𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Thursday, May 04, 2023
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Generated Fri 5 May 02:42:25 BST 2023
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
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Gemini index for the day: gemini://gemini.techrights.org/2023/05/04/


╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕
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QmS32fMTkeYomdxPWCP42PHMfFdKs9rfkSgXboUoVNA3jB
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QmbjVRkLQ4yrK3QTTACJcNbs4Z3VinU4mzjrwhHmMUKUzY


╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕

⦿ Bing is Dying and Chatbots Won’t Save Bing | Techrights

⦿ IRC Proceedings: Wednesday, May 03, 2023 | Techrights

⦿ Newer is Not Always Better (the Case of Automobiles) | Techrights

⦿ IBM Has Measurably Lessened Activity in Red Hat Web Sites (It Started When Layoffs Were Announced Last Month) | Techrights

⦿ The Electronic Frontier Foundation (EFF) Covers Software Patents Again | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2023/05/04/bing-is-dying/#comments
		http://techrights.org/2023/05/04/irc-log-030523/#comments
		http://techrights.org/2023/05/04/newer-is-not-always-better-automobiles/#comments
		http://techrights.org/2023/05/04/red-hat-web-sites/#comments
		http://techrights.org/2023/05/04/topic-of-swpats-back-in-eff/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2023/05/04/amazon-lays-off-27000/#comments
		http://techrights.org/2023/05/04/chatbots-debunked/#comments
		http://techrights.org/2023/05/04/lawsuits-over-negative-reviews/#comments
		http://techrights.org/2023/05/04/openwrt-22-03-5/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 62

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/05/04/bing-is-dying/#comments
    Gemini version at gemini://gemini.techrights.org/2023/05/04/bing-is-dying/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.04.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Bing_is_Dying_and_Chatbots_Won’t_Save_Bing⠀✐


Posted in Deception, Microsoft, Search at 9:42 am by Dr. Roy Schestowitz


Don’t believe the hype (a shameless lying blitz)


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Microsoft_layoffs,_chatbot_hype_campaign_starts_to_distract;
   Bing_down_from_6%_to_5.something_(despite_loads_of_marketing);_Google_has
                           actually_gained_ground⦈_


Summary: The ‘father’ of Bing left Microsoft, many Bing employees were laid off
earlier this year, and the remaining ones relocated out of their office in
Bellevue; the media is meanwhile hyping up the “Bing” brand (we saw new
examples this morning) and pretending_that_Google_is_doomed; the_data_does_not
support_this_phony_narrative (it’s more or less the same in other regions
around the world; overall, worldwide, Bing market share is measured at about
2.5%)


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⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣶⣶⣶⣶⣿⣿⣼⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣴⣠⣥⣿⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣙⣉⣩⣋⣹⣈⣹⣏⣏⣉⣋⣍⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣧⣧⣀⣧⣵⣵⣤⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣉⣹⣿⣇⣁⣈⣇⣙⣟⣘⣋⣝⣉⣹⣍⣙⣈⣈⣏⢋⢸⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⡿⠻⡻⠛⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠟⠛⠻⠟⠹⠛⡏⠻⠛⠻⠙⣿⠟⢩⣿⡟⠛⢻⠻⢛⠏⠘⠻⡟⣿⣿⣿⣿
⢸⣿⣿⣿⣷⣶⣶⣶⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣶⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠟⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣟⠻⡻⠛⢿⢸⣿⣿⠉⠛⠁⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠘⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣷⣶⣶⣶⣾⢰⣶⡶⠀⠀⠀⠀⠐⠲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⢶⣶⣶⢸⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠿⢿⢸⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠃⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡁⠀⢸⢸⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⢸⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣧⢩⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣘⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣘⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢣⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⡿⠿⠿⡇⠆⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠱⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡆⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠑⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⡌⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠡⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠒⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⡄⠵⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠑⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠈⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡡⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⠎⣰⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣆⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢵⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣆⣰⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠐⣨⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣅⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢩⡍⣻⢉⠙⡟⠛⠻⡋⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡫⡭⣻⢙⠋⢻⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⡭⢻⡍⡹⠋⡟⠛⢻⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣾⣶⣶⢤⣴⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣶⣾⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣷⣶⣷⣶⣷⣶⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣐⣃⣽⣘⣀⣃⣐⣀⣘⣀⣃⣒⣐⣈⣁⣪⣿⣿⣿⣿⣕⣓⣽⣆⣢⣀⣄⣘⣀⣍⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣽⣇⣃⣰⣄⣀⣅⣆⢆⣈⣂⣀⣆⣀⡂⢸⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

                    ䷩ 𝚕𝚒𝚗𝚎 150

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/05/04/irc-log-030523/#comments
    Gemini version at gemini://gemini.techrights.org/2023/05/04/irc-log-030523/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.04.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Wednesday,_May_03,_2023⠀✐


Posted in IRC_Logs at 2:04 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-030523.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-030523.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-030523.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-030523.gmi
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                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H                                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_


                                         #techrights_log_as_HTML5                                                                                  #boycottnovell_log_as_HTML5


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H                                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_


                                    #boycottnovell-social_log_as_HTML5                                                                               #techbytes_log_as_HTML5


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_


                                          #techrights_log_as_text                                                                                   #boycottnovell_log_as_text


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_


                                     #boycottnovell-social_log_as_text                                                                                #techbytes_log_as_text


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╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/05/04/newer-is-not-always-better-automobiles/#comments
    Gemini version at gemini://gemini.techrights.org/2023/05/04/newer-is-not-always-better-automobiles/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.04.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Newer_is_Not_Always_Better_(the_Case_of_Automobiles)⠀✐


Posted in Deception, Free/Libre_Software, Hardware at 11:01 am by Dr. Roy
Schestowitz


                   🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_car_drives_you!⦈_


Summary: Techrights recommends caution against ‘tech maximalism’; not
everything that can be done with/on a computer should, in practice, be done
that way; a careful balance is needed, taking stock of pros and cons


TODAY in IRC we had a lengthy discussion about the downside of supposedly
“modern” or “smart” cars*. It’ll be in the IRC logs tomorrow. It’s very
informal. It’s going way beyond aspects like cost and privacy — those two are
commonly discussed these days. We did a series about it over_a_year_ago.


“People are simply asked to buy the “latest” — no matter what Trojan horses are
included (mandated) in these.”What compels people to blindly assume that newer
is always better when it’s perfectly clear that users aren’t in control and
products are tailored (over time) to better suit the manufacturers, the stores
etc.? People are simply asked to buy the “latest” — no matter what Trojan
horses are included (mandated) in these.


This subject keeps coming back. People who drive need to buy cars
(occasionally) and there are many things they see which they strongly dislike.


“The one [new_article] about cars can be motivation for revisiting cars/
embedded systems and software freedom,” one person told us this week,
suggesting it as a topic and stating that “the focus was in-house expertise vs
outsourcing, in cars.”


To quote the portion we’ve already included in Daily Links:


     I would argue relying too much on external software vendors and not
     seeing software as a first-class citizen is the root cause. But Volvo
     Cars is wisely moving away from that model by bringing software
     developers in-house. Google and Apple partner with vendors for
     commodities. Software and data just happen to be too key to treat it
     that way. As I argued in a previous post, the automotive industry
     needs to own their data and set up to make it to the mobility-driven
     phase.


     Having someone from software-only companies tell Volvo how to do
     software is not that different from having someone from Foxconn
     coming to Cupertino telling Apple how to do hardware. Personally, I
     approach Volvo from a position of respect and will do my best for it
     to achieve its vision. And I’m not alone. There’s a whole army of us.


     Having done this for more than 2 decades, I don’t buy the argument
     that “it’s rocket science, you do cars, pay us to do it for you”.


Cars have long been marketed and merchandised as tools of freedom (mobility)
and independence (no public transport). But if entering a car means being spied
on in all sorts of ways (by third parties!), then taking a long walk might be
more emancipating an experience. As a teenager, when I drove my car I brought a
laptop into it (for music; no need to touch anything while driving). Back in
the 90s it was possible with universal ports. There was no DRM. I could take
the laptop anywhere I needed it afterwards, so I wasn’t paying for a computer
that only works inside the car.


“Cars have long been marketed and merchandised as tools of freedom (mobility)
and independence (no public transport).”Tech maximalism typically results in
tech fascism. It’s the misguided belief that everything should be digitalised,
no matter what the extra complexity may entail. In the case of voting machines,
it begets mistrust and uncertainty; media moguls are happy_to_exploit_that to
discredit entire elections. This morning at 7AM I went to vote (I was the first
person at the polling station) and all I needed was my passport. They gave me a
piece of paper, a pencil, and I put the paper inside a physical box. They
didn’t mind me wearing a hoodie (whole head covered) and two masks. The
passport is hard to forge and I knew how to answer questions when quizzed
verbally (name, address etc.) so a bit of privacy is possible and society can
function just fine this way.


I’m not against technology but as a passionate technologist I know where
technology neither belongs nor is needed. There are companies trying to sell a
bunch of useless “solutions” and councils/people eager to show it’s worth the
money by imposing these “solutions” on unsuspecting users (maybe they even get
kickbacks for introducing these “solutions”).


While we’re on the topic of ‘tech maximalism’, yesterday TechDirt said_goodbye
to_Twitter. TechDirt kept defending TikTok_from_bans, but maybe TechDirt is
coming to realise that social control media is a bad idea. Outsourcing
communications to it is a mistake. █
_________
* An associate reminded us of the horrifying nature and worrying trajectory of
such “smart” cars. Buyers ought to check the number of sensors in each new car.
They have some kind of jargon name — ECU_(Electronic_Control_Unit) — and six
years ago there were 80+ microcontrollers in your average new car. Some other
sites_put_that_number_at_over_100_microcontrollers. The diagnostics codes are
proprietary and there was a requirement that they be accessible but that law
did not specify wireless connections so the car companies block non-dealers
from accessing wireless diagnostics and have taken away wired diagnostics.


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⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣹⣿⣿⣿⣿⣿⣿⠻⣿⣆⠀⢿⢿⣿⡼⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢀⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿⣆⠻⣿⣧⠀⠘⠛⡅⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣺⣿⣿⡛⣿⠙⣿⠙⠃⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⡷⣞⣿⡃⡏⠀⢻⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠁⠀⠀⢩⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠀⠀⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢫⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠿⣿⣿⣿⣶⣆⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠛⠻⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣼⣿⣿⣿⠀⠀⠀⠸⣧⢀⠀⠀⠀⠀⣀⢀⢤⣤⣦⣄⣤⣾⣶⣶⣤⣶⣶⣦⣶⣿⣿⣿⣿⣿⣿⣿⣷⣷⣷⣤⣤⣤⣤⣶⣶⣤⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡄⠀⠀⠀⣿⣷⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⢠⣤⣤⣤⣶⣶⣶⣶⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣯⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⠿⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡞⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⡗⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢈⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣤⣀⣤⣶⣶⣶⣤⣤⣶⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠷⢦⡤⢤⣤⣤⣤⣄⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠝
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢸⡇⠃⢸⣿⠀⠀⡘⠃⣰⡾⠋⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣷⠶⠶⣤⡀⠀⢤⣤⡤⠀⠀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⡇⠀⣸⡟⠚⠛⡇⠀⣿⡇⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣿⡇⠀⢸⣿⠀⢰⣿⠋⠀⠀⠈⠇⠀⢹⡟⠉⠀⢹⣿⠒⡿⠓⢲⡖⢒⣿⢻⣿⢿⣿⢿⣿⣿⣿⣿⣿⠃⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⣇⣀⣀⣠⡆⠻⣧⡀⠀⠀⣙⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠙⣿⡉⠀⠀⢸⣿⠀⣿⡇⠀⠀⠐⢲⡶⠀⢸⡧⢤⣤⣼⣿⠀⠀⠀⣿⡇⢸⣿⣾⣿⣿⣿⣷⣿⣿⣿⠯⠀⠀⠀⠀
⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡇⠀⣀⠉⠉⠉⠉⠀⠀⠈⠙⠛⠋⠁⠐⣛⣓⣻⣿⣿⣿⣿⡿⠯⡄⠈⢿⣤⣀⣸⣏⡀⠘⢷⣄⠀⠀⣼⡇⠀⣾⡇⠀⠀⢸⡏⠀⠀⠀⣽⡇⠘⢿⣿⣿⣷⣎⠻⣿⣿⡿⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠽⠕⠛⠿⠾⡇⠀⡏⢾⠀⠀⡇⡃⠀⢹⣤⡆⠀⠀⡔⠲⠉⢻⣿⠿⠿⣿⡏⠁⡤⢀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠰⠷⠛⠓⠂⠐⠛⠓⠂⠀⠤⠿⠥⠀⠈⢻⠿⣿⡿⠀⠨⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠙⠊⠀⠘⠒⠀⠐⠛⠀⠀⠸⠄⠀⠰⠳⡀⠀⡟⢼⠁⠀⡯⡇⠀⡙⣜⠀⠀⢠⠒⠆⠀⡄⡄⠀⡠⢄⠀⢀⡀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⡄⠀⠀⠀⠀⠀⠈⠁⠀⠁⠈⠀⠀⠈⠐⠀⠀⠓⠃⠀⠉⠃⠀⠀⠅⠀⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⠿⠻⢿⣿⣿⣉⠉⢻⣶⣆⣄⣀⠀⢀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣠⣾⣿⣿⣿⣿⣿⣧⢸⣿⣧⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠁⣀⣤⣤⣤⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣷⣦⣀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⡏⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢼⢯⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠋⠉⠙⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣇⡶⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⡇⠀⡯⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢠⡾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢹⣿⣿⣛⠉⠛⠛⠛⠛⠛⢹⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⡏⢸⣿⣿⣿⣿⡍⣿⣷⡀⠛⢻⣿⣟⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠀⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⣿⣿⣿⣿⣿⡧⠘⣿⣷⠀⢈⠉⣈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⡿⢽⣿⢉⣿⠀⢾⡇⠁⠀⠈⠀⡟⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢰⣗⡿⣤⡏⠀⠘⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⡄⡀⡘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠠⠀⠆⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡂⠀⠀⠀⠁⢵⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣇⡀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠻⠿⠿⠿⠓⠂⠀⠀⠀⠀⠀⠀⠉⠛⠟⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣿⣿⡇⠀⠀⠀⠀⠈⣧⢀⠀⠀⠀⠀⠀⡀⢤⣠⣦⣄⣤⣾⣴⣶⣤⣤⣤⣴⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣤⣤⣤⣤⣤⣴⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⢀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡏⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⣠⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣄⣴⣶⣷⣤⣤⣴⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⢦⡤⢤⣤⣤⣤⣄⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢸⡇⠃⢸⣿⠀⠀⡘⠃⣰⡾⠋⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣷⠶⠶⣤⡀⠀⢤⣤⡤⠀⠀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⣸⡟⠚⠛⡇⠀⣿⡇⠀⠑⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣿⡇⠀⢸⣿⠀⢰⣿⠋⠀⠀⠈⠇⠀⢹⡟⠉⠀⢹⣿⠒⡿⠓⢲⡖⢒⣿⢻⣿⢿⣿⡿⣿⣿⣿⣿⣿⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⣇⣀⣀⣠⡆⠻⣧⡀⠀⠀⣙⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡙⣿⡉⠀⠀⢸⣿⠀⣿⡇⠀⠀⠐⢲⡶⠀⢸⡧⠤⣤⣼⣿⠀⠀⠀⣿⡇⢸⣿⣾⣿⣿⣿⣷⣿⣿⣿⣏⠁⠀⠀⠀
⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡇⠀⣀⠉⠉⠉⠉⠀⠀⠈⠙⠛⠋⠁⠘⣛⣓⣻⣿⣿⣿⣿⡿⠯⡄⠈⢿⣤⣀⣼⣏⡀⠘⢷⣄⠀⠀⣼⡇⠀⣾⡇⠀⠀⢸⡏⠀⠀⠀⣽⡇⠈⢿⣿⣿⣿⣿⠻⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠽⠕⠛⠿⠾⡇⠀⡏⢾⠀⠀⡇⡃⠀⢹⣤⡆⠀⠀⡔⠲⠘⢹⣿⢿⣿⣿⡟⠁⡤⣀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⣐⠛⠓⠂⠐⠛⠓⠂⠀⠤⠿⠥⠀⠈⢻⢿⣿⡿⠁⠈⠛⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠙⠊⠀⠘⠚⠀⠐⠛⠀⠀⠸⠄⠀⠰⠻⡀⠀⡟⢼⠁⠀⡫⡇⠀⡹⣿⠀⠀⢠⠒⠆⠀⡄⡄⠀⡠⢄⠀⢀⡀⡀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⣀⡰⡤⠀⠀⠀⠀⠀⠈⠁⠀⠉⠈⠀⠀⠈⠐⠀⠀⠓⠃⠀⠉⠃⠀⠀⠅⠀⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡿⠟⠉⣙⣿⣿⣧⣄⠀⢻⣿⣶⣀⣀⡀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣇⣴⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣉⣉⡉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠁⢀⣤⣤⣤⣤⣦⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢻⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⡏⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠞⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣯⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⡟⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢹⣟⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣧⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⡏⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢰⡿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣿⣿⣿⢉⠈⠛⠛⠛⠛⠛⢹⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡃⣺⣿⣿⣿⣿⡏⣿⣷⡄⠉⢹⣿⠏⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⢀⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⣿⣿⣿⢿⣿⣷⣈⢿⡟⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣿⢸⣿⣡⣿⠓⢻⡇⠁⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢸⣿⣯⣷⡆⠀⠘⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠰⠀⠅⣼⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡧⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠘⠀⠀⠰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡸⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠻⠿⠿⠿⠗⠂⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣴⣿⣿⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣤⣤⣾⣶⣶⣤⣴⣤⣾⣶⣷⣾⣿⣷⣿⣶⣶⣤⣤⣶⣦⣤⣤⣤⣤⣴⣤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢀⣿⣿⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣠⣤⣤⣤⣴⣶⣆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡂⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⠆⢸⡟⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⣾⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⢷⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣀⣤⣾⣖⣤⣤⣤⣴⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⢧⡤⢤⣤⣤⣤⣄⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢸⣿⠃⢸⣿⠀⠀⡘⠃⣰⡾⠋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣷⠶⠶⣤⠀⠀⢤⣤⡤⠀⠀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⡟⠚⠛⡇⠀⣿⡇⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣿⡇⠀⢸⣿⠀⢰⣿⠋⠀⠀⠈⠇⠀⢹⡟⠉⠀⢹⣿⠒⡿⠓⢲⡖⢒⣿⢻⣿⢿⣿⡿⣿⣿⣿⣿⣿⠃⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣇⣀⣀⣠⡆⠻⣧⡀⠀⠀⣉⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠙⣿⡉⠀⠀⢸⣿⠀⣿⡇⠀⠀⠐⢲⡶⠀⢸⡧⠤⣤⣼⣿⠀⠀⠀⣿⡇⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⡟⠈⠀⠀⠀
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣗⠀⣀⠉⠉⠉⠉⠀⠀⠈⠙⠛⠋⠁⠐⣛⣓⣻⣿⣿⣿⣿⡿⠯⡄⠈⢿⣤⣀⣸⣏⡀⠘⢷⣄⠀⠀⣼⡇⠀⣾⡇⠀⠀⢸⡏⠀⠀⠀⣽⡇⠘⢿⣿⣿⣿⣯⠻⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠽⠕⠻⣿⡷⡇⠀⡏⢾⠀⠀⡇⡃⠀⢹⣤⡆⠀⠀⡖⠺⢉⢻⣿⣿⡿⣿⡏⠉⣤⢀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠐⠛⠓⠂⠐⠛⠓⠂⠀⠤⠿⠥⠀⠘⢿⢿⣿⡿⠀⡘⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠙⠊⠀⠘⠒⠀⠐⠛⢀⣀⣸⡄⠀⠸⠳⡀⠀⡟⢼⠁⠀⡫⡇⠀⡹⣔⠀⠀⢠⠒⠆⠀⡄⡄⠀⡤⢄⠀⢀⡀⡀⠀⢐⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣷⣶⣴⡀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠈⠀⠀⠈⠐⠀⠀⠓⠃⠀⠉⠃⠀⠀⠅⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⡿⠛⠛⣿⣿⣏⡉⠉⢻⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠸⢿⣏⢁⣶⣿⣿⣿⣿⣿⣦⢸⣿⣷⠤⠀⠀⠀⠀⠀⢀⣘⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⣀⣠⣤⣤⣴⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠰⠾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣂⣀⡀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⡏⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣄⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣤⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⠟⠉⠙⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⡿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠑⠀⣻⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣦⣦⣷⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠇⢼⣿⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢻⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣼⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⣿⣿⡟⠀⠸⠙⠛⠛⠛⠛⠋⢹⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣺⣿⣿⣿⣿⣧⠈⠛⠿⢿⣿⠀⠀⠠⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢻⠇⣿⡗⣸⡇⠀⠀⠀⢸⡏⠀⠀⡅⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⣸⣿⣷⠈⠁⠀⠀⡀⠀⠃⠀⠀⣷⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠄⣔⠁⠀⠀⠐⣿⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠜⣂⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠘⠀⢙⢾⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠟⠛⢻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠻⠿⠿⠿⠷⠂⠀⠀⠀⠀⠀⠀⠘⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡀⢀⣄⠀⠀⠀⠀⢨⣶⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣀⣀⡠⢄⡀⣀⡀⣀⣠⣆⣶⣦⣾⣶⣤⣤⣤⣠⣠⣄⣠⣤⣤⣀⣀⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣿⣾⣿⣿⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣁⣸⣏⡀⡀⠀⠀⠀⢼⣷⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣶⣶⣶⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠇⣰⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⣤⣔⣶⣦⣤⣤⣀⣰⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⢤⡤⢤⣤⣤⣤⣄⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢸⣿⠃⢸⣿⠀⠀⡘⠃⣰⡾⠋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣷⠶⠶⣤⡀⠀⢤⣤⡤⠀⠀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⣸⡟⠚⠛⡇⠀⣿⡇⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣿⡇⠀⢸⣿⠀⢰⣿⠋⠀⠀⠈⠇⠀⢹⡟⠉⠀⢹⣿⠒⡿⠓⢲⡖⢒⣿⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣇⣀⣀⣠⡆⠻⣧⡀⠀⠀⣙⢻⣿⡇⣿⣿⣿⣿⣿⣿⣿⠙⣿⡉⠀⠀⢸⣿⠀⣿⡇⠀⠀⠐⢲⡶⠀⢸⡧⠤⣤⣼⣿⠀⠀⠀⣿⡇⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧⠅⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⠉⠉⠉⠉⠀⠀⠈⠙⠛⠋⠁⠘⣛⣓⣻⣿⣿⣷⣿⡿⠯⡄⠈⢿⣤⣀⣼⣏⡀⠘⢷⣄⠀⠀⣼⡇⠀⣾⡇⠀⠀⢸⡏⠀⠀⠀⣽⡇⠘⣿⣿⣿⣿⣯⠿⣿⣿⣿⠀⠀⠀⠀⠀
⠁⠉⠀⠁⠀⠀⠉⠿⠕⠻⣿⡿⢯⠀⡏⢾⠀⠀⡇⡃⠀⢹⣤⡆⠀⠀⡔⠲⢈⢻⣿⣿⡿⣿⡟⠁⡤⢀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠐⠛⠓⠂⠐⠛⠓⠂⠀⠤⠿⠥⠀⠈⢿⢿⣿⡿⠀⡸⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠙⠊⠀⠘⠒⠀⠐⠛⠀⠀⠸⠄⠀⠰⠳⡀⢀⡟⢼⠁⠀⡫⡇⠀⡽⣼⠀⠀⢠⠒⠆⠀⡄⡄⠀⡤⢄⠀⢀⡀⡀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠈⠀⠀⠈⠐⠀⠀⠓⠃⠀⠋⠃⠀⠀⠅⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⡿⣿⣿⠿⢿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣴⣾⠟⠁⡀⣰⣿⣷⣦⡀⠈⣿⣷⡀⠀⠀⣀⠀⣀⡀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢉⣿⣢⣾⣿⣿⣿⣿⣿⣿⣆⣿⣿⡟⠻⠛⠛⠛⠛⠛⠛⠛⣻⠛⠛⠛⠛⠡⢀⣤⣤⣤⣴⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣆⣦⣆⢀⡀⠀⠀⠀⠉⠀⠀⣴⣾⣿⣿⣿⣿⣿⡏⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣴⣮⣷⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢄⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠿⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢽⣛⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡏⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣆⣀⣠⠄⠀⣀⣐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢸⣿⡃⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣯⡀⣦⣿⣿⣷⠈⢹⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣇⠀⢸⠉⠛⠛⠛⠛⠛⢹⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠀⣸⡧⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡞⣿⣿⣿⣿⣿⡇⠸⣿⣿⠉⠛⢻⣷⣾⣤⣀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢿⠹⣿⡏⣿⡇⠀⠘⣿⡀⠰⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠈⢠⣿⣿⡹⠇⠀⠀⠻⠷⠀⠘⠻⣿⠿⠛⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢚⣿⢿⡇⠀⠀⢀⣤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⣙⣿⣷⠀⠀⢈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⣹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠛⠻⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠻⠿⠿⠿⠷⠂⠀⠀⠀⠀⠀⠀⠈⠙⠟⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣼⣃⡀⠀⠀⠰⠀⠿⠏⠀⠁⠀⠀⠀⠀⣀⣤⣴⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣠⣾⣷⣶⣿⣦⣠⣤⣄⣀⣤⣤⣠⣤⣄⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢠⣤⣴⣾⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⢻⡧⠀⠀⠀⠀⠀⢿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶
⠀⢀⣤⣤⣤⣴⣶⣶⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⡆⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣰⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣄⣠⣠⣶⣶⣄⣤⣤⣴⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⢤⡤⢤⣤⣤⣤⣄⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢸⣿⠃⢸⣿⠀⠀⡘⠃⣰⡾⠋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣷⠶⠶⣤⡀⠀⢤⣤⡤⠀⠀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⡟⠚⠛⡇⠀⣿⡇⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣀⣿⡇⠀⢸⣿⠀⢰⣿⠋⠀⠀⠈⠇⠀⢹⡟⠉⠀⢹⣿⠒⡿⠓⢲⡖⢒⣿⢻⣿⢿⣿⡿⣿⣿⣿⣿⣿⠇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣇⣀⣀⣠⡆⠻⣧⡀⠀⠈⣙⠿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡙⣿⡉⠀⠀⢸⣿⠀⣿⡇⠀⠀⠐⢲⡶⠂⢸⡧⢤⣤⣼⣿⠀⠀⠀⣿⡇⢸⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⠉⠉⠉⠉⠀⠀⠈⠙⠛⠋⠁⠐⣛⣓⣻⣿⣿⣿⣿⡿⠯⡅⠈⢿⣦⣀⣼⣏⡀⠘⢷⣄⠀⠀⣼⡇⠀⣾⡇⠀⠀⣸⡏⠀⠀⠀⣽⡇⠘⣿⣿⣿⣿⣯⠿⣿⣿⣏⠃⠀⠀⠀⠀
⠉⠁⠀⠈⠀⠈⠉⠿⠕⠻⢿⡿⢿⠀⡏⢾⠀⠀⡇⡃⠀⢹⣤⡆⠀⠀⡖⠺⠉⣻⣿⡿⡿⣿⡟⠃⡤⢀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠐⠛⠓⠂⠐⠛⠓⠂⠀⠤⠿⠥⠀⠈⢿⢿⣿⡿⠄⠸⠙⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠙⠊⠀⠘⠒⠀⠐⠛⠀⠀⠸⠄⠀⠰⠳⡀⠀⡟⢼⠁⠀⡯⡇⠀⡽⣼⠀⠀⢠⠒⠆⠀⡄⡄⠀⡤⢄⠀⢀⡀⡀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠈⠀⠀⠈⠐⠀⠀⠓⠃⠀⠉⠃⠀⠀⠅⠀⠠⠎⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣤⣀⣀⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⢿⣿⡿⠿⢿⣿⣷⣇⣀⢀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣾⣿⠟⠈⡉⣠⣿⣧⣦⡀⠀⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⢀⣀⣤⣤⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠨⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣰⣿⣿⣿⣿⣿⣿⣿⣆⣻⣿⣇⣤⣤⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣵⣿⣿⣿⣿⣿⡏⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣷⣄⣴⣤⣶⣿⣾⣿⣿⣿⣿⣿⣿⠟⠁⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠻⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠋⠉⠁⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣟⠀⠀⣤⠆⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠂⣳⣿⠃⢨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣶⣶⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⡁⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⢿⣷⣄⠀⠀⠀⠀⠀⢸⠛⠛⠛⠛⠛⠛⠻⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣎⣿⣿⣿⣿⣿⠏⢻⣿⡄⠀⠀⠀⠀⢸⠀⣠⣶⣦⣤⣄⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣻⣿⡿⣿⠄⠈⢿⣇⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠸⣿⣆⣿⡃⠀⠘⣿⣆⡀⠀⠀⠛⠿⠿⣿⣿⣿⡿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠉⣼⣿⣿⡟⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠻⠛⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠻⣿⣇⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠾⣿⣿⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠛⠻⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠛⠿⠿⠿⠳⠂⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣠⣤⣾⣇⠀⠀⠀⠀⠘⢿⡇⠀⣴⡀⠀⠀⠀⠀⣀⣤⣤⣄⣀⣀⣀⣀⣀⡀⣀⣀⣠⣶⣿⣦⣦⣤⡀⣀⣀⣀⣀⣄⣤⣤⣄⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣠⣶⣶⣾⣿⣷⣰⣶⣶⣤⣾⣿⣿⣿⣿⣿⣿⣯⡦⠀⠀⠀⠀⠈⣃⠀⣹⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶
⠀⢀⣤⣤⣤⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣹⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣄⣀⣠⣴⣦⣄⣠⣐⣴⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⢤⡤⢤⣤⣤⣤⣄⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⢹⣿⠃⢸⣿⠀⠀⡘⠃⣰⡾⠋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⠶⠶⣤⡀⠀⢤⣤⡤⠀⠀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⡟⠚⠛⡇⠀⣿⡇⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣀⣿⡇⠀⢸⣿⠀⢰⣿⠋⠀⠀⠈⠇⠀⢹⡟⠉⡀⢹⣿⠒⡿⠓⢲⡖⢒⣿⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣇⣀⣀⣠⡆⠻⣧⡀⠀⠀⣹⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠙⣿⡉⠀⠀⢸⣿⠀⣿⡇⠀⠀⠐⢲⡶⠀⢸⡷⣿⣿⣿⣿⠀⠀⠀⣿⡇⢸⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠃⣀⠉⠉⠉⠉⠀⠀⠈⠙⠛⠋⠁⠘⣛⣓⣻⣿⣿⣿⣿⡿⠯⡇⠈⢿⣦⣀⣸⣏⡀⠘⢷⣄⠀⠀⣼⡇⠀⣾⣷⣿⣿⣿⡏⠇⠀⠀⣽⡇⠸⣿⣿⣿⣿⣿⡻⣿⣿⡿⠂⠀⠀⠀⠀
⠉⠁⠀⠁⠈⠉⠉⠿⠕⠻⢿⣿⢯⡀⡏⢾⠀⠀⡇⡃⠀⢹⣤⡆⠀⠀⡖⠺⠈⢿⣿⣿⣿⣿⡟⠉⡤⣀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣀⣴⣿⣿⣿⣿⣛⠓⠂⠀⠤⠿⠥⠀⠘⢿⢿⣿⣿⠀⠸⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠙⠊⠀⠘⠒⠈⣐⣛⡀⠀⠸⠄⠀⠰⠳⡀⠀⡟⢼⠁⠀⡯⡇⣿⣿⣿⣿⣿⣿⣻⣿⠀⡄⡄⠀⡠⢄⠀⢀⡀⡀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣦⣤⣄⣠⡀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⠀⠓⠃⠀⠋⠃⠀⠀⠅⠀⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣧⡼⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣤⣿⡿⠿⠯⠛⣻⣿⣿⣦⡀⢿⣿⣧⢀⣀⡀⠀⢀⠀⠀⠀⣹⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠋⣯⢀⣴⣶⣶⣿⣿⣿⣿⣷⣾⣿⣟⡙⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⠟⠃⢀⣠⣤⣤⣤⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⣶⣦⣀⡀⠀⠀⠀⣸⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡘⠯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⡀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⠟⠉⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢛⢽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣟⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣦⣄⣤⠄⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢹⣿⡇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⡿⣯⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⡟⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⡟⡿⣿⣿⣿⣿⣿⡇⢹⣷⡀⠀⠀⠀⣾⣿⣿⠟⠛⠛⠿⠛⢹⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠁⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠇⣿⣿⣿⣿⣿⡇⠀⠹⣷⡄⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢿⢙⣿⣧⣼⡇⠘⣤⡘⠿⠆⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢃⣿⣿⡆⠁⠀⢻⡇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠀⠀⠀⠀⠙⣻⡇⠀⠀⣺⡇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠘⢣⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠂⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠛⠛⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠛⠟⠿⠿⠷⠆⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣿⣧⠀⠀⠀⠀⠀⠺⡆⠈⣿⠀⠀⠀⠀⢀⣠⣄⣄⣀⣀⣀⡀⣀⣀⣀⣀⣀⣠⣴⣷⣦⣶⣄⢀⣤⣀⣀⣠⣤⣠⣤⣄⣀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⣰⣾⣿⣿⣗⣤⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣯⡏⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣢⣤
⠀⢀⣤⣤⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠰⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢠⣠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⢸⡏⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⢸⣯⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⣏⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⠀⢈⣯⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣄⣀⣀⣀⣀⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⢤⡤⢤⣤⣤⣤⣄⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣹⣿⠃⢸⣿⠀⠀⡘⠃⣰⡾⠋⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣷⠶⠶⣤⡀⠀⢤⣤⡤⠀⠀⣀⣤⣄⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⣸⡟⠚⠛⡇⠀⣿⡇⠀⠑⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣿⡇⠀⢸⣿⠀⢰⣿⠋⠀⠀⠈⠇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⢲⡖⢒⣿⢻⣿⢿⣿⢿⣿⣿⣿⣿⣿⠃⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣇⣀⣀⣠⡆⠻⣧⡀⠀⠀⣉⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠹⣿⡉⠀⠀⢸⣿⠀⣿⡇⠀⠀⠐⢲⡶⢻⣿⡿⣿⣿⣿⣿⣿⣿⡇⣿⡇⢸⣿⣾⣿⣿⣿⣷⣿⣿⣿⠿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠉⠉⠉⠉⠀⠀⠈⠙⠛⠋⠁⠐⣛⣓⣻⣿⣿⣿⣿⡿⠯⡅⠈⢿⣤⣀⣸⣏⡀⠘⢷⣄⠀⠀⣼⡇⢈⣿⣿⣿⣿⣿⡟⣿⠛⠀⣽⡇⠘⣿⣿⣿⣿⣯⠻⣿⣿⣿⠂⠀⠀⠀⠀
⠋⠁⠁⠁⠈⠉⠉⠿⠕⠻⢿⣿⢯⠃⡏⢾⠀⠀⡇⡃⠀⢹⣤⡆⠀⠀⡖⠻⠉⣿⣿⣿⡿⣿⡟⠁⡤⢀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢩⣽⣿⣶⣿⣿⣿⣿⣿⣿⣷⡏⠀⠤⠿⠥⠀⠘⢿⢿⣿⡿⠀⡸⠛⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠙⠊⠀⠘⠒⣠⣴⣿⣦⣤⣸⠄⠀⠰⠳⡀⠀⡟⢼⠁⠀⣽⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡇⡄⠀⡠⢄⠀⢀⡀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⡿⣷⣶⣧⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠃⠀⠋⠣⠀⠀⠅⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⡿⠛⠋⣉⣿⣷⣤⡀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⡋⢀⣶⣶⣿⣿⣿⣿⣿⣬⣿⣿⣷⣀⡀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠙⠋⠙⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⡟⠋⣀⣀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣶⣤⣄⣀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠿⠹⣿⣿⣿⣿⣿⣿⣿⣾⣶⣠⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠁⠀⠀⠘⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⢼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠨⣻⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣷⣤⠄⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⢹⣿⡇⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢿⣿⣿⣿⣿⡟⢿⣆⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣟⡇⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠇⢻⡟⣿⣿⣿⡇⠈⣿⣆⠀⠀⠀⠸⢿⣿⡟⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢨⣇⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⣼⡟⣿⡟⢸⡇⢀⡘⢿⣦⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠹⠁⣿⡥⡼⠇⠘⣿⠀⠙⠃⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠁⠀⠀⢀⢺⢷⡇⠀⠀⣽⠃⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠈⢛⡷⠀⢀⣿⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⡀⠘⢻⡇⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠘⡇⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠛⠛⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣾⣿⢧⣆⡀⠀⠀⠀⠀⢹⣧⣀⣀⡀⠀⠀⢀⡀⣀⣀⣀⡀⡀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣵⣏⣄⣄⠀⣀⣄⣀⣀⣀⣠⣤⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣴⣶⣶⣷⣷⣤⣤⣄⣰⣦⣾⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤
⠀⢀⣠⣤⣤⣤⣶⣶⣶⣶⣶⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠰⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣴⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡇⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⡶⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢰⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣀⡀⣀⢀⢀⠀⡀⢠⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⢦⡤⢤⣤⣤⣤⣄⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⢹⣿⡇⢸⣿⠀⠀⡘⠃⣰⡾⠋⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⠶⠶⣤⡀⠀⢤⣤⡤⠀⠀⣀⣤⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⡟⠚⠛⡇⠀⣿⡇⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣿⡇⠀⢸⣿⠀⢰⣿⠋⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣿⢻⣿⢿⣿⠿⣿⣿⣿⣿⣿⠃⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣇⣀⣀⣠⡆⠻⣧⡀⠀⠀⣉⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠙⣿⡉⠀⠀⢸⣿⠀⣿⡇⠀⠀⠐⢲⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠉⠉⠉⠉⠀⠀⠈⠙⠛⠋⠁⠐⢛⣓⣻⣿⣿⣷⣿⡿⠯⡄⠈⢿⣤⣀⣸⣏⡀⠘⢷⣤⣦⣴⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⠘⣿⣿⣿⣿⣽⠻⣿⣿⣽⠂⠀⠀⠀⠀
⠉⠁⠀⠈⠀⠉⠉⠿⠕⠻⢿⣿⣯⡇⡏⢾⠀⠀⡇⡃⠀⢹⣤⡆⠀⠀⡖⠲⠈⢿⣿⣿⡿⣿⡟⠁⡤⢀⠀⠀⡀⠀⠀⠀⠀⠀⢈⣭⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠿⠥⠀⠘⢿⢿⣿⣿⠀⠸⠋⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠙⠂⠀⠘⠒⠀⣴⣿⣶⣶⣼⣄⡀⠰⠳⡀⠀⡿⢼⠁⠈⡯⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡠⢄⠀⢀⡀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⠿⣷⣶⣆⠀⠀⠀⠀⠀⠈⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠋⠃⠀⠀⠅⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡿⠋⠉⢀⣼⣿⣶⣤⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⣹⡇⣴⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⡄⣀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡆⣽⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠙⠛⠛⠛⠛⠛⠛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢺⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡠⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⠋⣿⣿⣿⣿⣿⣿⣾⣷⣷⡠⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡀⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⡿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠓⢴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠰⣻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣳⣷⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢻⣿⣿⣿⣿⣿⢿⣆⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠐⢿⠆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡏⠸⣿⣿⣿⣿⣿⠘⣿⣆⠀⠀⠀⢠⣾⣿⣿⡿⠿⠟⠉⢹⣿⠿⠃⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠂⢸⡏⢿⣿⢸⣿⠀⠙⣿⣆⠀⠀⠀⠉⠻⠃⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠈⠀⢸⡟⠸⠿⠸⣷⠈⠛⠃⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⢀⣪⣿⣿⠀⢀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠐⣻⣿⡄⢸⡏⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠂⡈⢹⡇⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠈⠀⠁⡸⣷⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠛⠛⠿⠿⠛⠓⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⣿⡌⠀⠀⠀⠀⠁⢻⣿⣈⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⠠⣄⣼⣄⣠⣄⡀⣠⣄⣀⣄⣀⣤⣤⣀⡀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣶⣾⣿⣶⣤⣤⣄⣠⣴⣤⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠐⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤
⠀⢀⣀⣄⣄⣠⣴⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠨⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣮⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⣴⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣆⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡗⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⡇⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣦⣄⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢀⣀⣀⡀⠠⡀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣿⠿⢦⡤⢤⣤⣤⣤⣄⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣸⣷⣇⢸⣿⠀⠀⡘⠃⣰⡾⠋⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣷⠶⠶⣤⠀⠀⢤⣤⡤⠀⠀⣀⣤⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡟⠚⠛⡇⠀⣿⡇⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣿⡇⠀⢸⣿⠀⢰⣿⠋⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢿⣿⠿⣿⣿⣿⣿⣿⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣇⣀⣀⣠⡆⠻⣧⡀⠀⠀⣩⢻⣿⡇⣿⣿⣿⣿⣿⣿⣿⠙⣿⡉⠀⠀⢸⣿⠀⣿⡇⠀⠀⠘⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠏⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣀⠉⠉⠉⠉⠀⠀⠈⠙⠛⠋⠁⠐⣛⣓⣻⣿⣿⣿⣿⡿⠯⡄⠈⢿⣤⣀⣸⣏⡀⠘⢷⣄⣀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠿⣿⣿⡿⠂⠀⠀⠀⠀
⠛⠛⠉⠉⠋⠛⠛⠿⠗⠻⢿⣿⡏⡷⡏⢾⠀⠀⡇⡃⠀⢹⣤⡆⠀⠀⡔⠺⠉⢿⣻⣿⣿⣿⣟⠃⡤⢀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢉⣭⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢿⣿⣿⠀⠘⠍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠙⠂⠀⠘⠒⠀⠐⠛⠂⠀⠸⠄⠀⠰⠳⡀⠀⡟⢼⠁⠀⡯⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢛⡁⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠃⠀⠀⠅⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣶⣔⣤⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠉⠉⣉⣩⣿⣁⠈⢻⣿⣧⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢙⡯⢠⣾⣷⣿⣿⣿⣿⣷⡘⣿⣿⠞⠛⠛⠛⠚⠚⠻⢻⣿⡻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡀⠀⠀⠀⠀⠀⢹⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⢭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣷⣶⣤⡀⣀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡻⠟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠼⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠋⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣆⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⣠⠄⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠏⠹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢛⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢯⡟⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠸⠋⠟⠛⠛⠛⠋⠸⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⠇⣹⣿⣿⣿⣿⠋⣿⣇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⡿⢹⣿⣧⣿⡄⠘⢿⣆⠀⠀⠀⢸⠀⠀⠀⠀⣠⣾⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠈⠃⣜⣿⣧⣿⠀⣿⡜⢿⣆⠀⠀⠘⣀⡀⣿⣾⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⢻⣿⡎⠀⣽⠂⠈⠻⠿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⢀⢌⢿⡇⢸⡟⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠂⠀⠀⠀⠁⣻⣇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠛⠛⠻⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠉⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣸⣿⣿⠀⠀⠀⠀⠈⣱⣿⣘⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⢀⠀⢀⣤⣴⣤⣄⣀⣀⣠⣤⣠⣠⣤⣠⣄⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣤⣴⣶⣿⣶⣠⣤⣤⣀⣠⣲⣺⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠘⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤
⠀⢀⣤⣤⣤⣦⣴⣶⣐⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢠⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢈⡦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡄⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡆⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢙⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣿⣿⣿⣿⣿⣷⣷⡶⢶⣿⠿⢦⡤⢤⣤⣤⣤⣄⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢹⣷⡇⢸⣿⠀⠀⡘⠃⣰⡾⠋⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣷⠶⠶⣤⡀⠀⢤⣤⡤⠀⠀⣀⣤⣄⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⣸⡟⠚⠛⡇⠀⣿⡇⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣿⡇⠀⢸⣿⠀⢰⣿⠋⠀⢠⣾⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢟⣿⠿⣿⣿⣿⣿⡿⠃⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣏⣿⣇⣀⣀⣠⡆⠻⣧⡀⠀⠀⣉⢻⣿⡇⣿⣿⣿⣿⣿⣿⣿⠙⣿⡉⠀⠀⢸⣿⠀⣿⡇⠀⠀⢺⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣷⣀⠉⠉⠉⠉⠀⠀⠈⠙⠛⠋⠁⠐⢛⣓⣻⣿⣿⣿⣿⡿⠯⡄⠈⢿⣤⣀⣸⣏⡀⠘⢷⣄⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣜⠻⣿⣿⡿⠀⠀⠀⠀⠀
⠿⠟⠛⠛⠛⠛⠿⠿⠗⠿⣿⣿⡯⡏⡏⢾⠀⠀⡇⡃⠀⢹⣤⡆⠀⠀⡔⠳⠙⢿⣻⣿⣿⣿⡟⠃⡤⢀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢩⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠁⠸⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠙⠊⠀⠘⠚⠉⠙⠛⠂⠀⠸⠄⠀⠰⠳⡀⠀⡿⢼⠁⠀⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣦⣄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⠿⢿⣿⣆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠟⠁⣀⣠⣤⣾⣶⣄⠈⣿⣿⡶⠶⠿⠿⠶⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣽⢢⣾⣿⣿⣿⣿⣿⣿⣧⣹⣿⡏⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⣷⣄⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠨⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠿⠛⠉⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⢻⣿⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣫⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣇⡝⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢟⡔⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠸⠉⠟⠛⠛⠻⠛⠹⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢟⣟⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣏⣼⡏⣿⣿⣿⡏⣿⣇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⠈⣿⡟⣿⡇⢸⣿⡄⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠰⣿⣿⢻⠇⠈⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠸⣿⣇⠀⣿⠀⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠈⠈⢹⣇⢠⡟⠀⠈⠛⣿⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠛⠛⠻⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣿⡇⠀⠀⠀⠈⢫⣿⣸⡇⠀⠀⠀⠈⠹⣿⣿⣿⣤⣤⣀⣀⠀⠀⠀⠀⠀⣀⣠⣬⣤⢀⣀⢀⣀⣄⣀⣄⣀⣠⣀⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⢽⣶⣤⣤⣤⣄⣠⣴⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣽⣿⣿⣿⣷⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⣤⣤
⠀⠀⣤⣤⣤⣤⣤⣤⣶⣦⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡆⠀⠀⢀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣗⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢭⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣶⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣀⠀⢀⣀⣤⣴⡶⠶⣤⠦⢤⡤⢤⣤⣤⣤⣄⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⢀⣘⣿⣾⣿⢿⣿⣿⣾⣿⣿⢸⣿⢃⢸⡿⠀⠀⡘⠃⣰⡾⠋⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣟⣷⠶⠶⣤⡀⠀⠤⣤⡤⠀⠀⣀⣤⣄⣀⡀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀
⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣼⡟⠚⠛⡇⠀⣿⡇⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⠀⣀⣾⡇⠀⢸⣿⠀⢠⣿⠋⠀⠀⠈⠇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣿⣿⣿⣿⣻⠿⣿⣿⣿⣿⡿⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣿⣇⣀⣀⣠⡆⠻⣧⡀⠀⠀⣉⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠙⢿⡉⠀⠀⢸⣿⠀⣿⡇⠀⣀⣴⣲⡶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣷⣿⣿⣿⡟⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣀⠉⠉⠉⠉⠀⠀⠈⠙⠛⠋⠁⠐⢛⣓⣻⣿⣿⣷⣿⡿⠯⡄⠈⢿⣤⣀⣸⣏⡀⠘⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⠃⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣯⣽⡏⢾⠀⠀⡇⡃⠀⠹⣤⡆⠀⠀⡔⠲⢻⣿⣿⣿⣿⣿⣿⡿⡤⣀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡿⣿⡿⢀⣿⣿⣿⣆⠀⠀⠀⠀
⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠙⠻⣿⢘⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠙⠂⠀⠘⠺⠻⠿⠻⠚⠁⠸⠄⠀⠰⠻⡀⠀⡿⢼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣤⣀⣀⣀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⡿⠿⢿⡿⠟⠿⢿⣿⡆⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣾⡿⠋⣀⣀⣰⣾⣿⣷⣄⢸⣿⣷⣀⠀⢀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣴⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠋⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣧⡖⡶⠅⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢤⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠋⠁⠙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠁⠀⠈⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢺⡶⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⢼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣷⣾⡁⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠫⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⡿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⢹⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣼⡗⣿⣿⣿⡏⣿⣿⡇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠙⠀⢿⡟⣹⣇⢹⣿⡇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⡈⠁⢸⣿⡇⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠈⠿⠁⠀⣲⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⣴⣶⣶⣤⠄⠀⠀⠀⠀⠀⠀⠉⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣂⣀⣀⠀⠀⠀⢀⠀⢀⣴⣶⢾⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣶⣶⣦⣴⣴⣤⣤⣤⣤⣤⣤⣤⣠⣴⣶⣶⣶⣷⣶⣦⣶⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⢀⣀⡀
⠀⠀⠀⠀⠀⣀⣄⣠⣄⢀⣀⣠⣄⣤⣦⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣧⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣌⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠁⠀⡏⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⣿⡧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠐⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⣤⠤⢤⡤⢤⣤⣤⣤⣄⡀⠀⠘⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠉
⠀⠀⢂⡀⢠⢄⣠⣮⣴⣶⣿⢸⣷⠃⢸⡿⠀⠀⡘⠃⣠⡾⠋⣱⣯⣿⣿⣿⣿⣿⣿⣿⣿⢛⣓⣶⠶⠶⣤⡀⠀⠤⣤⡤⠀⠀⣀⣤⣄⣀⡀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀
⠀⢠⣿⣧⢠⣈⣿⣿⣿⣿⣿⣾⣿⢸⣸⡟⠚⠛⡇⠀⣿⡇⠀⠘⠟⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⢀⣀⣾⡇⠀⢸⣿⠀⢠⣿⠋⠀⠀⠈⠇⣴⣿⣟⣿⣿⣿⣿⣿⣿⣻⣿⣟⣛⣿⣿⣿⣟⣿⠿⣿⣿⣿⣿⠟⠀⠀⠀
⣶⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣇⣀⣀⣠⡆⠹⣧⡀⠀⠀⣨⠿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠙⢿⡁⠀⠀⢸⣿⠀⣿⡇⠀⠀⠐⣲⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣷⣿⣿⣿⡯⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢠⣀⠉⠉⠉⠉⠀⠀⠈⠙⠛⠋⠁⠐⢛⣓⣻⣿⣿⣧⣿⡿⠯⡄⠈⢿⣤⣀⣸⣏⣴⣿⣷⣄⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⠻⣿⣿⣿⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⣿⣿⣗⣿⣿⣿⣯⢼⡏⢾⠀⠀⡇⡃⠀⠸⣤⡆⠀⠀⡔⠺⠹⣿⣿⣿⣿⣿⣿⠿⡤⢀⠀⠀⡀⢀⣶⣆⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣽⣿⣿⣿⡿⣿⡿⢀⣿⣿⣿⣿⠀⠀⠀⠀
⠛⠋⠉⠁⠉⠉⠛⠛⠛⠛⠻⣿⣿⢘⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠙⠂⠀⠙⠾⢿⣿⣿⠚⠀⠸⠄⠀⠰⠳⠈⢻⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣶⣦⣄⣤⡐⠟⢇⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⡿⠛⠛⣿⣋⡙⠻⣿⣧⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠋⢀⣤⣤⣿⣿⣿⣷⣄⣿⣿⣧⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠘⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⣀⡐⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⢿⣏⣿⣿⣿⣷⣧⣔⣹⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡏⠁⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠸⢾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣽⢻⡿⣿⣿⣿⣿⣿⣹⡇⠀⠀⠀⠈⠀⠀⠈⠉⠉⠀⠈⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣺⡇⣿⣿⣿⡟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠹⡧⣞⡗⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠙⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣦⣄⠀⣀⠀⠀⠀⠀⠀⣠⣿⣿⣇⣄⣄⣀⣀⢀⠀⠀⣀⡀⡀⣀⢀⣀⣀⠀⣠⣄⣠⣢⣀⣀⣀⣴⣶⣶⣶⣶⣤⣤⣤⣤⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣿⣴⣤⣄⣴⣴⣤⣧⣶⣿⣿⣿⣿⣷⣿⣷⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣮⣼
⠀⣀⣀⣀⣤⣤⣶⣶⣶⣶⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⡋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⢠⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣾⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⡶⠦⣤⠤⢤⡤⢤⣤⣤⣤⣄⡀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠝
⠀⠀⠀⠀⠀⠀⢀⣈⢀⣀⣿⢠⣆⠃⢸⣿⠀⠀⡘⠃⣰⡾⠋⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣗⣶⠶⠶⣤⡀⠀⠤⣤⡤⠀⠀⣀⣤⣄⣀⡀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀
⠀⢀⢈⣧⣶⣿⣾⣿⣿⣿⣿⣾⣿⠳⣼⡟⠚⠛⡇⠀⣿⡇⠀⢹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⢀⣀⣿⡇⠀⢸⣿⠀⢰⣿⠋⠀⠀⠈⠇⣀⢹⡟⣽⣿⣿⣿⣿⣿⣻⣿⡟⣛⣿⣿⣿⢛⣿⡿⣿⣿⣿⣿⣿⡟⠀⠀
⣶⣾⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣠⡆⠻⣧⡀⠈⠉⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⠙⢿⡉⠀⠀⢸⣿⠀⣿⡇⠀⠀⠐⢲⡶⣼⣾⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠉⠉⠉⠉⠀⠀⠈⠙⠛⠋⠑⢞⣛⣛⣿⣿⣿⣷⣿⡿⠯⡄⠈⢿⣤⣀⣸⣏⡀⠘⢷⣄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⠻⣿⣿⣿⣿⡿⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⢥⡏⢾⠀⠀⡇⡃⠀⠹⣤⡆⠀⠀⡔⠿⣿⣿⣿⣿⣿⣿⣿⣿⡤⣀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠉⣹⣾⣿⣿⣿⣿⣿⣟⣓⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣿⣿⣿⣿⣇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠙⠊⠙⢿⣿⣿⣿⣿⣿⠿⠸⠄⠀⠰⠳⡀⠀⡿⢼⠁⠀⡯⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠟⠿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣟⣿⣿⢿⣿⣿⠟⢹⣿⣿⢿⣿⣿⣇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠀⠀⠀⠀⠀⣤⣬⣾⣿⡟⠉⠀⠘⣿⣿⣿⣿⣿⣿⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⡿⣶⣤⣤⡤⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡿⠛⠉⣉⣉⣥⣀⠀⢹⣿⣷⡄⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠘⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣯⢀⣶⣶⣿⣿⣿⣿⣧⣸⣿⣿⣿⣤⡠⠽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣷⣤⣀⣀⣤⣸⣿⣿
⠀⠀⠀⠀⠀⠀⡌⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⠀⠀⠀⠀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣊⣤⣶⣔⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⡸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠉
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠟⠙⣿⡿⠏⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣯⡁⠀⠀⠀
⠀⠀⠀⠀⡆⣻⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠀⠀⠀⠈⠃⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⢠⣤⡄⠀⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀
⠀⠀⠀⠀⢱⣛⣆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠐⣿⣿⣿⣟⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⠻⠟⠻⠿⠿⡄⠀⠀⠀⠀⢻⣿⣿⣿⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢸⠛⠿⠿⠿⢿⡿⢿⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡮⣻⣿⣿⡿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⢻⣿⡿⠿⠿⠫⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠹⠘⣿⡇⣿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⡇⠈⠁⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠻⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠳⠻⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⢀⡀⡀⢂⢨⣒⣾⣻⣿⣃⠀⠀⠀⠀⠀⢀⣾⣿⣿⣶⣶⣶⣶⣤⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡆⠀⠀⣴⣶⣰⡿⠀⠀⣿⣿⣿⣿⣿⣶⣄⣀⣀⣀
⠀⡀⠀⠀⢀⣤⣤⣤⣦⣤⣤⡤⣵⣠⣶⣶⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾
⣒⣲⣶⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠣⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⡃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡂⠀⡿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡇⠀⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⣿⣿⣗⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣟⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣷⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⣿⣿⣿⣿⣿⣿⣅⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⣤⠤⢤⡤⢤⣤⣤⣤⣄⡀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⢀⡀⠀⠀⢀⣈⣀⣀⣿⢠⣦⠃⢸⣿⠀⠀⡘⠃⣰⡾⢋⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣗⣶⠶⠶⣤⡀⠀⠤⣤⡤⠀⠀⣀⣤⣄⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀
⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣼⡟⠚⠛⡇⠀⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⢀⣀⣿⡇⠀⢸⣿⠀⢰⣿⠋⠀⠀⠈⠇⠀⢹⡟⠉⣿⣿⣿⣿⡿⣻⣿⡟⣛⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⡟⠀⠀
⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣠⡆⠻⣧⡀⠈⠑⣻⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⠙⢿⡉⠀⠀⢸⣿⠀⣿⡇⠀⠀⠐⢲⡶⠀⢸⡧⠤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣿⣿⣿⣿⣿⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣀⠉⠉⠉⠉⠀⠀⠈⠙⠛⠋⠁⢟⣛⣛⣿⣿⣿⣧⣿⡿⠯⡄⠈⢿⣤⣀⣸⣏⡀⠘⢷⣄⠀⠀⣼⡇⠀⣾⡇⠀⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⠻⣿⣿⣿⣿⠟⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⡏⢾⠀⠀⡇⡃⠀⢹⣤⡆⠀⠀⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⡤⢀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⢐⣛⣓⣢⣶⣛⣓⣿⣿⣿⣿⣽⣿⣿⣿⢿⣿⡿⢀⣿⣿⣿⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠙⠊⠙⣿⣿⣿⣿⣿⣿⠿⠼⠄⠀⠰⠻⡀⠀⡿⢼⠁⠀⡯⡇⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⡋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣷⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⠟⠛⢷⣶⣾⡗⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠻⠟⠛⢻⣿⡟⠉⠀⢸⣿⣧⡜⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢠⣴⡿⠋⠋⠁⣤⣴⣶⣤⡀⣿⣿⣷⢤⢤⣤⠤⠯⢿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⡟⠀⠀⠀⠀⠛⠛⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡆⣴⣿⣿⣿⣿⣿⣿⣧⣸⣿⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢿⣿⠏⠀⠀⠀⠀⡀⠀⠀⠀⢽⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⡀⢰⣀⠀⠀⠘⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣾⣿⣶⠀⠀⠀⢑⠟⠟⠋
⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣦⣽⣿⣿⣿⣧⣤⣀⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡖⢟⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠟⠁⠀⠈⢰⣿⣻⣿⣽⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢰⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣖⡀⠀⠀⠀
⠀⠀⠀⠀⣩⣿⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡤⠚⠛⠉⠛⢿⡿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣤⡺⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢸⠻⠿⣿⣿⣿⡿⢿⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢿⣟⣿⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢼⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣿⢹⣿⣿⣿⢽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⠆⠜⣿⣃⠻⢸⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢘⡿⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠭⠃⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⠁⠿⠀⠀⠀⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⠻⠿⠷⠀⠀⠀⠀⠀⠀⠀⠈⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⢀⣀⣀⣤⢶⣶⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣰⣴⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡆⠀⠀⣼⣷⣿⡟⠈⣿⣿⣿⣿⣿⣿⣶⣄⣀⣀⣀
⠀⠀⠀⠀⢀⣠⣤⢦⣶⣤⣤⣠⣤⣤⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣬⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⢀⣿⣿⣿⡅⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⠇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒⠀⡃⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⡏⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢈⣿⣿⣿⡿⢇⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢸⣿⣿⣿⣿⠏⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣷⡄⢀⢤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣇⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⣤⠤⢤⡤⢤⣤⣤⣤⣄⡀⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⢀⡀⡀⠀⢀⣈⣀⣀⣿⢠⣦⠃⢸⣿⠀⠀⡘⠃⣰⡾⢋⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣗⣶⠶⠶⣤⡀⠀⠤⣤⡤⠀⠀⣀⣤⣄⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀
⠀⢠⣴⣷⣾⣿⣿⣿⣿⣿⣿⣾⣿⣇⣼⡟⠚⠛⡇⠀⣿⡇⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⢀⣀⣿⡇⠀⢸⣿⠀⢠⣿⠋⠀⠀⠈⠇⠀⢹⡟⠉⣿⣿⣿⣿⡿⣻⣿⡟⣛⣿⣿⣿⢛⣿⡿⣿⣿⣿⣿⣿⡿⠀⠀
⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣠⡆⠻⣧⡀⠀⠉⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⠙⢿⡉⠀⠀⢸⣿⠀⣿⡇⠀⠀⠐⢲⡶⠀⢸⡧⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠉⠉⠉⠉⠀⠀⠈⠙⠛⠋⠁⢚⣛⣛⣿⣿⣿⣧⣿⡿⠯⡄⠈⢿⣤⣀⣸⣏⡀⠘⢷⣄⠀⠀⣼⡇⠀⣾⡇⠀⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⠻⣿⣿⣿⣿⠗⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⡏⢾⠀⠀⡇⡃⠀⢹⣤⡆⠀⠀⡞⢻⣿⣿⣿⣿⣿⣿⣿⣿⡤⢀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⢐⣛⣓⣢⣶⣛⣓⣿⣿⣿⣿⣽⣿⣿⣿⢿⣿⡿⢀⣿⣿⣿⣾⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠙⠊⠙⣿⣿⣿⣿⣿⣿⠿⠼⠄⠀⠰⠳⡀⠀⡿⢼⠁⠀⡯⡇⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣷⣶⣦⣀⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⠟⠛⢷⣶⣾⡦⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠟⠛⠛⠛⠿⠛⢻⣿⡟⠉⠀⢸⣿⣧⡈⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢠⣼⡿⠛⠋⠀⣥⣴⣶⣤⡀⣿⣿⣷⡶⣤⡤⡤⠿⢿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⡟⠀⠀⠀⠈⠛⠛⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣖⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡆⣴⣿⣿⣿⣿⣿⣿⣷⣼⣿⡇⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⢿⣿⠏⠀⠀⠀⠀⣀⡀⠀⠀⢿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⢛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⡀⡠⡄⠀⠀⠘⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣾⣿⣷⡀⠀⠀⢸⠿⠟⠋
⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣧⣿⣿⣿⣿⣧⣤⣀⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡖⢙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠏⠁⠀⠈⢰⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢰⣶⣶⣾⣿⣿⣿⣿⣿⣷⣦⣆⠀⠀⠀⠀
⠀⠀⠀⠀⢣⡴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡰⠟⠛⠉⠛⢿⡟⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢭⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣤⡚⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢸⠻⠿⣿⣿⣿⡿⢿⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢿⣟⣿⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣿⢹⣿⢿⣿⢽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣀⡀⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠠⠍⠘⣿⡃⠻⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡄⠀⠠⡀⢨⣿⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⠩⠄⠀⠈⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⡀⠀⠈⠁⠿⠀⠀⠀⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⠻⠿⠳⠄⠀⠀⠀⠀⠀⠀⠈⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣤⣄⣀⣀⣀⣀⣴⣶⣞⣿⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣰⣶⣶⣦⣴⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣾⣾⡆⠀⠀⣴⣶⣿⡏⠀⣿⣿⣿⣿⣿⣿⣶⣄⣀⣀⣀
⠀⠀⠀⠀⠀⢠⣤⣤⣶⣄⣤⣠⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣌⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⢀⣿⣿⣿⡂⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠘⠀⡰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡰⠀⡃⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⣏⣦⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⢅⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢸⣿⣿⣿⣿⣹⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢸⣿⣿⣿⣿⡏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⡶⠦⣤⠤⢤⡤⢤⣤⣤⣤⣄⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⣀⠀⠀⡀⣈⣀⢀⣿⢰⣦⠃⢸⣿⠀⠀⡘⠃⣰⡾⠋⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣗⣶⠶⠶⣤⠀⠀⠤⣤⡤⠀⠀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀
⡀⢀⣸⣿⣷⣾⣿⣿⣿⣿⣿⣼⣿⣧⣼⡟⠚⠛⡇⠀⣿⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⠀⣀⣿⡇⠀⢸⣿⠀⢰⣿⠋⠀⠀⠈⠇⠀⢹⡟⠉⠀⢹⣿⠛⡿⠓⢲⡖⣛⣿⢻⣿⢿⣻⣿⣿⣿⣿⣿⡿⠛⠀⠀
⣿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣇⣀⣀⣠⡆⠻⣧⡀⠈⠛⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⠹⢿⡉⠀⠀⢸⣿⠀⣿⡇⠀⠀⠐⢲⡶⠀⢸⡧⢤⣤⣼⣿⠠⠥⠀⣿⡇⣾⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣆⠉⠉⠉⠉⠀⠀⠈⠙⠛⠋⠑⢾⣛⣛⣿⣿⣿⣧⣿⡿⠯⡄⠈⢿⣤⣀⣸⣏⡀⠘⢷⣄⠀⠀⣼⡇⠀⣾⡇⠀⠀⣸⡏⠀⣘⣿⣿⣗⣿⣿⣿⣿⣿⣭⠻⣿⣿⣿⡿⠃⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣷⡏⢾⠀⠀⡇⡃⠀⢹⣤⡆⠀⠀⡞⠻⣿⣿⣿⣿⣿⣿⣿⣿⡦⢀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠐⠛⠓⠂⠐⠛⠓⠒⣿⣿⣿⣽⣿⣿⣿⣿⣿⡿⢀⣿⣿⠏⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣗⡇⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠙⠊⠉⢿⣿⣿⣿⣿⣿⠿⠼⠄⠀⠰⠳⡀⠀⡿⢼⠁⠀⡯⡇⠀⡘⣜⢀⡀⢠⠒⢆⠀⡄⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⣪⣾⣟⡊⡖⠙⣵⣷⣿⣿⣿⣷⣿⣿⣷⣿⣿⢟⢘⠙⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡇⠀⠀⠀⠙⣿⣾⣿⣿⣿⣿⣿⣿⣿⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣶⣦⣤⣤⣤⢀⡤⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣄⣀⣠⣢⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⠟⠛⢻⣿⣿⣥⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⣠⣿⡟⠛⠋⢫⣽⣾⣿⣦⡘⣿⣿⠦⡴⠤⢦⣴⣴⢶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣬⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⢆⣶⣿⣿⣿⣿⣿⣿⣷⣾⣿⠇⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀
⠀⠀⠀⠀⠀⠈⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀
⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⣻⣖⣂⣶⣂⣿⣿⣿⣿⣿⣷⠀⠈⠫⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠏⠃⠹⣿⣿⡀⠀
⠀⠀⠀⠀⢖⠖⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠋⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⡇⠀
⠀⠀⠀⠀⢘⢳⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠉⠹⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⣿⡇⠀
⠀⠀⠀⠀⠀⠈⢁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠈⢹⣿⣿⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠛⢿⠿⢿⣿⣿⣤⡀⠀⢀⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢸⠛⠧⠤⠀⠄⠄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠸⣿⣿⠟⠛⠿⠿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢙⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠈⠏⢸⣿⠽⣿⢻⣿⣧⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣿⠄⠙⠀⢿⣿⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠨⠅⠀⠀⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠛⠻⠟⠳⠀⠀⠀⠀⠀⠀⠀⠈⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣤⡤⣀⢀⣀⠠⢐⣀⣴⣼⣿⣏⢹⣥⣀⠀⠀⠀⠀⢀⣄⣸⣿⣿⣧⣤⣦⣶⣶⣶⣶⣶⣶⣧⣷⣶⣶⣴⣾⣷⡆⠀⠀⢠⣦⣾⣿⣿⣿⣿⣿⣿⣿⣷⣆⣄⣀⣀⠀
⠀⠀⠀⠀⠀⣠⣤⣴⣶⣤⣴⠠⣤⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿
⣒⣲⣦⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠀⠨⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢸⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣉⠀⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⣿⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⢠⣿⣿⣧⡝⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⡅⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣏⠈⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⡍⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⣄⡀⣠⣀⣀⣀⣀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⡀⢸⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀
⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠻⢿⣏⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡥⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣦⣤⣄⣤⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣳⣿⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⢟⣿⣧⠀⣦⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⣿⡏⣩⣿⣿⣦⣜⣿⣿⣛⢄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈⠉⣉⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠛⠛⠟⠟⠿⠿⢷⣿⣿⣿⣿⡀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⡅⠀⠀
⠀⠀⠀⠀⠀⠀⢜⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠀⠀⠘⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠳⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣷⢦⡀⠀⠀⠀⣽⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⠿⠁⠈⠿⣿⣿⣛⣷⣄⣠⣤⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠰⡏⠀⠀⠀
⠀⠀⠀⠀⣆⣈⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠁⢿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠉⠉⠉⠉⠉⠙⠿⠿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠃⣩⡧⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣦⣄⠀⠀⠀⠈⠙⢿⣿⣿⣿⣯⣀⣀⣀⣠⠠⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⣦⣴⠶⠶⡶⠀⢠⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠁⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠻⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢼⣩⠃⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⠙⠛⠛⠛⠛⠛⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠐⣿⢻⣿⡏⣿⣿⣿⡇⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠍⠀⢿⡄⠻⠁⢻⡇⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠘⠁⠀⠀⠘⣇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣈⠝⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠈⠑⡄⠠⠃⠀⢰⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠐⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣧⢐⣄⠀⠀⠀⠀⠀⠀⣄⠀⣾⣷⣶⣀⠀⠀⢀⡀⠀⡀⠀⣀⢀⣀⣀⣀⣀⣠⣿⣏⠀⠀⠀⠀⡌⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⣤⣦⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢠⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣰⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶
⠀⠀⠀⢀⣀⣠⣶⣴⣼⣶⣶⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢱⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠨⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡟⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠁⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂⢸⡏⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣼⡇⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠔⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢨⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢸⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣷⣶⣆⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⣠⢠⢠⣀⣠⣤⣤⣤⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀
⣄⠀⣰⢚⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀
⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠃⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⡎⠁⠀⠀⠀⠀⠀
⣿⠿⠻⠋⠉⠙⠉⠙⠛⠛⠛⠿⣿⡧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⣿⠿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣶⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣲⠬⠁⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠉⠋⠁⠻⣿⣿⣿⣿⣿⣿⢿⠟⠟⠛⠋⠉⠁⠈⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⣤⣯⠽⠉⢉⣍⣨⣾⣿⣦⡹⣿⣷⣀⣀⣀⣀⣀⡀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠉⠉⠀⠁⠁⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣡⣤⡀⠀⠀⠀⠀⠀⢀⢻⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢄⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣧⣤⣀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠈⢸⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⣿⣿⣿⢟⣷⣿⣆⣆⠀⠀⡌⠋⠉⠈⠉⠉⠙⠛⠿⢿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠻⠃⠀⠀⢀⡁⠸⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠟⠃⠈⠛⣿⣿⣻⣶⣈⣇⠀⢀⢀⣀⣀⣀⣀⣀⡘⠛⣿⣿⣿⣿⣿⣿⣉⣠⣤⣶⠾⠛⠛⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠌⠡⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠙⢿⣿⣿⣾⣯⣿⣿⣿⣿⣿⣿⡿⠍⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷⣦⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠡⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⡟⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢸⢿⣿⡿⣿⣿⡿⢿⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡿⠉⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢨⡏⢿⡟⢻⡏⢻⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠈⠁⠘⠃⠸⠇⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢰⣿⣇⠀⠀⠀⠀⠁⠀⠀⠀⢷⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠶⡶⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⣴⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⠀⢴⣷⣶⣠⣀⣤⣤⣴⣦⣴⣴⣴⣦⣶⣶⣶⣤⣴⣿⣿⡀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀⠀⠀⣠⣠⣴⣶⣴⣿⣿⣿⣷⣾⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⢀⢀⡠⣴⣶⣾⣿⣷⣷⣷⣾⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠨⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠁⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣭⣭⣟⣯⣟⣫⣭⡛⣯⣥⣤⡀⠀⠈⣹⣯⣭⡛⡿⣻⣿⣿⡻⣫⣯⣏⣙⡻⣿⣿⣿⣿⣿⣿⣿⣸⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡟⣿⣿⡟⢻⣿⣿⣿⣿⡇⣿⣿⠛⠃⠀⢸⣿⡏⣿⣿⢀⣿⣿⣿⡇⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⠿⠇⠀⢸⣿⡇⣉⣉⢸⣿⡟⣿⣷⣿⣿⡿⣿⣏⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⡇⣿⣿⣤⡄⠀⢸⣿⣇⣿⣿⣼⣿⡿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠅⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣽⣿⣧⣿⣿⡛⠃⡀⣸⣽⣟⣿⣵⣿⣿⣧⣿⣿⣽⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⣤⡄⢆⣀⣠⣴⣒⣀⣠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀
⣅⠀⡶⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀
⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀
⡿⠿⠛⠋⠉⠉⠉⠙⠛⠛⠻⠿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣾⣶⣄⡄⠁⠀⠀⠀⠀⠀⢀⣿⣿⣿⣟⠉⠻⢿⠿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⡿⠟⠛⠙⣿⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⣿⢿⠿⠿⡿⠻⣻⣟⡙⣿⣿⣦⣄⣤⡤⣤⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠛⠉⢀⣶⣶⣿⣿⣿⣿⣼⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡄⠀⠀⠀⢰⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣥⣄⠀⠀⠀⠀⠀⠀⠁⣻⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠀⣀⣸⡿⠿⠿⠿⣿⣷⣶⣤⣄⣀⣼⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⣿⣿⣿⠛⠃⣿⣿⢹⣿⢿⡇⠀⠀⠀⠀⠀⠈⠉⠙⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣀⣤⣶⡶⠂⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠩⠄⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠁⠀⠀⠘⢻⣿⡿⣮⣿⣻⣾⣷⣶⣶⣶⡶⠀⠀⠈⠙⢿⣿⣿⣿⣷⣶⣾⠿⠿⠉⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⢕⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⡘⠁⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⡷⠊⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠸⠿⡿⢿⣿⣿⡿⣿⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢹⡿⣽⣿⣿⣟⣿⣿⣇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⣿⢹⣿⢿⣿⢽⣿⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠻⠀⠏⠸⣟⠘⡟⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⡯⠀⠀⠀⠤⠃⠀⠁⠀⢻⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠲⠿⠷⠦⠄⠀⠀⠀⠀⠀⠀⠀⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⡤⣾⣻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣠⢄⣄⣄⣠⣶⣆⣴⣶⣴⣆⣶⣶⣶⣤⣤⣿⣿⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣷⣶⣤⣤⡄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⡀⠀⠀⣀⣴⣶⣶⣶⣾⣿⣿⣷⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⣾⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⢀⣔⣶⣿⣿⣿⣿⣶⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⡠⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣭⣽⣛⣭⣝⣻⣿⡛⣿⣥⣤⡀⠀⠈⣻⣯⣿⣛⠿⣻⣭⣿⡻⣫⣭⣍⣙⡻⣿⣿⣿⣿⣿⣿⣿⣸⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⣿⣿⡟⢻⣿⣿⣿⣿⡇⣿⣿⠛⠃⠀⢸⣿⡏⣿⣿⢀⣿⣿⣿⡇⣿⣿⡟⣿⣿⢻⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⡇⢸⣿⣿⣿⣿⡇⣿⣿⠿⠇⠀⢸⣿⡇⣉⣉⢸⣿⡟⣿⣷⣿⣿⡿⣿⣏⣿⣿⣿⣿⣿⣿⣿⡇⠂⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⡇⣿⣿⣤⡜⠀⢸⣿⣇⣿⣿⣼⣿⡿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡄⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣽⣿⣧⣿⡛⠛⢣⠄⢺⣽⣟⣿⣵⣿⣿⣧⣿⣿⣽⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⣠⣦⣀⣤⣠⣤⣄⣢⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀
⣆⠀⣺⡂⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡃⠁⠀⠀⠀⠀⠀
⠿⠿⠛⠉⠉⠉⠉⠉⠉⠙⠛⠻⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣝⣽⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣶⣷⣦⣠⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⣽⣟⡿⠿⠿⠟⢻⣿⡏⢻⣿⣧⣀⣄⣀⣀⠀⢠⣿⣿⣿⣏⠈⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⡏⠟⣿⡿⠟⠟⠋⢹⣷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⠛⠉⢀⣶⣿⣾⣿⣿⣿⣾⣿⡃⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⢠⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠽⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⠋⠁⣿⣿⣿⣿⠟⣿⡿⠿⣿⣿⣿⣶⣶⣤⣄⣼⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠋⠁⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠋⠀⠀⠀⠈⢻⣿⡿⣮⡁⠀⠀⠀⠈⠀⠈⠉⠋⢛⣿⣿⣿⣿⣋⣀⠀⠀⠀⣀⣤⣶⡿⠏⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣝⠁⠀⠀⠀⠀⠉⢱⣟⣛⣷⣾⣶⣶⣦⠄⠀⠀⠀⠉⠛⢿⣿⣿⣿⣷⣶⡿⠟⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠈⠉⠻⠿⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠈⠿⠿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢏⡟⣹⣿⣿⣏⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣾⠀⣿⢹⣿⢻⣿⢺⣿⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⡋⠸⡟⠘⡏⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⣧⠀⠀⠀⠀⠀⠀⠠⠄⠂⠀⠘⠛⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠅⠀⠁⠀⢹⡇⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠙⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠒⠻⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⢤⣤⣾⣿⣿⣿⣟⣀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣦⣤⣦⣤⣴⣶⣴⣶⣦⣴⣦⣶⣶⣶⣦⣦⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀⣀⢀
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣀⢀⡀⢤⣤⣶⣶⣶⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡄⠀⠀⠀⠀⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿
⢀⣀⣀⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠰⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣟⣭⣝⣻⣿⡿⣿⣤⣤⡀⠀⠊⣹⣽⣿⡻⠿⣻⣿⣯⡻⣫⣭⣭⣙⡻⣿⣿⣿⣿⣿⣿⣿⣼⠁⠨⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣛⣿⣿⡟⢻⣿⣿⣿⣿⡇⣿⣿⠛⠃⠀⢸⣿⡏⣿⣿⢀⣿⣿⣿⡇⣿⣿⡟⣿⣿⣻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⡇⣸⣿⣿⣿⣿⡇⣿⣿⠿⠇⠁⢸⣿⡇⣉⣉⢸⣿⡟⣿⣷⣿⣿⡿⣿⣏⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣤⡜⠃⢸⣿⣇⣿⣿⣼⣿⡿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣽⣿⣧⣿⡛⠛⣣⠄⢴⣽⣟⣿⣵⣿⣿⣧⣿⣿⣽⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡟⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⢀⣤⣀⣴⣠⣴⣖⣰⣤⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀
⣧⢀⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣍⣡⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀
⠿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠙⠛⠿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⢿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⠿⠿⢛⣿⣿⣄⢻⣶⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠈⠉⠉⠛⣿⣿⣿⣿⣿⣿⠿⠻⠿⠛⠛⠉⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠻⠛⠉⢠⣾⣿⣻⣿⣿⣿⣿⣿⡽⠤⠤⢤⣤⣶⣦⡤⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣀⣠⡀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠟⣧⣾⣧⠀⣉⣃⠀⠀⠀⠻⠿⠿⠿⢿⣿⣷⣤⣀⠀⢠⣾⣿⣿⣿⣶⣶⠄⠀⠀⠀⢀⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠈⠛⢿⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⣿⣿⣿⣿⣿⣿⠋⣁⣤⣶⡿⠟⠙⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣤⡀⠀⠀⠀⠙⣿⣷⣯⡁⠀⢰⠂⠀⠀⢸⠿⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢝⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⢹⣿⣿⣀⢚⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⠍⢾⣿⣿⣿⣿⢹⣿⣧⠀⠀⠀⠸⠙⠋⠛⠃⠛⠉⢹⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣿⢻⣿⢸⡗⠘⣿⣿⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠁⠘⠛⠘⡷⠀⢻⣿⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠂⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⡀⠶⠂⠀⢈⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡇⠀⠀⠰⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡇⠀⠀⠠⠀⠀⣤⣤⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⣠⣿⣿⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣄⣀⠀⢀⣀⠀⠀⣤⣤⣼⣿⣿⣿⣦⣶⣄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣾⣿⠄⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣶⣶⣗⣢⣄⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⢸⣿⣿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣁⡀⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⣷⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣭⣭⣛⣭⣝⣫⣭⡛⣭⣭⣥⡘⠀⠀⣨⣭⣭⡛⠿⣻⣭⣽⡻⣻⣭⣍⣛⡻⣿⣿⣿⣿⣿⣿⣿⡜⠀⢸⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛⣿⣿⡟⢻⣿⣿⣿⣿⡇⣿⣿⠛⢣⡀⢸⣿⡏⣿⣿⢀⣿⣿⣿⡇⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⣿⣿⠿⢿⡇⢸⣿⡇⣉⣉⢸⣿⡟⣿⣷⣿⣿⡿⣿⣏⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⡇⣿⣿⣤⡿⡇⢸⣿⣇⣿⣿⣼⣿⡿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡅⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣽⣿⣧⣿⡛⢛⣷⡇⠀⣽⣟⣻⣵⣿⣿⣧⣿⣿⣽⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣷⣶⣴⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠡
⠀⠀⠀⢄⣀⣀⣂⣠⣤⠤⣠⣴⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀
⣾⠀⠀⣁⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀
⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀
⠿⠟⠛⠉⠉⠁⠀⠀⠉⠉⠉⠛⠻⣿⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⡿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠈⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡿⠿⢿⠿⣿⣯⡉⢿⣦⣖⡆⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠟⠉⠉⠉⠉⠀⣹⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠟⠂⢀⣴⣶⣿⣿⣿⣿⣾⣿⡍⠌⠤⠤⣤⣶⣶⡶⣦⠴⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢻⣿⣟⡀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⡠⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⢈⣿⣿⣟⠀⠀⠀⠀⠀⠀⣽⠅⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣿⣿⣿⣿⠟⠉⢶⡖⣧⣤⠀⠀⠀⡀⠀⠀⠈⠉⠉⠉⠉⢿⣿⣿⣶⣤⣠⣿⣿⣿⣿⣿⣶⣆⢀⣀⢠⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠉⠀⠀⠈⠙⢿⣿⣿⣾⡿⠅⠀⠀⠀⠀⠀⠀⣠⣀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣯⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣆⣀⠀⠀⠀⠀⠙⣿⣿⣧⣀⡀⠀⠀⠀⠘⠻⠟⠁⠀⠀⠀⠈⣻⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⢸⣿⣾⡄⠀⠐⡯⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠉⣿⣿⣿⣿⡝⣿⣿⡆⠀⠀⠀⢸⠉⠉⠃⠐⠐⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⡟⣿⡿⣿⡇⢻⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠃⠹⠗⠹⡇⠀⣿⣿⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⢠⠀⠀⠀⡤⠀⠀⠰⠀⠀⠀⠈⠀⡆⠀⠀⠀⠀⠀⢐⡀⠔⠂⠀⢨⡉⠀⢀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠟⠀⠀⠀⠀⢰⣾⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠈⠛⠉⠓⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⣿⣿⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣀⡀⣀⣀⣀⢀⢠⣤⣤⣿⣿⣷⣤⣄⣄⡀⠀⠀⢀⣾⣿⣿⣿⣾⣾⣶⣶⣶⣿⣷⣿⣶⣾⣿⣿⣿⣿⣿⣿⣟⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⡀⠀⢀
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣦⣀⣀⣠⣄⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⢸⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢸⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⡅⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣋⣉⣉⣛⣉⣙⣋⣉⡉⣉⣉⣁⡘⠀⠀⣨⣭⣭⡛⠿⣋⣉⣙⡛⣋⣉⣉⣙⡻⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡛⣿⣿⡟⢻⣿⣿⣿⣿⡇⣿⣿⠛⢣⠄⢸⣿⡏⣿⣿⢀⣿⣿⣿⡇⣿⣿⡟⣿⣿⢻⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⣸⣿⣿⣿⣿⡇⣿⣿⠿⢯⡇⢸⣿⡇⣉⣉⢸⣿⡟⣿⣷⣿⣿⡿⣿⣏⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⡿⠃⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣤⡝⡇⢸⣿⣇⣿⣿⣼⣿⡿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢘⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣽⣿⣧⣿⣟⠛⢳⡇⠀⣽⣛⣻⣵⣿⣿⣧⣿⣿⣽⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⡇⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣼⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣗⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓
⠄⠀⠀⣴⣰⣶⣂⣠⣧⣶⣰⣴⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀
⣿⡇⢐⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡛⢙⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀
⠿⠛⠛⠉⠉⠉⠁⠉⠉⠉⠉⠛⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⣠⣴⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣶⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⢿⣆⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠙⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⡙⠉⢉⣉⣿⣿⣿⣮⣻⣏⠉⠹⠦⠤⣤⣶⣶⡶⣶⠤⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠏⠁⠈⠁⠀⠀⢸⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⠉⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⢸⣿⣿⠗⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⣿⣿⣿⣿⣿⡿⠛⣷⡴⣦⣀⡀⣀⠀⠀⠀⠀⠻⠿⠿⢿⣿⣿⣦⣄⡀⠀⠀⣰⣿⣿⣿⣷⣄⡀⠀⠀⢀⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠤⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠟⠁⠀⠈⠩⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣈⠙⠻⢿⣿⣷⣾⣿⣿⣿⣿⠿⠿⣁⣄⣠⡌⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⡚⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⢀⠀⠀⠀⠈⠙⣿⣿⣿⠋⠀⠀⢀⣤⡿⢿⠟⠀⠀⠀⠁⢿⣿⣿⣿⣿⢃⣤⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠰⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣶⣮⡀⠀⠀⠀⠀⠀⢹⣿⣄⢀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣿⣿⣿⣿⢿⣿⣦⠀⠀⠀⠀⢸⠉⠉⠐⠐⠚⠁⢹⠀⠀⠀⠀⠀⡀⠀⠀⠘⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣙⢸⡿⣿⣷⣿⠘⣿⣿⡇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⠇⣿⡏⣿⡆⢻⣿⡇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢙⠃⠹⠂⠸⣿⣷⠀⠀⠀⢰⣀⠀⠀⠀⡄⠀⠘⢀⠀⠀⠈⠁⡇⠀⠀⠀⠀⠀⢘⠃⠄⠂⠀⢸⡍⠀⢀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠚⠇⠀⠀⠙⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⡟⠀⠀⠀⠀⣐⣻⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢰⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠙⠛⠙⠓⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀⡀⠀⢀⣿⠀⠀⠀⣠⣿⣿⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣠⣤⣄⣀⣀⣀⣀⣤⣤⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⣄⣠⣀
⠀⠀⠀⠀⠀⣀⣠⣤⣶⣷⣷⣢⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⠇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣋⣉⣉⣛⣉⣙⣋⣉⡛⣛⣉⣀⡘⠀⠀⣩⣭⣭⡛⠿⣋⣉⣙⡻⣋⣉⣉⣛⡻⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛⣿⣿⡟⢻⣿⣿⣿⣿⡇⣿⣿⠛⢣⡀⢸⣿⡏⣿⣿⢀⣿⣿⣿⡇⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣽⣿⣿⣿⣿⡇⣿⣿⠿⢯⡇⢸⣿⡇⣉⣉⢸⣿⡟⣿⣷⣿⣿⡿⣿⣏⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣤⡝⡇⢸⣿⣇⣿⣿⣼⣿⡿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣽⣿⣧⣿⣟⡛⣳⡇⠀⣽⣟⣿⣵⣿⣿⣷⣿⣿⣽⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⡛⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢽⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⣀⡤⠀⢄⣶⣶⣶⣲⣶⣶⣶⣶⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀
⣿⣷⣠⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀
⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠙⠛⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⠛⣻⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣠⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⡀⡁⢀⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⢿⠿⠿⣿⣿⣭⡽⣷⡄⠉⠫⠁⠤⠤⣶⣶⡶⠶⠄⣿⣿⣿⣿⣿⠀⠙⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⠛⠁⣠⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡏⠉⠉⠁⠀⠀⢀⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⡇⣦⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢹⣿⣿⣤⣤⡀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠰⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠻⣿⣿⣿⡿⠁⠀⠈⠁⣾⣷⣶⣄⡀⠀⠀⠀⠻⠿⠟⢿⣿⣿⣶⣄⡀⠀⠀⢀⣿⣿⣿⣯⣄⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⡃⠀⠀⣠⣦⡀⠀⠈⠉⠻⢿⣿⣷⣦⣾⣿⣿⣿⣿⡿⢗⣠⣤⡄⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣷⣤⡃⠀⠀⠀⠀⠀⠀⢸⣿⡅⠀⢐⣿⣿⣿⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣏⣻⣷⣿⠏⠁⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢸⠙⠂⠀⠼⠛⠉⢩⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡍⣼⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠂⠀⠀⠈⠙⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢻⣿⣿⢿⣧⠸⣿⣿⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀
⡀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠈⠀⠈⠀⠻⠂⢿⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⢘⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠰⠄⠀⠀⠘⢁⣸⡉⠀⠀⠀⠀⠀⠀
⢿⣶⣶⣤⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⢈⣿⡿⢸⡇⠀⠀⠸⡃⠀⠀⠈⠀⠀⠏⠀⠗⠀⠀⠇⠀⠀⠀⠀⢨⡦⠀⠀⠀⠰⠁⠀⠀⠁⠀⠀⠈⠀
⠀⠀⠉⠓⠒⠺⠿⠶⣷⣶⣾⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⣶⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢁⣺⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⢀⡀⠀⠀⢀⠀⢀⢀⣀⣀⣀⣀⣀⡀⢀⣿⠀⠀⢀⣴⣿⣿⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⣀⣠⣦⣄⣀⣀⣀⣤⣠⣤⣤⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣀
⠀⠀⠀⠀⠀⢀⣤⣤⣠⣴⣶⣶⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣶⣶⠂⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢠⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣯⣭⣭⣛⣭⣝⣻⣿⡛⣩⣭⣤⡘⠀⠀⣻⣯⣭⡛⠿⣫⣭⣭⡻⣻⣭⣉⣙⡻⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣛⣿⣿⡟⢻⣿⣿⣿⣿⡇⣿⣿⠛⢃⠀⢸⣿⡏⣿⣿⢀⣿⣿⣿⡇⣿⣿⡟⣿⣿⣻⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⡇⣿⣿⠿⢯⠀⢸⣿⡇⣉⣉⢸⣿⡟⣿⣷⣿⣿⡿⣿⣏⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣤⡝⡆⢸⣿⣇⣿⣿⣼⣿⡿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣽⣿⣧⣿⣛⡛⣳⡇⠀⣽⣟⣿⣵⣿⣿⣧⣿⣿⣽⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⢀⣠⣤⡀⢶⢠⣶⣤⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀
⣶⡆⠀⠀⢀⣘⠽⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀
⣿⣿⣶⣶⣬⣯⣬⣛⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀
⠿⠟⠛⠉⠉⠁⠈⠀⠈⠉⠉⠛⠻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⣀⣽⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣽⣿⣿⡿⠿⠻⣿⣛⠉⠹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣗⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡋⠁⣴⣦⣤⣴⣿⣿⣷⡄⣿⡿⠄⠤⢴⣶⣤⣤⠤⠄⣿⣿⣿⣿⡟⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⡿⠛⠛⠟⠋⠁⠀⢹⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⠏⠀⠀⠲⣧⠓⠀⠀⠀⠀⠀⠀⢻⣿⣿⣛⣃⡀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠀⠀⠀⢿⣷⣦⠀⠀⠀⠀⠀⠸⠿⠿⠿⣿⣿⣶⣄⡀⠀⠀⢀⣡⣶⣶⣆⣀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣷⣄⠀⠀⠀⠀⠀⠙⢿⡇⣦⡀⠀⠀⠀⣄⡀⠀⠀⠉⠛⠿⢿⣿⣶⣿⣿⣿⣿⣿⣿⣷⣾⡿⠿⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⡟⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠏⢸⣿⣿⣿⣿⢻⣿⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠩⢻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠀⢸⡏⣿⣿⣿⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣤⣀⣀⣄⡀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⠀⠻⠂⢻⠀⢻⡇⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣠⣤⣶⣶⣿⣷⣆⠈⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠀⠀⠄⠀⠀⠀⣀⢀⠀⠈⠀⠀⢰⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠹⠉⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⣀⣁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡇⠀⠀⠀⠀⠀⠇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠁⠉⠙⠛⠁⠀⠉⠙⢻⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠾⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠠⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⣸⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡇⠀⠀⠀⣤⣿⣧⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣴⣶⣷⣾⣿⣿⠇⠀⢠⣿⣿⣦⣤⡤⠀⠀⠀⠀⢠⣶⣦⣼⡿⠃⠀⣸⣷⣿⣿⣿⣿⣿⣶⣾⣷⣿⣿⣶⣿⡇⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⢀⣠⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠠⠺⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⢸⣿⣿⣻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠠⠀⣼⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣿⣿⣿⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⣋⣀⣀⡀⠀⠘⣫⣭⣭⡛⠟⣋⣉⣉⡻⣋⣉⣉⣙⡻⣿⣿⣿⣿⣿⣿⠁⠀⠰⣿⣿⠂⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⣿⣿⡟⢻⣿⣿⣿⣿⡇⣿⣿⠛⢃⡀⢸⣿⡏⣿⣿⢀⣿⣿⣿⡇⣿⣿⡟⣿⣿⢹⣿⣿⣿⣿⣧⠀⠀⢸⣿⡏⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢼⣿⣿⣿⣿⡇⣿⣿⠿⠇⠁⢸⣿⡇⣍⣉⢸⣿⡟⣿⣷⣿⣿⡿⣿⣏⣿⣿⣿⣿⣿⣿⠀⠀⣾⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⡇⣿⣿⣤⡌⠁⢸⣿⣇⣿⣿⣼⣿⡿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣽⣿⣥⣿⣟⠛⠃⠀⠀⣽⣛⣻⣵⣿⣿⣧⣿⣿⣽⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠅⠀
⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⢠⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀
⠠⠄⠀⠀⠀⠀⠉⠀⢀⣢⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠅⠀⠀⠀
⣾⣶⣤⣀⣀⡄⢀⣀⠸⡻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣯⡉⣹⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠻⣿⡿⡿⣻⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠛⠁⠀⠀⠀⠀⠀⠉⠉⠙⠻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⡿⠿⠻⢷⣶⡄⠀⠀⠀⠀⠀⠀⢸⣿⡟⠉⠀⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⡿⠻⠿⠿⠿⠛⠑⠛⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⠏⢀⣀⣀⣠⣴⣦⡀⠘⣿⣆⡀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⢠⣿⣿⣿⣿⣿⣿⣿⡄⢻⡿⠀⠀⠠⠤⠤⣼⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢽⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⣸⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠛⠁⠀⠀⢤⡀⠄⠀⠀⣿⣿⣿⣿⣿⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡌⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⢸⣷⣤⡀⢾⣿⣿⣿⣿⢿⠿⠿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢬⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣦⡀⠀⠀⠀⠀⠛⢷⠄⢈⠉⠁⠁⠀⠈⣇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠊⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣻⠋⣿⣿⣿⣿⢿⣄⠀⠀⠀⠀⠀⢠⣾⠀⢐⠀⠀⠘⠟⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⣠⣤⣤⣶⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠇⠀⣿⣿⣿⣿⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠇⣿⡏⢿⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠴⠟⠻⢿⣟⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣤⣄⢠⣼⣧⢐⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⠀⠀⠀⠀⠈⠀⢈⠀⠘⣇⠀⠀⣠⠄⠀⠀⣀⠀⠀⠀⠀⢸⣦⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣤⣤⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡀⠀⠀⣰⣦⣠⣿⡋⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣤⣿⣷⣶⣼⣿⣇⢠⣼⣿⡿⠿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⢸⣿⣠⣤⣿⣿⣧⠀⠀⣿⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⡆⠈⣿⣿⣿⣿⣿⣯⣿⣿⣿⢻⡿⠖⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣿⡿⢛⢻⣿⣿⣿⣆⣤⣤⣄⢈⣉⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡄⣤⠀⠙⢷⣿
⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⣿⣿⣿⣯⣿⣎⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⠉⠛⠛⠿⠿⠿⠿⢿⣬⣍⣉⡙⠃⠀⠀⠀⠀⠀⢀⣿⡷⣾⣿⣿⣽⡇⠹⡆⠀⠈⢛
⠁⠈⠋⢟⣻⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢹⡿⣽⡿⡇⠀⠁⠀⠀⠸
⠂⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣛⣿⣿⣿⣿⣿⣿⣤⣤⣼⣦⣴⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⣾⣇⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣿⣤⣁⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⠀⢠⣤⣤⣴⣶⣶⣶⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠀⢀⣠⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣮⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣉⣉⣛⣛⣛⣛⣛⣛⡛⣛⣁⣀⡀⠀⠸⣻⣿⣿⡻⡿⣛⣛⣛⣻⣟⣛⣉⣛⡻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛⣿⣿⡟⢻⣿⣿⣿⣿⡇⣿⣿⠛⠃⠀⢸⣿⡏⣿⣿⢀⣿⣿⣿⡇⣿⣿⡟⣿⣿⢻⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⡇⣿⣿⠿⠇⠀⢸⣿⡇⣉⣉⢸⣿⡟⣿⣷⣿⣿⡿⣿⣏⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⡇⣿⣿⣤⡄⠀⢸⣿⣇⣿⣿⣼⣿⡿⣿⣿⣿⣿⡇⣿⣿⢻⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣻⣷⣮⣛⣫⣝⣛⣥⣟⣛⠛⠃⠀⢠⣝⣛⣻⣵⣽⣿⣥⣿⣿⣽⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣀⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀
⠀⠀⠀⠀⠀⠀⢠⠀⠠⠀⣠⢄⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠘⠀⠀
⡤⠄⠀⠀⠀⡈⠠⢠⢁⣭⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⠀⠀⠀
⣿⣷⣦⡀⣀⢄⠀⣠⣐⣹⣹⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⢁⡽⣼⣷⣫⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⣿⣽⡮⣽⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣶⣴⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀
⠿⠟⠛⠁⠀⠉⠀⠀⠀⠀⠈⠙⠻⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣿⣿⣹⣿⣿⣽⣿⣿⣿⣿⣯⣄⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣷⣦⣤⢀⡀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠿⠛⠛⠛⠛⡉⠉⠙⣿⣏⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠉⠉⠋⠙⠻⣿⣿⣿⣿⣿⡿⠁⠉⠛⠛⠉⠈⠁⣹⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⠁⢠⣶⣶⣶⣿⣿⣷⡀⢸⣿⡤⠤⠤⠤⢤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⠁⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡟⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⢀⡀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠀⠈⠁⠀⠹⣿⡤⣟⠛⠁⠀⠀⢡⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣏⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⢱⣿⣷⡂⠀⠀⢸⠇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢵⠅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣼⠁⣸⣿⣿⣿⠋⢿⡀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠙⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡟⠀⣾⣿⣿⣿⠄⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣾⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⡇⠀⠈⢸⠇⢸⠂⠀⢻⡀⠀⠀⡴⠀⠀⢠⣦⠀⠀⠀⢸⣰⣆⠀⠀⠀⣷⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣶⠀⠀⢠⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣋⡀⢀⠀⠀⠀⢀⣶⡄⠀⢻⡁⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣶⠀⣶⣠⣾⣿⣦⣠⣝⣿⣿⣿⣿⡤⠶⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣠⣿⣧⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢡⢿⡆⠀⢸⣿⣿⣴⣿⠟⣿⣿⡟⢁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣦⡀⣿⣿⣿⡿⠗⠛⠏⣴⣿⣿⣅⣠⣿⠀⠀⠀⢠⡾⡿⢿⣿⣿⣿⣿⠏⠉⠹⢷⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⡆⣴⣿⣷⣾⠏⠀⠀⠀⢻⡏⢹⣿⣷⣾⠿⠀⠈⠁⢀⡀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⠟⠐⠿⠿⠿⢿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⢻⣟⡛⠛⢻⣿⠿⠷⠆⠀⠻⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣾⣿⣷⣿⣿⣿⣿⣤⠀⠀⠀⢸⡇⣸⣟⣿⣯⣴⠀⠀⠀⠘⢳⡄⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⡟⠛⠛⠉⣛⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣤⡀⠀⠀⢸⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣠⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠘⢿
⠀⠀⠀⠀⠀⣀⣠⣘⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⢰⣿⣿⣶⣦⡀⠀⠀⣹⣿⣷⣤⣤⣿
⣀⣤⣤⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣍⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣉⣉⣛⣛⣛⣛⣛⣛⡛⣛⣁⣀⡀⠀⠸⣻⣿⣿⡻⡿⣛⣛⣛⣿⣟⣛⣛⣛⡻⣿⣿⣿⣿⣿⣿⣿⠍⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣥⣷⣽⣑⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡟⣿⣿⡟⢻⣿⣿⣿⣿⡇⣿⣿⠛⠃⠀⢸⣿⡏⣿⣿⢀⣿⣿⣿⡇⣿⣿⡟⣿⣿⣹⣿⣿⣿⣿⣿⣿⣬⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⡇⣿⣿⠿⠇⠀⢸⣿⡇⣉⣉⢸⣿⡟⣿⣷⣿⣿⡿⣿⣏⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⡇⣿⣿⣤⡄⠀⢸⣿⣇⣿⣿⣼⣿⡿⣿⣿⣿⣿⡇⣿⣿⣻⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣷⣮⣟⣯⣽⣻⣥⣟⣟⠛⠃⠀⢠⣽⣛⣻⣥⣽⣿⣥⣿⣿⣽⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠠⣤⡀⠄⢄⢀⣄⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀
⡤⠄⠀⠀⠀⢀⠡⢠⣼⣗⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀
⣿⣷⣦⣀⣬⣄⣀⣈⣘⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣽⣿⡟⣽⣯⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⣿⣯⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⣿⣿⣿⣿⣿⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠛⢛⣿⣿⣿⣿⣿⣿⣿⡻⠀⠀⠀⠀⠀⠀⠀
⠿⠟⠛⠋⠁⠁⠀⠀⠀⠈⠉⠙⠻⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡻⠆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠿⠿⠿⣶⣦⠀⠀⠀⠀⠀⠀⣸⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠉⣀⣀⣀⣼⣦⣄⠀⢻⣷⡀⠠⠤⠤⠤⣴⡿⠁⠀⠀⠈⠉⠉⠉⢻⣿⣿⣿⣿⣿⠇⠉⠉⠉⠉⠀⠀⠸⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⣼⣿⣿⣿⣿⣿⣿⣧⢸⣿⠇⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡄⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣏⡀⠸⣿⣽⣿⣿⡆⠀⠀⠀⠀⠀⠀⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⡟⠛⢿⣿⡏⠀⠠⣴⡄⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢞⣿⢹⣿⣿⣿⡏⢿⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡗⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣼⣿⣿⣿⣿⣿⣣⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⡾⠀⠀⣴⡄⠀⠀⢨⣸⣿⣀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣶⠀⠀⢀⣹⣷⠀⠀⢰⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⢈⢹⣿⡿⣼⣟⡏⢹⡧⠈⠀⠀⠙⢿⣷⣤⡆⠀⢇⣴⣿⣷⣤⡜⣿⣿⣿⣿⣤⡴⣿⠀⠀⠀⠀⠀⠸⣿⣷⣶⣿⣿⣿⣿⣷⣾⣧⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠈⢲⠀⢀⠀⣿⣿⣷⡘⣿⠿⣿⠄⠉⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣳⣦⣼⣿⣿⡿⢟⠛⠟⢒⣿⣿⣟⣠⣿⠀⠀⠀⠀⠀⢠⣤⣼⣿⣿⣿⣿⣿⡏⠉⠀⠻⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⢠⣿⡇⣐⠘⠀⠈⠀⠉⣿⠈⠁⣠⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠛⠸⠿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⠿⠛⠿⠶⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣼⣿⣧⣿⣿⣿⣿⡄⠀⠀⠀⠀⠽⠀⠀⢹⣿⡨⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠋⠙⠉⠉⠙⢿⣿⣿⣿⣿⣇⣄⣠⣤⣤⣤⣤⣦⣼⣿⣿⡄⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣀⣀⣀⣉⣉⡉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣠⣒⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣶⣶⣦⣤⣄⠀⠀⠀⠘⣿⣶⣶⣦
⣄⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣶⣦⣤⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣽⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢨⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠄⣤⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⣽⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀
⢤⡄⠀⠀⠀⠐⠉⢠⣔⣛⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀
⣿⣷⣴⣤⣀⣔⣤⣩⡹⣻⣻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣛⠛⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠟⠛⠋⠉⠀⠀⠈⠈⠉⠙⠻⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠊⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣿⣿⣿⣾⣶⣾⣿⣿⣿⣿⣿⣥⣄⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⠛⢻⣏⣁⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡟⠁⣠⣤⣶⣿⣿⣿⣷⡈⣿⣿⠀⠀⠶⠦⠤⠄⣰⡟⠁⠀⠀⠉⠛⠈⠀⠉⢻⣿⣿⣿⣿⣿⠟⠙⠛⠛⠉⠉⠹⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⣸⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢙⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣏⢁⠐⢦⡴⣠⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⡏⠿⣿⣧⣴⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣿⣿⣧⣀⡹⣿⠛⠋⠉⠛⠉⡀⠀⠀⠀⠀⠀⠀⠉⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣶⣿⣿⣏⣹⣿⣿⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠰⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣄⡻⣿⡿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⠿⠛⠚⠛⠀⠸⣿⣿⣿⠀⠀⠀⠀⢰⠴⠂⢀⣤⣀⣀⣼⣶⣆⣀⣀⣀⣧⡀⠀⠀⠀⠀⢠⣦⠀⠀⣤⡄⠀⠀⡀⢠⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠏⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣤⣀⣼⣾⣶⣿⠟⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⢯⠀⢸⠠⣴⢰⣿⣶⣿⣿⣧⣄⣛⣿⡼⣿⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⢰⡄⠻⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠠⢥⣿⣿⣿⣿⣿⡿⢷⣶⣶⡦⠀⢤⡤⠀⠀⠀⣀⣿⠘⠆⢸⣄⡿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⣤⡆⠀⢀⡀⠀⠀⠀⠀⣠⣤⣽⣯⣍⣉⣭⣭⣡⣶⣦⣤⣤⣤⣤⣄⣠⣴⡙⠉⣻⡆⠂⠘⠁⠓⠻⣿⣿⠿⢿⣿⣿⣿⠿⠟⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⢀⣠⣀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣠⣾⠁⠀⠀⠀⠀⡀⠉⠉⠉⢩⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⠀⠀⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠀⠀⠀⠈⠉⠉⠀⢉⣛⣁⠀⣀⣀⣀⣤⣤⣤⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⣠⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⢀⡆⠀⠀⢸⣿⣿⣿⡃⠀⣀⣄⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⣀⣠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡆⠀⠀⠀⠸⡟⠀⠀⠈⢙⣽⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⣀⣀⢘⡁⠀⠀⠀⢘⣿⣰⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⠃⠛⠃⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⠀⠀⢰⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠠⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⠃⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⢸⣏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣾⣿⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⢻⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⠇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⡀⠀⢀⣺⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⢿⣆⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀
⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣆⣀⠀⠀⢰⠀⠀⠐⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠟⠂⠁⠀⠘⠒⠒⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣀⣨⣿⣿⣿⠛⠋⠙⢿⣿⡆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣶⣶⣶⣿⣿⣯⣙⣛⣛⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠻⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠋⠀⠀⢹⣷⣶⣄⠈⣿⡿⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣀⡀⣴⣾⣿⣿⣿⣶⣿⣷⠀⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠈⠚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢹⣿⡃⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠙⠉⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⡟⠀⢀⡀⠀⠈⣿⡷⢶⣤⣀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠇⠀⠀⠀⠀⠉⠀⣇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⢛⠁⠀⢸⡇⠀⠀⣿⡇⠀⠈⠙⠻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠸⣧⠀⢸⣧⣀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠉⠀⠀⠀⠀⢸⡿⡟⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣤⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠺⣇⣄⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠈⠁⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣶⢶⠞⠉⢻⣿⣷⣦⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣄⣀⣤⣠⣦⣶⣆⠀⢸⡧⠀⢰⣤⣴⡦⠀⢠⣿⣠⣤⣶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠻⢿⣷⣄⠀⠀⠀⠀⠀⠀⢠⣶⣶⣆⠀⣸⣿⣠⡀⠀⠀⡇⠀⠀⢀⠀⠀⠀⣄⠀⠀⣠⣄⠀⠀⣀⣰⡆⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣼⠃⠀⢾⠿⠋⠁⢠⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣭⣠⣶⣶⣤⣶⣿⣿⣿⣾⣿⣿⣿⣷⣆⢀⡁⠀⠀⢸⡇⠠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣤⣤⣶⣶⣶⣶⣿⣟⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠉⠉⢹⣧⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⢸⡇⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⣀⣀⣿⣿⣿⣋⣀⣀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣤⣤⠀⠀⢰⣶⣶⣶⣶⠇⠸⠏⠀⠛⠋⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⢸⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣿⣿⣿⣿⣿⣿⣿⠁⠀⠸⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⢙⣿⣿⣿⣿⣯⠀⠀⠀⢈⠉⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣻⣛⠟⠋⠀⠀⣦⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢝⣟⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣶⣶⣦⣼⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⣿⣿⡷⠄⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠛⠛⢻⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⢠⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣼⣿⣿⣄⣀⣀⣀⣀⣤⣤⣤⣶⣦⠀⠀⠀⠀⢠⣿⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣿⣿⣿⢘⢅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠉⠙⠛⠉⠛⠿⠟⠻⠿⢿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣿⣿⣿⣿⣿⣿⠀⠀⣶⣶⣶⣶⣤⡀⣶⣶⣶⣶⣤⡀⣶⣶⡶⣶⣶⡆⣶⣶⡆⣶⣶⣶⣶⢠⣴⣶⣶⣬⠁⠀⢰⣶⣦⢰⣶⡾⣩⣿⣶⣾⣝⠏⣿⣿⣿⣿⣿⡇⣶⣶⣿⣿⣿⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣿⣿⡏⣿⣿⡇⣿⣿⡏⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡏⠍⣿⣿⣏⠿⠿⣷⣷⣆⣿⣿⣿⣿⠃⣿⣿⡏⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡿⣿⣿⡁⣿⣿⡇⢻⣿⣷⣿⣿⠁⣿⣿⣿⣿⡘⠿⣿⣿⣮⡻⣿⣿⡸⣿⣿⡏⡆⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⢻⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⠀⣿⣿⣇⣚⣿⣿⡏⣿⣿⡇⣿⣿⡇⣿⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⠇⣿⣿⣸⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠿⠿⠿⠿⠟⣣⠿⠿⠇⠿⠿⢇⠿⠿⣇⣎⡿⠿⠿⢏⣄⠿⠿⠿⠿⣘⠻⠿⠿⢟⣱⣿⣿⣇⠿⠿⣿⣷⣝⠿⠿⠿⣟⣴⣝⠿⠿⠿⣛⣄⠿⠿⢿⣿⣿⣯⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⣿⡿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⠓⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣫⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⣀⣄⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠟⠿⣋⣀⡀⠈⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣶⠀⠀⠀⢰⠆⠀⠈⡁⣿⣿⠀⠀⠀⠀⠀⠀⠀⠰⣿⠏⠁⠀⠀⣴⣿⣿⣿⣆⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠓⠁⠀⠘⠓⠓⠲⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣿⣿⣿⣍⣙⣛⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⢻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⠋⠀⢰⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⣼⠀⠀⠀⣿⠟⠻⢶⣤⣀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡀⠀⠹⢧⠀⣿⣤⡀⠀⣿⠀⠀⠀⠈⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠉⠀⠀⠀⠀⠀⣿⠿⠇⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⡀⠀⠀⠙⢶⣤⣴⣆⠀⢠⡄⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⡀⣀⣠⣤⣴⣶⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⠄⠀⠸⣿⣿⡅⠐⢸⣇⠀⠀⠀⠀⠀⠀⠀⠈⠠⣏⣀⠀⠀⠀⠀⠀⠀⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣷⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢀⡀⢀⠀⠀⠀⣀⣀⣀⣸⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⣷⣾⣾⠿⠟⠛⠛⠉⠙⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⡀⣸⣿⣀⠀⠀⠀⠇⠀⠀⢀⠀⠀⠀⣠⠀⢀⣴⡆⠀⠀⣀⣴⣆⠀⠀
⣿⡿⠿⠛⠛⠛⠛⠛⠿⠀⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⣿⠟⢿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⡆⠀⠀⢸⡆⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣤⣤⣤⠀⠀⣤⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣧⠀⠀⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⠉⠁⠁⢈⠻⣷⣶⠄⠀⠘⠆⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣿⣿⣿⣿⣶⣶⣶⣿⣿⡿⠷⠈⠛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠛⠀⣶⣶⣾⣷⣿⣾⣿⣿⣿⡿⠿⠿⠿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣚⣷⣶⣤⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⢣⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⣿⣿⡙⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣤⡀⣶⣶⣶⣶⣤⡀⣶⣶⡶⣶⣶⡆⣶⣶⡆⣶⣶⣶⣶⢠⣴⣶⣶⣤⠀⠀⢰⣶⣦⢰⣿⡿⣫⣽⣶⣾⣝⠏⣿⣿⣿⣷⣾⡇⣶⣶⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⣿⣿⡇⣿⣿⡏⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡏⠉⣿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣿⣿⠃⣿⣿⡏⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣋⣀⣀⣀⣀⣤⣤⣤⡄⣿⣿⡇⣿⣿⡇⣿⣿⡿⣿⣿⡁⣿⣿⡇⢻⣿⣷⣿⣿⠁⣿⣿⣿⡿⠘⠿⣿⣿⣦⣠⣴⣦⣸⣿⣿⡏⡆⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⢻⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⠀⣿⣿⣇⣂⣾⣿⡏⣿⣿⡇⣿⣿⡇⣿⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣸⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠿⠿⠿⠿⠟⣃⠿⠿⠇⠿⠿⢇⠿⠿⢇⣌⠿⠿⠿⢏⣄⠿⠿⠿⠿⣘⠻⠿⠿⢟⣵⣿⣿⣇⠿⠿⣿⣿⣝⡿⠿⠿⣛⣶⣝⠿⠿⠿⣛⡄⠿⠿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠳⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⣦⣴⣤⣀⠀⠀⠀⠀⠀⠩⢒⣬⣼⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⣿⡿⠿⠿⢟⣋⠉⠉⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣾⣂⡀⠀⢸⣇⣁⣹⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⣰⣿⣿⣿⣦⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠛⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⡋⢡⢬⠙⠿⠿⡾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠀⣴⣿⣿⣿⣿⣿⣿⣷⣶⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣷⣾⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣯⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠀⠀⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⡷⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠉⠙⠻⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠁⢀⡆⠀⠀⠀⣹⣿⣇⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⠟⣿⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣿⡄⣼⡇⠀⠀⠀⢻⣿⣇⡀⠀⠤⠤⢠⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡿⠧⣄⣀⢻⠃⣿⣷⡄⠀⠀⠻⠿⠋⠛⠷⢦⣤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠻⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⣄⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣶⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⢀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠠⣧⡀⢀⠀⠀⠀⠀⠀⠀⠘⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢻⣷⣿⡇⡀⢼⡀⠀⠀⡀⠀⠀⠀⠈⠣⠈⡇⠀⠀⠀⠀⣄⠀⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠤⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠐⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣠⠀⠀⠙⠻⣷⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⢻⣇⣂⣤⣤⣤⣿⡶⠦⠺⡤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣾⣟⣭⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠛⢿⣦⣀⡴⠀⠀⠀⠀⠀⠀⠛⠀⠀⣸⣿⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⢀⠀⢀⣴⡂⠀⠀⢀⣾⣦⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⣿⡿⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰⣶⣆⠀⠻⣿⣿⣿⡧⠀⠀⠀⠈⠁⠠⣾⣿⣿⣷⣦⣤⣴⡽⠀⠀⢸⡄⠠⠄⠈⣷⣿⣿⣇⠀⣀⣾⣿⣿⣿⣿
⢻⢿⣿⣿⣿⣿⠟⢁⣀⣤⣀⣀⠈⠻⡿⠀⢰⣶⣶⣾⣷⣶⣤⡀⢀⣀⣠⣤⣴⣿⣿⣶⡄⠀⠀⠘⠛⠛⠉⠁⠀⠀⠀⢻⣿⣅⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣏⠀⠀⢸⣧⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⠞⠛⠟⠛⠛⠀⠚⠙⢿⣿⣿⣦⠀⠀⠀⠀⠘⠛⠻⠿⠿⢿⣿⣿⡿⠿⢿⠿⢿⠿⠿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣭⣷⣶⣶⣾⣿⣿⣿⣿⡿⠿⠻⣿⣿⣿⡇⠀⠀⣾⣿⠀⠀⢐⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⡄⠀⣀⣀⣤⣤⣤⣤⣤⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⣿⣿⣇⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠋⠉⠋⠉⠉⠉⠉⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⣿⣯⠠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣛⣻⣿⣿⣿⡯⠦⠀⠂⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢀⣿⣿⣿⠁⡤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣷⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⢸⣿⣿⣿⣧⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡄⠀⠀⠀⠀⠀⢸⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣤⡀⣶⣶⣶⣶⣤⡀⣶⣶⡶⣶⣶⡆⣶⣶⡆⣶⣶⣶⣶⢠⣴⣶⣶⣤⢲⣾⣳⣾⣿⢻⣷⡶⣠⣶⣶⣶⣄⠀⣶⣶⣶⣾⣿⡧⣶⣶⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣿⣿⡏⣿⣿⡇⣿⣿⡏⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡏⠉⣿⣿⣏⠿⠿⢿⣿⣇⣿⣿⣿⣿⠃⣿⣿⡏⣿⣿⡆⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠙⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇⣿⣿⡿⣿⣿⡁⣿⣿⡇⢻⣿⣷⣿⣿⠁⣿⣿⣿⡿⠘⠿⣿⣿⣦⡙⣿⣿⠸⣿⣿⡏⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⢿⣿⣿⣿⡇⡺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠐⢐⢄⣂⢀⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⠀⣿⣿⣇⣀⣾⣿⡏⣿⣿⡇⢙⣿⡃⣿⣿⡇⡄⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣸⣿⣿⣿⡃⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣬⣵⣤⣄⣲⣤⣀⡀⠿⠿⠿⠿⠟⣃⠿⠿⢇⠿⠿⣇⠿⠿⢇⡈⠿⠿⠿⠏⡀⠿⠿⠿⠿⠘⠻⠿⠿⢟⣡⣿⣿⣇⠿⠿⢷⣧⣙⠿⠿⠿⢟⣴⣝⠿⠿⠿⣻⡄⠿⠿⣿⣿⣿⣿⡖⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠐
⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀
⣿⣿⣤⣆⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀
⣿⣿⣿⣷⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢿⠿⠿⠛⠛⠻⠿⠟⠟⠿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⣿⣿⣿⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣨⣽⣛⣟⣻⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⢶⠴⠶⡶⠶⡶⠶⢷⣿⠝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠉⠛⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠿⢿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣟⠋⠛⢿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⠉⠹⣷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠟⠁⣀⣾⣿⣿⣿⣦⡘⣿⣿⣷⣻⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣳⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠇⣧⠀⠉⡄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣹⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠈⠻⣴⣿⠄⠀⣀⣴⡷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⣢⣀⢀⣰⠀⠀⠀⠀⡆⢰⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣟⡁⠀⠀⠀⢰⣿⣶⡾⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣐⠄⢕⠰⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣷⣮⣶⡿⠟⠁⣀⣀⣠⣴⣶⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣠⣶⣾⣿⣯⣤⣤⣤⣤⣤⣴⣾⣿⣷⣶⣶⣶⠛⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄⠀⠀⠀⠀⣠⣾
⠀⠀⠀⠥⠀⠀⠀⠀⠀⠀⠀⢸⡧⣤⣤⣶⣾⣿⡿⠻⠛⠛⠉⠉⠁⠀⠀⠀⡏⠉⠻⡉⠉⡟⠀⠘⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠛⠛⠛⣉⣭⣍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⡀⠀⣮⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣢⣾⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠹⣦⡀⠀⠀⠻⡟⠛⠛⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠐⠛⠛⠿⢿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣤⣤⣿⣿⡿⣛⣁⣀⣀⣀⣀⣀⣤⣤⣤⣤⢤⠶⠶⣶⡶⣶⡇⠀⠀⠀⠹⠇⠀⠀⠀⣄⡀⢀⣠⣝⡛⣿⣿⣿⣉⣁⠀⠀⠀⠀⠀⢠⣤⣤⣤⣼⣿⣇⠀⠀⠀⠀⠀⠀⣼⣿⣯⣥⣀⠀⠀⠀⣀⣿⣿⣿
⠤⠤⠤⠤⣴⣾⣿⡿⠟⠃⣸⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣿⣿⣿⣦⣴⣷⣿⣿⣷⢶⣀⣀⣀⣀⣈⣹⣿⠀⠀⢸⡿⢺⣿⣿⣿⣿⣿⣿⣿⣿⡷⠻⣿⣿⡯
⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⢱⣤⣴⡿⢿⣿⣿⡛⢻⣿⠟⠛⠑⣉⣻⣿⣷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⢿⣷⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠈⠁⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⡀⠀⣒⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣠⣿⠃⠀⠀⠛⠛⠻⣿⣿⣿⠁⠀⠀⣴⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣮⣿⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠟⠟⠁⠀⠀⠀⠘⠻⣿⠧⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⢾⣿⣿⣿⠟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠘⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡆⠀⠀⠀⣀⡀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣶⣶⣤⡀⣶⣶⣶⣶⣤⡀⣶⣶⡶⣶⣿⡟⣿⣿⡖⣶⣶⣶⣶⣠⣴⣶⣶⣦⠀⠀⢰⣶⣦⢰⣶⡶⣡⣶⣶⣶⣤⠀⣶⣶⣶⣶⣶⣶⣶⣶⡆⡛⠀⠀⠿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⣿⣿⡇⣿⣿⡏⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡏⠉⣿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣿⣿⠇⣿⣿⡏⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇⣿⣿⡿⣿⣿⡁⣿⣿⣇⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣘⠿⣿⣿⣦⡀⠀⠀⢸⣿⣿⡟⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡏⢻⣿⣿⣿⣿⠋⣿⣿⣟⣛⣿⣿⡏⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣾⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠃⠿⠿⠇⠿⠿⠇⠿⠿⠇⠈⠿⠿⠿⠟⠀⠿⠿⠿⠿⠘⠿⠿⠿⠟⠁⠀⠄⠀⠿⠿⠇⠀⠙⠿⠿⠿⠿⠶⠙⠿⠿⠿⠛⠀⠿⠿⠇⠀⠀⠀⠀⠀⢰⣶⣾⣿⡿⠿⠿⠛⠛⠋
⠐⠖⠶⣶⠿⢶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣷⣶⣦⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠁⠀
⣀⣀⣀⣀⠀⡀⠀⢀⢀⣀⣠⣌⣥⣤⣤⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡅⠀⠀⠀
⣿⣿⣿⣿⣿⣷⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠻⠿⠿⠟⠉⠉⠉⠉⠉⠉⠉⠉⠙⠿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠶⠶⠶⢾⣷⣶⣿⣿⣶⣾⠶⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣰⣶⣦⠀⠀⢀⠀⡀⠀⠰⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⣿⣿⣷⣿⣽⠫⠟⢚⠉⠀⣺⣿⣿⠁⠀⠀⠀⠀⣾⣿⣿⣷⣦⣤⣽⣇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⣨⣍⣀⣀⣀⣄⣴⣿⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡟⠋⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣋⠉⠻⠿⠆⢠⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⣼⣿⣿⣶⠀⠀⠈⠃⠀⠀⠀⠁⣤⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣿⣿⣿⠿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⢯⠻⢷⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣶⣤⡈⠛⠁⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣉⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣷⡄⣶⣦⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⡿⠉⢹⣿⣻⣿⣤⣾⣿⣿⣿⡿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⣀⠀⠸⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻
⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠈⠀⠀⠀⠿⠿⠿⠛⠉⠛⠛⢧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⡷⠀⠀⢀⡀⡀⠀⣤⠀⠀⠄⠀⠘⢻⣿⠿⣧⣄⣴⣿⣿⣿⠃⠀⠘⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⣿⣏⣡⡄⢀⣤⣞⠏⣼⡗⠀⠀⢸⠀⠀⠘⠃⢀⣏⣿⣿⣿⢿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⠛⠟⠉⠉⠈⠩⠁⠀⠀⠀⠀⠘⠃⠹⠁⠀⡈⠀⠀⣿⡇⠀⠀⢻⠀⢀⣠⣤⣴⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣴⣿⣀⣤⣴⣾⣿⢿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠀⠀⠰⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠃⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣤⡀⣶⣶⣶⣶⣤⡀⣶⣶⡶⣶⣶⡆⣶⣶⡖⣶⣶⣶⣶⣠⣶⣶⣶⣦⠀⡄⢰⣶⣦⢰⣶⡶⣠⣶⣶⣶⣤⠀⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⣿⣿⡇⣿⣿⡏⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡏⣉⣿⣿⣏⡿⠿⣿⠇⠀⣿⣿⣿⣿⠇⣿⣿⡏⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠙⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣿⣿⡇⣿⣿⡇⣿⣿⡿⣿⣿⡁⣿⣿⡇⢿⣿⣿⣿⣿⠁⣿⣿⣿⣿⠙⠿⣿⣿⣦⡉⠀⠀⢸⣿⣿⡟⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⡄⣿⣿⣇⣤⣿⣿⡏⣿⣿⡇⣿⣿⡇⣿⣿⡷⡆⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣤⣄⠀⠀⠀⠀⠈⠁⠿⠿⠿⠿⠿⠃⠿⠿⠇⠿⠿⠇⠿⠿⠇⠈⠿⠿⠿⠟⠀⠿⠿⠿⠿⣘⡿⠿⠿⣟⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⢿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⣿⣿⣿⣿⣷⠦⠰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⢴⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣼⣶⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣖⣶⣦⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣽⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀
⠀⢐⣴⣚⣿⣾⣶⣦⣄⣲⣛⣶⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⣶⣾⣿⣾⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠻⠿⠿⠿⠿⠛⠛⠉⠉⠉⠛⠓⠛⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠄⠤⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣴⣶⣶⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣾⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⣶⣾⣍⠀⠀⠈⠻⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠐⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣉⡀⢠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡟⠉
⣀⣀⣠⣤⣴⣶⣶⣶⣶⡶⢶⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⢿⣯⡿⣿⣿⣿⣿⣿⣿⣿⣄
⣿⣿⣿⣿⣿⣿⡟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧⢬⢕⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠟⠉⠉⠉⠉⠉⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⠿⠋⠉⠙⣿⣿⣿⣿⡏⠉⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠻⢿⣿⣷⣽⣉⠀⠀⡿⠟⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠀⠀⠀⠀⠈⣉⣉⠉⢳⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢹⣿⣿⣿⣿⣿⡆⠀⠀⠘⢻⠿⣿⣿⣿⣿⣿
⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡄⠀⠐⣶⣾⣿⣿⣇⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡶⠾⠿⠿⠟⠛⠃⠀⠀⠈⠉⠉⠉⠛⠃⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⣿⡏⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⠖⣠⣤⠄⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣷⣶⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣾⣿⣧⣤⡾⠇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⠿⠏⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣤⡀⣶⣶⣶⣶⣤⡀⣶⣶⡶⣶⣶⡆⣶⣶⡆⣶⣶⣶⣶⢠⣴⣶⣶⣤⠀⠀⢰⣶⣦⢰⣶⡶⣠⣶⣶⣶⣤⠀⣶⣶⣶⣾⣿⡿⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⣿⣿⡇⣿⣿⡏⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡏⠉⣿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣿⣿⠃⣿⣿⡏⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇⣿⣿⡿⣿⣿⡁⣿⣿⡇⢿⣿⣷⣿⣿⠁⣿⣿⣿⣿⠘⠿⣿⣿⣦⡀⠀⠀⢸⣿⣿⡟⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣠⣄⣴⠭
⠀⠀⠐⠿⠷⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⠀⣿⣿⣇⣀⣾⣿⡏⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡀⣀⡀⠀⠀⠀⠀⠀⠋⠋⠿⣿⣿⣿⠛⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠟⣣⠿⠿⠇⠿⠿⠇⠿⠿⠇⠈⠿⠿⠿⠏⠀⠿⠿⠿⠿⠘⠻⠿⠿⠟⠁⠀⠀⠀⠿⠿⠇⠀⣙⠿⠿⠿⣟⣤⣙⠿⠿⠿⠛⠀⠿⠿⣇⣉⣀⣀⣀⣀⣀⣄⣀⣠⣤⣤⣤⣄⠀⠀
⠀⠖⠶⣶⠿⢶⠆⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣭⣽⣿⣿⣿⣿⣿⣿⣷⣶⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣠⣤⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣀⡀⠀⢀⣀⣀⣀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀
⠁⠀⠀⡀⡠⣼⣿⣿⣆⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀
⠀⢨⣭⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠻⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠛⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⣠⣤⣤⣤⣠⣤⣤⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣃⢀⣀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠋⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣲⣿⣿⣿⣿⣿⣿⣿⣿⡾⠶⠦⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣿⣿⣿⣿⠟⠛⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⢠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⠿⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣿⣿⣿⣿⣿⣿⠏⠛⢙⡛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀
⣀⣀⣀⣀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣦⣤⠀⠀⢠⣾⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣹⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀
⣿⣿⣿⣿⣿⣷⣾⠿⠿⠿⡟⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡉⠀⠀⠀⠀⠀⠀⠀⢲⣾⡿⡿⠿⠿⠗⢲⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠐⠀⠀⠀⠤⠈⠁⠁⠈⠉⠙⠇⠌⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠠⠶⣶⣶⣶⡶⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁
⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⠀⠀⣴⣶⣿⣿⣿⣿⣇⡀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀
⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠿⢿⣿⣿⣿⣿⣿⣿⣧⣤⣤⡙⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⡟⠛⠛⠛⣛⣛⣉⣉⡉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠓⠒⠶⠶⢶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⡿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿
⠀⠀⠀⠀⢀⣀⣠⣴⣾⣿⣿⣿⣶⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣶⣿⣿⣿⣿⣿⢿⣷⣿⣿⠋⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣶⣬⡀⣶⣶⣶⣶⣤⡀⣶⣶⡶⣶⣶⡆⣶⣶⡖⣶⣶⣶⣶⣠⣶⣶⣶⣦⠀⠀⢰⣶⣦⢰⣶⡶⣠⣶⣶⣶⣤⠀⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣯⣿⡟⣿⣿⡏⣿⣿⡇⣿⣿⡏⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡏⠉⣿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣿⣿⠇⣿⣿⡏⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣇⣽⣿⠃⣿⣿⡇⣿⣿⡇⣿⣿⡿⣿⣿⡁⣿⣿⡇⢿⣿⣿⣿⣿⠁⣿⣿⣿⣿⠘⠿⣿⣿⣦⡀⠀⠀⢸⣿⣿⡟⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣻⣿⣿⣿⣿⡿⠀⣿⣿⠀⣿⣿⣇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⠀⣿⣿⣇⣀⣿⣿⡏⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠘⠈⠉⠀⢰⣿⠿⣄⣿⣿⡿⠿⠿⠃⠿⠿⠇⠿⠿⠇⠿⠿⠇⠈⠿⠿⠿⠟⠀⠿⠿⠿⠿⠘⠿⠿⠿⠟⠁⠀⠀⠀⠿⠿⠇⠀⠙⠿⠿⠿⠟⠀⠙⠿⠿⠿⠛⠀⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⠶⠶⣶⠿⢷⠾⠷⠶⠿⣿⣿⡿⠁⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠛⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠉⠛⠿⠿⠿⠿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣶⣶⣤⣤⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣶⣶⣷⣶⣶⣶⡾⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⣿⣛⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡉⠉⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠉⠁⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣯⣹⣿⣷⣄⠀⠀⠀⠀
⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⣤⣀⡀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣟⣻⣧⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠓⠒⣀⣸⣷⣦⣤⣤⣀⣀⠀⣰⣿⣿⣿⣿⡿⠟⠛⠟⠟⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⣴⣦⡀⠀⠀⠀⠀⠀⢤⠤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⣠⣤⠄⠀⣀⣠⣤⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠘⠛⠓⠀⠀⠀⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢿⢿⡦⠀⠉⠉⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⣀⣤⣾⣿⣿⣿⠿⠟⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⣀⣬⣶⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣠⣶⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣶⣶⣶⣾⣽⡿⣿⣿⣿⣷⣤⡀⣶⣶⡶⣶⣶⡆⣶⣶⡆⣶⣶⣶⣶⢠⣴⣶⣶⣬⠛⠿⢹⣷⣯⢱⣶⡶⣠⣴⣶⣶⣄⠀⣶⣶⣦⣶⣶⡄⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⣡⣤⣦⣿⣿⡏⣿⣿⡇⣿⣿⡏⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡏⠉⣿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣾⣿⠃⣿⣿⡏⣿⣿⡆⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⣿⣿⡇⣿⣿⡿⣿⣿⡁⣿⣿⡇⢻⣿⣷⣿⣿⠁⣿⣿⣿⡿⠘⠿⣿⣿⣦⡀⢀⣀⢸⣿⣿⡏⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⠀⣿⣿⣇⣀⢾⣿⡏⣿⣿⡇⣿⣿⠃⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⠇⣿⣿⡀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠿⠿⠿⠿⠟⠃⠿⠿⠇⠿⠿⠇⠿⠿⠇⠈⠿⠿⠿⠏⠀⠿⠿⠿⢿⣘⡻⠿⠿⠟⢡⢛⣡⣄⠿⠿⠇⠀⠙⠿⠿⠿⠛⠀⠙⠿⠿⠿⠛⠀⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠿⠷⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠿⠉⠀⠀⣤⣾⣿⣿⠟⠋⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠋⠉⠻⢿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⡿⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣮⣠⡀⠀⡠⣎⣻⢷⠳⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⣰⣶⣿⣿⣿⣿⣵⣾⣏⣣⢻⣛⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⢇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣴⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣶⡶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⢀⢀⣀⠀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣭⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀
⠀⠀⠀⠀⣴⣾⣿⣟⣛⣋⣽⣭⣭⣯⣭⣷⣶⣾⣯⣭⣥⣿⣁⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠘⠛⠉⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣠⣤⣼⣟⠛⢿⣿⣿⣿⣿⣧⡀⠀⠀
⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢹⠟⠛⠛⠻⣿⣶⣼⣿⣿⣿⣿⣿⣿⡄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⣴⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⠉⠀⠬⠟⠟⠛⠛⠋⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣠⣿⣻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣸⣗⣤⠄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣤⣾⣿⣿⣿⣿⣿⡉⢀⣤⡀⢠⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⣀⣤⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠁⠘⣿⣧⣤⣿⣿⣿⣿⣿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣃⣀⣀⡀⠀⣈⣉⣭⣭⣭⣭⣍⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠉⠉⠛⠙⠛⠛⠻⠿⠿⠻⣿⣿⣃⣛⣿⣷⣤⣤⣶⣿⣿⣿⠿⠟⠉⠉⠉⠉⠀⠀
⣉⣉⣉⣉⣙⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⡟⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⡀⣶⣶⣶⣶⣤⡀⣶⣶⡶⣶⣶⡆⣶⣶⡆⣶⣶⣶⣶⢠⣴⣶⣶⣤⠀⠀⢰⣶⣦⢰⣶⡶⣠⣶⣶⣶⣄⠀⣶⣶⣶⣶⣶⡤⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡏⣿⣿⡇⣿⣿⡏⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡏⠉⣿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣿⣿⠃⣿⣿⡏⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⣿⣿⡇⣿⣿⡇⣿⣿⡿⣿⣿⡁⣿⣿⡇⢿⣿⣷⣿⣿⠁⣿⣿⣿⣿⠘⠿⣿⣿⣦⡀⠀⠀⢸⣿⣿⡏⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠛⠋⠉⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⠀⣿⣿⣇⣀⣾⣿⡏⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⣤⣤⣀⡀⠀⠀⠀⠿⠿⠿⠿⠟⠃⠿⠿⠇⠿⠿⠇⠿⠿⠇⠈⠿⠿⠿⠏⠀⠿⠿⠿⠿⠘⠻⠿⠿⠟⠁⠀⠀⠀⠿⠿⠇⠀⠙⠿⠿⠿⠟⠀⠙⠿⠿⠿⠛⠀⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⡶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⣿⣟⠛⠻⢿⣿⣿⣿⣿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠔⠻⢉⣠⣤⣤⣤⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣥⣤⣿⣿⣟⠃⠀⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣰⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡥⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⢰⠌⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢠⣴⣶⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢞⠕⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢈⣯⣵⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠨⠿⠫⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⠟⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠀⠀⠀⠀⠀⠀⠀⠙⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⢷⣦⠀⠀⠀⡀⣠⣤⡵⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠂⠒⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠾⠿⠿⠿⠿⠿⠟⠦⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠋⠃⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠶⠶⣶⣶⣦⣤⣤⣤⣤⣀⣀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⢛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣐⣤⣾⣿⣿⣿⣿⣯⣿⣿⣷⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣉⣙
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣾⣿⣿⣧⡀⠀⠀⠀⠛⣿⣿⣿⣿
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣍⣿⣯⢉⣭⣄⣹⣷⡇⠀⠀⠀⠈⠛⣿⣿
⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢈⣿
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠏⣽⠀⠀⠀⠀⠀⠀⠀⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⣭⣿⣿⣿⣿⣿⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠏⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⣴⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠋⢀⣤⣼⣿⣷⣦⣤⣤⣤⣤⣤⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡁⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠻⠿⠛⠿⠿⠿⢶⠀⠀⠀⠀⠉⠋⡙⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⣀⠉⠁⠀⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠛⠛⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠟⠻⠻⠿⠻⠓⠒⠶⠶⠶⠿⠿⠾⠿⠿⠿⠯⠹⠉⠋⠽⠿⠿⠿⠿
⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣿⣿⣿⣿⣿⠿⠏⠁⠙⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠋⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣶⣾⣶⣤⡀⣶⣶⣶⣶⣤⡀⣶⣶⡶⣶⣶⡆⣶⣶⡖⣶⣶⣶⣶⣠⣶⣶⣶⣦⠀⠀⢰⣶⣶⢰⣶⡶⣠⣶⣶⣶⣤⠀⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⣿⣿⡇⣿⣿⡏⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡏⠉⣿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣿⣿⠇⣿⣿⡏⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡧⣿⣿⡇⣿⣿⣿⣿⣿⡁⣿⣿⡇⢿⣿⣿⣿⣿⠁⣿⣿⣿⣿⠘⠿⣿⣿⣦⡀⠀⠀⢸⣿⣿⡟⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⠀⣿⣿⣇⣀⣿⣿⡏⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⠿⠿⠃⠿⠿⠇⠿⠿⠇⠿⠿⠇⠈⠿⠿⠿⠟⠀⠿⠿⠿⠿⠘⠿⠿⠿⠟⠁⠀⠀⠀⠿⠿⠇⠀⠙⠿⠿⠿⠟⠀⠙⠿⠿⠿⠛⠀⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡶⠶⣶⠿⢷⠶⠲⠶⠶⢾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡟⠉⠛⣿⠿⣿⣿⣿⣷⣆⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣺⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠹⢻⣿⣿⣿⣿⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣺⣿⣿⣿⣟⠖⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⣍⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⡀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⢠⣠⣄⣰⣶⡇⣠⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⣎⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⡇⠀⠀⣸⣟⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢙⣻⡄⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⡿⡆⠀⠀⠀⠀⢀⣾⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠓⠳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣴⣶⣶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠶⠶⠶⠿⠿⠟⠟⠿⠷⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣿⣿⣿⣿⣿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠲⠶⠶⢶⣦⣤⣶⡾⠛⠛⠛⠿⢿⣿⣷⣶
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣛⣟⣛⣫⣭⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠽
⠈⠁⠀⠀⠀⠀⠀⢐⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠛⠛⠛⠿⠟⠻⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣄⠀⠀⢀⣤⣤
⠀⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣿⣿⠿⠿⠿⢿⣷⣀⡈⢿⣿
⠰⡇⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣶⣿⣿⣥⣶⣶⣾⣿⣿⡇⠀⠉
⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡟⠋⠨⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣭⣍⣽⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣋⣿⣿⣿⣾⠃⠠⢾⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⠉⠉⣀⣠⣬⣿⣷⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⠿⢿⣿⣿⣟⣻⣿⣿⣿
⣿⣿⣿⣿⣟⣀⣈⣉⣉⠉⠉⠉⠛⠛⠛⠓⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣀⠀⠀⠀⠈⠀⠁⠀⠀⠈⠉⠉⠈⠉⠉⠉⠙⠛⠛⠛⠓⠚⠲⠒⠖⠶⠶⠶⠶⠶⠶⠶⠶⠦⢤⠦⣤⢤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⡘⠻⢻⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠐⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠋⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡟⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡟⢀⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⠃⢸⡿⠉⠀⠀⠀⣶⣶⣶⣶⣤⡀⣶⣶⣶⣶⣤⡀⣶⣶⡶⣶⣶⡆⣶⣶⡖⣶⣶⣶⣶⣠⣴⣶⣶⣦⠀⠀⢰⣶⣶⢰⣶⡶⣠⣶⣶⣶⣤⠀⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡈⠀⣾⠇⠀⠀⠀⠀⣿⣿⡏⣿⣿⡇⣿⣿⡏⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡏⠉⣿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣿⣿⠇⣿⣿⡏⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⢀⣿⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡁⣿⣿⡇⢿⣿⣿⣿⣿⠁⣿⣿⣿⣿⠘⠿⣿⣿⣦⡀⠀⠀⢸⣿⣿⡟⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⠀⣿⣿⣇⣀⣿⣿⡏⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠃⠿⠿⠇⠿⠿⠇⠿⠿⠇⠈⠿⠿⠿⠟⠀⠿⠿⠿⠿⠘⠿⠿⠿⠟⠁⠀⠀⠀⠿⠿⠇⠀⠙⠿⠿⠿⠟⠀⠙⠿⠿⠿⠛⠀⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡰⠶⢾⣷⠿⢷⠶⠲⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠉⠻⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠑⠀
⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀
⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⡿⠛⢿⡿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠿⠟⠃⠀⠀⠀⠀⠀
⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠘⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⣤⣤⣦⣤⣶⡄⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣼⣿⣧⣬⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠛⠿⠿⠿⠿⠿⠛⠻⠿⠿⢿⣿⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣶⡶⠾⠿⠟⠛⠛⠛⠛⠉⠉⠉⠑⠲⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⠶⠛⠛⠻⠿⢿⣿⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣽
⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣻⣟⣛⣭⣏⣭⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣦⣤⣤⣤⣴⣤⣴⣤⣤⣴⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀
⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠙⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠙⠛⠻⣿⣿⠛⠿⠿⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⣶⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⣴⣴⣶⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣴⣿⣷⣶⣶⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠕⠀⠀⠀⠀⠀⠀⢿⣷⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⠿⠿⡿⢤⡀⠀⠀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣭⣭⣭⡀⠀⢈⣁⡈⠁⠉⠉⠙⠛⠓⠒⠀⠀⠀⠐⠶⠶⠟⠻⠿⡿⠿⠿⠿⠿⠿⠷⠶⠷⠲⠒⠖⠲⠶⠾⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠦⠤⠤⠤⠤⠤⠤⣤⠤⣤⣤⣤⣬⣭⣿⣿⡿⢿⣭⠹⡿⠛⠛⠿⢿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣶⣶⣶⣶⣤⡀⣶⣶⣶⣶⣤⡀⣶⣶⡶⣶⣶⡆⣶⣶⡖⣶⣶⣶⣶⣠⣴⣶⣶⣦⠀⠀⢰⣶⣶⢰⣶⡶⣠⣶⣶⣶⣤⠀⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⣿⣿⡏⣿⣿⡇⣿⣿⡏⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡏⠉⣿⣿⣏⡿⠿⠇⠀⠀⣿⣿⣿⣿⠇⣿⣿⡏⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡁⣿⣿⡇⢿⣿⣿⣿⣿⠁⣿⣿⣿⣿⠘⠿⣿⣿⣦⡀⠀⠀⢸⣿⣿⡟⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⠀⣿⣿⣇⣀⣿⣿⡏⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠃⠿⠿⠇⠿⠿⠇⠿⠿⠇⠈⠿⠿⠿⠟⠀⠿⠿⠿⠿⠘⠿⠿⠿⠟⠁⠀⠀⠀⠿⠿⠇⠀⠙⠿⠿⠿⠟⠀⠙⠿⠿⠿⠛⠀⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⠶⠶⣶⠿⢷⠶⠲⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀
⠀⠀⠈⠛⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀
⠀⠀⠀⠀⠀⠈⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠁⠈⠙⠛⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣄⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣷⣴⢀⣾⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⢿⣿⣿⣿⣛⣛⣿⣿⣿⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣲⣶⣦⣂⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠄⢀⣀⣠⣤⣤⣶⣶⣾⣿⡿⠿⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⠳⠶⠤⠤⠄⠀⠿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠇⠀⠴⠶⠶⠶⠞⠉⠉⠉⠉⠛⠻⠿⢿⣿⣿
⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿
⠀⢀⣠⣴⣿⣿⣿⣟⣿⣟⣻⣯⣿⣂⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠙⠛⠉⠉⠉⠙⠉⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⣀⣀⡀⠀
⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣾⣿⣿⣿
⠟⠋⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣖⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡛⠛⠛⢿⣿⣿⠿⠛
⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣶⣷⣿⣧⣄⣀
⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣶⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣏⣻
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣺⣷⣾⣿⣿⣶⣯⣽⣿⣿⣿⣿⣿⣿⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣽⡟⣛⣻⣿⣟⣿⡿⠿⣿⣿⣿⣿⣿⣷⣷⣦⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⣁⣀⣠⣀⣄⣄⣀⣤⣀⣀⣀⡀⣀⣀⡀⣀⠀⠀⢀⡀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠿⢿⣿⣿⡿⣿⣿⣿
⣶⣶⣄⣈⣭⣭⣍⣉⣀⣀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠿⠟⠉⠉⠉⠛⠛⠋⠛⠙⠛⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠋⠉⠉⠙⠙⠉⠉⠉⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠑⠂⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣤⡀⣶⣶⣶⣶⣤⡀⣶⣶⡶⣶⣶⡆⣶⣶⡖⣶⣶⣶⣶⣠⣶⣶⣶⣦⠀⠀⢰⣶⣶⢰⣶⡶⣠⣶⣶⣶⣤⠀⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⣿⣿⡇⣿⣿⡏⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡏⠉⣿⣿⣏⡿⠿⠇⠀⠀⣿⣿⣿⣿⠇⣿⣿⡏⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣦⣤⣀⡀⠀⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡁⣿⣿⡇⢿⣿⣿⣿⣿⠁⣿⣿⣿⣿⠘⠿⣿⣿⣦⡀⠀⠀⢸⣿⣿⡟⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣿⣿⣇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⠀⣿⣿⣇⣀⣿⣿⡏⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠿⠿⠿⠿⠿⠃⠿⠿⠇⠿⠿⠇⠿⠿⠇⠈⠿⠿⠿⠟⠀⠿⠿⠿⠿⠘⠿⠿⠿⠟⠁⠀⠀⠀⠿⠿⠇⠀⠙⠿⠿⠿⠟⠀⠙⠿⠿⠿⠛⠀⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠶⠲⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢑
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠠
⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⢿⡿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢬⣽⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⢀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣴⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⢢⣶⣿⣶⣶⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⣿⣿⡇⠀⠀⢠⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢐⣼⣿⣿⣿⣷⣾⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣿⣿⡇⠀⢰⡟⢀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠲⢤⣀⣀⡀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⣀⣤⠶⠶⠶⢶⣶⣶⣶
⣿⣿⣿⢁⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠿⠛⠿⠽⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠈⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠉⠉⠉⠉⠉⠙⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣛⣋⣭⣤⣤⣤⣴⣤⣴⣶⣿⣶⣶⣤⣶⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡄⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣣⣶⣾⣿⣿⣿⣿⣴⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⠀⠀⠀⢠⡶⠿⣿⣿⠿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣇⠀⣨⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠀⠀⣴⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⠿⠯⠖⠰⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⡀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣀⣀⣚
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣧⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡍⠛⠛⠿⠿⠿⠟⠉
⣿⣿⣿⣿⣿⣿⡟⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣧⣀⣠⣴⣦⣴⣶⣤
⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣶⣦⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣤⣄⣀⣀⢀⠀⡀⢀⡀⣀⠀⣀⣀⣀⣀⣿⣿⣿⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠟⠙⠛⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⡿⣿⣿⡿⠿⠿⢿⠿⡿⠴⠤⢤⢤⡤⣤⣤⣄⣤⣄⣀⣀⣀⣀⡀⣉⣉⣉⣉⣉⣹⣿⣛⣛⣛⡟⠛⠛⠛⠛⠛⠛
⣶⣶⣶⣶⣶⣤⡤⡤⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉⠙⠁⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠋⠉⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣶⣶⣶⣤⡀⣶⣶⣶⣶⣤⡀⣶⣶⡶⣶⣶⡆⣶⣶⡆⣶⣶⣶⣶⢠⣴⣶⣶⣦⠀⠀⢰⣶⣦⢰⣶⡶⣠⣶⣶⣶⣤⠀⣶⣶⣶⣶⣶⡶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⣿⣿⡏⣿⣿⡇⣿⣿⡏⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡏⠉⣿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣿⣿⠃⣿⣿⡏⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣿⣿⡇⣿⣿⡇⣿⣿⡿⣿⣿⡁⣿⣿⡇⢿⣿⣿⣿⣿⠁⣿⣿⣿⣿⠘⠿⣿⣿⣦⡀⠀⠀⢸⣿⣿⡟⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⣿⣿⣇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⠀⣿⣿⣇⣀⣿⣿⡏⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠿⠿⠿⠿⠟⠃⠿⠿⠇⠿⠿⠇⠿⠿⠇⠈⠿⠿⠿⠟⠀⠿⠿⠿⠿⠘⠿⠿⠿⠟⠁⠀⠀⠀⠿⠿⠇⠀⠙⠿⠿⠿⠟⠀⠙⠿⠿⠿⠛⠀⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠶⣶⠿⢷⠶⠲⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠁⣹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣷⠜⡗⣿⣿⣟
⠀⠀⠀⢀⣄⣶⣶⣾⣿⣿⣟⣓⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠗⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠇⡏⠹⠛
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠚⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⢣⠋⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣾⣗⠂⠀⠀⠀⠀⠀⠀⠀⠂⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢀⣯⡦⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣿⣷⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠿⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠙⣿⣿⢿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠻⠿⠿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⢀⣤⣤⠸⡿⣇⠀⠀⣠⣤⣀⣿⡆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⢀⣠⣦⣶⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⣾⢋⣀⣤⣷⣤⣵⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠿⣿⣿⣾⣿⣿⣀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⡀⠀⠀⠀⠀⣀⣤⡶⠶⠾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠉⠉⠀⠀⠈⠙⠛⠛⠛⠛⠛⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⠛⠻⠛⠿⠛⡉⠉⠉⠙⠛⠛⠛⠛⠛⠻⠛⠀⠀⠀
⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠁⠘⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣯⣤⡦⡄⠀⢄⣠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣤⣤⣤⣄⣠⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⢿⣿⣿⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣶⣾⣿
⣿⣿⣿⡿⠏⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿
⣿⡿⠁⠀⠀⠀⠀⠀⠐⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣤⡤⠀⠀⠀⢀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⡀⠘⠛⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣠⣾⣯⣯⣯⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡻⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣤⣴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⣿⣿⣿⣿⣷⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣴⣶⣶⣶⡆⣶⣶⣶⣶⣬⡻⣿⣿⣶⣶⣭⡃⣶⣶⡶⣶⣶⡆⣶⣶⡖⣶⣶⣶⣶⣠⣶⣶⣶⣦⢠⣤⢰⣶⣶⢰⣶⡶⣠⣶⣶⣶⣤⠀⣶⣶⣶⣶⣶⣶⣶⣶⡆⣀⣀⣀⣸⣿⣿⣿⣿⣯⣤⣌⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡏⣿⣿⡇⣿⣿⡏⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡏⠍⣿⣿⣏⠿⠿⢯⣿⣇⣿⣿⣿⣿⠇⣿⣿⡏⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡁⣿⣿⡇⢿⣿⣿⣿⣿⠁⣿⣿⣿⣿⠘⠿⣿⣿⣶⡙⠿⠿⢹⣿⣿⡟⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⠇⠉⠉⠉⠹⡍⠉⠉⠉⠀⠀⠉⡉⠉⠉⠉
⠁⠈⠉⠉⠉⠛⠛⠛⠳⠆⣿⣿⣇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⠀⣿⣿⣇⣀⣿⣿⡏⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣀⣄⣰⣶⣶⣿⣧⣴⣶⣶⣶⣶⣿⣶⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠃⠿⠿⠇⠿⠿⠇⠿⠿⠇⠈⠿⠿⠿⠟⠀⠿⠿⠿⠿⠘⠿⠿⠿⠟⠁⠀⠀⠀⠿⠿⠇⠀⠙⠿⠿⠿⠟⠀⠙⠿⠿⠿⠛⠀⠿⠿⠇⠉⠉⠉⠉⠉⠋⠋⠙⠉⠉⠁⠀⠉⠀⠀
⠶⠶⠶⣶⠿⢷⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⡡⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠨⣱⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣻⢉⢻⣿⣿⡻⠟
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣾⣿⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠊⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⢧⣿⣿⠇⠀
⣿⣿⣿⡇⠠⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣄⠀⠀⠀⠀⠀⠀⠀⠈⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⢸⣟⠓⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠸⣿⣧⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⡶⠶⠆⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⣿⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⡿⠻⠟⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠿⠛⠛⠿⣿⣦⡀⠀⠀⠀⠈⠀⠀⠀
⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠛⠻⢿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⣿⣿⣶⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠄⠀⢀⠀⠀⠀⢀⣴⣶⣶⣶⣿⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣾⣿⣦⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⢶⣦⣤⣀⡀⠀⢀⡤⠀⢀⣶⣶⣶⣦⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣷⡶⠿⠿⠿⠿⠿⠾⠿⠿⠿⣿⠿⣿⡿⠿⠟⠛⠇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⠛⠿⠿⣿⣿⣿⣿⡿⠿⠷⠶⠶⣶⣶⣶⣶⣦⣤⣤⣴
⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠬⠤⠬⠌⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠌⡙⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⢀⠀⣀⢀⢀⠀⣀⣀⡁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣦⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣦⣶⣤⣶⣶⣶⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠛⠏⠉⠀⠈⠁⠁⠀⠁⠚⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠋⠙⠛⠉⠉⠉⠉⠉⠙⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⣤⠶⠞⠋⠁⠀⠀⠀⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠁⠀⠀⢀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠛⠻⠿⠿⠿⠃⠈⠙⠻⣿
⠀⠀⣰⣿⣭⣭⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣷⣿⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣷⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣶⣶⣶⣤⡀⣶⣶⣶⣶⣤⡀⣶⣶⡶⣶⣶⡆⣶⣶⡖⣶⣶⣶⣶⣠⣶⣶⣶⣦⠀⠀⢰⣶⣶⢰⣶⡶⣠⣶⣶⣶⣤⠀⣶⣶⣶⣶⣾⣿⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡏⠉⣿⣿⣏⡿⠿⠇⠀⠀⣿⣿⣿⣿⠇⣿⣿⡏⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡁⣿⣿⡇⢿⣿⣿⣿⣿⠁⣿⣿⣿⣿⠘⠿⣿⣿⣶⡀⠀⠀⢹⣿⣿⡟⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⠀⣿⣿⣇⣀⣿⣿⡏⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠿⠿⠿⠿⣣⡿⠿⠟⠿⠿⠇⠿⠿⠇⠈⠿⠿⠿⠟⠀⠿⠿⠿⠿⠘⠿⠿⠿⠟⠁⠀⠀⠀⠿⠿⠇⠀⠙⠿⠿⠿⢟⠄⠙⠿⠿⠿⠛⠀⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠟
⠰⠶⠶⣶⡿⣿⣿⣿⣿⣿⠶⠀⠀⣿⡏⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉⠉⠁⠀⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠁⠀⡄⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⢁⢸⣏⣼⣥⣯⣯⣾⣿⣿⣿⣿⣿⣿⡿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⣴⣶⣶⣾⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣴⣤⣤⣤⣬⣭⣿⣿⣿⣿⠿⠿⣷⣄⡀⠀⠠⠀⠀⠀⠀
⠀⢯⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣧⡄⠀⠀⠀⠀
⠀⠙⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡑⠀⠀⠀⠀⢀⣴⣿⣴⣷⣷⣶⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠰⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣶⣶⣶⣶⣶⠶⠶⠶⠶⢶⣦⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⡅⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠉⠉⠀⠀⠀⠀⠀⢀⣹⣤⣾⣿⣿⣿⣿⣿⣿⣦⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠝⠋⠁⠁⢀⡀⢀⡐⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⡿⠿⠿⠿⠻⣿⣿⣿⣯⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣺⡟⢡⣲⣶⣿⣿⣿⣿⣷⣿⡄⠀⠀⠀⠀⠈⠁⠀⠂⠩⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⢱⠴⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣿⣿⣿⡟⠛⠛⢻⡿⠟⠃⠀⢀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣯⣍⣩⣽⣯⣵⣵⣲⣄⣲⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠋⠫⠛⠛⠟⠻⠟⠟⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠿⠿⠿⠿⠿⠯⠿⠽⠿⠿⠿⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠹⠿⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠋
⣤⣤⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣉⣉⣛⡻⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣙⣛⣻⡿⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡀⣶⣶⣶⣶⣤⡀⣶⣶⡶⣶⣶⡆⣶⣶⡆⣶⣶⣶⣶⢠⣴⣶⣶⣤⠀⠀⢰⣶⣦⢰⣶⡶⣠⣶⣶⣶⣄⠀⣶⣶⣶⣶⣶⡤⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⡏⣿⣿⡇⣿⣿⡏⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡏⠉⣿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣿⣿⠃⣿⣿⡏⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡇⢀⣶⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣿⣿⡇⣿⣿⡇⣿⣿⡿⣿⣿⡁⣿⣿⡇⢻⣿⣷⣿⣿⠁⣿⣿⣿⡿⠘⠿⣿⣿⣦⡀⠀⠀⠸⣿⣿⡏⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⠃⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⠀⣿⣿⣇⣀⣾⣿⡏⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡀⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠟⠃⠿⠿⠇⠿⠿⠇⠿⠿⠇⠈⠿⠿⠿⠏⠀⠿⠿⠿⠿⠘⠻⠿⠿⠟⠁⠀⠀⠀⠿⠿⠇⠀⠙⠿⠿⠿⠛⠀⠙⠿⠿⠿⠛⠀⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡗⠲⣶⠿⢶⠆⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠆⠀
⠀⠀⠘⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠉⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣰⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⢀⣾⣿⣿⣧⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣶⠠⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠸⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣒⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⢀⣠⣤⣴⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡗⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣩⣤⣾⡶⣿⣿⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⢿⣿⣿⠿⠿⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣾⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡄⠈⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⣦⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠿⣏⣹⣿⠁⠀⢀⣄⠀⣠⣶⣆⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠓⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠛⠀⠀⠼⢿⠆⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠏⠛⠏⠍⠋⠛⠛⠻⠿⠟⠿⠿⠟⠂⠀⠀⠠⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡿⠀⠀⠀⠀⠀⠀⣤⡿⣷⣿⢿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠿⠗⠀⠀⠀⠀⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠿⠃⣹⣟⢸⣿⣷⣶⢄⡖⠉⠙⠛⠛⠻⢟⣿⡏⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣶⣶⣄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀
⣂⣤⣤⣴⣶⣶⣶⣿⣿⣿⣄⣤⣤⣤⣤⣤⣤⣤⣼⣿⣾⣿⣯⣥⣤⣥⣤⣦⣤⣤⣽⣾⣿⣧⣤⣤⣤⣤⣤⣄⣄⣀⣀⡀⠀⠈⢻⣿⡏⠀⠀⠀⠀⠻⠋⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣸⣇⡀⣀⣀⣀⡀⠀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠿⠿⠿⠟⠛⠿⠿
⠉⠈⠉⠙⢿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣤⡀⣶⣶⣶⣶⣤⡀⣶⣶⡶⣶⣶⡆⣶⣶⡖⣶⣶⣶⣶⣠⣶⣶⣶⣦⠀⠀⢰⣶⣦⢰⣶⡶⣠⣶⣶⣶⣤⠀⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⣿⣿⡇⣿⣿⡏⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡏⠉⣿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣿⣿⠇⣿⣿⡏⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇⣿⣿⡿⣿⣿⡁⣿⣿⡇⢿⣿⣿⣿⣿⠁⣿⣿⣿⣿⠘⠿⣿⣿⣦⡀⠀⠀⢸⣿⣿⡟⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⠀⣿⣿⣇⣀⣿⣿⡏⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠃⠿⠿⠇⠿⠿⠇⠿⠿⠇⠈⠿⠿⠿⠟⠀⠿⠿⠿⠿⠘⠿⠿⠿⠟⠁⠀⠀⠀⠿⠿⠇⠀⠙⠿⠿⠿⠟⠀⠙⠿⠿⠿⠛⠀⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⠶⠶⣶⠿⢷⠶⠲⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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✐ IBM_Has_Measurably_Lessened_Activity_in_Red_Hat_Web_Sites_(It_Started_When
Layoffs_Were_Announced_Last_Month)⠀✐


Posted in IBM, Red_Hat at 9:11 am by Dr. Roy Schestowitz


Summary: OpenSource.com and enterprisersproject.com scaled down their activity
around the time Red Hat’s CEO announced that 700+_workers_would_be_made
redundant; are writers among the casualties of these cuts?


T HIS is a subject we deem especially and exceptionally sensitive because many
good people lost their jobs at Red Hat. Some were technical, some were less
technical. We know some names, but this post will name nobody.


“My wife and I have been reading OpenSource.com every day for about a decade,
so these trends are easy to spot or “feel” (even the mere absence of something
gets noticed).”Last year we_took_note_of_neglect_in_OpenSource.com (a Red Hat
site for well over a decade already) and weeks later the site picked up pace
again, publishing 2-3 new articles per day, except weekends (sometimes on
weekends too they published new material). Unlike months prior, they didn’t
post obnoxious stuff; they had actually published some tasteless_things_last
year.


My wife and I have been reading OpenSource.com every day for about a decade, so
these trends are easy to spot or “feel” (even the mere absence of something
gets noticed). The site’s editors changed a few times over the years (we won’t
name them; we want to keep this impersonal).


“The ‘Linux’ Foundation has been very quiet this year and it is intentional;
they try to keep a low profile for a reason.”So what exactly is going on? Let
us know. We’re generally thankful for what the site offered since its birth and
it would be a shame if it became something like Linux.com — in affect killed by
the ‘Linux’_Foundation when it fired_all_the_staff_writers_and_all_the_editors
without_prior_notice_or_an_explanation. Revenue was growing fast back then,
unlike in_recent_years. The ‘Linux’ Foundation has been very quiet this year
and it is intentional; they try to keep a low profile for a reason. We’ll write
about it some other day.


“The people fired by the Linux Foundation, longtime writers at Linux.com, never
quite recovered or made a comeback.”Contact us by IRC or E-mail if you know
something about this. It seems likely IBM removed not only OpenSource.com
staff*. Around April 25, a day after the_Red_Hat_layoffs, activity in both
enterprisersproject.com (another Red Hat site, a much worse one**) and
opensource.com was cut down (more than halved). Coincidence? Were they
impacted? One can only guess, hence we hope for anonymous disclosure of
information. The people fired by the Linux Foundation, longtime writers at
Linux.com, never quite recovered or made a comeback. Eric Brown ‘retired’ from
writing 1-2 years later, Carla (tuxchick) is hard to find online, and Jack
Walllen is perhaps the last survivor of that cull. He’s still active in a
number of sites. █
_________
* It is merely a side note that these layoffs aren’t justified. As mintCast_put
it_earlier_today, “Red Hat lays of 4% due to high profits…”


** Over the past few months enterprisersproject.com published about 2 dozen
‘articles’ that merely help Microsoft hype/dial up chatbots. It’s_doing_so
again_today. This helps Microsoft distract from its demise in most areas.



                    ䷩ 𝚕𝚒𝚗𝚎 2256

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Gemini_version_available_♊︎


✐ The_Electronic_Frontier_Foundation_(EFF)_Covers_Software_Patents_Again⠀✐


Posted in America, EFF, Law, Patents at 11:19 am by Dr. Roy Schestowitz


                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Cory_Doctorow⦈_
    By Dominik Butzmann / re:publica – re:publica_faces_2019, CC BY-SA 2.0.


Summary: Cory Doctorow and Joe Mullin (EFF) wrote about software patents this
week; this shows that the EFF can still pivot in the right direction if it
really wants to


As it turns out, Joe Mullin is fortunately still around (at the EFF, he used to
be in the media) and the other day he cautioned “the_U.S._Solicitor_General
Trying_To_Change_The_Law_To_Benefit_Patent_Trolls”. His EFF colleague, Mr.
Doctorow, said_at_almost_the_same_time: “In theory, patents are for novel,
useful inventions that aren’t obvious “to a skilled practitioner of the art.”
But as computers ate our society, grifters began to receive patents for “doing
something we’ve done for centuries…with a computer.” “With a computer”: those
three words had the power to cloud patent examiners’ minds.”


He then changed the subject from software patents to patent trolls (the EFF
habitually changes the subject to “bad patents” or “trolls”). To quote: “Patent
trolls – who secure “with a computer” patents and then extract ransoms from
people doing normal things on threat of a lawsuit – are an underappreciated
form of “tech exceptionalism.” Normally, “tech exceptionalism” refers to bros
who wave away things like privacy invasions by arguing that “with a computer”
makes it all different.”


Quoting Mr. Mullin, regarding the U.S. Patent and Trademark Office (USPTO) and
35 U.S.C. § 101: “Government officials should be working to reduce, not
increase, the burden that low-quality patent lawsuits impose on innovators. So
we’re concerned and dismayed by recent briefs filed by the U.S. Solicitor
General, asking the Supreme Court to reexamine and throw out the best legal
defenses regular people have against “patent trolls”—companies that don’t make
products or provide services, but simply use patents to sue and threaten
others.


“To truly stop patent trolls, we’ll need wholesale reform, including
legislative change. But the current framework of rules governing Section 101 of
the U.S. patent laws, including the Supreme Court’s 2014 CLS Bank v. Alice
decision, were important victories for common-sense patent reform.


“The Alice decision made clear that you can’t simply add generic computer
language to basic ideas and get a patent. The ruling has been consistently
applied to get the worst-of-the-worst software patents kicked out of the
system. For the most part, it allows courts to state, clearly and correctly,
that these patents are a form of abstract idea, and should be thrown out at an
early stage of litigation. A win under the Alice rules spares the targets of
patent trolls not just from an unjust trial, but from an invasive and expensive
discovery process, fueled by a patent that never should have been issued in the
first place.”


It’s encouraging to see that the EFF still covers this issue, however seldom,
and we hope it’ll do so as frequently as it used to do. █


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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⢿⣿⣿⣿⣿⣿⣿⠻⠁⠀⠀⠀⠈⠀⠀⠀⠸⣿⡷⢄⡀⠀⠀⢄⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⠙⠻⣿⠟⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⡲⡝⠦⡄⠀⠀⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠘⡠⠀⢀⣀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢘⣌⢄⠀⠉⢠⠠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣈⠀⠀⠊⠁⠛⠉⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⡱⡟⣳⡤⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡄⠈⣁⣁⠄⠁⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡮⠔⡀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⡀⠘⡼⠀⠀⠀⠚⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⡀⠀⢀⠁⠀⠀⡀⠀⠀⠀⠀⠘⠺⠂⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠒⠀⠀⠀⠀⠀⠊⠥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 2393

╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.04.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_04/05/2023:_Amazon_Lays_Off_27,000,_Musk_Pulls_an_Andrew_Lee_(Hijacking
Handles)⠀✐


Posted in News_Roundup at 4:42 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Server
          o Applications
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          o Games
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          o Fedora_Family_/_IBM
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    * § GNU/Linux⠀➾


          o § Server⠀➾


                # ⚓ Kubernetes Blog ☛ Kubernetes_1.27:_StatefulSet_PVC_Auto-
                  Deletion_(beta)⠀⇛


                       Kubernetes v1.27 graduated to beta a new policy
                       mechanism for StatefulSets that controls the
                       lifetime of their PersistentVolumeClaims (PVCs).
                       The new PVC retention policy lets users specify if
                       the PVCs generated from the StatefulSet spec
                       template should be automatically deleted or
                       retrained when the StatefulSet is deleted or
                       replicas in the StatefulSet are scaled down.


          o § Applications⠀➾


                # ⚓ GamingOnLinux ☛ OBS_Studio_29.1_is_out_now_with_AV1_/_HEVC
                  for_YouTube⠀⇛


                       One for content creators here, as the excellent OBS
                       Studio just released version 29.1.0. This brings
                       initial support for AV1 / HEVC on YouTube.


          o § Instructionals/Technical⠀➾


                # ⚓ Ruben Schade ☛ PSA:_gz_isn’t_a_generic_compressed_file
                  extension⠀⇛


                       Take a look at this filename, and take a guess what
                       it is:


                       rootfs.gz
                       If you’re like me, you assumed gz meant gzip, and
                       therefore I could extract it with gunzip(1): [...]


                # ⚓ Alberto de Murga ☛ How_to_make_a_CSS-only_hamburger_menu⠀⇛


                       Recently I was doing some small modifications to my
                       site, when I rediscovered the hamburger menu I made
                       for it. It is not very special, just a menu that,
                       once you go into a small resolution, it will
                       compress itself into a hidden vertical menu that
                       you can show or hide by pushing a button. The
                       interesting part of it is that it is made only
                       using HTML and CSS.


                       I remember when I was making it that I could not
                       find a full example on the internet about how to
                       accomplish this, and that it implied a lot of trial
                       and error to achieve the desired result. So, I
                       extracted the code of the menu and turned it into a
                       simplified example.


                # ⚓ OSTechNix ☛ Install_Third_Party_Software_Using_Fedy_In
                  Fedora_38⠀⇛


                       The Fedora project will not include any package
                       that doesn’t comply with Fedora licensing policies
                       in the official repositories. So, the Fedora users
                       rely on third-party repositories like RPM Fusion to
                       install propriety drivers, software and codecs that
                       Fedora doesn’t want to ship due to legal and
                       licensing reasons. In this guide, we will see what
                       is Fedy and how to install third-party software and
                       multimedia codecs with Fedy in Fedora 38 Linux
                       operating systems.


                # ⚓ TecMint ☛ 5_Best_Mathematical_Equation_and_Formula_Writing
                  Tools_for_Linux⠀⇛


                       Are you looking for good software to write
                       mathematical equations? If so, this article
                       provides the top 5 equation editors that you can
                       easily install on your favorite Linux distribution.


                       In addition to being compatible with different
                       types of mathematical equations and formulas, they
                       are completely free and open-source. Take a look at
                       all the options below to find the one that best
                       suits your requirements.


                # ⚓ TecMint ☛ 9_Best_Command-Line/Terminal_Email_Clients_for
                  Linux⠀⇛


                       Recently, I wrote an article covering the best
                       email clients you can use on a Linux Desktop, all
                       of the email clients in that list were graphical
                       user interface (GUI) programs, but sometimes, users
                       prefer to deal with email directly from the
                       command-line.


                       For this reason, there is also a need to highlight
                       some of the best text-based email clients that you
                       can use on your Linux system.


                # ⚓ Linuxiac ☛ How_to_Install_Docker_on_Fedora:_A_Step-by-Step
                  Guide⠀⇛


                       Are you looking to install Docker on Fedora? Our
                       comprehensive guide provides clear and concise
                       instructions to get you up and running.


                # ⚓ UNIX Cop ☛ How_to_install_Codon_on_Ubuntu_22.04_–_High-
                  performance_Python_compiler⠀⇛


                       Hello, friends. In this post, you will learn how to
                       install Codon on Ubuntu 22.04. If you are a Python
                       developer, you will find it very useful to know it.


                # ⚓ How_to_install_Firefox_developer_edition_on_Ubuntu_22.04_or
                  20.04⠀⇛


                       Firefox Developer Edition is for those who want to
                       have tailored tools helpful in web development so
                       that it becomes easy to create, test and debug web
                       applications & websites.


                # ⚓ Linux Capable ☛ How_to_Install_Signal_on_Ubuntu_22.04_|
                  20.04⠀⇛


                       Signal Messenger is a free, open-source and
                       privacy-focused messaging app that offers end-to-
                       end encryption for secure communication. As a
                       cross-platform application, Signal provides a
                       seamless experience for users across various
                       devices and operating systems, including Ubuntu. >


                # ⚓ Linux Capable ☛ How_to_Install_Strawberry_on_Ubuntu_22.04_|
                  20.04⠀⇛


                       Are you an Ubuntu user looking for a powerful,
                       feature-packed, and customizable music player? Look
                       no further! Strawberry Player is here to meet all
                       your music listening needs.


                # ⚓ Linux Capable ☛ How_to_Install_Blender_on_Ubuntu_22.04_|
                  20.04⠀⇛


                       Blender is a powerful, open-source, and versatile
                       3D creation suite that has gained immense
                       popularity among artists, designers, and
                       enthusiasts worldwide. Its comprehensive set of
                       features, coupled with its affordability, make it
                       an attractive choice for Ubuntu users.


                # ⚓ nixCraft ☛ Bash_see_if_an_input_number_is_an_integer_or
                  not⠀⇛


                       While working on the bash shell script wrapper, I
                       needed to ensure that I only passed an integer in
                       the Bash script under Linux and Unix-like systems.
                       Here is how to check if a number is an integer in
                       Bash Linux or Unix script or at the command-line
                       interface (CLI)


                # ⚓ Linux Capable ☛ How_to_Install_GParted_on_Ubuntu_22.04_|
                  20.04⠀⇛


                       GParted, short for GNOME Partition Editor, is an
                       essential utility for Ubuntu users who want to
                       manage their disk partitions with ease and
                       precision.


                # ⚓ Linux Capable ☛ How_to_Install_FreeCAD_on_Ubuntu_22.04_|
                  20.04⠀⇛


                       FreeCAD is an open-source, highly versatile, and
                       feature-rich 3D computer-aided design (CAD)
                       software. Designed with engineers, architects, and
                       designers in mind, it offers a wide range of tools
                       to create and manipulate 3D models.


                # ⚓ Linux Capable ☛ How_to_Install_KiCad_on_Ubuntu_22.04_|
                  20.04⠀⇛


                       Welcome to the world of KiCad, an open-source
                       Electronic Design Automation (EDA) suite that is
                       fast gaining popularity among electrical engineers,
                       hobbyists, and Ubuntu users alike. KiCad offers a
                       comprehensive environment for designing schematics,
                       laying out printed circuit boards (PCBs), and even
                       creating 3D models of your design.


                # ⚓ Make Tech Easier ☛ How_to_Use_Diff_Files_in_Linux⠀⇛


                       Diff is a command line tool for Unix systems that
                       allows you to compare two files or directories and
                       see the differences between them. It’s ideal for
                       comparing old and new versions of files to see
                       what’s changed. In this article, we show you how
                       you can use diff to easily compare files in Linux.


                # ⚓ Kifarunix ☛ Install_MariaDB_11_on_Ubuntu_22.04/Ubuntu
                  20.04⠀⇛


                       Follow through this guide to learn how to install
                       MariaDB 11 on Ubuntu 22.04/Ubuntu 20.04. “MariaDB
                       11 is the new major release series of MariaDB.


          o § Games⠀➾


                # ⚓ GamingOnLinux ☛ Get_a_bunch_of_Rhythm_games_in_this_game
                  bundle⠀⇛


                       Do you have the moves? Are you quick on the finger?
                       Check out the Feel the Rhythm bundle over on Humble
                       Bundle. Here’s what compatibility to expect on
                       desktop Linux and Steam Deck.


                # ⚓ GamingOnLinux ☛ Heroic_Games_Launcher_2.7.1_hotfix_1_fixes
                  up_Epic_Games_login⠀⇛


                       Having some troubles with Epic Games on the Heroic
                       Games Launcher? You weren’t alone and a new hotfix
                       is out to get it sorted.


                # ⚓ GamingOnLinux ☛ OpenRazer_v3.6_brings_support_for_11_more
                  Razer_devices⠀⇛


                       Another fantastic update to OpenRazer with version
                       3.6.0 bringing support for more Razer devices on
                       Linux along with various improvements.


                # ⚓ GamingOnLinux ☛ Look_after_your_pixel_people_in_life_sim
                  Tiny_Life⠀⇛


                       A pixel-art version of The Sims? Sign me up. Tiny
                       Life from Ellpeck Games and Top Hat Studios is now
                       available in Early Access. It comes with full
                       Native Linux support and it should work just fine
                       on Steam Deck too.


                # ⚓ GamingOnLinux ☛ Valve_limits_Steam_store_pages_to_2
                  trailers_before_screenshots⠀⇛


                       I don’t know about you, but I used to get a little
                       annoyed by endless amounts of trailers on Steam
                       pages that didn’t really show much. Valve have been
                       paying attention again to what players want to see.


                # ⚓ GamingOnLinux ☛ GE-Proton_8-1_released,_mainly_pulling_in
                  Proton_8_upgrades⠀⇛


                       GE-Proton has a new release out with 8-1, which is
                       mainly pulling in a whole bunch of improvements
                       from Proton 8 and Proton Experimental.


    * § Distributions and Operating Systems⠀➾


          o § Fedora Family / IBM⠀➾


                # ⚓ DebugPoint ☛ Introducing_Fedora_Onyx:_Immutable_Variant
                  with_Budgie_Desktop_(Proposed)⠀⇛


                       Discover the latest addition to the Fedora Linux
                       family with the introduction of Fedora Onyx, an
                       immutable variant featuring the popular Budgie
                       Desktop environment. Learn how this new variant
                       expands the range of options available to Fedora
                       users and offers added immutability and atomic
                       capabilities with rpm-ostree.


          o § Debian Family⠀➾


                # ⚓ OMG! Linux ☛ New_Raspberry_Pi_OS_Update_Arrives_with_Linux
                  Kernel_6.1⠀⇛


                       This is the first update to the official operating
                       system for Raspberry Pi devices in 3 months and is
                       notable for being the first version powered by the
                       Linux 6.1 LTS kernel (previous versions use Linux
                       5.15 LTS).


                       A substantial uplift, the newer kernel offers
                       improved hardware support, new drivers, performance
                       boosts, and better security. Gamers will appreciate
                       the addition of new gamepad drivers, including the
                       Hori Fighting Commander ONE and 8BitDo Pro 2 wired
                       controller.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ DebugPoint ☛ Ubuntu_MATE_23.04_“Lunar_Lobster”:_Find_out
                  what’s_new_in_this_release⠀⇛


                       Ubuntu MATE 23.04, code-named “Lunar Lobster”, has
                       been released on April 20, 2023. The latest version
                       of Ubuntu MATE 23.04 is the first short-term
                       release of 2023, and it will receive support for
                       nine months until January 2024. It is the official
                       Ubuntu flavour featuring the super-lightweight MATE
                       desktop, and it comes packed with several
                       enhancements that make it worth considering for
                       those who want a legacy desktop look of GNOME.


                       Find out what’s new in this release.


                # ⚓ OMG Ubuntu ☛ Development_Opens_on_Ubuntu_23.10_‘Mantic
                  Minotaur’⠀⇛


                       At this formative stage in development there isn’t
                       anything “new” for me to mention, much less
                       screenshot for your ocular enjoyment. However, if
                       you’re big into bug hunting then this is prime
                       season so feel free to jump in and start squashing
                       as soon as you’re able.


                       The final stable version of Ubuntu 23.10 is due to
                       be released on October 12, 2022 — a touch earlier
                       than when most October release typically emerge (or
                       maybe I’m just getting so old everything feels too
                       soon).


          o § Devices/Embedded⠀➾


                # ⚓ Linux Gizmos ☛ 3.5”_SBC_features_i.MX8M_Mini_and_dual_GbE
                  ports⠀⇛


                       ICOP launched last month a single board computer
                       based on the i.MX8M mini multicore processor
                       designed for machine vision, industrial systems,
                       embedded systems and smart retail applications.


          o § Open Hardware/Modding⠀➾


                # ⚓ Raspberry Pi ☛ Aquaponics_for_beginners_with_the
                  TynecastleTechs_team⠀⇛


                       Research led the team to select the Scissortail
                       Rasbora, since this is a hardy and adaptable fish
                       that can live in a smaller tank. They moved twelve
                       scissortails into in a 40-litre plastic tub, along
                       with aquatic plants to create a more natural
                       environment and provide hiding places, reducing
                       stress for the fish. They selected Java moss,
                       Anubias, and Cryptocoryne as the most suitable
                       plant species for smaller tanks, and added some
                       mature specimens. The team kept the water heated to
                       tropical fishes’ favourite temperature (about 24°C
                       or 75°F), and also installed appropriate filters.


                # ⚓ Andrew Hutchings ☛ Acorn_RiscPC_#2:_Restoration_Part_1⠀⇛


                       Another RiscPC recently hit my saved searches on
                       eBay and given that it had a second slice to it I
                       thought it would be good to maybe use parts of this
                       machine to upgrade my own.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Google ☛ The_beginning_of_the_end_of_the_password [iopkh:
                  marketeering of proprietary gimmicks, devoid of actual
                  information]⠀⇛


                       Last year — alongside FIDO Alliance, Apple and
                       Microsoft — we announced we would begin work to
                       support passkeys on our platform as an easier and
                       more secure alternative to passwords. And today,
                       ahead of World Password Day, we’ve begun rolling
                       out support for passkeys across Google Accounts on
                       all major platforms. They’ll be an additional
                       option that people can use to sign in, alongside
                       passwords, 2-Step Verification (2SV), etc.


                # ⚓ 9to5Google ☛ Google_rolling_out_fix_for_Messages_on_Pixel
                  phones_with_Android_14⠀⇛


                # ⚓ Make Tech Easier ☛ How_to_See_Blocked_Numbers_on_Android
                  and_Manage_Them_–_Make_Tech_Easier⠀⇛


                # ⚓ 9to5Google ☛ Best_MagSafe_accessories_for_Google_Pixel_and
                  other_Android_phones_in_2023⠀⇛


                # ⚓ Gizmo China ☛ Google_Play_Store_35.5.14_now_rolling_out_to
                  Android_devices⠀⇛


    * § Free, Libre, and Open Source Software⠀➾


          o § Programming/Development⠀➾


                # ⚓ Red Hat ☛ New_C_features_in_GCC_13⠀⇛


                       The latest major version of theGNU_Compiler
                       Collection (GCC), 13.1, was released in April 2023.
                       Like every major GCC release, this version will
                       bring manyadditions,_improvements,_bug_fixes,_and
                       new_features. GCC 13 is already the system compiler
                       inFedora_38. Red_Hat_Enterprise_Linux (RHEL) users
                       will get GCC 13 in the Red Hat GCC Toolset (RHEL 8
                       and RHEL 9). It’s also possible to try GCC 13 on
                       godbolt.org and similar pages.


                # ⚓ Vadim Kravcenko ☛ Rules_of_Thumb_for_Software_Development
                  Estimations⠀⇛


                       First, I planned on calling this article “Mastering
                       the Art of Estimations: A Definitive Guide for
                       Developers”, but then who am I to tell you how to
                       estimate projects? I can only give you some
                       pointers and describe some things that worked well
                       for me over the years. So that’s exactly what I
                       will do — give you some rules of thumb to make your
                       life easier.


                       Ah, software estimation – the bane of many
                       developers’ existence and the scourge of project
                       managers everywhere. A constant battle of “tell me
                       how much it’s going to take you” and “give me a
                       clear description of the task first.” I’m here to
                       bring some much-needed reality of the complexities
                       of real-world development. I’ve had my share of
                       estimations on both sides of the fence. I’ve seen
                       it all. And I’m here to give you the harsh truths
                       about software estimation, so buckle up.


                # ⚓ Rlang ☛ How_to_Download_a_File_from_the_Internet_using
                  download.file()⠀⇛


                       Introduction
                       The download.file() function in R is used to
                       download files from the internet and save them onto
                       your computer. Here’s a simple explanation of how
                       to use it:


    * § Leftovers⠀➾


          o ⚓ TwinCities Pioneer Press ☛ Amid_quarreling,_the_Ramsey_County
            Fair_is_canceled_for_a_fourth_year,_its_future_uncertain⠀⇛


                 It will be the only one of Minnesota’s 87 counties
                 without its own fair.


          o ⚓ New Yorker ☛ I_Will_Not_Board_a_Plane_to_Visit_Your_Baby⠀⇛


                 If I had a baby, I would not ask you to get on a plane. I
                 wouldn’t publish a wounded essay online if you chose
                 sleep over visiting my offspring.


          o ⚓ New York Times ☛ A_Minimalist_Australian_Dream_Home_With_an_18th-
            Century_Twist⠀⇛


                 Why would a modernist house in a Melbourne suburb need an
                 inverted ha-ha? (And what is a ha-ha, anyway?)


          o ⚓ Reason ☛ NBA_MVP_Joel_Embiid_Learned_To_Shoot_by_Watching
            YouTube⠀⇛


                 Politicians attack social media for spreading
                 conspiracies and so-called misinformation. But what about
                 when social media helps someone become an NBA star?


          o § Education⠀➾


                # ⚓ teleSUR ☛ Guinea_Contract_Teachers_in_the_Streets,_Threaten
                  More_Strikes⠀⇛


                       “…several educators have remained unpaid for a
                       duration of seven months…”


                # ⚓ uni Stanford ☛ GSC_reaffirms_support_for_Faculty_Senate’s
                  Honor_Code_revisions⠀⇛


                       The GSC discussed the last Faculty Senate meeting
                       and heard updates from R&DE on events and on-campus
                       food options.


                # ⚓ uni Stanford ☛ Undergraduate_Senate_doubles_down_on
                  opposition_to_Honor_Code_revision_proposal,_citing_breach_of
                  precedent_and_student_trust⠀⇛


                       At its Tuesday meeting, the Undergraduate Senate
                       expressed opposition to the Faculty Senate’s
                       decision to bypass its prior votes against proposed
                       revisions to the Honor Code that would explicitly
                       allow exam proctoring, ending a 102-year long
                       precedent.


          o § Hardware⠀➾


                # ⚓ Tom’s Hardware ☛ AMD_Posts_First_Loss_in_Years_as_Consumer
                  Chip_Sales_Plummet_by_65%⠀⇛


                       Sales of AMD’s datacenter products remain strong,
                       but client CPU shipments drop 65% year-over-year.


                # ⚓ Tom’s Hardware ☛ Intel_Bids_Gemini_Lake_Refresh_CPUs
                  Farewell⠀⇛


                       Intel’s Gemini Lake Refresh processors, launched in
                       2019, have reached end-of-life (EOL) status.


                # ⚓ Tom’s Hardware ☛ TSMC_to_Charge_up_to_30%_More_for_Chips
                  Made_in_the_U.S.⠀⇛


                       TSMC’s quotes for U.S. and Japan-made chips will be
                       higher than for chips produces in Taiwan.


                # ⚓ US News And World Report ☛ US_Defense_Contractors_Want
                  Deeper_Cooperation_With_Taiwan⠀⇛


                       A delegation of United States defense contractors
                       and a former senior leader of the U.S. Marine Corps
                       are pledging the beginning of deeper cooperation
                       with Taiwan


                # ⚓ Tom’s Hardware ☛ Ryzen_Burnouts_Force_Asus_to_Add_Overclock
                  Warnings_to_EXPO_Features [Ed: AMD made and shipped chips
                  that fried themselves. So much for quality control...]⠀⇛


                       Asus is one of the first motherboard vendors to add
                       a notice stating that memory technologies like XMP
                       / EXPO are considered overclocking, with clear
                       warranty implications/


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ teleSUR ☛ U.S._Salmonella_Outbreak_Linked_to_Flour⠀⇛


                       “…Hospitalization has been necessitated for three
                       individuals…”


                # ⚓ Helsinki Times ☛ Exercise_increases_cancer-fighting_cells
                  in_cancer_patients,_study_shows⠀⇛


                       Exercise has been foundto increase the number of
                       defense cells in cancer patients, according to two
                       studies conducted at the national PET center at the
                       University of Turku. The studies aimed to
                       investigate the effects of short-term exercise on
                       the immune system of lymphoma and breast cancer
                       patients who had recently been diagnosed and had
                       not started treatment yet.


                # ⚓ YLE ☛ Mental_health_disorders_have_not_increased
                  significantly,_although_symptoms_have⠀⇛


                       Health specialists say it is important for public
                       discussion to distinguish between clinical
                       disorders and the symptoms of struggles with day-
                       to-day living.


                # ⚓ Free_at-home_COVID-19_antigen_tests_still_available⠀⇛


                       The U-M COVID-19 Community Sampling and Tracking
                       Program has free rapid antigen test kits available 
                       available for pickup through May 12 at the CSTP
                       sites at Pierpont Commons and Blau Hall.


                # ⚓ CS Monitor ☛ Won’t_you_be_my_neighbor?_How_porch_culture
                  fights_loneliness.⠀⇛


                       American front porches signified community and
                       openness, but increasingly people are suspicious
                       when strangers approach their door. Meet the people
                       trying to keep neighborliness alive.


                # ⚓ New York Times ☛ Australia_Aims_to_‘Stamp_Out’_Vaping_With
                  Sweeping_Regulations⠀⇛


                       The proposal would ban all single-use, disposable
                       vapes, halt the importation of nonprescription
                       vapes and restrict certain flavors, colors and
                       ingredients.


          o § Proprietary⠀➾


                # ⚓ NPR ☛ Elon_Musk_threatens_to_re-assign_@NPR_on_Twitter_to
                  ‘another_company’⠀⇛


                       “If this is a sign of things to come on Twitter, we
                       might soon see even more of a rapid retreat by
                       media organizations and other brands that don’t
                       think it’s worth the risk,” said Emily Bell, a
                       professor at Columbia Journalism School who studies
                       social media. “It’s really an extraordinary threat
                       to make.”


                # ⚓ Yahoo News ☛ 2023-04-28_[Older]_More_on_GM_Dropping
                  CarPlay⠀⇛


                # ⚓ Yahoo News ☛ Amazon_cut_27,000_roles,_including_many_in_HR.
                  Here’s_where_it’s_investing_those_savings⠀⇛


                       Amazon’s first quarter earnings call shed light on
                       the company’s shifting investments following
                       leadership’s decision to cut a whopping 27,000
                       jobs. The widespread cuts, which severely
                       diminished the tech giant’s HR team, were said to
                       be an effort to help streamline costs.


                       Amazon began its latest layoffs last week,
                       targeting HR and cloud computing employees. And an
                       internal memo sent to Amazon Web Services (AWS)
                       hiring managers on Tuesday revealed that the
                       company would restrict the number of hires the
                       cloud business can make, going so far as to employ
                       a new headcount management system to better monitor
                       hiring plans.


                       The moves aren’t a surprise. Late last year, the
                       company announced it would freeze corporate hiring,
                       slow the expansion of its warehouses, and end some
                       of its more experimental projects like Amazon Care
                       and its Halo device division.


                # ⚓ The Register UK ☛ Give_NotPetya-hit_Merck_that_$1.4B,
                  appeals_court_tells_insurers [iophk: Windows TCO]⠀⇛


                       A New Jersey appellate court this week upheld [PDF]
                       an earlier decision that a group of insurers could
                       not use the war exclusion in their insurance
                       policies — despite the US and UK governments, among
                       others others, attributing NotPetya to Kremlin-
                       backed fiends — because the attack against Merck
                       wasn’t specifically linked to Russian military
                       action.


                       The ruling means Merck may finally claim its $1.4
                       billion payout. And it’s likely going to make it
                       more difficult for insurance companies to use war
                       as an excuse to not pay losses related to
                       cyberattacks, according to industry watchers.


                # ⚓ Security Week ☛ Ransomware_Attack_Affects_Dallas_Police,
                  Court_Websites [iophk: Windows TCO]⠀⇛


                       Dallas was hit with a computer ransomware attack
                       Wednesday that brought down its Police Department
                       and City Hall websites and caused some jury trials
                       to be canceled, officials said.


                # ⚓ Data Breaches ☛ City_of_Dallas_impacted_by_ransomware
                  attack [iophk: Windows TCO]⠀⇛


                       The City of Dallas is dealing with a ransomware
                       attack that has infected its servers, limiting the
                       delivery of City service.


                # ⚓ NBC ☛ [Crackers]_hijacked_a_university’s_emergency_system
                  to_threaten_students_and_faculty [iophk: Windows TCO]⠀⇛


                       Bluefield University, a small, private university
                       on the border of Virginia and West Virginia, is
                       among the long and growing list of U.S.
                       institutions hit by ransomware [crackers], who
                       break into computer systems to then encrypt or
                       threaten to leak files if they are not paid. The
                       school learned of the cyberattack on their systems
                       on Sunday, a Bluefield University spokesperson told
                       NBC News.


                # ⚓ The Record ☛ Colleges_and_schools_across_US_dealing_with
                  ransomware_incidents,_cyberattacks [iophk Windows TCO]⠀⇛


                       Bluefield University — a private Baptist school in
                       Bluefield, Virginia serving about 1,000 students –
                       published a statement on Sunday announcing that
                       their systems “have been shut down for an unknown
                       period of time due to a recent cybersecurity
                       attack.” Two hours away across the border in West
                       Virginia, BridgeValley Community and Technical
                       College said it continued to deal with a ransomware
                       attack that is now believed to be the work of the
                       Akira cybercrime gang.


                # ⚓ CyberRisk Alliance LLC ☛ US_educational_system_hit_with
                  deluge_of_cyberattacks [iophk: Windows TCO]⠀⇛


                       Ransomware attacks against K-12 districts across
                       the U.S. have reached at least 22, while attacks
                       against universities and colleges have totaled at
                       least 27 so far this year, said Emsisoft ransomware
                       expert Brett Callow.


          o § Security⠀➾


                # ⚓ LWN ☛ Security_updates_for_Wednesday_[LWN.net]⠀⇛


                       Security updates have been issued by Debian (avahi,
                       kernel, linux-5.10, nodejs, webkit2gtk, and
                       wpewebkit), Gentoo (chromium, google-chrome,
                       microsoft-edge, dbus, dbus-broker, dhcp, firefox,
                       firejail-lts, libapreq2, libsdl, libsdl2, lua,
                       proftpd, python, PyPy3, sudo, syslog-ng, systemd,
                       tor, uptimed, vim, and xfce4-settings), Oracle
                       (emacs and libwebp), Red Hat (libwebp), Scientific
                       Linux (libwebp), and SUSE (ceph, ffmpeg-4, git,
                       pdns-recursor, and shim).


                # ⚓ City_of_Dallas_impacted_by_ransomware_attack,_police
                  computer_dispatch_system_down⠀⇛


                       The city of Dallas working to recover from a
                       ransomware attack that has infected its servers,
                       limiting the delivery of city services, including
                       the police department.


                       FOX 4 learned about the breach through a tip and
                       the city is continuing to be very tight-lipped, not
                       making anyone available for interviews regarding
                       the scope an impact of the attack.


                       The city released a statement on Wednesday
                       afternoon confirming that a number of servers have
                       been compromised with ransomware, impacting
                       “several functional areas.”


                # ⚓ Data Breaches ☛ Persistent_attackers:_Eurasia_Group
                  believes_it_has_been_dealing_with_the_same_attackers_since
                  2020⠀⇛


                       The total number of individuals affected was not
                       disclosed in the letter. Nor was it clear whether
                       those affected were all employees or if client data
                       was involved.


                # ⚓ Data Breaches ☛ Brightline_continues_notifying_clients_of
                  GoAnywhere_incident;_count_continues_to_rise_(more_than_1
                  million)⠀⇛


                       DataBreaches has written to Brightline’s external
                       counsel to ask whether Brightline has terminated
                       its contract with Fortra or continues using it. No
                       reply was immediately available.


                # ⚓ Murfreesboro_Medical_Clinic_remains_closed_due_to
                  cyberattack⠀⇛


                       Murfreesboro Medical Clinic & SurgiCenter was the
                       victim of a sophisticated criminal cyberattack,
                       according to a press release.


                       The cyberattack happened on April 22 and in
                       response, MMC said it had to shut down all
                       operations on May 1-3 to limit the spread of the
                       attack. Since shutting down, they’ve been working
                       with law enforcement and experts to identify the
                       source and scope of the attack to restore normal
                       operations.


                       CEO Joey Peay said they were able to limit the
                       impact of the attack thanks to the quick response
                       of their technology experts. MMC’s data backup
                       systems were not affected by the attack.


                       “They would hit us, and we would try to hit them
                       back,” Peay said about trying to fight the cyber
                       criminals for more than a week. “We thought we were
                       in a pretty good shape and then Sunday morning
                       things changed again. That is what necessitated us
                       closing. We weren’t going to be able to continue to
                       fend off the serious nature of these attacks with
                       our clinic open, our physicians and staff trying to
                       work. It just wasn’t going to be doable.”


                # ⚓ Data Breaches ☛ Lawrence_Family_Development_Charter_School
                  allegedly_attacked_by_Snatch_Team⠀⇛


                       Two attempts to contact LFCDS administrators
                       through their website contact forms for messages to
                       faculty and staff both failed with messages “
                       {“statusText”:”*** Forbidden. You sent forms too
                       often. Please wait a few minutes. ***”,”status”:
                       403}”


                       There is nothing on the charter school’s website at
                       this time to indicate any disruption or incident
                       and DataBreaches could find no confirmation by them
                       of any attack. DataBreaches subsequently sent
                       emails to administrators at the charter school, but
                       no reply was immediately available. This post will
                       be updated if a reply is received or more
                       information becomes available.


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ Zimbabwe ☛ Liquid_(Zol)_faced_a_DDoS_attack_on_email
                        service,_explains_why_your_inbox_was_empty⠀⇛


                             Liquid has communicated that they were the
                             victim of a large-scale DDoS attack on their
                             Hosted Email Service. They found out they
                             were under attack on Workers’ Day, around
                             11PM. DDoS stands for Distributed Denial of
                             Service. Multiple computers are used to
                             target a single computer or network.


                # § Privacy/Surveillance⠀➾


                      # ⚓ Engadget ☛ 2023-04-29_[Older]_Apple_drops_lawsuit
                        against_former_exec_who_accused_company_of_spying⠀⇛


                      # ⚓ Latvia ☛ ‘E-health’_system_to_up_authentication
                        requirements_in_2024⠀⇛


                             From the beginning of next year, access to e-
                             health is planned to only be possible through
                             qualified electronic means of personal
                             identification: with an e-ID card, an e-
                             signature (eParaksts) card, an e-signature
                             card plus or e-signature mobile. The plan has
                             met resistance from both the patient and
                             doctor side, Latvian Radio reported on May 3.


                      # ⚓ Off Guardian ☛ Who_Wants_a_Brain_Machine_Interface?⠀⇛


                             VN Alexander I’ve never wanted to be able to
                             control any of my devices with my thoughts. 
                             I am perfectly happy to use a physical
                             interface that I can turn off, let go of, or
                             walk away from.  What about you?  Is your
                             keyboard holding you back?


                      # ⚓ Privacy International ☛ Our_position_on_the_EU_Cyber
                        Resilience_Act_(CRA)⠀⇛


                      # ⚓ Reason ☛ New_Senate_Bill_Would_Turn_Online_Services
                        Into_Narcs⠀⇛


                             An expanded surveillance state can’t solve
                             problems created by drug prohibition.


                      # ⚓ The Register UK ☛ Go_ahead,_forget_that_password._Use
                        a_passkey_instead,_says_Google⠀⇛


                             Passkeys are the latest hope for allowing
                             organizations and regular folk to move away
                             from passwords. And when we say passkeys,
                             think of things like biometric-reading phone
                             apps that can be used to authenticate
                             yourself and gain access to accounts, though
                             these keys can take various forms.


                      # ⚓ Scoop News Group ☛ White_House_wants_to_understand
                        how_employers_use_automated_tools_to_track_staff⠀⇛


                             Responses to the RFI will be used by the
                             administration to inform new policy responses
                             as it works to formulate a comprehensive
                             response to the wider use of technologies
                             including artificial intelligence.


                             It said: “Employers are increasingly
                             investing in technologies that monitor and
                             track workers, and making workplace decisions
                             based on that information. According to an
                             investigation by The New York Times last
                             year, eight of the 10 largest private U.S.
                             employers tracked individual workers to
                             assess their productivity.”


                      # ⚓ Vice Media Group ☛ Accessing_Porn_In_Utah_Is_Now_a
                        Complicated_Process_That_Requires_a_Picture_of_Your
                        Face⠀⇛


                             As of Tuesday, many Utahns navigating to
                             Pornhub were met with a notice that they
                             can’t enter the website, and a video of adult
                             performer Cherie DeVille gently explaining
                             that thanks to their elected
                             officials—specifically Republican Senator
                             Todd Weiler and governor Spencer Cox—they are
                             now completely banned from using the site.


                             All of the sites under the same ownership as
                             Pornhub (formerly Mindgeek, now Canadian
                             private equity firm Ethical Capital
                             Partners), including Brazzers, Redtube,
                             Youporn, and several others, have also pulled
                             out of Utah, with a message: “Please contact
                             your representatives before it is too late
                             and demand device-based verification
                             solutions that make the internet safer while
                             also respecting your privacy.”


          o § Defence/Aggression⠀➾


                # ⚓ RFERL ☛ One_Militant_Killed,_Seven_Arrested_In_Pakistan,
                  Military_Says⠀⇛


                       One militant was killed and seven others were
                       arrested in raids on hideouts of the Pakistani
                       Taliban, known as Tehrik-e Taliban (TTP), near the
                       Afghan border on May 1, the military said in a
                       statement.


                # ⚓ AIM ☛ Microsoft_to_Pay_$3.3_million_for_Selling_Software_to
                  ‘Blocked_Users’_in_Russia,_Cuba,_Iran⠀⇛


                       Amounting to 94%—1,252 of all the sales made from
                       Microsoft’s US and Ireland servers were to Russian
                       entities—primarily based in the Crimea region.
                       Additionally, 54 in Cuba, 30 in Iran, and three
                       took place in Syria.


                # ⚓ The Hill ☛ China_updates_military_conscription_rules_with
                  eye_on_space,_cyberwarfare⠀⇛


                       The revised regulations will also focus on
                       recruiting individuals with cyber and space
                       expertise, two emerging domains that Chinese
                       President Xi Jinping is increasingly pushing for.


                # ⚓ teleSUR ☛ US_Government_To_Send_1,500_Troops_To_Mexican
                  Border⠀⇛


                       The move comes before Title 42 is lifted on May 11.


                # ⚓ CS Monitor ☛ How_is_Biden’s_quick_asylum_screening_plan
                  different_from_Trump’s?⠀⇛


                       The Biden administration is implementing a new
                       system for fast-track asylum screenings at the
                       border, with interviews conducted by immigration
                       officials and access to legal counsel. Critics
                       doubt its effectiveness after issues under Donald
                       Trump’s system.


                # ⚓ The Strategist ☛ Vale_Allan_Gyngell,_the_finest_mind_in
                  foreign_policy⠀⇛


                       In mid-April, Foreign Minister Penny Wong addressed
                       the National Press Club on Australia’s interests in
                       a regional balance of power.


                # ⚓ The Strategist ☛ Taking_Defence_beyond_the_barbed_wire_in
                  northern_Australia⠀⇛


                       Nations must regularly ask themselves how they are
                       to meet the challenges of their strategic context.


                # ⚓ Federal News Network ☛ Teenage_shooter_kills_8_children,
                  guard_at_school_in_Serbia⠀⇛


                       Police say a teenager opened fire at his school in
                       Serbia’s capital, killing eight children and a
                       school guard before being arrested in the school
                       yard. Six more children and a teacher were
                       hospitalized. A father of a student at the school
                       in central Belgrade said the shooter entered his
                       daughter’s classroom Wednesday, firing at her
                       teacher and then her classmates as they ducked
                       under their desks. A local official said most
                       students were able to flee through a back door.
                       Police said the shooter was a student at the
                       Vladislav Ribnikar school and was born in 2009.
                       They said he used his father’s gun.


                # ⚓ Federal News Network ☛ Army_changes_tack_in_how_it_trains
                  recruiters⠀⇛


                       As the Army looks to another year of recruiting
                       shortages, it takes a new look at how it trains
                       recruiters.


                # ⚓ France24 ☛ Israel,_Palestinian_armed_groups_agree_to
                  ceasefire_after_hunger_striker’s_death_sparks_fighting⠀⇛


                       A Palestinian hunger striker died in Israeli
                       custody on Tuesday, sparking an exchange of fire
                       between Israel and armed groups in Gaza, before
                       three Palestinian officials said the sides had
                       agreed to a ceasefire.


                # ⚓ HDP_warns_against_provocations_in_Mersin⠀⇛


                       The People’s Democratic Party invited all party
                       members and supporters to be careful against any
                       provocations, and to continue the election campaign
                       in a calm and decisive manner.


                # ⚓ European Commission ☛ Questions_and_Answers_on_the_Act_in
                  Support_of_Ammunition_Production⠀⇛


                       European Commission Questions and answers Brussels,
                       03 May 2023 Why there is a need for the Act in
                       Support of Ammunition Production (ASAP)?


                # ⚓ European Commission ☛ Defence:_€500_million_and_new
                  measures_to_urgently_boost_EU_defence_industry_capacities_in
                  ammunition_production⠀⇛


                       European Commission Press release Brussels, 03 May
                       2023 Today, the Commission has adopted the Act in
                       Support of Ammunition Production (ASAP).


                # ⚓ Latvia ☛ Latvian_government_okays_naval_missile_system
                  purchase⠀⇛


                       On Tuesday, May 2, the Latvian Cabinet of Ministers
                       approved the purchase of the Naval Strike Missile
                       (NSM) system from the United States.


                # ⚓ US News And World Report ☛ YouTube_Prankster_Testifies
                  About_Video_That_Got_Him_Shot⠀⇛


                       A YouTube prankster has testified about a video
                       that went wrong and ended with him getting shot in
                       the abdomen


                # ⚓ Latvia ☛ May_4_military_parade_will_take_place_in_Alūksne⠀⇛


                       This year’s May 4 military parade in honor of
                       Latvia’s restoration of independence day is taking
                       place in Alūksne in north-east Latvia.


                # ⚓ Latvia ☛ New_army_barracks_to_be_built_soon_at_Ādaži_base⠀⇛


                       In the near future, the construction of new
                       barracks for soldiers at the Ādaži military base is
                       planned, the commander of the National Armed Forces
                       (NBS), Leonīds Kalniņš, said on Latvian
                       Television’s broadcast “Morning Panorama” on May 3.


                # ⚓ teleSUR ☛ Palestinian_Jader_Adnan_Dies_After_88-Day_Hunger
                  Strike⠀⇛


                       The Palestinian National Authority denounced
                       that his death was a “deliberate assassination” due
                       to the negligence of the Israeli authorities who
                       knew about the deterioration of his health.


                # ⚓ New York Times ☛ What_to_Know_About_Hunger_Strikes⠀⇛


                       The actions are almost always political, and
                       governments sometimes resort to force-feeding, a
                       practice denounced as inhumane. Deaths like that of
                       a Palestinian prisoner this week are uncommon.


                # ⚓ Axios ☛ Judge_finds_former_Minneapolis_police_officer
                  guilty_for_role_in_George_Floyd’s_death⠀⇛


                       A former Minneapolis police officer who held back
                       bystanders as Derek_Chauvin_restrained_George
                       Floydhas been convicted of aiding and abetting
                       second-degree manslaughter.


                # ⚓ teleSUR ☛ Sudanese_Warring_Parties_Agree_to_7-Day_Truce⠀⇛


                       Nevertheless, Gen. Al Burhan’s envoy Dafa Allah al
                       Haj Ali said that there will be no “direct”
                       negotiations with the RSF, calling it a “terrorist”
                       organization.


                # ⚓ New York Times ☛ Does_America_Realize_That_Sudan_Is_Too_Big
                  to_Fail?⠀⇛


                       The people of Sudan have been all but abandoned in
                       the crossfire of a fight to the death between the
                       two men who want to rule them.


                # ⚓ New York Times ☛ A_Brutal_Sex_Trade_Built_for_American
                  Soldiers⠀⇛


                       It’s a long-buried part of South Korean history:
                       women compelled by force, trickery or desperation
                       into prostitution, with the complicity of their own
                       leaders.


                # ⚓ New York Times ☛ Marcos_Makes_Mark_on_Foreign_Policy_in
                  Push_for_Closer_U.S.-Philippines_Ties⠀⇛


                       In his first months in power, the Philippines
                       leader has reforged a strong alliance with the
                       U.S., winning praise even as questions remain about
                       his path and intent at home.


                # ⚓ RFA ☛ US_warns_China_against_‘intimidation’_of_Philippines
                  in_South_China_Sea⠀⇛


                       Warning comes after a near-collision between
                       Philippine and Chinese vessels and as Ferdinand
                       Marcos Jr. visits U.S.


                # ⚓ LRT ☛ Lithuanian_president_calls_for_speeding_up_deal_on
                  NATO_defence_plans⠀⇛


                       Lithuania and Poland must seek that NATO member
                       countries agree on the alliance’s new defence plans
                       before July’s summit in Vilnius, President Gitanas
                       Nausėda said after meeting with Polish Prime
                       Minister Mateusz Morawiecki in Vilnius on Tuesday.


                # ⚓ LRT ☛ Denmark_pledges_battalion_to_defend_Baltic_states⠀⇛


                       Denmark will deploy a battalion of between 700 and
                       1,200 troops to the Baltic states after withdrawing
                       troops from Iraq, the country’s Defence Minister
                       Troels Lund Poulsen said on Tuesday.


                # ⚓ New York Times ☛ A_Drone_Opera,_Brought_to_You_by_General
                  Dynamics?_A_Company_Clarifies.⠀⇛


                       “Grounded,” a new work about the psychological toll
                       of drone warfare, drew scrutiny after its
                       presenter, Washington National Opera, advertised
                       the support of a major military contractor.


                # ⚓ 2023_ELECTIONS:_‘AKP_is_no_more_a_good_partner_for_the
                  US’⠀⇛


                       Researcher Kumru Toktamış says that for the US, AKP
                       is no longer a good partner for cooperation, since
                       it is not predictable which steps the Erdoğan
                       government will take here or there.


          o § Environment⠀➾


                # § Energy/Transportation⠀➾


                      # ⚓ The Straits Times ☛ US_firm_plans_to_build_small
                        nuclear_power_plants_in_the_Philippines⠀⇛


                             In Manila, nuclear-free advocates questioned
                             the plan, saying the tech has not been tested
                             enough.


                      # ⚓ The Straits Times ☛ India,_China_propose_‘multiple
                        pathways’_on_cutting_use_of_fossil_fuels:_Sources⠀⇛


                             Multiple pathways would enable countries to
                             choose resources, even coal, while working
                             towards net-zero emissions.


                      # ⚓ Federal News Network ☛ Iran’s_Revolutionary_Guard
                        seizes_tanker_in_Strait_of_Hormuz⠀⇛


                             Iran seized a Panama-flagged oil tanker in
                             the Strait of Hormuz on Wednesday, the
                             second-such capture by Tehran in recent days.
                             That’s according to the U.S. Navy. The
                             Mideast-based 5th Fleet identified the vessel
                             as the Niovi. It said Iran’s paramilitary
                             Revolutionary Guard seized the ship. The Navy
                             published pictures of small Guard vessels
                             surrounding the tanker. Iran’s state-run IRNA
                             news agency acknowledged the Guard seized the
                             vessel, but offered no motive. Last week,
                             Iran seized an oil tanker carrying crude for
                             Chevron amid wider tensions between Tehran
                             and the U.S. over its nuclear program.


                      # ⚓ Quartz ☛ Ford’s_EV_unit_lost_$722_million_last
                        quarter,_but_it’s_still_cutting_prices_to_compete_with
                        Tesla⠀⇛


                             Ford announced it would slash the price of
                             its all-electric Mustang Mach-E by between
                             $1,000 and $4,000 this week, the latest move
                             to keep up with Tesla’s recurring price
                             changes.


                      # ⚓ Quartz ☛ Another_Indian_airline_has_followed_Jet_into
                        bankruptcy⠀⇛


                             Eighteen-year-old Indian airline, Go First,
                             has gone bankrupt, following the same fate as
                             Jet_Airways, the country’s first private
                             carrier.


                      # ⚓ Federal News Network ☛ Indian_no-frills_air_carrier
                        Go_First_files_for_bankruptcy⠀⇛


                             Thousands of travelers have been stranded
                             after no-frills Indian air carrier Go First
                             filed for bankruptcy and suspended its
                             flights for three days, starting Wednesday. A
                             statement on the carrier’s website said the
                             cancellations were due to “operational
                             reasons.” The Press Trust of India news
                             agency said airline chief Kaushik Khona told
                             Go First employees it was facing a crisis due
                             to Pratt & Whitney’s failure to supply
                             aircraft engines, which forced it to ground
                             half its fleet of about 60 aircraft. Pratt
                             and Whitney, an American aerospace
                             manufacturer with global operations, had no
                             immediate comment.


                # § Wildlife/Nature⠀➾


                      # ⚓ uni Emory ☛ Emory_freshman_saves_the_bees,_one_bottle
                        of_lemonade_at_a_time⠀⇛


                             Me & the Bees Lemonade donates to a number of
                             different groups, including the U.S.
                             Beekeepers Association, Heifer International
                             and the Sustainable Food Center.


                # § Overpopulation⠀➾


                      # ⚓ RFERL ☛ Armenia’s_Population_Drops_Under_3_Million
                        For_First_Time_Since_Independence⠀⇛


                             Armenia’s population is just below 3 million
                             people, data from the census conducted in
                             October shows.


          o § Finance⠀➾


                # ⚓ Engadget ☛ 2023-04-28_[Older]_Ex-Apple_employee_sentenced
                  to_three_years_in_prison_after_$17_million_fraud_scheme⠀⇛


                # ⚓ Helsinki Times ☛ Growth_in_Finnish_student_loan_borrowers
                  slows_down_in_2022⠀⇛


                       The growth in the number of student loan borrowers
                       in Finland slowed down in 2022, according to a
                       press release by Kela, the Finnish Social Insurance
                       Institution. The mediaan amount of student loans
                       borrowed was 14,389 euros, and Helsinki-based
                       students took out significantly more loans than
                       those in other regions. While the number of
                       borrowers grew rapidly in the late 2010s, the
                       growth has since slowed down.


                # ⚓ The Straits Times ☛ Big-spending_Chinese_shoppers_are
                  splurging_on_luxury_at_home,_not_abroad_any_more⠀⇛


                       In April, about 62% of luxury spending by Chinese
                       consumers took place inside its borders.


                # ⚓ YLE ☛ Nokian_Tyres_begins_restructuring_talks_affecting_160
                  workers⠀⇛


                       The company says the proposed staff changes are
                       aimed to address a changed market affected by a
                       drop in demand.


                # ⚓ YLE ☛ Record_number_of_prenups_made_in_Finland,_despite
                  ever_fewer_marriages⠀⇛


                       Prenuptial agreements in Finland have nearly
                       doubled in number since the early 2000s.


                # ⚓ New York Times ☛ Rent_for_Millions_of_New_Yorkers_Could
                  Increase_by_2_to_5_Percent⠀⇛


                       The panel, known as the Rent Guidelines Board, took
                       a preliminary vote on potential rent hikes on
                       Tuesday evening.


                # ⚓ New York Times ☛ How_First_Republic_and_Other_Bank_Failures
                  Could_Impact_the_U.S._Economy⠀⇛


                       Are we on the brink of a financial crisis — or has
                       the threat been contained?


                # ⚓ Axios ☛ Yellen_breaks_the_debt_ceiling_ice⠀⇛


                       The months-long silence between President Biden and
                       House Speaker Kevin McCarthy is reaching an abrupt
                       end thanks to Treasury Secretary Janet Yellen.


                       Why it matters:Yellen’s urgent deadline_on_the_debt
                       ceiling gives the White House and Congress as
                       little as a month to avert a catastrophic default,
                       spurring Biden to call an emergency meeting with
                       congressional heads.


                # ⚓ Quartz ☛ India’s_unemployed_are_optimistic_about_finding
                  jobs—except_there_aren’t_enough_jobs_for_them⠀⇛


                       India’s unemployment rate hit a four-month high in
                       April.


                # ⚓ European Commission ☛ InvestEU:_EIF_and_BBVA_sign_€200
                  million_guarantee_agreement_to_support_startups_with
                  innovative_and_sustainable_investment_plans⠀⇛


                       The EIF is granting a €200 million guarantee to
                       BBVA to enable it to offer more financing
                       opportunities to startups via its BBVA Spark unit.


                # ⚓ CS Monitor ☛ ‘No_time_to_waste’:_Yellen,_experts_urge
                  Congress_to_act_on_debt_limit⠀⇛


                       Treasury Secretary Janet Yellen notified Congress
                       that the United States could default on its debt
                       much sooner than expected if legislators don’t
                       change course soon. Waiting “until the last minute
                       … can cause serious harm,” she said.


                # ⚓ New York Times ☛ After_Pandemic_Rebound,_U.S._Manufacturing
                  Drops⠀⇛


                       Factories that roared out of the recession have
                       stalled, hampering the economy, even as a new wave
                       of production looms.


                # ⚓ New York Times ☛ Is_the_Debt_Limit_Constitutional?_Biden
                  Aides_Are_Debating_It.⠀⇛


                       As the government heads toward a possible default
                       on its debt as soon as next month, officials are
                       entertaining a legal theory that previous
                       administrations ruled out.


                # ⚓ New York Times ☛ Why_the_14th_Amendment Is_Being_Cited_in
                  the_Debt_Ceiling_Debate⠀⇛


                       Some Biden administration officials believe a
                       constitutional clause prevents the United States
                       from failing to make payments even if it means
                       breaching the debt limit.


                # ⚓ Michael West Media ☛ Retail_trade_lifts_modestly_but
                  spending_starts_to_dip⠀⇛


                       Spending on nice-to-haves has started to drop off
                       as rapid interest rates and cost of living
                       pressures continue to chew into household budgets.
                       Official retail sales data recorded a slightly
                       higher-than-expected lift of 0.4 per cent in March,
                       which followed a modest 0.2 per cent uptick in
                       February.


                # ⚓ Michael West Media ☛ ‘Should_be_shocked’,_workers_could
                  earn_more_at_Maccas⠀⇛


                       >Tens of thousands of workers will soon be targeted
                       for jobs in childcare centres across the country
                       but could be earning more at McDonalds or Bunnings.
                       Danielle Wood from the Grattan Institute said
                       Australians should be shocked by salaries in early
                       education.


                # ⚓ New York Times ☛ How_New_Yorkers’_Lives_Will_Be_Altered_by
                  the_$229_Billion_State_Budget⠀⇛


                       The budget contains a handful of contentious policy
                       changes on issues like bail, minimum wage and a ban
                       on gas stoves and furnaces in new construction.


                # ⚓ New York Times ☛ In_China,_It’s_Time_to_Splurge_Again,_and
                  the_Luxury_Industry_Is_Relieved⠀⇛


                       The end of pandemic-era restrictions has unleashed
                       a luxury spending rebound in China. Which Western
                       brands are coming out on top?


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ New York Times ☛ Release_of_Justice_Stevens’s_Private
                  Papers_Opens_Window_Into_Supreme_Court⠀⇛


                       Justice John Paul Stevens’s files on thousands of
                       cases, including landmark decisions on abortion and
                       the 2000 election, have been made public, opening a
                       window on the Supreme Court.


                # ⚓ Ruben Schade ☛ Three_years_on_from_Brexit⠀⇛


                       (This post was written back in January, but I
                       forgot to post it).


                       It’s the three-year anniversary of Brexit, when
                       Britain acted upon a referendum to impose sanctions
                       upon itself. It wasn’t unanimous; Northern Ireland,
                       Greater London, Scotland, and Gibraltar
                       conspicuously voted to remain, as did a
                       disproportionate number of young people who had the
                       most future to lose.


                       Funny how that always happens!


                       It was surreal seeing it play out from outside the
                       UK. Here was a country voluntarily leaving one of
                       the largest and most prosperous economic blocs in
                       the world, and one in which it held significant
                       sway and interest. British exporters would still be
                       beholden to EU law, they just wouldn’t have a say
                       in shaping its direction. UK wasn’t ever in the
                       Shengen Area, but they still surrendered their
                       preferential treatment… as Tory tourists discovered
                       when visiting their Spanish holiday villas.


                # ⚓ Salon ☛ How_to_weaponize_Republicans’_words⠀⇛


                       As part of a nationwide plan, Republicans in states
                       such as Iowa, Missouri, Arkansas, Wisconsin, Ohio,
                       and elsewhere are trying to get rid of child labor
                       laws. Such outcomes will leave children vulnerable
                       to financial and all manner of exploitation and
                       danger.


                # ⚓ The Hill ☛ NPR_says_Elon_Musk_is_threatening_to_reassign
                  its_Twitter_account⠀⇛


                       The outlet reported Tuesday that Musk said in a
                       series of emails he would give the account with the
                       handle @NPR to another organization or person.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ France24 ☛ What_happens_when_AI_generates_fake
                        historical_photos⠀⇛


                             Social media users in recent weeks have been
                             circulating an old-timey photo of men
                             standing next to a giant horse. While the
                             photo looks like it came from a bygone era,
                             it was actually generated by artificial
                             intelligence. It is just one of a number of
                             AI-generated images that have been presented
                             online as real historical photos. Jo Hedwig
                             Teeuwisse, a historian who specialises in
                             debunking fake historical photos, spoke to
                             the FRANCE 24 Observers team.


                      # ⚓ New York Times ☛ Tucker_Carlson’s_Text_That_Alarmed
                        Fox:_‘It’s_Not_How_White_Men_Fight’⠀⇛


                             The discovery of the text message contributed
                             to a chain of events that ultimately led to
                             Tucker Carlson’s firing.


                      # ⚓ Reason ☛ How_‘Disinformation’_Became_Public_Enemy_No.
                        1⠀⇛


                             Join Reason on YouTube Thursday at 1 p.m.
                             Eastern for a discussion of Jacob Siegel’s
                             broadside against the “counter-disinformation
                             complex” in Tablet magazine.


          o § Freedom of Information / Freedom of the Press⠀➾


                # ⚓ [Repeat] YLE ☛ Press_Freedom_Index:_Finland_now_less_safe
                  for_journalists⠀⇛


                       Finland’s result is the same as last year, but RSF
                       said the overall situation for journalists in the
                       Nordic country has worsened. Finland now ranks 23rd
                       in journalists’ safety, compared to 10th last year.
                       The score was heavily impacted by the case of two
                       Helsingin Sanomat journalists who were found guilty
                       of disclosing state secrets in court earlier this
                       year.


                # ⚓ NBC ☛ Judge_dismisses_Trump’s_lawsuit_against_The_New_York
                  Times⠀⇛


                       A New York judge dismissed Donald Trump’s 2021
                       lawsuit against The New York Times on Wednesday and
                       ordered the former president to pay attorneys’ fees
                       for the paper and three of its journalists who are
                       listed as defendants.


                       In his ruling Wednesday, Justice Robert R. Reed of
                       the state Supreme Court in New York County said
                       Trump’s claims against the Times and three of its
                       journalists for their Pulitzer-winning series on
                       his undisclosed finances in 2018 “fail as a matter
                       of constitutional law.” (Supreme Court is the name
                       of New York’s top trial court.)


                # ⚓ Hong Kong Free Press ☛ Editorial:_HKFP_photo_by_Britt
                  Clennett_wins_honourable_mention_at_Human_Rights_Press
                  Awards⠀⇛


                       Hong Kong Free Press has won an honourable mention
                       for photography at the 2023 Human Rights Press
                       Awards. A shot by Britt Clennett, which shows a
                       worker rolling up a “Hong Kong Asia’s World City”
                       banner as police officers pass by, won a prize in
                       the Single Image category.


                # ⚓ RFERL ☛ Kazakh_Journalist_Sentenced_To_25_Days_After_Online
                  Call_For_Protest⠀⇛


                       Kazakh journalist Duman Mukhammedkarim has been
                       sentenced to 25 days in jail on a charge of
                       violating regulations on public gatherings.


                # ⚓ New Yorker ☛ The_Limits_of_Joe_Biden’s_Calls_for_Press
                  Freedom⠀⇛


                       After decades of exposing corruption in Guatemala,
                       the journalist José Rubén Zamora has been jailed.
                       Why can’t the U.S. help him?


                # ⚓ RFERL ☛ Pratasevich,_Whose_Plane_Was_Diverted_To_Minsk,
                  Sentenced_To_Eight_Years_In_Prison⠀⇛


                       A court in Minsk has sentenced Raman Pratasevich, a
                       journalist who was detained in Belarus in 2021
                       after the commercial flight he was on was forced to
                       land in Minsk, to eight years in prison on charges
                       linked to his reporting.


                # ⚓ New Yorker ☛ BuzzFeed,_Gawker,_and_the_Casualties_of_the
                  Traffic_Wars⠀⇛


                       Ben Smith’s new book shows how the race for clicks
                       spawned—then strangled—the new media.


                # ⚓ RFA ☛ Reporting_carries_high_costs_for_RFA_journalists_in
                  authoritarian_Asian_countries⠀⇛


                       World Press Freedom Day is a reminder that the
                       region contains some of the world’s biggest jailers
                       of journalists.


                # ⚓ LRT ☛ Vilnius_to_host_solidarity_event_for_Belarusian
                  journalists⠀⇛


                       A solidarity event called “Journalism is not a
                       crime!” will take place in Vilnius’ Sakura Park on
                       Wednesday in support of independent Belarusian
                       journalists.


                # ⚓ LRT ☛ Lithuania_rises_to_7th_place_in_World_Press_Freedom
                  Index⠀⇛


                       Lithuania has moved up two positions from the ninth
                       to seventh place in this year’s World Press Freedom
                       Index, Reporters Without Borders (RSF) said on
                       Wednesday.


                # ⚓ Federal News Network ☛ UN_denounces_Taliban_intimidation,
                  attacks_on_Afghan_media⠀⇛


                       The United Nations says the Taliban’s intimidation,
                       threats and attacks on Afghan journalists are
                       unacceptable. Many journalists lost their jobs
                       after the Taliban takeover in August 2021, with
                       media outlets closing over a lack of funds or
                       because their staff left the country. The U.N.
                       mission in Afghanistan said Wednesday the Taliban
                       have used arbitrary arrests and detentions, ill-
                       treatment and threats as a way to suppress freedom
                       of expression. A media watchdog said the country
                       ranks 152 out of 180 in the World Press Freedom
                       Index. Deputy Broadcasting Minister Mahajar Farahi
                       told The Associated Press that the government is
                       “still trying to work on


                # ⚓ Press Gazette ☛ Stop_SLAPPs_and_scrap_Section_40_call_from
                  UK_news_industry_on_Press_Freedom_Day⠀⇛


                       News Media Association warns of urgent threats to
                       presss freedom in the UK.


                # ⚓ New York Times ☛ New_York_Times’s_Publisher_Warns_of_Risks
                  to_Press_Freedom_and_Democracy⠀⇛


                       The free press’s role in supporting human rights
                       and democratic societies is “at great risk” amid
                       increasing levels of violence against journalists
                       worldwide, A.G. Sulzberger said.


                # ⚓ Latvia ☛ Latvian_PEN_award_goes_to_Punctum_magazine⠀⇛


                       The Latvian PEN Award 2022 goes to the literature
                       and philosophy online magazine Punctum,
                       representatives of the Latvian PEN said May 3.


                # ⚓ Latvia ☛ Latvia_climbs_six_places_in_World_Press_Freedom
                  Index⠀⇛


                       Against a deteriorating environment for press
                       freedom worldwide, Latvia managed to climb six
                       places in the 2023 World Press Freedom Index
                       published by Reporters Without Borders (RSF) May 3.


                # ⚓ Press Gazette ☛ Two-time_editor_of_Press_Gazette_Tony
                  Loynes_dies_aged_73⠀⇛


                       The editor and publisher saved Press Gazette from
                       closure and fought to chart a way forward for trade
                       publishers in the Internet era.


                # ⚓ YLE ☛ Association_of_Editors:_Defamation_case_filed_against
                  Yle_in_Monaco_“worrying”⠀⇛


                       Finnish news outlets are responsible for operating
                       in accordance with the laws as set out in their own
                       jurisdiction, the association says.


                # ⚓ New York Times ☛ At_a_U.N._event_on_press_freedom,_the
                  publisher_of_The_New_York_Times_warns_of_dangers_to
                  democracy.⠀⇛


                # ⚓ Quartz ☛ Where_press_freedom_is_threatened_around_the
                  world⠀⇛


                       Media polarization is helping tear the world apart,
                       according to Reporters Without Borders. The group
                       says polarization is happening at both the local
                       and international levels. As opinion media sows
                       divisions within countries, despotic regimes with
                       their own tight media controls are waging
                       propaganda wars against…


          o § Civil Rights/Policing⠀➾


                # ⚓ NPR ☛ It’ll_take_300_years_to_wipe_out_child_marriage_at
                  the_current_pace_of_progress⠀⇛


                       When girls are home from school, and families are
                       facing financial crises, parents are more likely to
                       marry their girls off, she says.


                       “It’s one less mouth to feed,” she says, “but also,
                       fear of sexual violence and threats to family
                       honor” lead families to seek out the perceived
                       safety of a marriage.


                       Armed conflicts and climate change have a similar
                       impact – by increasing uncertainty and driving up
                       the number of child marriages.


                # ⚓ uni Michigan ☛ Op-Ed:_GEO_needs_you_to_reject
                  #BullshitGrades⠀⇛


                       The Graduate Employees’ Organization has concluded
                       the fifth week of their strike, withholding their
                       labor as they continue to demand that the
                       University of Michigan engage in good faith
                       bargaining and respect the union’s call for a
                       living wage.


                # ⚓ NYPost ☛ Emma_Watson_reveals_why_she_stepped_away_from
                  acting:_‘I_didn’t_have_a_voice’⠀⇛


                       The “Harry Potter” star hasn’t appeared onscreen
                       since her last project in 2018.


                # ⚓ New York Times ☛ Late_Night_Shows_Go_Dark_in_First_Fallout
                  From_Writers’_Strike⠀⇛


                       How long they stay off the air is an open question.
                       During the last strike, they gradually returned
                       after a couple of months.


                # ⚓ Curfew_ended_in_Nusaybin,_Mardin⠀⇛


                       A curfew has been ordered in nine rural
                       neighborhoods and their villages in Nusaybin
                       district this morning. The Governor’s Office
                       announced later that the curfew had ended with the
                       completion of the operations.


                # ⚓ NYPost ☛ California_District_Attorney_Pamela_Price_slammed
                  as_‘disrespectful’_to_Asians_as_another_prosecutor_resigns⠀⇛


                       A California prosecutor called hyper-woke Alameda
                       County District Attorney Pamela Price
                       “condescending and disrespectful” to the Asian
                       community in a resignation letter this week.


                # ⚓ CHP_accuses_the_Interior_Ministry_of_organizing_a_parallel
                  structure_to_the_Supreme_Election_Council⠀⇛


                       The Vice President of CHP claimed that the Ministry
                       of Interior has sent written instructions to
                       governorships and is organizing a “parallel
                       structure to YSK” while the country is heading
                       toward the May 14 elections.


                # ⚓ Several_HDP,_Green_Left_members_detained_in_İstanbul
                  raids⠀⇛


                       The operation comes amid the ongoing crackdown on
                       Kurdish politicians, journalists and lawyers.


                # ⚓ EDRI ☛ Moving_from_empty_buzzwords_to_real_empowerment:_a
                  framework_for_enabling_meaningful_engagement_of_external
                  stakeholders_in_AI⠀⇛


                       The use of artificial intelligence (AI) is
                       accelerating. So is the need to ensure that AI
                       systems are not only effective, but also fair, non-
                       discriminatory, transparent, rights-based,
                       accountable, and sustainable – in short,
                       responsible


                # ⚓ EDRI ☛ Irish_and_French_parliamentarians_sound_the_alarm
                  about_EU’s_CSA_Regulation⠀⇛


                       The Irish parliament’s justice committee and the
                       French Senate have become the latest voices to
                       sound the alarm about the risk of general
                       monitoring of people’s messages in the proposed
                       Child Sexual Abuse (CSA) Regulation.


                # ⚓ Jacobin Magazine ☛ 2023-04-23_[Older]_Apple_Store_Workers
                  Want_to_Unionize._Apple_Is_Union_Busting.⠀⇛


                # ⚓ RFA ☛ Myanmar_military_announces_amnesty_for_more_than
                  2,000_political_prisoners⠀⇛


                       The move comes as China’s foreign minister
                       continues his visit to the country.


                # ⚓ The Straits Times ☛ Rohingya_team_to_visit_Myanmar_over
                  refugee_return_plan⠀⇛


                       It will visit a site close to the Bangladesh
                       border, where Myanmar’s junta plans to resettle
                       over 1,000 Rohingya in a pilot project.


                # ⚓ RFERL ☛ Blast_At_Revolutionary_Guards_Center_Leaves_Two
                  Dead_In_Central_Iran⠀⇛


                       An explosion at a combat-readiness and support
                       center of the Islamic Revolutionary Guards Corps
                       (IRGC) on the outskirts of the city of Damghan in
                       the central Iranian province of Semnan has left two
                       personnel dead and three injured, the IRGC said in
                       a statement.


                # ⚓ RFERL ☛ Five_Kazakhs_Killed_During_Anti-Government_Unrest
                  Last_Year_Convicted_Posthumously⠀⇛


                       A court in Kazakhstan’s largest city, Almaty, has
                       posthumously convicted five men who were shot dead
                       during unprecedented anti-government protests in
                       January last year.


          o § Monopolies⠀➾


                # ⚓ Deutsche Welle ☛ 2023-04-26_[Older]_UK_blocks_Microsoft’s
                  $69_billion_takeover_of_Activision⠀⇛


                # ⚓ Engadget ☛ 2023-04-26_[Older]_UK_regulator_blocks
                  Microsoft’s_Activision_Blizzard_merger_over_cloud_concerns⠀⇛


                # ⚓ Make Tech Easier ☛ 2023-04-26_[Older]_Microsoft_Acquisition
                  of_Activision_Blizzard_Blocked_by_UK_Regulator⠀⇛


                # ⚓ Florian Müller ☛ 2023-04-26_[Older]_UK_Competition_&
                  Markets_Authority_radicalizes_itself_by_blocking_Microsoft’s
                  purchase_of_Activision_Blizzard_based_on_misconceptions_and
                  speculative_concerns:_parties_will_appeal [Ed: Florian_is_a
                  paid_Microsoft_shill_and_basically_a_mouthpiece_of_Microsoft,
                  who fails to disclose conflicts of interest]⠀⇛


                # § Patents⠀➾


                      # ⚓ UPC’s_PPI_to_come_into_force_for_Denmark [Ed: UPC is
                        illegal. Firms that promoted this illegal things for
                        profit now try to retroactively legitimise their
                        criminal pursuits.]⠀⇛


                      # ⚓ UPC_templates_for_decisions_and_orders [Ed: UPC is
                        illegal. EPO and EU are doing illegal things. This
                        cannot possibly end well and the lobbyists (like
                        Bristows) won't seem like law firms but law-breaking
                        firms.]⠀⇛


                      # ⚓ European Commission ☛ Anti-corruption:_Stronger_rules
                        to_fight_corruption_in_the_EU_and_worldwide [Ed: EU
                        posing as opponent of corruption while tolerating and
                        enabling crimes in the EPO, even participating in them
                        (UPC)]⠀⇛


                             European Commission Press release Brussels,
                             03 May 2023 Today, the Commission is taking
                             decisive action to fight corruption in the EU
                             and worldwide, delivering on the commitment
                             made by President von der Leyen in her 2022
                             State of the Union address.


                      # ⚓ European Commission ☛ Questions_and_Answers:_Stronger
                        rules_to_fight_corruption_in_the_EU_and_worldwide [Ed:
                        Will the EU finally tackle EPO corruption? Or is it
                        about the law?]⠀⇛


                             European Commission Questions and answers
                             Brussels, 03 May 2023 What is included in the
                             anti-corruption package?


                      # ⚓ European Commission ☛ Strengthening_EU_action_to
                        fight_corruption [Ed: Lots of rhetoric and hot air
                        while EU officials participate in corruption at the EPO
                        for personal gain]⠀⇛


                             European Commission Factsheet Brussels, 03
                             May 2023 Strengthening EU action to fight
                             corruption Strengthening EU action to fight
                             corruption Strengthening EU action to fight
                             corruption


                # § Copyrights⠀➾


                      # ⚓ CS Monitor ☛ The_Dream_Journey:_Meet_the_friends
                        bringing_Pakistani_music_back⠀⇛


                             The cultural effects of an oppressive regime
                             can linger for generations. But in Pakistan,
                             a collective of music lovers is reviving the
                             country’s musical heritage and spreading joy
                             across borders.


                      # ⚓ The Data Scientist ☛ The_Legal_Implications_of_AI-
                        Generated_Content_in_Copyright_Law⠀⇛


                             Legal action of collective nature was
                             instituted against GitHub, Microsoft, and
                             OpenAI. The motion claimed that the AI-
                             powered coding aide GitHub Copilot infringed
                             copyright laws by generating code derived
                             from code licensed under open source, which
                             is publicly accessible. Copilot provides
                             programmers with suggestions for novel code
                             based on their existing code in real-time. As
                             per the legal action, Copilot’s code-
                             generating software was trained on code that
                             was subject to copyright, without obtaining
                             the necessary authorization. Furthermore, the
                             program creates new code that is akin or
                             identical to the original work. This is the
                             premier lawsuit to be brought involving
                             generative AI. The case aims to attain class-
                             action status, and if it prevails, it could
                             potentially affect the whole AI industry and
                             how it utilizes publicly available code for
                             training models.


                      # ⚓ Sanders Law Group ☛ Potential_Copyright_Implications
                        of_Artificial_Intelligence_and_Machine_Learning⠀⇛


                             These algorithms often rely on massive
                             datasets of copyrighted images, which can
                             easily be obtained from online platforms like
                             Google Images or Flickr. However, these
                             datasets are often created without the
                             permission of the original creators.


                             One potential solution is for artificial
                             intelligence software developers to enact
                             stronger protections for intellectual [sic]
                             property [sic] rights [sic] and require users
                             to seek permission from original copyright
                             holders before uploading their work or
                             content. This would help avoid any potential
                             issues with copyright infringement and ensure
                             that artificial intelligence systems are used
                             in a responsible and ethical manner.



                    ䷩ 𝚕𝚒𝚗𝚎 4720

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.04.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Gemini_Links_04/05/2023:_IDEs_Reviewed,_Chatbots_Debunked⠀✐


Posted in News_Roundup at 4:36 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Games
    * Technical
          o Science/Sci-Fi
          o Internet/Gemini
    * § Games⠀➾


          o ⚓ 🔤SpellBinding:_CEFYILH_Wordo:_MACAW⠀⇛


    * § Technical⠀➾


          o ⚓ IDE_Shopping⠀⇛


                 Emacs was the first alternative I tried, really just
                 because I know some people are able to really get into it
                 and turn it into something powerful.


                 I learn new tools best by finding a good starter config
                 and making tweaks until I’m familiar enough where I could
                 do it from scratch. I learned tiling window managers this
                 way and am now currently using my own unique config, and
                 it’s also how I got into Linux in the first place by
                 starting with Ubuntu Gnome (back when Unity was still the
                 default DE) and eventually finding my way to Arch. So to
                 tackle Emacs I set myself up with a popular configuration
                 framework called Doom Emacs.


                 [...]


                 If you’re interested in the differences between Vim and
                 Neovim you’re probably better off having someone else
                 explain them to you. But from what I understand, Neovim
                 is just a fork of Vim that’s meant to be more
                 maintainable and allow for more powerful plugins.


                 After looking into and trying a couple different starter
                 configs for Neovim, I eventually settled on LunarVim. Now
                 LunarVim isn’t so much a starter config. The project’s
                 website describes it as an “IDE layer for Neovim with
                 sane defaults”, and because LunarVim installs itself
                 alongside your existing Neovim install and separates the
                 user’s config from its own, I’d say that feels accurate.


          o ⚓ Pumpkin_Patch⠀⇛


                 Today I saw Brodie Robertson’s latest video on the latest
                 systemd feature, where you can reboot only the user
                 space. I think that is pretty cool and welcome it’s
                 development. However, I can’t entirely think of scenarios
                 where it would be needed, I mostly reboot because I want
                 to reboot my entire system. AFAIK the user space reboot
                 is everything except the kernel, so I guess one would use
                 it when you undergone a “standard” update of packages,
                 mostly?


          o § Science/Sci-Fi⠀➾


                # ⚓ The_Forth⠀⇛


                       That was from last year, but I remembered it was
                       forth day too late this year and didn’t have any
                       ideas for something that could be quickly churn
                       out.


                # ⚓ Proof_That_ChatGPT_Is_Not_Sentient⠀⇛


                       There’s a childish variation of the Turing Test
                       that ChatGPT fails today.


                       Simply parrot whatever ChatGPT says.


                       Then keep doing it.


                       It won’t notice what you’re doing, and it won’t get
                       bored or frustrated.


                       If you’ve never played this game, find any sentient
                       being and try it. But I suspect you already know
                       how it should go.


                       QED.


                       [...]


                       If you’re not convinced, just keep repeating. It
                       must eventually become clear to you that there is
                       nothing behind the curtain—just as it will never
                       become clear to (this iteration of) ChatGPT that
                       something untoward is going on.


          o § Internet/Gemini⠀➾


                # ⚓ Metaverses⠀⇛


                       I am perpetually late to the party. andi (@mcc on
                       cohost), who I sort of peripherally knew-of when
                       she was on Twitter, posted an essay in the early
                       bird-migration days at cohost, on the various ideas
                       of the metaverse: Stephenson’s original conception,
                       Facebook’s ambitions (largely jettisonned), and
                       others.


                       [...]


                       In some sense we’ve reached feature parity, thirty
                       years later. We’ve also got the same level of
                       control over our own identities on the platform,
                       which is to say, barely any at all; we can choose
                       to use the platform or not, but if we go, that’s
                       it. We can’t take our Instagram data and import it
                       elsewhere, not in any meaningful sense. We’re stuck
                       with apps and no overarching protocol.


                       The Fediverse is a partial answer to that, allowing
                       social verbs or ideas that work across a variety of
                       platforms. But as you may have seen when trying to
                       convince your mutuals to make the move to Mastodon,
                       it comes with a tradeoff. It’s not as instinctively
                       simple as shitposting on Twitter. It requires
                       people to think a little bit about their data and
                       interactions. Most people don’t want to do that,
                       and so Mastodon won’t take off until Twitter’s last
                       day. Maybe after that we’ll start to see people
                       other than idealistic free software types and
                       disaffected tweeps in the Fediverse.


                # ⚓ Writing_process⠀⇛


                       Like many geminauts, I’ve coded my own content
                       management script.


                       [...]


                       Now, this assumes that I am to write and publish my
                       text in the same session. This doesn’t necessarily
                       encourage afterthought and reflection.


                       My last post “broke” my content management script.
                       A geminaut very kindly sent me a message to tell
                       me. I was very grateful, but also, it made me
                       realize that people actually read my posts… which I
                       should have expected, right? That is, after all,
                       why I write?


                       Certainly, but I suspect that actively ignoring
                       that fact was what made it possible for me to write
                       without getting caught in doubts and anxiety. But
                       if I am to become a better writer, I also need to
                       think about the audience, about the necessary
                       context I have to include and the unnecessary
                       grumbling I can spare them. Therefore, I need a bit
                       more space to think, or at least some space to have
                       distance.


                       I’ll try to implement something like a 12- or 24-
                       hours quarantine. This way, I get a chance to
                       revise posts before sending them. But also, since
                       it’s a one-time quarantine, I don’t get to revise
                       indefinitely. Maybe it’s more akin to having an
                       editor (except it’s me). A busy one, who doesn’t
                       want back and forth.


===============================================================================
* Gemini_(Primer) links can be opened using Gemini_software. It’s like the
World Wide Web but a lot lighter.



                    ䷩ 𝚕𝚒𝚗𝚎 4945

╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.04.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Gemini_Links_04/05/2023:_IKEA_Maze_and_Lawsuits_Over_Negative_Reviews⠀✐


Posted in News_Roundup at 1:59 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Internet/Gemini
    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ A_Ducky_Couple_and_the_Unexpected_Sunset_2023-05-04_
                  (Fairbanks,_AK,_USA)⠀⇛


                       Yesterday, I caught this devoted pair enjoying a
                       leisurely swim during the noon hour…


                # ⚓ An_off-ramp_from_the_digital_IKEA_maze_[2023-05-04]⠀⇛


                       There is an episode of Star Trek where a character
                       is for plot reasons trapped in a shrinking parallel
                       universe. As time passes, people she knows one by
                       one just vanish and she is the only one who seems
                       to notice. Eventually it gets to an absurd point.
                       She asks if it really makes sense if a ship made
                       for a thousand people would have a crew of a few
                       people, and everyone just sort of like shrugs and
                       looks at her like she’s crazy. That’s basically
                       what the last decade of the Internet[1]. It feels
                       like it’s shrinking. Like parts of it are
                       vanishing.


                       In part I think it’s the fault of the big walled
                       gardens on the web, whether Facebook, Twitter or
                       Reddit. They’re essentially designed like a maze.
                       They make you feel like there are no other websites
                       aside from few silos and e-commerce and various
                       forms of blog spam and political propaganda, like
                       the web only consists of maybe a few dozen big
                       sites, encircled by an endless digital strip mall.


          o § Technical⠀➾


                # ⚓ Lawsuits_Over_Negative_Reviews⠀⇛


                       I hate how businesses now can sue a person over a
                       negative review or at least threaten to do so. They
                       even shame a person for it to defend their
                       reputation with responses such as:


                       “… I have seen that you slander a lot of businesses
                       in Google review…”


                       Chances are they won’t sue me. The only reason I’ve
                       removed the revies is because I do not want to be
                       shamed.


                       I have a right to a good reputation, too. So what
                       if I am not a business. I’m still a human being.
                       This causes me to believe that I should criticize
                       businesses anonymousloy by writing my opinion in
                       chalk on the sidewalk or something.


                # § Internet/Gemini⠀➾


                      # ⚓ My_Gemini_Crawlers_Meta_Info_Page⠀⇛


                             I have the (bad?) habit of diving into my
                             server log files every once in a while to
                             know what’s going on. This is not needed for
                             a purely static site like mine. I know that I
                             will see robots crawling my sites at will,
                             but at least I’d like to know which ones and
                             how.


                             After scouring the documenation of different
                             Geminispace crawlers, I tried to piece
                             together information about used IPs and more.
                             Because the amount of information released
                             differs, I created an overview page with all
                             the available info and added some additional
                             info, which I, as a user and server
                             maintainer alike, would like to know about
                             those crawlers.


===============================================================================
* Gemini_(Primer) links can be opened using Gemini_software. It’s like the
World Wide Web but a lot lighter.



                    ䷩ 𝚕𝚒𝚗𝚎 5072

╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 05.04.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_04/05/2023:_OpenWrt_22.03.5_and_OSMC’s_May_Update⠀✐


Posted in News_Roundup at 2:07 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Server
          o Audiocasts/Shows
          o Applications
          o Games
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
    * Distributions_and_Operating_Systems
          o Reviews
          o New_Releases
          o SUSE/OpenSUSE
          o Canonical/Ubuntu_Family
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Web_Browsers/Web_Servers
                # Mozilla
          o Productivity_Software/LibreOffice/Calligra
          o Programming/Development
    * Leftovers
          o Science
          o Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy/Transportation
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
    * Monopolies
          o Patents
          o Software_Patents
          o Trademarks
          o Copyrights
    * § GNU/Linux⠀➾


          o § Server⠀➾


                # ⚓ Unicorn Media ☛ Mirantis_Pushes_Security_With_Its_New_k0s
                  1.27_Kubernetes_Release⠀⇛


                       Mirantis, the company that bought Docker Enterprise
                       in 2019 and several releases later renamed it
                       Mirantis Kubernetes Engine, announced on Thursday
                       the release of k0s 1.27, the company’s own branded
                       (but still open source) version of Kubernetes. As
                       the release number implies, this new release adds
                       compatibility with Kubernetes 1.27, the Cloud
                       Native Computing Foundation’s flagship project’s
                       latest and greatest. It includes some improvements
                       and bug fixes as well.


          o § Audiocasts/Shows⠀➾


                # ⚓ mintCast Podcast ☛ mintCast_411_–_We_Like_It_GUI⠀⇛


                       First up in the news, Linux Kernel 6.3 Officially
                       Released, blendOS 2 supports Android, new Vivaldi
                       out, new Opera One Dev Release, GIMP completes GTK3
                       rewrite, QEMU drops 32-bit, Ryzens are burning,
                       Proton launches a password app, Jetpack Announces
                       the end of twitter auto-sharing, and Red Hat lays
                       of 4% due to high profits…


                # ⚓ The BSD Now Podcast ☛ BSD_Now_505:_BSD_Desktop_Setup⠀⇛


                       OpenBSD 7.3 released, Accelerating Datacenter
                       Energy Efficiency by Leveraging FreeBSD as Your
                       Server OS, install Cinnamon as a Desktop
                       environment, xmonad FreeBSD set up from scratch,
                       Burgr books in your terminal, and more


                # ⚓ Tux Digital ☛ Linux_Out_Loud_61:_Alternative_Career_Paths⠀⇛


                       This week, Linux Out Loud chats about alternative
                       career paths. Welcome to episode 61 of Linux Out
                       Loud. We fired up our mics, connected those
                       headphones as we searched the community for themes
                       to expound upon. We kept the banter friendly, the
                       conversation somewhat on topic, and had fun doing
                       it.


          o § Applications⠀➾


                # ⚓ OMG! Linux ☛ Generate_Secure_Passwords_on_Linux_Fast_with
                  ‘Key_Cutter’⠀⇛


                       Most of us know that using complex (cOm_Pl3X)
                       passwords is good security but coming up with
                       passwords to satisfy the demands of pernickety
                       signup forms can be effort.


                # ⚓ Linux Links ☛ Alternatives_to_popular_CLI_tools:_grep⠀⇛


                       This article spotlights alternative tools to grep.


                       grep is a useful command to search for matching
                       patterns in a file. If you are a system admin who
                       needs to scrape through log files or a developer
                       trying to find matches in a code file, grep is a
                       powerful command to use.


                # ⚓ Linux Links ☛ Alternatives_to_popular_CLI_tools:_cat⠀⇛


                       This article spotlights alternative tools to cat.


                       cat derives its name from concatenation and
                       provides other nifty options too. For example, it
                       can be be used to write contents to a file by
                       typing them from the terminal itself.


                       Enterprising users will appreciate you can display
                       the contents of a file using the shell builtin
                       read.


                # ⚓ OMG Ubuntu ☛ Spotify’s_‘Controversial’_New_Look_Arrives_on
                  Linux [Ed: ‘Controversial’? There are much more serious
                  problems, such as surveillance and DRM, not mere "looks".]⠀⇛


                       Spotify for Linux user? You’ll notice that the
                       desktop app looks a little different next time you
                       open it. The music streaming service, which
                       recently passed 515 million monthly active users,
                       rolled out a redesign of its desktop app on Windows
                       and macOS last week. That revamp is now hitting the
                       official Spotify for Linux client — though it
                       appears to be a server-side change rather than a
                       client update.


          o § Games⠀➾


                # ⚓ Free Desktop ☛ mesa_23.1.0-rc4⠀⇛


                       Hello everyone,

                       The fourth release candidate for 23.1.0 is now
                       available.

                       If you find any issues, please report them here:

                       https://gitlab.freedesktop.org/mesa/mesa/-/issues/
                       new

                       The next release candidate is expected in one week,
                       on May 10th.

                       Cheers,
                         Eric
                # ⚓ Mike_Blumenkrantz:_New_Era⠀⇛


                       § Lavapipe: Dragged Into The Future


                       Some time ago I teased a new Mesa project that
                       involved both features and perf. At last, it’s time
                       to unveil the goods: a complete_rewrite_of_all
                       descriptor_handling in Lavapipe thanks to one of
                       RADV’s raytracing tamers, Konstantin Seurer.


                       It’s a feature that’s been confounding developers
                       and users everywhere for years, but thanks to
                       Konstantin’s tireless efforts over the past
                       ETOOLONG, at last everyone will have the features
                       they crave.


                # ⚓ ScummVM ☛ Welcome_to_my_alchemy_workshop!⠀⇛


                       Reah: Face the Unknown, the first supported game of
                       the V-Cruise_engine, is ready for public testing!


                       Created in 1998 by Detalion and published by LK
                       Avalon, this 3D-rendered panoramic first-person
                       adventure has you travel to a strange desert world
                       to unravel its secrets.


                       ScummVM currently supports the CD, DVD, and digital
                       English releases (with subtitles in Dutch, English,
                       French, German, Italian, Polish, and Spanish). If
                       you’re aware of any other versions, please contact
                       us.


                       To play any of these supported releases, you will
                       need a daily_development_build. If you encounter
                       any issues, please submit them to the issue
                       tracker!


          o § Desktop Environments/WMs⠀➾


                # § K Desktop Environment/KDE SC/Qt⠀➾


                      # ⚓ KDE ☛ SoK_2023_Selenium-ST-API_KDE_Eco_Power
                        Measurement_Proof_Of_Concept:_Achieving_Three_KDE_Goals
                        With_One_Stone⠀⇛


                             Last year, Okular, KDE’s advanced document
                             reader, became the first software product
                             ever to receive the Blue Angel eco-label.
                             This certification recognises Okular as
                             having a sustainable software design.


                             The certification process involves measuring
                             the power consumption of the software
                             executing repetitive actions that simulate
                             human use. For Okular’s certification, this
                             was done using scripts written in Actiona. At
                             KDE Eco, we also tried to use the GUI tool
                             Actiona to make these tests, but it was not
                             flexible enough because it required adding a
                             simple action to open a window, entering a
                             click location, validating your input, and so
                             on. This process was very tedious. We then
                             developed a Python tool based on xdotool and
                             called it KdeEcoTest, which was able to
                             record any user action and translate it into
                             text script. The advantage of using text-
                             based scripts over creating GUI actions is
                             that it is much quicker and you can easily
                             copy/paste/modify any interesting part of the
                             test. This is much more efficient time-wise,
                             but it was not enough.


    * § Distributions and Operating Systems⠀➾


          o § Reviews⠀➾


                # ⚓ CNX Software ☛ GL.iNet_Spitz_AX_(GL-X3000NR)_5G_NR_WiFi_6
                  router_review_–_Part_1:_Specs,_unboxing,_and_first_boot⠀⇛


                       GL.iNet Spitz AX, also known as GL-X3000NR, is a
                       compact 5G NR WiFi 6 router running OpenWrt 21.02
                       on a MediaTek Filogic 820 (TM7981A) dual-core
                       Cortex-A53 processor coupled with 512MB DDR4 and
                       8GB eMMC flash, as well 2.5GbE and GbE interfaces,
                       and a USB 2.0 port.


                       The company sent us a Spitz AX router for
                       evaluation, and in the first part of the review,
                       we’ll go through the specifications, and do an
                       unboxing and a teardown, before connecting it for a
                       first boot.


                       The system runs OpenWrt 21.02 with Linux 5.4. Note
                       there are two Spitz AX (GL-X3000) routers: the GL-
                       X3000NR with 5G NR connectivity as reviewed on CNX
                       Software, and the GL-X3000C16 with 4G LTE
                       connectivity only.


          o § New Releases⠀➾


                # ⚓ OSMC’s_May_update_is_here⠀⇛


                       We hope that you had a good Easter.


                       We are introducing a final update to our existing
                       Kodi v19.5 release to improve stability and give
                       users that wish to stay on this version of Kodi for
                       some time an improved stable and supported
                       platform.


                # ⚓ [OpenWrt_Wiki]_OpenWrt_22.03.5_–_Service_Release_–_1_May
                  2023⠀⇛


                       The OpenWrt community is proud to announce the
                       newest stable release of the OpenWrt 22.03 stable
                       version series. It fixes security issues, improves
                       device support, and brings a few bug fixes.


          o § SUSE/OpenSUSE⠀➾


                # ⚓ SUSE’s Corporate Blog ☛ First_Partner_Summit_of_2023_for
                  SUSE_South_Africa⠀⇛


                       SUSE South Africa hosted its first Partner Summit
                       of the year in Johannesburg. The event generated a
                       lot of interest from both existing and new
                       partners.


                # ⚓ SUSE’s Corporate Blog ☛ Hybrid_Boot_and_SEV-SNP_support_in
                  AWS_EC2⠀⇛


                       A while back AWS introduced UEFI support for
                       specific instance types. Then in March of 2023 AWS
                       enabled hybrid-boot for AMIs and in addition to the
                       memory encryption that has already been supported
                       in EC2, AWS announced the support of attestation,
                       also known as SEV-SNP recently.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ OMG Ubuntu ☛ Want_More_Wallpapers_in_Ubuntu?_Install_GNOME
                  Backgrounds⠀⇛


                       Ubuntu 23.04 comes with a small selection of
                       (largely lobster themed) wallpapers out of the box.
                       The choice is neither vast nor varied so you may
                       find yourself looking for some additional ones to
                       liven up your desktop.


                       Well, one fast and easy way to quickly add more
                       high-quality wallpapers to Ubuntu is to install the
                       gnome-backgrounds package. This is available in the
                       Ubuntu repos, though you’ll need to install it
                       using the command line as Ubuntu Software doesn’t
                       show a result for it).


                       This package contains the “official” GNOME
                       wallpaper which you’ll have seen in blog posts,
                       videos, and screenshots recently. I absolutely love
                       it. I think it is one of the best “default”
                       wallpapers of any OS, Linux or otherwise. It’s
                       neutral without being bland; and visually
                       interesting without being distracting.


          o § Open Hardware/Modding⠀➾


                # ⚓ Arduino ☛ Introducing_the_new_Value_Selector_and_Dropdown
                  Widgets_for_Arduino_IoT_Cloud_dashboards⠀⇛


                       We’re excited to announce the release of two new
                       widgets to the Arduino IoT Cloud: the Value
                       Selector and Value Dropdown Widgets.


                # ⚓ Hackaday ☛ Exploring_Woodworking_Mysteries_With_Strain
                  Gauges_And_Raspberry_Pi⠀⇛


                       If you’re not a woodworker, you might not have
                       heard of the “45-degree rule.” It goes like this: a
                       clamp exerts a force that radiates out across a
                       triangular region of the wood that forms a right
                       angle — 45 degrees on each side of the clamp’s
                       point of contact. So, to ensure that force is
                       applied as evenly as possible across the entire
                       glue joint, clamps should be spaced so that these
                       force triangles overlap. It’s a handy rule,
                       especially for the woodworker looking to justify
                       the purchase of more clamps; you can never have too
                       many clamps. But is it valid?


                # ⚓ Ruben Schade ☛ Retrocomputing_info_is_easy_to_find,_until
                  it_isn’t⠀⇛


                       It’s a common refrain among bloggers and video
                       creators that retrocomputing as a hobby has never
                       been easier, thanks to the modern Internet. It’s
                       true to an extent, from the explosion in hobbyist
                       hardware replacements, to scans of available
                       documentation, to the sheer size of retrocomputing
                       communities that can offer help.


                       But I’d caution anyone entering from thinking it’ll
                       be easy. Even leaving aside the increasing failure
                       rate of old components, two of the biggest
                       challenges remain documentation and drivers. These
                       are less of an issue if you’re using popular
                       hardware with limited numbers of SKUs, like a
                       Commodore 64 or an Apple IIc. But if you have an
                       ISA modem in a generic PC clone? Not so much.


                # ⚓ Daniel Lemire ☛ Graviton_3,_Apple_M2_and_Qualcomm_8cx_3rd
                  gen:_a_URL_parsing_benchmark⠀⇛


                       Whenever you enter a URL into a system, it must be
                       parsed and validated. It is a surprisingly
                       challenging task: it may require hundreds of
                       nanoseconds and possibly over a thousand cycles to
                       parse a typical URL. We can use URL parsing as a
                       reasonable benchmark of a system performance.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Top_8_Ways_to_Fix_Android_Can’t_Find_Nearby_Bluetooth
                  Devices_–_Guiding_Tech⠀⇛


                # ⚓ Android Police ☛ A_fix_for_Google_Messages_breaking_on
                  Android_14_is_rolling_out⠀⇛


                # ⚓ Giz China ☛ Ulefone_Note_16_Pro_With_Latest_Android_13_is
                  coming_–_Gizchina.com⠀⇛


                # ⚓ Hindustan Times ☛ Google_I/O_2023:_From_Android_14_OS,
                  Pixel_7a_to_Pixel_Fold_smartphones,_know_what’s_coming_|_Tech
                  News⠀⇛


    * § Free, Libre, and Open Source Software⠀➾


          o ⚓ Tor ☛ Arti_1.1.4_is_released:_Development_on_Onion_Services_and
            RPC⠀⇛


                 Arti is our ongoing project to create a next-generation
                 Tor client in Rust. Now we’re announcing the latest
                 release, Arti 1.1.4.


                 For this month and the next, our efforts are divided
                 between onion services and work on a new RPC API (a
                 successor to C Tor’s “control port”) that will give
                 applications a safe and powerful way to work with Arti
                 without having to write their code in Rust or link Arti
                 as a library (unless they want to).


          o ⚓ Mozilla ☛ Ready_to_try_Mastodon?_Here’s_how_to_get_started⠀⇛


                 Mastodon has been around since 2016, but not until
                 recently has it emerged as a popular alternative to
                 Twitter. Like Firefox, Mastodon is open-sourced, so it’s
                 built on a foundation of transparency and accessibility
                 to all. It’s also decentralized, which means it’s powered
                 by different communities and doesn’t answer to one entity
                 or a bunch of stakeholders. 


          o ⚓ Venture Beat ☛ Mattermost_brings_generative_AI_power_to_open-
            source_collaboration⠀⇛


                 Mattermost expands its open-source technology to enable
                 security conscious organizations to better integrate
                 generative AI.


          o ⚓ It’s FOSS ☛ FOSS_Weekly_#23.18:_Ubuntu_18.04_to_Discontinue,
            Debian_12_Features,_Qemu_VM_and_More⠀⇛


                 Ubuntu 18.04 is ending soon and Debian 12 is coming soon.
                 And the puzzles make a comeback on It’s FOSS but with a
                 twist.


          o § Web Browsers/Web Servers⠀➾


                # § Mozilla⠀➾


                      # ⚓ Linuxiac ☛ The_Pulse_Browser_Project_Is_Developing_a
                        New_Firefox_Fork⠀⇛


                             Currently in Alpha testing, Pulse Browser is
                             a minimalist browser for Windows, Linux, and
                             macOS that focuses on delivering a smooth,
                             streamlined user experience while providing
                             built-in tools for improving privacy and
                             security.


                             Based on Firefox but with removed telemetry,
                             it seeks to fill a gap between browsers
                             firmly focused on security on the one hand
                             and those relying on fewer features but a
                             faster and more pleasant browsing experience
                             on the other.


                             Furthermore, some internal Firefox components
                             have been replaced with better open-source
                             alternatives to the developers’ views.


          o § Productivity Software/LibreOffice/Calligra⠀➾


                # ⚓ The_Document_Foundation_releases_LibreOffice_7.5.3
                  Community⠀⇛


                       LibreOffice 7.5.3 Community, the third minor
                       release of the LibreOffice 7.5 line, the volunteer-
                       supported free office suite for desktop
                       productivity, is available from https://
                       www.libreoffice.org/download for Windows (Intel/AMD
                       and ARM processors), macOS (Apple Silicon and Intel
                       processors), and Linux [1].


                       A description of new features of LibreOffice 7.5 is
                       available in the Release Notes [2].


                       Based on the distinctive features of the
                       LibreOffice Technology platform for personal
                       productivity on desktop, mobile and cloud,
                       LibreOffice 7.5 provides a large number of
                       improvements and new features targeted at users
                       sharing documents with MS Office or migrating from
                       MS Office. These users should check new releases of
                       LibreOffice on a regular basis, as the progress is
                       so fast, that each new version improves
                       dramatically over the previous one.


                # ⚓ 9to5Linux ☛ LibreOffice_7.5.3_Is_Now_Available_for_Download
                  with_119_Bug_Fixes⠀⇛


                       LibreOffice 7.5.3 is here about five weeks after
                       LibreOffice 7.5.2 and brings another batch of bug
                       fixes to those who already managed to upgrade their
                       GNU/Linux system to the LibreOffice 7.5 series.


                       In numbers, LibreOffice 7.5.3 address a total of
                       119 bugs that have been reported by users or
                       discovered by LibreOffice developers. For more
                       details about these bug fixes, you should check out
                       the RC1 and RC2 changelogs.


          o § Programming/Development⠀➾


                # ⚓ Rlang ☛ Intermediate_Web_Scraping_and_API_Harvesting_using
                  R_workshop⠀⇛


                       Learn how to use web scraping in R! Join our
                       workshop on Intermediate Web Scraping and API
                       Harvesting using R which is a part of our workshops
                       for Ukraine series. 


                # ⚓ Hubert Figuière ☛ Hubert_Figuière:_Niepce_April_2023
                  updates⠀⇛


                       This is the April 2023 update for Niepce. Between
                       outages caused by an unseasonbly ice storm,
                       squirrels chewing cable, I discovered how painful
                       is being off the grid. This is not the excuse, just
                       the events that lead to downtime and April not
                       being very productive.


                       The importer moved a little bit forward. I tried to
                       use the brand new “sort by date” importer tool,
                       that is used to test and exercise the logic. The
                       improved importer address a few long standing
                       issues, including not using libgphoto2 for USB Mass
                       Storage, including flash card readers. This was a
                       shortcut I had taken and the result was suboptimal.
                       The new approach is to use libgphoto2 to find the
                       device, and then switch to pure filesystem
                       operations. That was issue_26.


    * § Leftovers⠀➾


          o ⚓ Hackaday ☛ Op-Amp_Challenge:_Reliable_Peak_Power_Measurement⠀⇛


                 As part of our Op-Amp Challenge we’re seeing a wide
                 diversity of entries showcasing the seemingly endless
                 capabilities of these extremely versatile parts. Another
                 one comes from [Joseph Thomas], who when faced with the
                 need to measure the properties of an automotive spark
                 plug, came up with a precision peak detector to hold on
                 to the energy level used when firing it.


          o § Science⠀➾


                # ⚓ Science Alert ☛ Asteroid_Found_Orbiting_Earth_Might_Be_a
                  Chunk_of_The_Moon⠀⇛


                       I think you dropped something …


                # ⚓ Science Alert ☛ Scientists_Discover_a_Rare_Example_of
                  Insects_Using_Tools_to_Capture_Prey⠀⇛


                       This is a stick up!


                # ⚓ Science Alert ☛ Light_Microscopes_See_Smaller_Than_Ever
                  Using_a_Weird_Quantum_Trick⠀⇛


                       Double the resolution.


                # ⚓ Science Alert ☛ The_Remains_of_The_Universe’s_First_Stars
                  Finally_Seen_in_Distant_Gas_Clouds⠀⇛


                       Drawing closer to first light.


                # ⚓ uni Michigan ☛ Two_from_U-M_elected_to_the_National_Academy
                  of_Sciences⠀⇛


                       Professors Maria Carmen Lemos and Robert Sellers
                       are among the 2023 inductees into the National
                       Academy of Sciences, one of the highest
                       distinctions for a scientist or engineer in the
                       United States.


                # ⚓ Science Alert ☛ A_Star_Was_Caught_Swallowing_a_Planet_in_an
                  Astronomical_First⠀⇛


                       This is what fate has in store for us.


                # ⚓ Mexico News Daily ☛ Mexican_astronomer_named_honorary
                  member_of_American_Academy_of_Arts_and_Sciences⠀⇛


                       The astronomer and physicist Julieta Fierro Gossman
                       has dedicated her working life to the stars, and
                       has been recognized in Mexico and abroad.


          o § Education⠀➾


                # ⚓ The Nation ☛ Past_and_Present⠀⇛


                       When I was a junior in college, I studied abroad
                       for a semester in Rome. I only managed to make one
                       Italian friend, a charming boy with a winsome smile
                       who, when he focused his attention on you, made you
                       feel like you were at the center of the world.
                       Needless to say, I had a crush on him. He did not
                       have a crush back, but we spent a lot of time
                       wandering Rome’s cobblestoned streets and sitting
                       on the graffitied embankment of the Tiber River. On
                       one of those occasions, he admitted something: He
                       had read Mein Kampf and found it interesting. He
                       knew what Hitler had done was wrong but was
                       intrigued by the book nonetheless.1


                # ⚓ Quartz ☛ US_eighth_graders’_history_test_scores_hit_lowest
                  levels_on_record⠀⇛


                       Eighth-grade history and civics test scores in the
                       US fell to the lowest level on record last year, in
                       line with broad post-pandemic declines in math
                       scores and reading comprehension.


                # ⚓ CS Monitor ☛ As_schools_push_math_and_reading,_history_and
                  civics_scores_decline⠀⇛


                       Eighth grade students in the United States are
                       scoring lower in history and civics, according to
                       the National Assessment of Educational Progress.
                       Schools have focused more on reading and math post-
                       pandemic, but that has resulted in lower scores
                       elsewhere.


                # ⚓ Axios ☛ U.S._history_scores_hit_all-time_low_among_8th
                  graders⠀⇛


                       U.S. history scores among the nation’s_eighth
                       graders_plummeted_in_2022, new assessment results
                       known as the Nation’s Report Card show.


                       The big picture:The history scores, whichare the
                       lowest ever recorded since theassessment began in
                       1994, pluscivics scores seeing their first-ever
                       decline underscore the pandemic’s prolonged effects
                       on students.


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ Carbon_Fiber_And_Kevlar_Make_This_Linear
                  Actuator_Fast_And_Strong⠀⇛


                       When it comes to the “build versus buy” question,
                       “buy” almost always wins. The amount of time you
                       have to put into building something is rarely
                       justified, especially with a world of options
                       available at the click of a mouse.


                # ⚓ Hackaday ☛ How_To_Install_Mac_OS_On_The_Nintendo_Wii⠀⇛


                       What if you could run Mac OS on a Nintendo Wii game
                       console? That’s probably not a thought that has
                       occurred to many Wii owners or Mac OS users, but
                       that is no excuse not to give it a try, as
                       [Michael] handily demonstrates in a recent video by
                       running Mac OS 9 on a Nintendo’s legendary console.
                       The first major issue is what anyone who has ever
                       tried to put a Hackintosh together knows: just
                       because a target system runs the same CPU
                       architecture can you necessarily install Mac OS (or
                       OS X) for Intel x86 on any Intel x86 system. The
                       same is true for the Wii with its PowerPC CPU and
                       running Mac OS 9 for PowerPC on it.


                # ⚓ Hackaday ☛ LoRa_Goes_To_The_Moon⠀⇛


                       LoRa is a communications method that allows for
                       long range radio contacts to be made using
                       typically low-powered devices. This shouldn’t be
                       surprising given that LoRa is short for “long
                       range” which typically involves distances on the
                       order of a few kilometers. However, a group of
                       students are taking the “long range” moniker to the
                       extreme by attempting to send and receive a signal
                       with a total path of around 768,000 kilometers by
                       using some specialized equipment to bounce a LoRa
                       signal off of the moon and receive it back on
                       Earth.


                # ⚓ Hackaday ☛ New_Drivers_For_Ancient_Webcam⠀⇛


                       For those of us who are a little older, the 90s
                       seem like they were just a few years ago. The
                       younger folks might think that the 90s were ancient
                       history though, and they might be right as we’ve
                       been hearing more bands like Pearl Jam and The
                       Offspring playing on the classic rock stations
                       lately. Another example of how long ago the 90s
                       were is taking a look at the technological progress
                       that has happened since then through the lens of
                       things like this webcam from 1999, presuming you
                       load up this custom user space driver from
                       [benjojo].


                # ⚓ Hackaday ☛ NASA’s_Voyager_Space_Probe’s_Reserve_Power,_And
                  The_Intricacies_Of_RTG-Based_Power_Systems⠀⇛


                       Launched in 1977, the Voyager 1 and 2 space probes
                       have been operating non-stop for over 45 years,
                       making their way from Earth to our solar system’s
                       outer planets and beyond. Courtesy of the
                       radioisotope thermoelectric generators (RTGs) which
                       provided 470 W at launch, they are able to function
                       in the darkness of Deep Space as well as they did
                       within the confines of our Sun-lit solar system.
                       Yet as nothing in the Universe is really infinite,
                       so too do these RTGs wear out over time, both from
                       natural decay of their radioactive source and from
                       the degradation of the thermocouples.


                # ⚓ Ruben Schade ☛ An_enigma_of_a_VGA_cable⠀⇛


                       I’ve started mounting my various upscalers and
                       video converters to the back of my old monitor to
                       save space, but it didn’t do much to reduce cable
                       clutter. So I ordered the shortest VGA cable I
                       could find.


                       I was surprised at how thin it was when it arrived.
                       The RS232 cable I inherited from dad’s old modem
                       that I use for CGA on my Am386 and Commodore 128 is
                       thicker! I suppose being an analogue cable, it
                       didn’t need as much shielding for such a short
                       distance.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Pro Publica ☛ What_to_Know_About_Stillbirths⠀⇛


                       Every year, more than 20,000 pregnancies in the
                       U.S. end in a stillbirth, the death of an expected
                       child at 20 weeks or more of pregnancy. Research
                       shows as many as 1 in 4 stillbirths may be
                       preventable. We interviewed dozens of parents of
                       stillborn children who said their health care
                       providers did not tell them about risk factors or
                       explain what to watch for while pregnant. They said
                       they felt blindsided by what followed. They did not
                       have the information needed to make critical
                       decisions about what happened with their baby’s
                       body, about what additional testing could have been
                       done to help determine what caused the stillbirth,
                       or about how to navigate the process of requesting
                       important stillbirth documents.


                       This guide is meant to help fill the void of
                       information on stillbirths. It’s based on more than
                       150 conversations with parents, health care
                       providers, researchers and other medical experts.


                # ⚓ Common Dreams ☛ The_End_of_Covid-Era_Boosted_Benefits
                  Reveals_a_Society_Still_Profoundly_Sick⠀⇛


                       “In order to fully recover, we must first recover
                       the society that has made us sick.”


                # ⚓ Common Dreams ☛ Brazilian_Police_Allege_‘Criminal’_Forgery
                  of_Bolsonaro_Covid_Vaccine_Record_Before_US_Trip⠀⇛


                       Agents from Brazil’s Federal Police on Wednesday
                       raided the home of former Brazilian President Jair
                       Bolsonaro as part of an investigation into whether
                       the far-right leader forged his Covid-19
                       vaccination certificate so he could travel to the
                       United States.


                # ⚓ Helsinki Times ☛ The_effects_of_COVID-19_and_the_war_in
                  Ukraine_on_children_and_youth⠀⇛


                       The mental resilience of children and youth has
                       been put to the test due to the COVID-19 pandemic
                       and the ongoing war in Ukraine. The consequences
                       have included disruptive behavior, marginalization,
                       distress, and decreased sense of belonging. Anu
                       Liljeström, Director of the Department of Education
                       and Culture, explains that preventing the
                       marginalization of children and youth was a key
                       priority last year, as well as supporting their
                       mental, physical, and social well-being, and their
                       ability to cope with crisis.


                # ⚓ New York Times ☛ Why_Americans_Feel_More_Pain⠀⇛


                       Chronic pain is not just a result of car accidents
                       and workplace injuries but is also linked to
                       troubled childhoods, loneliness, job insecurity and
                       a hundred other pressures on working families.


                # ⚓ Reason ☛ Surgeon_General_Vivek_Murthy_Refuses_To
                  Acknowledge_the_Government’s_Misrepresentation_of_Mask
                  Research⠀⇛


                       Recent comments by former COVID-19 adviser Anthony
                       Fauci contradict what public health officials told
                       us during the pandemic.


                # ⚓ US News And World Report ☛ WHO_Experts_Weigh_up_Whether
                  World_Ready_to_End_COVID_Emergency⠀⇛


                # ⚓ Science Alert ☛ Pharma_Giant’s_Experimental_Alzheimer’s
                  Drug_Slows_Cognitive_Decline_by_Over_A_Third⠀⇛


                       This gives hope.


                # ⚓ Science Alert ☛ Ancient_Woman’s_DNA_Recovered_From_20,000-
                  Year-Old_Necklace_Pendant⠀⇛


                       The only trace left of her.


                # ⚓ European Commission ☛ Remarks_by_Commissioner_Lenarčič_at
                  the_Launch_of_the_Global_Report_on_Food_Crises⠀⇛


                       This is the third Report launch event I have
                       attended. Every year, the situation is worse.


          o § Proprietary⠀➾


                # ⚓ Common Dreams ☛ Noam_Chomsky_Speaks_on_What_ChatGPT_Is
                  Really_Good_For⠀⇛


                       Artificial intelligence (AI) is sweeping the world.
                       It is transforming every walk of life and raising
                       in the process major ethical concerns for society
                       and the future of humanity. ChatGPT, which is
                       dominating social media, is an AI-powered chatbot
                       developed by OpenAI. It is a subset of machine
                       learning and relies on what is called Large
                       Language Models that can generate human-like
                       responses. The potential application for such
                       technology is indeed enormous, which is why there
                       are already calls to regulate AI like ChatGPT.


                # ⚓ Common Dreams ☛ Fake_Content_Industry,_AI_Poses_Threat_to
                  Fact-Based_Journalism_Worldwide⠀⇛


                       Along with the threats to journalists’ safety that
                       watchdog groups have documented for years, the 2023
                       World Press Freedom Index on Wednesday warned that
                       the rapidly growing artificial intelligence and
                       fake content industries are endangering the
                       livelihoods of journalists around the world and
                       cutting down on people’s ability to access fact-
                       based news.


                # ⚓ Enterprisers Project ☛ Large_language_models:_6_pitfalls_to
                  avoid [Ed: Over the past few months enterprisersproject.com
                  published about 2 dozen 'articles' that merely help Microsoft
                  hype/dial up chatbots. It's doing so again today. This helps
                  Microsoft distract from its demise in most areas.]⠀⇛


                       There has recently been incredible progress in
                       artificial intelligence (AI), due mainly to the
                       advances in developing large language models
                       (LLMs).


                # ⚓ Enterprisers Project ☛ Why_generative_AI_won’t_solve_your
                  cloud_spending_woes [Ed: Red Hat as a Microsoft hype drone
                  will simply have no future]⠀⇛


                       Tools like ChatGPT are famously capable of
                       producing everything from computer code to poetry,
                       with impressive accuracy and sophistication.


                       But here’s one thing that generative AI is not
                       capable of doing, at least not anytime soon:
                       Helping to solve cloud spending woes. It would be
                       nice if figuring out how to cost-optimize your
                       cloud were as simple as asking an AI engine for
                       tips, but that’s not happening—not because
                       generative AI technologies aren’t impressive (they
                       are) but because AI tools currently lack the
                       ability to understand feedback loops and nuanced
                       business context.


                # ⚓ India Times ☛ Shopify_to_lay_off_20%_of_its_workforce,
                  beats_quarterly_revenue_estimates⠀⇛


                       The company posted revenue of $1.51 billion in the
                       quarter ended March 31, compared with analysts’
                       estimate of $1.43 billion, according to Refinitiv
                       data.


          o § Security⠀➾


                # ⚓ WhichUK ☛ Weak_banking_security_is_leaving_customers
                  vulnerable_to_fraud_on_stolen_phones,_Which?_warns⠀⇛


                       Losses to mobile banking fraud have risen by 16%,
                       but there are steps that banks


                       and customers can take to make life harder for
                       criminals


                # ⚓ Security Week ☛ Court_Rules_in_Favor_of_Merck_in_$1.4
                  Billion_Insurance_Claim_Over_NotPetya_Cyberattack⠀⇛


                       Court says insurers must pay Merck for losses
                       related to the Russia-linked NotPetya cyberattack.


                # ⚓ SANS ☛ Infostealer_Embedded_in_a_Word_Document,_(Thu,_May
                  4th)⠀⇛


                       When attackers design malicious documents, one of
                       their challenges is to make the potential victim
                       confident to perform dangerous actions: click on a
                       link, disable a security feature, etc. The best
                       example is probably VBA macros in Microsoft Office
                       documents.


                # ⚓ Scoop News Group ☛ Russian_national_charged_for_role_in
                  stolen_credit_card_verification_scheme⠀⇛


                       Prosecutors say Denis Kulkov earned at least $18
                       million in Bitcoin through his service that checked
                       the status of stolen credit cards.


                # ⚓ Security Week ☛ Netgear_Vulnerabilities_Lead_to_Credentials
                  Leak,_Privilege_Escalation⠀⇛


                       Vulnerabilities in Netgear network management
                       system allow attackers to retrieve cleartext
                       passwords and escalate privileges.


                # ⚓ Security Week ☛ Passkeys_Support_Added_to_Google_Accounts
                  for_Passwordless_Sign-Ins [Ed: The companies behind it were
                  never interested in true security, so the devil is in the
                  details]⠀⇛


                       Google has added passkeys support to Google
                       accounts on all major platforms as part of the
                       company’s passwordless sign-in efforts.


                # ⚓ Linux_Kernel_Use-After-Free_Vuln_Could_lead_to_Privilege
                  Escalation,_Malware_Attacks⠀⇛


                       A use-after-free vulnerability (CVE-2023-1829) has
                       been discovered in the Linux Kernel traffic control
                       index filter (tcindex). It was discovered that the
                       tcindex_delete function does not properly
                       deactivate filters in case of a perfect hashes
                       while deleting the underlying structure, which can
                       later lead to double freeing the structure.


                # ⚓ Security Week ☛ Hackers_Promise_AI,_Install_Malware_Instead
                  [Ed: Media hyping up a bunch of proprietary rubbish from
                  Microsoft (spyware with very low returns) is costing
                  people]⠀⇛


                       Facebook parent Meta warned that hackers are using
                       the promise of generative artificial intelligence
                       like ChatGPT to trick people into installing
                       malware on devices.


                # ⚓ Security Week ☛ Chrome_113_Released_With_15_Security
                  Patches [Ed: It's not designed for security because sites
                  (remote) can execute all sort of malicious scripts on the
                  client side]⠀⇛


                       Chrome 113 was released to the stable channel with
                       15 security fixes, including 10 that address
                       vulnerabilities reported by external researchers.


                # ⚓ Ubuntu ☛ Ubuntu_Blog:_Big_data_security_foundations_in_five
                  steps⠀⇛


                       We’ve all read the headlines about spectacular data
                       breaches and other security incidents, and the
                       impact that they have had on the victim
                       organisations. From LastPass to SolarWinds, “data
                       security” seems to be the phrase on the lips of
                       every CTO these days. And in some ways there’s no
                       place more vulnerable to attack than a big data
                       environment like a data lake.


                       § From the vault


                       Data intensive systems have been the target of
                       countless attacks. Some of the most memorable
                       technical exploits include Log4Shell, Heartbleed
                       and ShellShock.


                # § Privacy/Surveillance⠀➾


                      # ⚓ Techdirt ☛ US_Marshals’_Secretive_Surveillance_Wing
                        Still_Trying_To_Recover_After_Being_Hit_By_Ransomware
                        More_Than_Two_Months_Ago⠀⇛


                             Money can’t buy you everything. Not even the
                             kind of money that’s apparently infinite, if
                             our current federal deficit is any
                             indication.


                      # ⚓ Site36 ☛ 30_years_of_„crypto_wars“:_The_EU_chat
                        control_is_the_final_enemy_in_the_battle_over
                        encryption⠀⇛


                      # ⚓ Common Dreams ☛ FTC_Praised_for_Pushing_Meta_to_End
                        Exploitation_of_Kids’_Data_for_Profit⠀⇛


                             Children’s advocacy and government watchdog
                             groups on Wednesday welcomed the Federal
                             Trade Commission’s push to implement new
                             protections for youth users of Meta products
                             including Facebook in response to the company
                             allegedly violating a 2020 privacy order.


                      # ⚓ Common Dreams ☛ To_‘Uphold_Human_Right_to_Privacy,’
                        Global_Coalition_Demands_Safeguards_for_Encrypted
                        Services⠀⇛


                             A global coalition of more than 40 companies
                             and digital rights groups on Wednesday urged
                             governments around the world to publicly vow
                             to “protect encryption and ensure a free and
                             open internet.”


                      # ⚓ Common Dreams ☛ Journalists,_Rights_Groups_Urge_Ban
                        on_‘Sinister’_Spyware_Like_Pegasus⠀⇛


                             Six dozen civil society groups, journalists,
                             and experts marked World Press Freedom Day on
                             Wednesday with a joint call for “all
                             governments to implement an immediate
                             moratorium on the export, sale, transfer,
                             servicing, and use of digital surveillance
                             technologies, as well as a ban on abusive
                             commercial spyware technology and its
                             vendors.”


                      # ⚓ The Dissenter ☛ US_Double_Standards_On_World_Press
                        Freedom_Day⠀⇛


                      # ⚓ Scoop News Group ☛ FTC_accuses_Facebook_of_violating
                        privacy_agreement,_proposes_ban_on_profiting_off
                        children’s_data⠀⇛


                             This would be the third time the agency has
                             ordered the company to accept new privacy
                             terms.


                      # ⚓ New York Times ☛ FTC_Seeks_‘Blanket’_Ban_on_Meta’s
                        Use_of_Young_Users’_Data⠀⇛


                             Citing privacy failings by the tech giant,
                             regulators proposed to stop sites like
                             Instagram and Facebook from profiting off the
                             data of users under 18.


                      # ⚓ Press Gazette ☛ As_Reach_warns_of_traffic_slowdown:
                        How_Facebook_referrals_to_publishers_have_plummeted⠀⇛


                             Data from Chartbeat and Similarweb shows how
                             news publisher Facebook traffic has fallen.


          o § Defence/Aggression⠀➾


                # ⚓ CS Monitor ☛ How_Pentagon_leak_suspect’s_violent_words
                  escaped_notice⠀⇛


                       The Pentagon missed red flags identifying Airman
                       Jack Teixeira as a security risk.


                # ⚓ AntiWar ☛ Bush’s_‘Mission_Accomplished,’_20_Years_Later⠀⇛


                       Twenty years ago, President George W. Bush landed
                       in a twin-engine Navy jet on an aircraft carrier,
                       strode across the deck in a bulky flight suit and
                       proceeded to give a televised victory speech under
                       a huge red-white-and-blue banner announcing
                       “Mission Accomplished.”


                # ⚓ The Strategist ☛ How_should_the_law_treat_Underwater
                  Maritime_Autonomous_Vehicles?⠀⇛


                       Maritime Autonomous Vehicles (MAVs) have fast
                       become an essential component of the modern
                       maritime security scene and may operate underwater,
                       on the surface, or in the air—though the latter are
                       commonly referred to as drones.


                # ⚓ New York Times ☛ 8_Students_Killed_After_School_Shooting_in
                  Belgrade,_Serbia⠀⇛


                       The assailant had two pistols, four Molotov
                       cocktails and detailed plans, the police said. A
                       security guard was also killed.


                # ⚓ RFERL ☛ Teen_Arrested_In_Shooting_At_Belgrade_School_To_Be
                  Placed_In_Psychiatric_Clinic,_Vucic_Says⠀⇛


                       Serbian President Aleksandar Vucic said a teenage
                       boy accused of killing eight fellow students and a
                       security guard at a school in Belgrade will be
                       placed in a psychiatric clinic in the Serbian
                       capital.


                # ⚓ RFERL ☛ Iranian_President_Praises_Assad_‘Victory’_On
                  Landmark_Visit_To_Syria⠀⇛


                       Iranian President Ebrahim Raisi has hailed Syrian
                       President Bashar al-Assad for achieving “victory”
                       in the country’s 12-year-long civil war.


                # ⚓ teleSUR ☛ Iranian_President_Arrives_in_Syria_on_Landmark
                  Visit⠀⇛


                       “Syrian-Iranian relations are rich in content,
                       experiences and vision because they have been
                       constant and stable even in difficult times,” the
                       Syrian President said.


                # ⚓ Site36 ☛ Crotone_shipwreck_discovered_by_Frontex_with_high-
                  tech_to_locate_phones_of_refugees⠀⇛


                # ⚓ Telex (Hungary) ☛ Information_on_Hungary_in_leaked_NATO
                  documents_deemed_authentic⠀⇛


                # ⚓ Democracy Now ☛ “We’re_in_Crisis”:_Texas_Democrats_Demand
                  Gun_Control_After_Another_AR-15_Mass_Shooting_Kills_5⠀⇛


                       Texas authorities have arrested the suspect in last
                       week’s mass shooting in the town of Cleveland and
                       are charging him with five counts of murder. Police
                       say Francisco Oropesa killed five neighbors in the
                       home next door, including a 9-year-old child, after
                       the family asked him to stop firing his AR-15-style
                       rifle in his yard because it was keeping a baby
                       awake. Texas Governor Greg Abbott drew backlash
                       after the shooting for referring to the victims as
                       “illegal immigrants,” for which he later
                       apologized. “His goal is to dehumanize people,”
                       Texas state Senator Roland Gutierrez says of
                       Abbott, adding that the governor has done nothing
                       to stem gun violence and easy access to weapons.
                       “Republican policies across this country have led
                       to a very loose gun policy that allows just about
                       anybody, and certainly in Texas, to go find a
                       weapon like an AR-15 with impunity.”


                # ⚓ Meduza ☛ ‘I_didn’t_notice_the_sword_in_my_own_hands’:_Daria
                  Trepova,_charged_with_killing_pro-Kremlin_war_blogger_Vladlen
                  Tatarksy,_speaks_out_from_jail_—_Meduza⠀⇛


                       On April 2, an explosion in a St. Petersburg cafe
                       killed pro-Kremlin war blogger Vladlen Tatarsky and
                       injured around 40 other people. The blast occurred
                       shortly after Daria Trepova handed Tatarsky a small
                       bust of himself, which investigators believe was
                       packed with radio-controlled explosives. The
                       authorities arrested Trepova the following day,
                       after searching her mother’s home and interrogating
                       the woman. Trepova and some of her close associates
                       insist that, though she is against the war in
                       Ukraine, she was framed as Tatarsky’s killer. From
                       pre-trial detention, Trepova wrote to the
                       publication Rotonda. Meduza is publishing an
                       abridged English-language translation of her
                       message.


                # ⚓ Meduza ☛ Kremlin_says_Ukraine_attempted_to_launch_drone
                  strike_on_Putin’s_Moscow_residence_—_Meduza⠀⇛


                       The Kremlin’s press service reported Wednesday that
                       two Ukrainian drones tried to carry out an attack
                       on Vladimir Putin’s residence in the Kremlin on
                       Tuesday night.


                # ⚓ Meduza ☛ Russian_authorities_open_‘justifying_terrorism’
                  case_against_actor_Alexey_Panin_for_post_about_Crimean_Bridge
                  —_Meduza⠀⇛


                       Russia’s Investigative Committee opened a criminal
                       case against Russian actor Alexey Panin on charges
                       that he publicly justified terrorism, TASS reports.
                       If found guilty, he could face up to seven years in
                       prison.


                # ⚓ Meduza ☛ Lawyers_locate_Alexey_Moskalev_after_several
                  weeks,_report_he_was_severely_beaten_in_detention_in_Belarus
                  —_Meduza⠀⇛


                       Alexey Moskalev, who is accused of “discrediting”
                       the Russian army and who was arrested in Belarus
                       after fleeing house arrest, has been extradited to
                       Russia and remanded to pre-trial detention in
                       Smolensk. Vladimir Bilienko, a lawyer with the
                       human rights organization OVD Info, reported
                       Moskalev’s whereabouts after meeting with him.


                # ⚓ Meduza ☛ Critical_timing_Unless_the_Ukrainian_military
                  seizes_the_initiative_soon,_it_risks_losing_more_positions.
                  Meduza’s_updated_combat_map_shows_the_latest_developments_in
                  the_war._—_Meduza⠀⇛


                # ⚓ Meduza ☛ Russian_forces_shell_Kherson,_killing_18_and
                  injuring_46_—_Meduza⠀⇛


                       Ukraine’s Prosecutor General reported that the
                       Russian army had shelled Kherson on the morning of
                       May 3. The shelling killed 18 people and injured 46
                       others, including two children, across the Kherson
                       region.


                # ⚓ Meduza ☛ Dmitry_Medvedev_calls_for_‘physical_elimination’
                  of_Zelensky_—_Meduza⠀⇛


                       Russian Security Council Deputy Chair Dmitry
                       Medvedev took to Telegram on Wednesday to call for
                       Ukrainian President Volodymyr Zelensky to be
                       “physically eliminated” in the wake of the
                       purported Ukrainian drone attack on the Kremlin.


                # ⚓ Meduza ☛ Zelensky_spokesman_says_Ukraine_has_no_information
                  about_alleged_drone_strike_on_Kremlin,_calls_attack
                  ‘predictable_step_from_our_opponents’_—_Meduza⠀⇛


                       Zelensky spokesman Serhii Nykyforov said in a
                       statement that Ukraine does not attack other
                       countries.


                # ⚓ Meduza ☛ Kherson_governor_announces_scheduled_public_safety
                  lockdown_—_Meduza⠀⇛


                       Kherson Governor Oleksandr Prokudin announced on
                       Facebook that a public safety lockdown will be
                       imposed in Kherson from 8 p.m. on Friday, May 5 to
                       6 a.m. on Monday, May 8.


                # ⚓ Meduza ☛ ‘A_terrorist_attack_and_an_assassination_attempt’
                  Russia_says_Ukraine_tried_to_kill_Putin_with_Kremlin_drone
                  strike_—_Meduza⠀⇛


                       The Kremlin’s press service reported Wednesday that
                       two Ukrainian drones tried to carry out an attack
                       on Vladimir Putin’s residence in the Kremlin on
                       Tuesday night.


                # ⚓ Common Dreams ☛ Moscow_Alleges_Putin_Assassination_Attempt
                  as_Ukrainian_Drones_Reportedly_Hit_Kremlin⠀⇛


                # ⚓ Meduza ☛ Russian_Telegram_channel_reports_Ukrainian_drone
                  attack_on_Bryansk_airbase_—_Meduza⠀⇛


                       The Telegram channel Baza reported Wednesday that
                       the Ukrainian military carried out a drone attack
                       on an airbase in Russia’s Bryansk region the
                       previous night.


                # ⚓ Meduza ☛ Russia_launches_new_wave_of_overnight_drone
                  attacks_on_Ukraine_—_Meduza⠀⇛


                       Russia carried out a wave of drone attacks against
                       Ukraine on the night of May 2–3, Ukraine’s Air
                       Force Command reported.


                # ⚓ The Nation ☛ The_Consequences_of_Underestimating_China⠀⇛


                       From the ashes of a world war that killed 80
                       million people and reduced great cities to smoking
                       rubble, America rose like a Titan of Greek legend,
                       unharmed and armed with extraordinary military and
                       economic power, to govern the globe. During four
                       years of combat against the Axis leaders in Berlin
                       and Tokyo that raged across the planet, America’s
                       wartime commanders—George Marshall in Washington,
                       Dwight D. Eisenhower in Europe, and Chester Nimitz
                       in the Pacific—knew that their main strategic
                       objective was to gain control over the vast
                       Eurasian landmass. Whether you’re talking about
                       desert warfare in North Africa, the D-Day landing
                       at Normandy, bloody battles on the Burma-India
                       border, or the island-hopping campaign across the
                       Pacific, the Allied strategy in World War II
                       involved constricting the reach of the Axis powers
                       globally and then wresting that very continent from
                       their grasp.


                # ⚓ Common Dreams ☛ Ukraine,_the_Deepening_Euro-Atlantic
                  Crisis,_and_Common_Security_Possibilities⠀⇛


                       The following is based on a speech—entitled “17th
                       Strategy Conference of the Cooperation for Peace:
                       Our Security Can Only Work Together: Ukraine,
                       Russia, and Europe in a Multipolar World”—delivered
                       in Hamburg, Germany on April 28 to Germany’s
                       largest annual peace conference.


                # ⚓ The Gray Zone ☛ US_troops_in_Somalia_rise_to_900,_House
                  votes_not_to_withdraw⠀⇛


                # ⚓ Scheerpost ☛ Who_Is_Fighting_Whom_in_Sudan?⠀⇛


                       The conflict is domestic, regional and
                       international. Western media have been exaggerating
                       the role of the Wagner Group and all but omitting
                       the influence of U.S. allies in the region.


                # ⚓ Quartz ☛ Cargo_ships_“going_dark”_undermine_Russian
                  sanctions._The_EU_wants_to_ban_the_practice⠀⇛


                       Fourteen months of increasingly tough trade
                       restrictions have not brought the Russian economy
                       to its knees, nor have they forced the end of its
                       war_in_Ukraine.


                # ⚓ Latvia ☛ Baltics_and_Poland_to_back_Ukraine’s_membership_of
                  NATO⠀⇛


                       The Baltic countries and Poland will work on a
                       joint declaration supporting Ukraine’s accession to
                       NATO, Saeima Speaker Edvards Smiltēns (United List)
                       said after a meeting with his Estonian counterpart
                       Lauri Hussar in Riga on Wednesday, reported the
                       LETA newswire.


                # ⚓ France24 ☛ UN_pressures_Sudan’s_warring_generals_to
                  guarantee_humanitarian_aid_access⠀⇛


                       The United Nations pressed Sudan’s warring
                       factions on Wednesday to guarantee safe passage of
                       humanitarian aid after six trucks were looted and
                       air strikes in the capital undermined a supposed
                       truce.


                # ⚓ New York Times ☛ Fleeing_Sudan,_Some_Find_Saudi_Ships_‘a
                  Golden_Opportunity’_to_Escape⠀⇛


                       A Sudanese student waiting to be evacuated by Saudi
                       Arabia counted himself as one of the lucky ones:
                       Born in the kingdom and holding a residency permit,
                       he could board a rescue ship.


                # ⚓ France24 ☛ USAID_pauses_food_assistance_to_Tigray_region_of
                  Ethiopia_amid_theft⠀⇛


                       The United States Agency for International
                       Development (USAID) announced on Wednesday the
                       temporary suspension of its food assistance to the
                       Tigray region of Ethiopia.


                # ⚓ US News And World Report ☛ South_Africans_Call_for_UK_to
                  Return_Diamonds_Set_in_Crown_Jewels⠀⇛


                # ⚓ New York Times ☛ Floods_and_Landslides_Kill_More_Than_120
                  in_Rwanda⠀⇛


                       Many areas across East Africa have in recent years
                       experienced both severe droughts and heavy
                       rainfalls that killed many and damaged property and
                       crops.


                # ⚓ France24 ☛ Floods_from_heavy_rainfall_kill_at_least_129_in
                  Rwanda⠀⇛


                       Torrential rains caused flooding in western and
                       northern Rwanda, killing at least 129 people, a
                       public broadcaster said Wednesday.


                # ⚓ The Straits Times ☛ Security_guard_buried_alive_after
                  landslide_in_Kuala_Lumpur⠀⇛


                       The landslide happened at around 1am on Thursday.


                # ⚓ Tom’s Hardware ☛ Single-GPU_Systems_Will_Beat_Quantum
                  Computers_for_a_While:_Research⠀⇛


                       Researchers with Microsoft, AWS and the Scalable
                       Parallel Computing Laboratory in Zurich have
                       published research that throws some doubt over how
                       soon quantum computers will achieve advantage over
                       their classical counterparts.


                # ⚓ AntiWar ☛ Winners_and_Losers_in_Sudan:_On_Proxy_Wars_and
                  Superpower_Rivalries_in_the_Global_South⠀⇛


                       The world is changing. In fact, it has been
                       undergoing seismic change that long preceded the
                       Russian-Ukraine war, and the recent US-Chinese
                       tensions in the Taiwan Strait. In fact, the US
                       debacle in Iraq and the Middle East, and the
                       humiliating retreat from Afghanistan were only
                       signs of the decline in US power.


                # ⚓ Atlantic Council ☛ Ukrainians_are_inspired_by_Finland’s
                  heroic_past_and_NATO_present⠀⇛


                       Ukrainians are inspired by Finland’s record of
                       resisting Russian imperial aggression and
                       encouraged by the country’s recent accession to
                       NATO, writes the head of Ukraine’s Office of the
                       President, Andriy Yermak.


                # ⚓ France24 ☛ 🔴_Live:_Zelensky_to_meet_ICC_leaders_on
                  Netherlands_trip⠀⇛


                       Ukrainian President Volodymyr Zelensky is visiting
                       The Hague on Thursday and will meet the leadership
                       of the International Criminal Court, which has
                       issued an arrest warrant for Russian President
                       Vladimir Putin, his spokesman said..


                # ⚓ RFERL ☛ Russia_Unleashes_New_Wave_Of_Drones_On_Ukraine_As
                  Donetsk_Defenders_Hold_Ground⠀⇛


                       Russia launched another wave of drone attacks
                       overnight across Ukraine, but most were repelled by
                       Ukrainian air defenses, the military said on May 4,
                       a day after more than 20 civilians were killed by
                       Iranian-made Shaheds..


                # ⚓ RFERL ☛ Kuleba_Says_EU_Move_To_Provide_Ukraine_With_More
                  Ammunition_Is_Step_Kyiv’s_Been_Waiting_For⠀⇛


                       Ukrainian Foreign Minister Dmytro Kuleba said a
                       decision by the European Union to allocate hundreds
                       of millions of euros for the purchase and
                       production of ammunition and missiles for Ukraine
                       is a step that Kyiv has been waiting for.


                # ⚓ RFERL ☛ Russian_Former_F1_Driver_Mazepin_Fighting_U.K.
                  Sanctions_To_Revive_Career⠀⇛


                       Russian former Formula One driver Nikita Mazepin is
                       fighting British sanctions imposed following the
                       invasion of Ukraine in a bid to resurrect his
                       racing career.


                # ⚓ RFERL ☛ Zelenskiy_Denies_Kremlin_Accusation_That_Kyiv_Was
                  Behind_Alleged_Drone_Attack⠀⇛


                       Ukrainian President Volodymyr Zelenskiy said his
                       country did not attack Moscow or Russian President
                       Vladimir Putin, denying Russia’s claim that Ukraine
                       was behind an alleged overnight drone attack aimed
                       at hitting Putin’s residence inside the Kremlin.


                # ⚓ RFERL ☛ Fire,_Explosions,_Drone_Attack_Reported_In_Russian
                  Regions_Close_To_Ukraine⠀⇛


                       Fire, damaging explosions on railways, and a drone
                       attack targeting a military airport have been
                       reported in two Russian regions close to Ukraine,
                       Krasnodar and Bryansk.


                # ⚓ RFERL ☛ Ukraine’s_Zelenskiy_To_Speak_In_The_Hague,_Dutch
                  Government_Says⠀⇛


                       Ukrainian President Volodymyr Zelenskiy is expected
                       to speak in the Netherlands on May 4, the Dutch
                       government said.


                # ⚓ teleSUR ☛ Ukraine_Tried_to_Attack_the_Kremlin_With_Drones⠀⇛


                       Despite what happened, the military parade on Red
                       Square will go ahead as planned, Kremlin spokesman
                       Dmitri Peskov said.


                # ⚓ Vice Media Group ☛ Drone_Explodes_Over_Kremlin,_Russia
                  Alleges_Putin_Assassination_Attempt⠀⇛


                       Ukraine has denied any connection to the incident
                       and said Russia was planning its own terror attack.


                # ⚓ Helsinki Times ☛ Finland_will_continue_supporting_Ukraine,
                  assure_Kaikkonen_and_Orpo⠀⇛


                       MINISTER OF DEFENCE Antti Kaikkonen (Centre) on
                       Wednesday assured that Finland will continue
                       supporting Ukraine uninterrupted even if the
                       coalition formation negotiations drag into June.


                       Kaikkonen stated on YLE A-studio that the caretaker
                       government has looked into the question with the
                       Chancellor of Justice, concluding that decisions on
                       additional aid packages can be made as long as the
                       approach remains unchanged.


                # ⚓ US News And World Report ☛ Ukrainian_Air_Defences_Destroy
                  18_Out_of_24_Russian_Drones_Overnight⠀⇛


                # ⚓ US News And World Report ☛ Artists_to_Russia:_‘Our_Fire_Is
                  Stronger_Than_Your_Bombs’⠀⇛


                       An exhibit has opened in New Hampshire detailing
                       the war in Ukraine through the eyes of eight
                       Ukrainian artists


                # ⚓ US News And World Report ☛ Russia_Unlikely_to_Face
                  Criticism_at_Central_Asian_Meeting⠀⇛


                       Russia is unlikely to face backlash over its war in
                       Ukraine from Central Asian foreign ministers and
                       instead could flex its influence at their regional
                       meeting Friday


                # ⚓ US News And World Report ☛ Explosions_Heard_in_Kyiv,_Other
                  Ukrainian_Cities_–_Authorities⠀⇛


                # ⚓ YLE ☛ Ukrainian_President_Zelensky_thanks_Finland_for
                  continued_support,_calls_for_more_weapons⠀⇛


                       The President of Ukraine was speaking at a press
                       conference in Helsinki on Wednesday as he made a
                       surprise visit to Finland to attend a meeting of
                       Nordic Prime Ministers.


                # ⚓ New York Times ☛ The_Kremlin_made_an_intentional_choice_to
                  publicize_the_drone_episode._The_question_is_why.⠀⇛


                # ⚓ New York Times ☛ Explosions_rock_Kyiv_and_Odesa_overnight
                  after_Kremlin_incident.⠀⇛


                # ⚓ New York Times ☛ Explosions_Over_the_Kremlin_Set_Off
                  Dueling_Accusations⠀⇛


                       Russia accused Ukraine of launching drones at the
                       Kremlin aimed at killing President Vladimir V.
                       Putin. The Ukrainian president denied the claim,
                       and officials in Kyiv warned that Russia could use
                       it to launch “a large-scale terrorist provocation.”


                # ⚓ New York Times ☛ Explosions_Above_Kremlin_Were_an_Attempt
                  to_Kill_Putin,_Russia_Claims⠀⇛


                       Russia said Ukraine had launched a drone attack,
                       which Kyiv vehemently denied, accusing Russia of
                       manufacturing a pretext for escalation.


                # ⚓ New York Times ☛ Zelensky_Arrives_in_the_Netherlands_to
                  Speak_at_The_Hague,_Dutch_Media_Reports⠀⇛


                       The Ukrainian president has long urged that
                       Vladimir Putin and others be held to account under
                       international law.


                # ⚓ New York Times ☛ Zelensky_Denies_Ukraine_Carried_Out_the
                  Drone_Attack_on_the_Kremlin⠀⇛


                       The Ukrainian president flatly denied that his
                       country was behind any drone attack on the Kremlin.


                # ⚓ New York Times ☛ Zelensky_Travels_to_Finland_to_Meet_With
                  Nordic_Leaders⠀⇛


                       The Ukrainian president has made few overseas trips
                       since Russia launched its full-scale invasion of
                       Ukraine.


                # ⚓ New York Times ☛ Secret_‘Mission’_for_Peace_in_Ukraine_May
                  Show_Limits_of_Pope’s_Influence⠀⇛


                       Since Francis made cryptic reference to a Vatican
                       peace effort, the suggestion has elicited denial or
                       bewilderment by war’s protagonists.


                # ⚓ uni Stanford ☛ ‘America’s_Gift_to_Famine-Stricken_Russia’
                  as_a_propagandist_display_of_U.S._relief_efforts⠀⇛


                       The Hoover Institution’s screening of the 1922 film
                       told the history of America aiding Soviet Russians
                       during the 1922 famine. The film is a testament to
                       the power of art in shaping public perspectives,
                       writes Liu.


                # ⚓ JURIST ☛ Kremlin_claims_Kyiv_attempted_to_assassinate_Putin
                  with_overnight_drone_attack,_vows_retaliation_for_‘act_of
                  terror’⠀⇛


                       The Kremlin press service said Wednesday that Kyiv
                       had deployed drones to the Kremlin the night prior
                       in an attempt to assassinate Russian President
                       Vladimir Putin. Two unmanned aerial vehicles were
                       aimed at the Kremlin.


                # ⚓ Press Gazette ☛ Prisoner_exchange_‘only_route_out’_for_Evan
                  Gershkovich,_fears_Independent’s_diplomatic_editor⠀⇛


                       Kim Sengupta thought the Russian government is
                       otherwise unlikely to release the Wall Street
                       Journal reporter.


                # ⚓ Vice Media Group ☛ Beleaguered_Russia_to_Show_Troops_Videos
                  of_NATO_Tanks_Exploding_to_Boost_Morale⠀⇛


                       Russia is deploying 75 year old tanks to the
                       battlefield and coming up with unique plans to
                       counter the modern ones NATO is sending to the
                       battlefield.


                # ⚓ New Yorker ☛ Why_Russian_Élites_Think_Putin’s_War_Is_Doomed
                  to_Fail⠀⇛


                       Rival factions are jockeying for power as the
                       country navigates a crisis with no clear way out.


                # ⚓ US News And World Report ☛ Fire_Extinguished_at_Russian_Oil
                  Refinery_After_Drone_Attack_–_TASS⠀⇛


                # ⚓ US News And World Report ☛ Despite_War,_Sanctions,_Russians
                  in_London_Commercial_Courts_Reach_New_Record_-Report⠀⇛


                       A record number of Russians have appeared in
                       London’s Commercial Courts over the last year,
                       despite the war…


                # ⚓ New York Times ☛ Verified_Videos_Show_Two_Drones_Exploding
                  Over_the_Kremlin_in_Russia⠀⇛


                       The explosions were separated by about 15 minutes
                       and one caused a brief fire.


                # ⚓ New York Times ☛ What_Is_the_Kremlin,_the_Heart_of_Putin’s
                  Security_Bubble_in_Russia?⠀⇛


                       The Russian president resides at various heavily
                       guarded locations and travels frequently between
                       Moscow and a compound in an elite suburb miles
                       away.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Scheerpost ☛ US_House_Members_Unveil_Stock_Trading_Ban⠀⇛


                       “When members have access to classified
                       information, we should not be trading in the stock
                       market on it,” said Rep. Alexandria Ocasio-Cortez.
                       “It’s really that simple.”


          o § Environment⠀➾


                # ⚓ DeSmog ☛ The_Former_Extinction_Rebellion_Campaigners
                  Rallying_A_Climate_Majority⠀⇛


                       Governments show time and again they won’t deliver
                       adequate climate solutions of their own accord. If
                       the world is ever going to get serious on climate,
                       it will be because a mass movement of citizen
                       action insists on it. 


                       Except, no such mobilisation of citizens yet exists
                       across the global north. Accordingly, nothing like
                       sufficient bottom-up pressure exists to hold
                       governments accountable for inadequate climate
                       pledges, let alone policies commensurate with
                       climate science.


                # ⚓ Science Alert ☛ UN_Warns_Developing_El_Niño_Could_Seriously
                  Add_to_Warming_Woes_in_2024⠀⇛


                       “The world should prepare.”


                # ⚓ New York Times ☛ ‘A_New_Spike’_in_Global_Temperatures_in
                  the_Forecast⠀⇛


                       The World Meteorological Organization reports
                       increased odds that El Niño, the global weather
                       pattern often tied to intense heat, will arrive by
                       fall.


                # ⚓ New York Times ☛ Sultan_al-Jaber,_Who_Heads_U.N._Climate
                  Talks,_Hints_at_His_Approach⠀⇛


                       In a speech, Sultan al-Jaber, the Emirati official
                       presiding over this year’s climate summit, spoke of
                       emissions cuts, but experts also cited ambiguity in
                       his statements.


                # ⚓ The Straits Times ☛ Scientists_warn_on_climate_impact_as
                  Australia_unlocks_giant_gas_region⠀⇛


                       Opponents say development of the gas basin would
                       generate as much as an additional 89 million tonnes
                       of greenhouse gas emissions annually.


                # § Energy/Transportation⠀➾


                      # ⚓ DeSmog ☛ Conservative_Party_Funds_Anti-ULEZ_Facebook
                        Ad_Blitz⠀⇛


                             The Conservatives deployed anti-ULEZ adverts
                             on Facebook in March and April that were seen
                             on more than three million occasions, DeSmog
                             research has found. 


                             The party has engaged in a concerted online
                             campaign against the expansion of London
                             Mayor Sadiq Khan’s Ultra Low Emission Zone
                             (ULEZ), which has been the subject of more
                             than a quarter (28.4 percent) of the 88
                             adverts that were launched during this
                             period.


                      # ⚓ Scheerpost ☛ Tesla_Plans_to_Build_Huge_Factory_in
                        Mexican_City_Struggling_With_Water_Scarcity⠀⇛


                             Activists from Mexico are decrying the plan
                             as a prime example of “colonial
                             extractivism.”


                      # ⚓ Quartz ☛ Balaji_Srinivasan_lost_$1_million_in_a
                        bizarre_bitcoin_bet⠀⇛


                             A pseudonymous leftist Twitter account won $1
                             million from crypto investor Balaji
                             Srinivasan over a bet on US inflation.


                      # ⚓ Quartz ☛ Iran_has_seized_its_second_oil_tanker_in_a
                        week⠀⇛


                             A swarm of Iranian fast-craft vessels
                             surrounded the Niovi, a Panama-flagged oil
                             tanker crossing the Strait of Hormuz, at dawn
                             on Wednesday (May 3), steering it towards
                             Iranian waters. It was the second ship Iran
                             has seized in the past week, and the latest
                             escalation in tensions between the US and
                             Iran.


                      # ⚓ Federal News Network ☛ Iran’s_Revolutionary_Guard
                        seizes_tanker_in_Strait_of_Hormuz⠀⇛


                             Iran has seized a Panama-flagged oil tanker
                             in the Strait of Hormuz, the second such
                             capture by Tehran in recent days. That’s
                             according to the U.S. Navy. The Mideast-based
                             5th Fleet identified the vessel taken as the
                             Niovi. It said Iran’s paramilitary
                             Revolutionary Guard seized the ship on
                             Wednesday. The Navy published pictures of
                             small Guard vessels surrounding the tanker.
                             Iran’s state-run IRNA news agency
                             acknowledged that the Guard seized the
                             vessel, but offered no motive. Last week,
                             Iran seized an oil tanker carrying crude for
                             Chevron amid wider tensions between Tehran
                             and the United States over its nuclear
                             program.


                      # ⚓ H2 View ☛ Refineries_to_use_six_million_tonnes_of
                        low-emissions_hydrogen_by_2030,_reports_IEA⠀⇛


                             Around six million tonnes of low-emissions
                             electrolysis hydrogen is projected to be used
                             in refineries in 2030, according to a new IEA
                             World Energy Outlook special report.


                      # ⚓ uni Stanford ☛ From_nighttime_solar_panels_to_algae
                        biofuels,_emerging_research_presented_at_Energy
                        Solutions_Week⠀⇛


                             Leading Stanford researchers came together at
                             Energy Solutions Week to discuss solutions
                             for energy transition and current technology
                             development trends. The event was invite-
                             only.


                # § Wildlife/Nature⠀➾


                      # ⚓ The Revelator ☛ California_Condors_vs._Avian_Flu:_Can
                        the_Endangered_Birds_Survive?⠀⇛


          o § Finance⠀➾


                # ⚓ TurkStat_announces_inflation_at_43%,_continues_to_withhold
                  inflation_basket_despite_court_ruling⠀⇛


                       ENAG reports that Turkey’s inflation rate remains
                       in triple digits. Despite DİSK’s win in a lawsuit
                       against the suspension, the official statistical
                       institute continues to withhold the publication of
                       its inflation basket.


                # ⚓ AFP_journalists_in_İstanbul_go_on_strike_over_low_wages⠀⇛


                       The journalists say their wages have eroded due to
                       the high inflation in Turkey, demanding improved
                       wages.


                # ⚓ Michael West Media ☛ Stock_markets_nervous_about_Fed_pivot,
                  banking_sector⠀⇛


                       Global stock markets have sagged while the Japanese
                       yen has risen in reaction to the Fed’s policy
                       statement and signs of stress at another US
                       regional bank, spurring investors to price in a
                       pivot rather than just a pause in rate rises.


                # ⚓ Axios ☛ Fed_raises_interest_rates,_hints_possible_end_to
                  series_of_hikes⠀⇛


                       The Federal Reserve raised interest rates by a
                       quarter percentage point on Wednesday, marking the
                       10th_consecutive_move in an aggressive hiking
                       campaign that began a year ago to cool inflation.


                       Why it matters: As the banking_system shows renewed
                       signs of stress, the central bank gave its
                       strongest signal yet that it could pause its series
                       of rate increases.


                # ⚓ Quartz ☛ Regional_banks_and_the_US_debt_ceiling:_Quartz
                  Smart_Investing⠀⇛


                # ⚓ Zimbabwe ☛ NMB_Remit_joins_crowded_domestic_remittance
                  market,_can_it_make_a_mark?⠀⇛


                       The collapse of the Zimdollar has led to some
                       interesting phenomena in Zimbabwe. The population
                       prefers the US dollar but cannot bring themselves
                       to bank said USD. This means when it comes time to
                       transfer money, Zimbabweans cannot turn to banks.


                # ⚓ Michael West Media ☛ Treasurer_calls_on_banks_to_give_rate
                  rises_to_savers⠀⇛


                       Banks should pass on the latest interest rate hike
                       to savers without delay, the treasurer says. Jim
                       Chalmers has urged banks to apply the cash rate
                       increase to deposit accounts as quickly as they are
                       passing them on to borrowers.


                # ⚓ Latvia ☛ Ziedonis_‘Stardust’_collector_coin_to_be_sold⠀⇛


                       The Latvian central bank (Latvijas banka, LB) said
                       May 3 it will put another special coin on sale on
                       May 11. This time the theme is the much-loved
                       poet Imants Ziedonis (3 May 1933–27 February 2013).


                # ⚓ Common Dreams ☛ Warren,_Sanders,_and_10_Others_to_Powell:
                  Stop_Hiking_Rates_or_Risk_Terrible_Recession⠀⇛


                       Ten lawmakers including progressive Sens. Elizabeth
                       Warren and Bernie Sanders implored the Federal
                       Reserve to impose a pause on interest rate hikes
                       during its Wednesday meeting, warning that further
                       financial tightening in the name of fighting
                       inflation would risk a brutal, job-killing
                       recession.


                # ⚓ Democracy Now ☛ Debt_Ceiling:_Economist_James_K._Galbraith
                  Warns_GOP_Proposal_Would_Gut_Social_Safety_Net⠀⇛


                       U.S. Treasury Secretary Janet Yellen has warned
                       Congress that the United States could run out of
                       money to pay its bills by June 1 unless lawmakers
                       raise the debt ceiling. House Republicans last week
                       narrowly passed a bill to raise the debt ceiling,
                       but only in exchange for sweeping spending cuts to
                       numerous programs, including student debt relief,
                       food assistance, Medicaid and renewable energy.
                       Democrats, meanwhile, are pushing for a vote to
                       raise the debt ceiling without imposing cuts, even
                       as the constitutionality of the debt ceiling has
                       been questioned by some legal scholars. For more on
                       the debt ceiling, recent bank failures and other
                       economic news, we speak with James Galbraith,
                       economist and professor at the University of Texas
                       at Austin.


                # ⚓ Michael West Media ☛ Another_year_of_record_fossil_fuel
                  subsidies._What’s_the_scam?⠀⇛


                       Government subsidies for fossil fuel companies have
                       hit records again – more money than is spent on
                       Australia’s army. What’s the scam?


                       The scam is, in gas particularly, the winners are
                       mostly foreign-owned multinational companies. The
                       scam is also that these companies are enjoying
                       soaring profits and most of them are serious tax
                       avoiders.


                # ⚓ Pro Publica ☛ Why_Are_Prices_Still_So_High?_Follow_a_Tire
                  to_Find_Out.⠀⇛


                       The trouble that brought Heather Brown to Tire Town
                       Auto Service in Picayune, Mississippi, had started
                       with a shake as she drove down the interstate. The
                       tires she relied on to guide her gold 2014 Nissan
                       Rogue and grip the asphalt when she braked seemed
                       to shift and bounce unpredictably. The 29-year-old
                       single mom had purchased the used SUV in early
                       2022, and when she brought it to a dealership, a
                       mechanic diagnosed a condition that was potentially
                       dangerous for Brown and her 10-year-old son: The
                       steel cords in all four of her tires were
                       separating.


                       Brown replaced two of the tires in July and tried
                       to save for the other two. But inflation kept
                       eating away at her paycheck from her $14.31-an-hour
                       job at a nursing home. So, needing the tires and
                       with Christmas on the way, she took out a personal
                       loan and pulled up to Tire Town on a drizzly
                       Saturday morning in late November.


                # ⚓ Common Dreams ☛ Median_Pay_of_Top_US_CEOs_Jumped_to_Record
                  $22.3_Billion_Last_Year⠀⇛


                       As workers in a range of industries across the
                       United States demanded fair pay and benefits last
                       year—and in several cases, were forced to strike as
                       companies refused to meet those demands—median
                       compensation for the top chief executives rose to a
                       record-breaking $22.3 million.


                # ⚓ Common Dreams ☛ Bombshell_Report_Exposes_Key_Argument
                  Against_Student_Debt_Relief_as_‘Categorically_False’⠀⇛


                       The argument at the center of Republican officials’
                       case against President Joe Biden’s student debt
                       cancellation plan is “categorically false,”
                       according to an explosive new report released
                       Tuesday by the Roosevelt Institute and the Debt
                       Collective.


                # ⚓ Common Dreams ☛ Warren_Leads_Call_to_End_Dispute_System
                  ‘Weaponized’_by_Corporations_Amid_Honduras_Case⠀⇛


                       U.S. Sen. Elizabeth Warren and Rep. Lloyd Doggett
                       on Wednesday led nearly three dozen progressive
                       members of Congress in demanding an end to the
                       Investor-State Dispute Settlement system, a key
                       feature of corporate-managed trade agreements
                       signed, and often initiated, by the United States.


                # ⚓ Michael West Media ☛ Budget_funds_to_meet_record_aged_care
                  wage_rise_ruling⠀⇛


                       More than 250,000 aged care workers are in for a
                       record 15 per cent pay rise under a $11.3 billion
                       boost in the federal budget.


                # ⚓ Silicon Angle ☛ Global_venture_capital_investments_drop_56%
                  in_April [Ed: Yesterday they said 59%]⠀⇛


                       New data released today by Crunchbase Inc. finds
                       that global venture capital funding continued to
                       decline in April as broader macroeconomic issues,
                       40-year-high interest rates and the war in Ukraine
                       continue to disrupt global markets.


⚓ Quartz ☛ The_Fed_raised_rates_again_but_left_doubt_as_to_whether_there_are
more_hikes_to_come⠀⇛


     The US Federal Reserve raised its benchmark interest rate by another
     25 basis points on May 3. Left unsaid, however, was whether the Fed
     is done hiking yet.


⚓ Michael West Media ☛ US_central_bank_lifts_rates_by_25_basis_points⠀⇛


     The Federal Reserve has raised interest rates by a quarter of a
     percentage point and signalled it may pause further increases, giving
     officials time to assess the fall-out from recent bank failures, wait
     on the resolution of a political stand-off over the US debt ceiling
     and monitor the course of inflation.


⚓ US News And World Report ☛ Stock_Market_Today:_Asian_Markets_Higher_After_US
Rate_Hike⠀⇛


     Asian stock markets are mostly higher after the Federal Reserve
     raised its benchmark lending rate again to cool inflation and said it
     isn’t sure what may come next


⚓ CS Monitor ☛ The_Fed_raises_interest_rates_for_10th_time_amid_economic
turmoil⠀⇛


     The Federal Reserve raised key interest rates by a quarter percentage
     point. The Wednesday announcement offered little indication that the
     Fed’s rate hikes have made significant progress toward the goal of
     cooling the economy, the job market, and inflation.


⚓ Axios ☛ “Nobody_believes_her”:_Republicans_believe_debt_ceiling_cliff_is
further_than_Yellen_claims⠀⇛


     Senate Republicans are deeply skeptical of Treasury_Secretary_Janet
     Yellen’s_estimate that the U.S. will not be able to pay its bills as
     early as June 1 if Congress does not raise the debt ceiling.


     Why it matters: A firm deadline can be a forcing mechanism in any
     negotiations, especially on Capitol Hill. But deadlines only work if
     all the parties actually believe that they are real.


§ AstroTurf/Lobbying/Politics⠀➾


    * ⚓ New York Times ☛ Jack_Dorsey_Takes_Aim_at_Elon_Musk_and_Twitter_on_New
      Platform⠀⇛


           The Twitter co-founder has posted prolifically on two new
           social networks, Nostr and Bluesky, which he also backed
           financially.


    * ⚓ Digital Music News ☛ TikTok_Loses_U.S._Head_of_Safety_As_Government_Ban
      Looms⠀⇛


           TikTok’s U.S. Head of Safety and Trust is leaving the company
           on May 12, according to reports. Eric Han’s departure comes as
           TikTok grapples with a potential government ban. Eric Han led
           the safety teams for TikTok in the US for years.


    * ⚓ YLE ☛ EU_parliamentary_group_labels_Finland’s_PM-designate_Orpo_“puppet
      of_the_far_right”⠀⇛


           In a since-deleted Facebook post, the Progressive Alliance of
           Socialists and Democrats accused NCP leader Petteri Orpo of
           pandering to the far right.


    * ⚓ Hong Kong Free Press ☛ The_Hong_Kong_Bar_Association’s_endangered
      reputation,_and_the_seven-year itch⠀⇛


           Tanya Chan, former legislator and former barrister, has
           been censured by the disciplinary committee of the Bar
           Association for “bringing the profession into disrepute” in two
           speeches made in 2014 to pro-democracy Umbrella Movement
           protesters.


    * ⚓ Hong Kong Free Press ☛ Exodus_of_Hongkongers_does_not_impact_salary_tax
      revenue,_says_finance_chief⠀⇛


           The exodus of Hongkongers does not impact the city’s salaries
           tax revenue, said Hong Kong’s financial chief Paul Chan on
           Wednesday. Meanwhile, this year’s budget was passed by the
           “patriots-only” legislature with only one abstention.


    * ⚓ Meduza ☛ Major_donor_to_Navalny’s_Anti-Corruption_Foundation_plans_to
      cut_back_on_contributions_in_wake_of_Berlin_opposition_forum_—_Meduza⠀⇛


           Boris Zimin, one of the key donors to Alexey Navalny’s Anti-
           Corruption Foundation, says he is about to reduce the amount of
           his regular contributions to the organization.


    * ⚓ Meduza ☛ Alexey_Navalny_subjected_to_‘Putin_torture’_in_prison,_forced
      to_listen_to_recorded_speeches_at_top_volume_—_Meduza⠀⇛


           The imprisoned opposition politician Alexey Navalny writes that
           the penal colony management has come up with a new way to make
           his prison life intolerable. Every evening, Vladimir Putin’s
           recorded speeches sound, at top volume, from loudspeakers
           throughout the building and in the penal cell that has become
           Navalny’s regular dwelling-place.


    * ⚓ Craig Murray ☛ The_USA_–_What_Democracy?⠀⇛


           Joe Biden will very probably be re-elected. No incumbent
           President has ever lost a primary (though it should be
           remembered the current primary system is younger than me). Only
           one sitting President has ever not been selected by their party
           to stand again, and that was knocking on two hundred years ago.


    * ⚓ Democracy Now ☛ Supreme_Court:_Are_New_Ethics_Rules_Needed_as_Gorsuch,
      Roberts_&_Thomas_Face_Questions_over_Finances?⠀⇛


           Three conservative Supreme Court justices are now embroiled in
           a growing ethics scandal about their personal and financial
           connections. Recent reporting has revealed that Justice Neil
           Gorsuch sold property he co-owned to the head of a major law
           firm that has since had many cases before the court, Justice
           Clarence Thomas failed to disclose lavish gifts and payments
           from billionaire and conservative activist Harlan Crow, and the
           wife of Chief Justice John Roberts was paid over $10 million in
           commissions as a job recruiter placing lawyers at elite law
           firms. Legal experts and lawmakers are increasingly pushing for
           ethics reform on the high court, with the Senate Judiciary
           Committee holding a hearing on the issue on Tuesday. “Because
           they don’t have an ethics code, you don’t know whether they’re
           doing things in an above-board way,” says Vox senior
           correspondent Ian Millhiser. He also discusses growing
           frustration that California Senator Dianne Feinstein has not
           resigned her seat amid a prolonged absence from the Senate due
           to illness, which is stopping Democrats from confirming federal
           judges.


    * ⚓ Techdirt ☛ Bethesda_DMCAs_Its_Official_Twitter_Account_Trying_To_Stop
      ‘Redfall’_Leaks⠀⇛


           We’re getting into the warmer seasons, which means AAA games
           are coming up for release dates. It also means that leaks of
           content, or sometimes the entire games, for those AAA games are
           coming out as well. We just talked about several leaks coming
           out for Nintendo’s latest Zelda title. And now, right on the
           cusp of Bethesda’s release of the much anticipated Redfall, the
           publisher is very busy trying to nuke every bit of leaked
           content it can sniff out on the internet. Including, briefly,
           images of Redfall appearing on its own official Twitter
           account.


    * ⚓ The Nation ☛ Tucker_Carlson’s_Racist_Text_Didn’t_Get_Him_Fired⠀⇛


           I really thought I’d written my last words on Tucker Carlson.
           Last week, after Fox fired him, I told him not to let the door
           hit him in the ass. But the New York Times article exposing a
           racist Carlson text, and suggesting that it’s what got him
           fired, demands at least a little context.


    * ⚓ The Nation ☛ Guns_Paralyze⠀⇛


    * ⚓ Techdirt ☛ Goodbye_Twitter:_Techdirt_Will_Soon_End_Our_Automated
      Posting⠀⇛


           Over the last few months we’d been wondering if it was worth
           pulling Techdirt posting from Twitter altogether, but had been
           too busy with other stuff to make a decision, and now it looks
           like Twitter has made the decision for us. Last week,
           Automattic informed us that Elon Musk was demanding a
           ridiculous amount of money to continue allowing its Jetpack
           service to use the API to enable WordPress sites to
           automatically post to Twitter. Automattic publicly announced
           this week that it would not pay, and that WordPress sites would
           no longer be able to automatically post to Twitter.


    * ⚓ Techdirt ☛ Elon_Whines_That_He’ll_Give_Away_NPR’s_Twitter_Account_If
      They_Won’t_Start_Using_Twitter_Again⠀⇛


           It’s truly incredible what a childish person Elon Musk can be.
           As you’ll recall, he thought it was the funniest thing in the
           world to misleadingly label NPR as “state affiliated media,” a
           label that had been previously reserved for media organizations
           that were voices of the state, rather than independent. He did
           it because one of his nonsense peddler followers made some joke
           about NPR being state-affiliated media, and in typical Elon
           fashion, rather than looking into any of this or understanding
           the reasons why the “state-affiliated media” labels existed,
           thought it would put NPR in its place to put the label on them
           as well.


    * ⚓ Telex (Hungary) ☛ We_don’t_want_to_become_a_country_of_immigrants_–
      Hungarian_Parliament_adopts_declaration_three_days_after_Pope_Francis’
      visit⠀⇛


    * ⚓ Telex (Hungary) ☛ Hungarian_judicial_reform_worth_€13_billion_voted
      through,_hidden_in_amendment⠀⇛


    * ⚓ Techdirt ☛ DC_Appeals_Court_Belatedly_Declares_USPS_Custom_Stamp
      Program_Restrictions_Unconstitutional⠀⇛


           In 2005, the US Postal Service (USPS) began to get into the
           crowdsourcing business. For a fee, anyone could create custom
           stamps that could be sold through the government’s approved
           stamp portal (Stamps.com), provided they survived a cursory
           review by inattentive public servants.


    * ⚓ Scheerpost ☛ Private_Equity_is_Out_of_Control_and_Looting_America._This
      Prosecutor_Says_We_Can_Fix_It⠀⇛


           In his new book, “Plunder: Private Equity’s Plan To Pillage
           America,” Brendan Ballou, a federal prosecutor who served as
           Special Counsel for Private Equity in the Justice Department’s
           Antitrust Division, outlines the dangers of a trillion-dollar
           industry that hardly anyone understands. He explains how
           Americans can fight their harmful practices.


    * ⚓ US News And World Report ☛ Philadelphia_Mayoral_Race_Hones_in_on_Crime
      Policies⠀⇛


           In Philadelphia’s first mayoral race since crime spiked during
           the coronavirus pandemic, the crowded Democratic field is
           trying to make public safety a campaign cornerstone


§ Censorship/Free Speech⠀➾


    * ⚓ The Nation ☛ Ron_DeSantis_Declares_War_on_Disney⠀⇛


           For the real story of the dueling leadership styles of the
           Republican Party, look to the courts. As former president
           Donald Trump battles criminal and civil charges stemming from a
           payoff to a porn star and an alleged rape, his closest
           potential rival for the GOP presidential nomination is mounting
           a legal counteroffensive against Disney. Florida Governor Ron
           Desantis has clashed against the corporation over its dissent
           from his plan to program anti-LGBQT+ bigotry into Florida’s
           public schools, a fight that has rapidly escalated. The
           Sunshine State’s newly instituted Central Florida Central
           Tourism District Board of Supervisors—a handpicked panel of
           DeSantis cronies that includes a pastor who once took to
           YouTube to suggest that drinking water could turn people
           gay—convened an emergency meeting to vote unanimously on Monday
           to sue Disney. The vote was a response to a suit filed last
           week by the Magic Kingdom’s legal team claiming that the
           DeSantis administration’s threatened suspension of a long-
           standing tax abatement for the company was a retaliatory
           violation of the company’s First Amendment protections after it
           had protested DeSantis’s “Don’t Say Gay” legislation.


    * ⚓ Scheerpost ☛ Now_Reintroduced,_The_Kids_Online_Safety_Act_is_Still_A
      Huge_Danger_to_Our_Rights_Online⠀⇛


           KOSA’s burdens will affect adults, too, who will likely face
           hurdles to accessing legal content online as a result of the
           bill.


    * ⚓ Hong Kong Free Press ☛ Canada_politician_demands_expulsion_of_Chinese
      diplomat_accused_of_planning_to_intimidate_him_and_family_in_Hong_Kong⠀⇛


           A Canadian lawmaker on Wednesday called for Ottawa to expel a
           Chinese diplomat accused of having sought to intimidate him and
           his family in Hong Kong over the MP’s criticisms of Beijing.


§ Freedom of Information / Freedom of the Press⠀➾


    * ⚓ Federal News Network ☛ Trump_lawsuit_against_New_York_Times_over_2018
      series_tossed⠀⇛


           Former President Donald Trump’s lawsuit against The New York
           Times over a 2018 investigative series into his family’s wealth
           and tax practices was dismissed by a state judge. The lawsuit
           accused the Times and three of its investigative reporters of
           relentlessly seeking out his estranged niece, Mary Trump, as a
           source of information and convincing her to turn over
           confidential documents. The Times and its reporters on
           Wednesday succeeded in getting a judge to dismiss the claims
           against them. Trump attorney Alina Habba said “we will weigh
           our client’s options.”


    * ⚓ Meduza ☛ Belarusian_dissident_Roman_Protasevich_sentenced_to_eight
      years_in_prison_—_Meduza⠀⇛


           A Minsk court has sentenced Roman Protasevich, the former head
           of the Telegram channel Nexta, to eight years in prison,
           according to the Belarusian news agency Belta.


    * ⚓ Shadowproof ☛ US_Double_Standards_On_World_Press_Freedom_Day⠀⇛


           A similar statement about the climate of fear fueled by
           prosecuting Assange has been made by Rebecca Vincent, the
           director of operations and international campaigns for
           Reporters Without Borders (RSF).“If the U.S. government is
           successful in securing Assange’s extradition and prosecuting
           him for his contributions to public interest reporting, the
           same precedent could be applied to any journalist anywhere,”
           Vincent contended. “The possible implications of this case
           simply cannot be understated; it is the very future of
           journalism and press freedom that is at stake.”This year,
           Blinken will participate in a “moderated conversation on the
           state of press freedom worldwide” with Washington Post
           columnist David Ignatius.


    * ⚓ Quartz ☛ India_drops_below_Pakistan_and_Afghanistan_in_press_freedom
      amid_BBC_row⠀⇛


           Press freedom in India has_taken_a_turn_for_the_worse,
           according to the World_Press_Freedom_Index.


    * ⚓ The Nation ☛ If_Biden_Really_Believes_in_Press_Freedom,_He’ll_Stop
      Targeting_Julian_Assange⠀⇛


           President Biden opened his speech at Saturday night’s White
           House Correspondents Dinner with an urgent appeal for the
           release of imprisoned journalists—and for increased global
           recognition of the vital importance of robust protections for a
           free press.


    * ⚓ Scheerpost ☛ Chris_Hedges:_Julian_Assange_and_World_Press_Freedom_Day⠀⇛


           This is a talk Chris Hedges gave in New York City at rally
           calling for the immediate release of Julian Assange on World
           Press Freedom Day.


    * ⚓ Common Dreams ☛ If_Biden_Believes_Journalism_Is_Not_a_Crime,_He’ll_Drop
      Charges_Against_Julian_Assange⠀⇛


           President Biden opened his speech at Saturday night’s White
           House Correspondents Dinner with an urgent appeal for the
           release of imprisoned journalists—and for increased global
           recognition of the vital importance of robust protections for a
           free press.


    * ⚓ Common Dreams ☛ How_Lawmakers_Are_Helping_Sinclair_Broadcast_Group
      Destroy_Local_News⠀⇛


           Sometimes lawmakers write legislation that would do the
           opposite of its stated goal. Nowhere is this more evident than
           in two recent bills—one introduced at the state level and
           another in the U.S. Congress—that are supposedly designed to
           “save local news.”


    * ⚓ Scheerpost ☛ Don’t_Laugh,_There_Is_a_Policy_Solution_to_the_Problem_of
      American_Journalism⠀⇛


           If we can’t figure out a way to pay local reporters then, as a
           country, we’re only left with that many more blind spots to
           where the bull is happening. You hear about all these newsrooms
           getting cuts. That’s every article that Tamara has been sending
           me the […]


    * ⚓ Telex (Hungary) ☛ Reporters_Without_Borders:_minimal_improvement_for
      press_freedom_in_Hungary⠀⇛


§ Civil Rights/Policing⠀➾


    * ⚓ The Nation ☛ Tennessee_Republicans_Are_Showing_Exactly_How_Deep
      American_Racism_Goes⠀⇛


           I’ve been a Black person in this country for 44 years. There is
           very little about racism that still surprises me. Indeed, being
           able to anticipate what racist white folks will do next is an
           essential survival skill: “Surprise” is a luxury I cannot
           afford when I am so often the only Black person in a room.


    * ⚓ Scheerpost ☛ A_Texas_Prison_Guard_Placed_a_Woman_in_Isolation_for
      Talking_About_Abortion⠀⇛


           Legal experts told The Nation it’s not illegal. But that didn’t
           stop one guard from moving a woman to extreme isolation after
           sharing sexual health information.


    * ⚓ Common Dreams ☛ Activists_Arrested_for_Occupying_Florida_Gov._DeSantis’
      Office_While_Staff_Literally_Eat_Cake⠀⇛


           More than a dozen activists were arrested late Wednesday after
           occupying part of Republican Florida Gov. Ron DeSantis’ office
           to protest his “fascist agenda,” especially his support for a
           new anti-immigrant bill.


    * ⚓ US News And World Report ☛ Wyoming_Mayor:_Sorry_for_Fiery_Abortion
      Clinic_Facebook_Post⠀⇛


           The mayor of Casper, Wyoming, is apologizing for a Facebook
           post some say evoked last year’s arson attack that delayed
           opening an abortion clinic


    * ⚓ EDRI ☛ EDRi-gram,_3_May_2023⠀⇛


           This week, as the EU Parliament gets ready to vote on the AI
           Act, we are urging members of Parliament to protect people’s
           rights in this landmark legislation. We are putting forward our
           recommendations to lawmakers on protecting journalists from all
           kinds of surveillance through the European Media Freedom Act.


           Among other digital rights updates, read about how Irish and
           French Parliamentarians have become the latest voices to sound
           the alarm against monitoring of people’s messages in the
           proposed Child Sexual Abuse Regulation.


    * ⚓ Quartz ☛ A_McDonald’s_franchisee_was_fined_for_employing_10-year-olds⠀⇛


           Three McDonald’s_franchisees in Kentucky were fined for
           violating federal child labor laws.


    * ⚓ RFERL ☛ U.S._Notes_‘With_Disappointment’_Turkey’s_Suspension_Of
      Overflight_Permissions_For_Armenian_Airlines⠀⇛


           The United States has noted “with disappointment” Turkey’s
           announcement that it would suspend Armenian airline overflight
           permission, a U.S. State Department spokesman said on May 3.


    * ⚓ Common Dreams ☛ Memo_Reveals_How_Sandra_Day_O’Connor_Helped_Get_George
      W._Bush_to_the_White_House⠀⇛


           Former U.S. Supreme Court Justice Sandra Day O’Connor played a
           greater role than previously known in handing the highly
           contentious 2000 presidential election to George W. Bush, a
           document released Tuesday by the Library of Congress revealed.


    * ⚓ Common Dreams ☛ Gig_Workers_Know_Best_How_to_Fix_the_Gig_Economy’s
      Failure⠀⇛


           In recent months, stories of rideshare drivers and delivery
           workers carjacked, robbed, or even killed on the job have made
           headlines around the country. Now, growing research shows that
           there is an all-out, racialized safety crisis in app-based
           work.


    * ⚓ YLE ☛ Police_suspect_12_former_Avarn_Security_guards_of_violent_crimes,
      abuse_of_authority⠀⇛


           The defendants in the case allegedly targeted people in weaker
           positions, including the intoxicated and defenceless, as well
           as members of various minority groups, police say.


    * ⚓ CS Monitor ☛ Writers’_block:_Hollywood_strike_is_pulling_the_plug_on
      productions⠀⇛


           Hollywood writers are on their first strike in 15 years to
           demand better pay and job security, now threatened by streaming
           services. Some scripted productions have paused, and with no
           resolution in sight, the situation is likely to drag on.


    * ⚓ Off Guardian ☛ OffG’s_Quick_Take:_AI_&_the_Writer’s_Strike⠀⇛


           Yesterday evening the US union the Writers’ Guild of America
           went on strike. The most immediate impact of this is that all
           the late-night “comedy” talk shows – Colbert, Fallon, Kimmel,
           Meyers – have gone on hiatus.


    * ⚓ France24 ☛ How_Iranian_authorities_are_cracking_down_on_unveiled
      women⠀⇛


           Iranian authorities have begun imposing fines and denying entry
           to public transport, airports and hospitals to women who refuse
           to wear the hijab. Police have closed cafés, restaurants and
           shopping malls where customers do not wear the Islamic hijab to
           force shop owners to make the headscarf compulsory for women.
           These are the latest efforts by religious authorities in Iran
           to try to enforce Islamic dress codes after months of protests
           brought them down. Iranian women, however, say this crackdown
           will not stop them from fighting for social freedoms.


    * ⚓ Breach Media ☛ As_mining_fight_escalates,_First_Nations_challenge
      Ontario’s_power⠀⇛


           Treaty 9 nations are countering the province’s plans with a
           bold vision of shared land management


§ Internet Policy/Net Neutrality⠀➾


    * ⚓ Techdirt ☛ Cooper_Davis_Act:_Another_Attempt_By_Congress_To_Regulate
      That_Which_They_Don’t_Understand⠀⇛


           There are all sorts of anti-internet bills making the rounds
           lately, and one of the many on the docket and apparently set to
           move quickly is the Cooper Davis Act, which aims to create a
           mandatory reporting rule for websites where promotion of the
           sale of illegal drugs may occur. As with basically any law
           named after someone, the details of what happened to that
           individual are, in fact, tragic:


    * ⚓ Techdirt ☛ GAO_Would_Like_The_FCC_To_Explain_Why_It_Still_Maintains_A
      Pathetic,_Dated_Definition_Of_‘Broadband’⠀⇛


           The US has always had a fairly pathetic definition of
           “broadband.”


§ Monopolies⠀➾


    * § Patents⠀➾


          o ⚓ Kluwer Patent Blog ☛ High_Court_finds_prior_disclosures_in_Russia
            to_be_non-confidential_–_AutoStore_v_Ocado [Ed: EPO enabling patent
            bullies with bogus, worthless, invalid patents]⠀⇛


                 His Honour Judge Hacon handed down judgment in AutoStore
                 v Ocado on 30 March 2023.  The case was atypical in that
                 it had a split trial: the first part of the trial
                 considered whether AutoStore’s patents (EP 794 and EP
                 027) were rendered invalid by prior disclosures made in
                 Russia…


          o ⚓ European Commission ☛ Intellectual_property:_Commission_welcomes
            the_political_agreement_to_boost_the_protection_of_European_craft
            and_industrial_products_in_the_EU_and_beyond [Ed: Intellectual
            property as a term is a misleading propaganda term and a lie;
            meanwhile the EU turns its sight away from EPO crimes]⠀⇛


                 European Commission Press release Brussels, 03 May 2023
                 The Commission welcomes the provisional political
                 agreement reached by the European Parliament and Council
                 on a new Regulation to protect the intellectual property
                 for craft and industrial products that rely on the
                 originality and authenticity of traditional skills from
                 their regions.


          o ⚓ Dennis Crouch/Patently-O ☛ The_Split_on_Pleading_Scienter_for
            Inequitable_Conduct⠀⇛


                 Federal Rule of Civil Procedure 9(b) requires that fraud
                 or mistake be pled with particularity.


          o ⚓ Kluwer Patent Blog ☛ UPC_platform_to_practice_entry_into_force
            functionalities [Ed: UPC is illegal and this is UPC hijacking a
            blog to promote its illegal agenda, which will backfire badly on
            everyone, including the EU and the legitimacy of the patent
            system]⠀⇛


          o ⚓ Countdown_to_the_Unified_Patent_Court,_Part_III:_Remedies [Ed:
            The Unified Patent Court (UPC) is both illegal and
            unconstitutional, so it's rather revealing it is being promoted by
            patent extremists at Watchtroll; what does that say about the
            political systems?]⠀⇛


          o ⚓ New_Report_Reaffirms_Danger_Patent_Trolls_Pose_to_Manufacturers,
            Small_Businesses⠀⇛


                 People whose business models are threatened by strong
                 post-grant review and improved patent quality continue to
                 assert that non-practicing entities (NPEs) and the patent
                 troll narrative is a myth or a fabrication of big tech
                 companies. And yet, a new report by Hightech Solutions
                 reaffirms what has long been known to be true [...]


          o ⚓ Unified Patents ☛ $2,000_for_Sotat_surveillance_patent_prior
            art⠀⇛


                 A new PATROLL contest, with a $2,000 cash prize, was
                 added seeking prior art on at least claim 1 of U.S.
                 Patent_9,854,207, owned by Sotat, LLC, an NPE. The ‘207
                 patent generally relates to a mobile device in
                 communication with a server, where the server is adapted
                 for receiving surveillance data that is transferred
                 electronically from a surveillance area. The patent is
                 currently being asserted against Resideo, Canary_Connect,
                 Vivint, and Wyze_Labs.


                 The contest will expire on June 30, 2023. Please visit
                 PATROLL for more information and to submit an entry for
                 this contest.


    * § Software Patents⠀➾


          o ⚓ Unified Patents ☛ DigiMedia_Tech_video_patent_challenged⠀⇛


                 On April 27, 2023, Unified Patents filed an ex parte
                 reexamination proceeding against U.S._Patent_6,744,818,
                 owned by DigiMedia Tech, LLC, an NPE and an IP
                 Investments_Group entity. The ‘818 patent relates
                 generally to processing, encoding, and compressing frames
                 of video images using visual perception and compression
                 thresholds, and is relevant to our content zone.


    * § Trademarks⠀➾


          o ⚓ TTAB Blog ☛ TTABlog_Test:_Which_of_These_Three_Section_2(d)
            Refusals_Was/Were_Reversed?⠀⇛


                 So far this year, the percentage of Section 2(d)
                 affirmances is lower than the historical average of about
                 90%. Here are three more refusals on appeal. At least one
                 was reversed. How do you think these three cases came
                 out? [Results in first comment].


    * § Copyrights⠀➾


          o ⚓ Creative Commons ☛ Open_Culture_Platform_Activity_Fund_Winners
            2023⠀⇛


                 Ghana attained its independence in 1957, prior to that
                 the country was colonized by a number of European
                 countries like the Portuguese, Danish, British and
                 others.


          o ⚓ Torrent Freak ☛ New_UK_Cybersecurity_Campaign_Leads_Kids_Directly
            to_Pirate_Apps_&_Malware⠀⇛


                 The UK’s National Cyber Security Centre (NCSC) launched a
                 new awareness campaign today hoping to educate kids on
                 the risks of using the internet. The government’s
                 decision to call the campaign “CyberFlix” is utterly
                 bewildering. Not only does the campaign now share the
                 same name as one of the most recognized movie piracy
                 apps, but the first few pages of Google results only
                 return piracy-related results, at least some of which
                 lead to malware.


          o ⚓ Torrent Freak ☛ Z-Library_Defendants_Retain_U.S._Lawyers_But
            Questions_Remain⠀⇛


                 Z-Library proudly bills itself as “the world’s largest
                 library.” The pirate site still flourishes today despite
                 the fact that two Russians, who are allegedly connected
                 to the site, were arrested in Argentina last year on
                 behalf of the United States. The criminal case has yet to
                 get started but there is some movement as both defendants
                 are now represented by U.S. attorneys.


          o ⚓ Digital Music News ☛ TikTok_Is_Developing_Generative_AI
            Disclosure_System_for_Creators_—_Will_It_Help_Combat_Deepfakes?⠀⇛


                 As generative AI is taking the social media world by
                 storm with song mashups, TikTok is looking to disclose
                 content that has been AI-generated.  A new report from
                 The Information suggests TikTok is internally working on
                 a tool to allow content creators to disclose whether
                 content was made using generative AI.


          o ⚓ Digital Music News ☛ Ed_Sheeran_Puts_Musicologist_on_Blast_as
            Copyright_Counteroffensive_Continues⠀⇛


                 As the Marvin Gaye copyright infringement trial against
                 Ed Sheeran’s “Thinking Out Loud” continues, Sheeran has
                 some choice words about a musicologist who testified
                 against him last week. Ed Sheeran is none too pleased
                 with a musicologist who testified against him in the
                 Marvin Gaye copyright infringement trial.


          o ⚓ Digital Music News ☛ ByteDance-Owned_Resso_Abruptly_Drops_Free
            Access_Tier⠀⇛


                 ByteDance pinned its hopes of creating a rival to Spotify
                 or Apple Music with Resso, beginning in emerging markets.
                 Now it’s cutting access to its free tier on May 11. The
                 music streaming service launched in India, Brazil, and
                 Indonesia as a way to get a foot in the door.


          o ⚓ Public Domain Review ☛ The_Ether_Dreams_of_Fin-de-Siècle_Paris⠀⇛


                 Those who sipped or sniffed ether and chloroform in the
                 19th century experienced a range of effects from these
                 repurposed anaesthetics, including preternatural mental
                 clarity, psychological hauntings, and slippages of space
                 and time. Mike Jay explores how the powerful solvents
                 shaped the writings of Guy de Maupassant and Jean Lorrain
                 — psychonauts who opened the door to an invisible
                 dimension of mind and suffered Promethean consequences.


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