𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Saturday, July 16, 2022
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Generated Sun 17 Jul 02:39:43 BST 2022
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
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Gemini index for the day: gemini://gemini.techrights.org/2022/07/16/
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Previous bulletins in IPFS (past 21 days, in chronological order):
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╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕
⦿ The EPO Bubble — Part IV — A Cashflow Problem Looming on the Horizon? | Techrights
⦿ [Meme] Grinning at Immunity | Techrights
⦿ [Meme] The EPO’s Kangaroo Tribunals Explained | Techrights
⦿ IRC Proceedings: Friday, July 15, 2022 | Techrights
⦿ Microsoft Cuts Off Free and Open Source Software From Using the Windows Store for Donations | Techrights
⦿ Illegally Monetising an Attack on the European Patent Convention (or How National Delegates Participate in a Coordinated Patent Collusion, a Form of Organised Crime) | Techrights
䷼ Bulletin articles (as HTML) to comment on (requires login):
http://techrights.org/2022/07/16/epo-cashflow-problem/#comments
http://techrights.org/2022/07/16/epo-hubris/#comments
http://techrights.org/2022/07/16/epo-iac-kangaroo-tribunal/#comments
http://techrights.org/2022/07/16/irc-log-150722/#comments
http://techrights.org/2022/07/16/microsoft-cuts-off-freesw/#comments
http://techrights.org/2022/07/16/patent-microcosm-collusion/#comments
䷞ Followed by Daily Links (assorted news picks curated and categorised):
http://techrights.org/2022/07/16/gnu-rush-2-3/#comments
http://techrights.org/2022/07/16/openbgpd-7-5/#comments
䷩ 𝚕𝚒𝚗𝚎 63
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(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/16/epo-cashflow-problem/#comments
Gemini version at gemini://gemini.techrights.org/2022/07/16/epo-cashflow-problem/
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✐ The_EPO_Bubble_—Part_IV—_A_Cashflow_Problem_Looming_on_the_Horizon?⠀✐
Posted in Europe, Finance, Patents at 1:08 am by Dr. Roy Schestowitz
Overview: [Teaser]_The_EPO’s_Deflating_Patent_Bubble_and_Pursuit_of_Illegal
Software_Patents_(With_Kangaroo_Courts,_UPC,_and_Bullied_Examiners)
Series parts:
🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇EPO_Dukatenesel⦈_
Is the legendary EPOnian “Dukatenesel” at risk of developing constipation?
Summary: The EPO has become unsustainable since the days of Benoît_Battistelli
as suitably-qualified examiners left in droves, new suitably-qualified
examiners_are_impossible_to_recruit, and quality_of_patents_plunged_along_with
compliance_rates; the revenue incurred by handing out hundreds of thousands of
fake European Patents was just a temporary ‘luxury’; the EPO is in fact being
destroyed_by_managers_who_break_the_law,_violate_constitutions,_and_trash
treaties/conventions
In the last part we saw how both the senior management of the EPO and their
“friends” on the Organisation’s governing body – the Administrative Council –
have a “vested interest” in a high level of granted patents.
Any developments which impact negatively on the number of grants will threaten
the lucrative cashflow from EPOnia’s “Dukatenesel” and are likely to be a cause
for concern in these circles.
“Any developments which impact negatively on the number of grants will threaten
the lucrative cashflow from EPOnia’s “Dukatenesel” and are likely to be a cause
for concern in these circles.”As we noted in the second part of the series, the
number of grants at the EPO took a significant downturn in 2020 and 2021. This
downward trend is expected to continue during 2022 because of ongoing
industrial action by the EPO staff union SUEPO.
In the normal course of events it takes some time before the renewal fees due
at national offices are paid and, likewise, before the national offices hand
over the EPO’s share.
“In the normal course of events it takes some time before the renewal fees due
at national offices are paid and, likewise, before the national offices hand
over the EPO’s share.”Because of this, there will typically be a time lag of
one or more years before changes in the number of granted patents give rise to
any visible impact on NRF revenues.
For this reason, the impact of the recent downturn in EPO “production” is not
yet visible in the EPO’s NRF revenue for 2021 (reported as € 640,71 million).
However, if the “grant bubble” were to continue deflating, this would
inevitably lead to a stagnation or drop in future NRF revenues.
🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇EPO_NRF_revenue⦈_
The downturn in the number of grants is not yet reflected in the EPO’s NRF
revenue figures. However, if the “grant bubble” continues to deflate, this will
inevitably lead to a stagnation or drop in future NRF revenues.
In other words, a sustained decline in the level of granted patents over the
course of the coming years would ultimately lead to a decline in the level of
NRF revenues accruing to both the EPO and its contracting states.
“Against this background, it becomes apparent that EPO management has strong
motives for trying to prop up the “grant bubble” and stave off any impending
decrease in NRF cashflow.”Such a development obviously has worrying
implications for all those dependent on the largesse of EPOnia’s legendary
“Dukatenesel”.
Against this background, it becomes apparent that EPO management has strong
motives for trying to prop up the “grant bubble” and stave off any impending
decrease in NRF cashflow.
In the next part, we shall explain why insiders have good reason to believe
that Team Campinos is currently gearing up to take “pre-emptive action” in this
regard. █
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⢸⠇⠀⣿⠁⢸⡇⠐⡸⠉⣿⣿⣿⡟⢛⠿⠿⠇⠀⠀⢸⣿⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣿⣶⣾⣿⣿⣿⣿⣿⡇⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣴⠴⠶⠶⣶⣶⣶⣶⣖⣃
⣨⣒⡼⣿⠀⢸⠀⠀⡇⢠⡏⣿⣷⡆⠈⠉⠀⡁⠀⠀⢸⣿⡄⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⡀⣀⠀⠀⣀⣤⣴⠀⠀⠰⠿⠀⠀⠸⣿⣿⣛⣛⣛⣛⣿⣿⣿⣭⣭⣭⣽⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣮⣝⡀⠀⡇⢸⡇⠀⠀⠀⣀⣀⣠⣧⠤⠤⠾⢿⣷⠀⠀⠀⢘⣛⡇⠀⠀⣨⣭⠝⣈⠠⠄⢐⢶⣶⠀⠀⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠟
⠻⠿⣿⣿⣿⡟⠅⣵⣾⣽⣇⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠘⣿⠇⠀⠰⠏⠀⠀⠀⠙⠀⠂⠀⠘⠂⢰⣿⣿⡇⠘⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠿⠋⠙⠇⠠⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢟⣟⢿⣿⣿⣟⣿⡿⣟⣿⣟⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣭⣯⣯⣤⣿⣿⣴⣵⣽⣥⣿⣿⣥⣼⣯⣼⣾⣿⣥⣿⣧⣽⣵⣿⣿⣶⣵⣵⣼⣿⣮⣿⣴⣵⣼⣿⣯⣼⣵⣼⣼⣿⣧⣼⣯⣿⣿⣿⣿⣭⣮⣯⣽⣿⣿⣯⣿⣵⣿⣿⣯⣽⣼⣿⣿⣼⣿⣿⣿⣯⣿⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣯⡛⡝⣿⣿⣿⡻⣻⡻⠻⣻⣻⡏⣿⣻⡛⡻⣻⣛⢻⣟⣟⠟⢻⣟⠛⣽⢩⣿⡝⢟⡿⣟⡟⠛⣿⣻⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣿⡿⢿⣿⣿⠿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣼⣯⣿⣟⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣽⣿⣯⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⣿⣿⣿⣿⡿⣿⢛⣿⣿⣿⣧⣿⣷⣿⣿⣾⣾⣿⣿⣭⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣽⣿⣿⣿⣯⣿⣿⣿⣿⣽⣿⣿⣿⣯⣿⣿⣿⣿⣽⣿⣿⣿⣯⣿⣿⣿⣿⣽⣿⣿⣿⣯⣿⣿⣿⣿⣽⣿⣿⣿⣯⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣭⣭⣭⣽⣿⣿⣿⣿⣽⣿⣿⣿⣿⣯⣽⣯⣿⣿⣽⣿⣽⣿⣯⣿⣭⣿⣿⣯⣿⣽⣿⣯⣽⣭⣿⣿⣯⣯⣿⣿⣯⣿⣭⣿⣿⣿⣯⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡾⣾⡿⡾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
䷩ 𝚕𝚒𝚗𝚎 224
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/16/epo-hubris/#comments
Gemini version at gemini://gemini.techrights.org/2022/07/16/epo-hubris/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.16.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ [Meme]_Grinning_at_Immunity⠀✐
Posted in Europe, Patents at 1:57 am by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Court of Justice of the European Union; ILOAT; EPO
management⦈
Summary: The Hubris of EPO management is quite a spectacle
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠋⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠉⠓⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣤⣤⣤⣤⣤⣄⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡿⣟⣿⠶⠫⠶⢾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⠛⣾⡟⠁⠀⠀⠀⠀⠀⠘⣂⣘⣇⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡟⠀⣼⠟⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⡘⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⢻⠉⠉⠙⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⢀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⣻⣿⣿⣿⣷⠀⠀⠀⠀⢠⣴⣤⣀⡠⣴⣿⣧⣄⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡟⠀⠀⠀⠀⠀⠀⠐⢛⣛⠛⠛⢛⡿⠿⠿⣿⡇⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠉⢿⣿⡟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⢠⣆⣀⣀⣀⣀⣰⣷⡀⠀⢙⣷⢻⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠛⠃⠀⠶⠾⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠄⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⠿⡿⣿⣿⣿⣿⡏⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⢩⣿⣷⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠄⠀⢸⣧⡀⠀⠀⠀⠀⠈⣸⣦⣄⣠⣿⣽⣿⠃⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠆⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣒⣖⣉⢿⣇⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠟⠀⢰⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⣨⣩⣽⡿⠏⠀⢹⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣼⣿⣷⣾⣿⣿⡙⢻⣿⣿⣿⣿⣿⣿⡇
⠸⠂⠀⠻⣿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⠇⠀⠀⠀⠙⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⡿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡆⠀⠀⠀⠐⠻⠿⣿⣿⣦⣄⣀⣀⣀⣄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠛⣻⣿⠘⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣧⠀⠀⠀⠀⠀⢈⢳⣤⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢰⣦⣤⣤⣾⣿⣿⣿⣶⣶⣿⣧⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⡀⠠⣤⣀⠀⠀⣀⣾⣿⣧⣀⣀⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠻⣿⣿⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣷⣶⣾⣿⣿⣿⣿⣷⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⡇⠀⣤⠀⠀⠀⠰⠟⠶⠾⠿⢇⣿⣿⡟⣹⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⠿⣿⣿⡿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣇⠀⠀⠀⠀⠠⢤⣤⣬⣿⣿⣾⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣀⣼⣿⣿⡟⣿⠋⠀⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠀⠘⢺⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠲⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢈⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⢿⣿⣧⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡆⠀⠀⠀⠀⠀⠀⠉⠉⠻⠻⠋⢸⣿⠟⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⣿⣿⣿⣿⡿⠛⠷⠀⠀⣰⣿⣿⣿⣿⣉⣴⠟⠋⠻⣿⡟⢿⣿⣿⣿⣿⣿⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠀⠀⠀⠀⠀⠀⡏⢻⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠄⠀⠄⠀⠀⠨⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣼⠟⠁⠀⠀⠀⢀⠐⠾⣿⣿⣿⣿⣿⡿⢧⠀⠀⠀⠻⣿⣾⣿⣿⣿⣿⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⣠⣷⣾⣿⣿⣿⣿⣿⣿⣿⣀⡐⠁⠄⠀⠀⠄⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⠀⠀⠀⠈⠙⠛⠋⠩⠿⢿⠂⠋⠉⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡠⠄⢀⣠⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠶⠶⣶⠂⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣦⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠈⠙⠏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢠⣤⣤⣤⣤⣤⣄⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡿⢟⣿⠖⠧⠶⡾⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⢫⣾⠟⠁⠀⠀⠀⢀⠀⢛⣀⣺⣜⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡏⠀⣼⠏⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣦⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⣏⠉⠉⠙⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢢⣴⣀⣀⣤⣼⣿⣦⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡏⠀⠀⠀⠀⠀⠀⠘⢛⡟⠛⠛⢻⡿⠿⢿⣿⡆⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠙⢿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⢲⣆⣀⣀⣀⣀⣼⣧⡀⢀⣙⡇⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⠙⠀⠀⠾⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⡿⢿⢿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣸⣦⡀⠀⠀⠀⠀⠁⣾⣦⣄⣴⣯⣻⡿⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠛⠻⠏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣲⣆⣙⣿⡇⠀⣴⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠏⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣬⣭⣽⡿⠇⠈⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢡⣿⣿⣶⣿⣿⣍⠻⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠀⠀⠻⣿⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⠁⠀⠀⠈⢹⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠇⠀⢸⢿⣿⣿⣿⣿⣿⣆⣹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠿⠀⠀⠀⠀⠈⠻⠿⢿⣷⣤⣤⣀⢀⣤⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠋⢛⣿⡌⢻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠰⢾⣤⣀⠀⠀⠀⠀⣸⡵⣴⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣶⣦⣤⣴⣿⣿⣿⣷⣶⣾⣷⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣴⣾⣷⠀⠀⠀⢀⣤⣾⣿⣿⣄⣀⢀⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠈⠻⠿⣟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣷⣶⣾⣿⣿⡧⢸⣿⣄⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⠏⣸⣿⣿⣿⣿⣷⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⠀⢠⡄⠀⠀⠀⠛⠓⠺⠿⠷⢹⣿⡿⣻⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣇⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷⠀⠛⢿⣿⠿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠁⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠶⢶⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠃⠈⠛⠻⣿⣿⣿⣿⣿⣿⡇⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⣿⣿⣿⠟⠉⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⣤⣴⡾⠛⠉⣹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠛⠉⣿⡿⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⡿⠋⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠀⠀⠀⠀⠀⠸⠉⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠠⠤⠄⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢾⣿⣿⣾⢿⣿⣿⣿⣿⣿⣟⣟⣿⣿⠀⠀⢰⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣆⡀⠐⠀⠀⠀⠢⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠭⠿⠶⠊⠁⠁⠙⠻⠄⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⡰⣤⠄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠶⠶⣶⠀⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⡻⠿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠙⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠉⠻⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣠⣤⣤⣤⣤⣤⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡿⣟⡿⠟⠭⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⢻⣾⠛⠁⠀⠀⢀⣀⠈⢓⣀⣷⡘⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠏⠀⣾⠋⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣎⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⡏⠉⠉⢹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡟⠀⠀⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⡄⠀⠀⠀⠀⣤⣦⣀⣠⢤⣿⣷⣤⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡏⠀⠀⠀⠀⠀⠀⠚⢻⠿⠛⠛⢿⡟⠻⣿⣿⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠻⣿⣟⠛⠙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⣲⣅⣀⣀⣀⣠⣾⣧⡀⣈⣹⡞⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠀⠐⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⠿⠿⣿⣿⣿⣿⠁⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠈⢉⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣸⣧⡀⠀⠀⠀⠈⢉⣿⠦⢤⣴⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠘⠛⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢤⣶⣆⣙⣿⡄⠀⣼⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠋⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⣠⣤⣬⣽⠿⠁⠈⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⣾⣿⣿⣿⣿⣯⡙⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠀⠀⠻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡿⠀⠀⠀⠈⢻⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⠗⠀⠐⠿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠙⠯⠀⢰⣿⠄⠘⠟⢩⣿⣧⣦⣴⣂⣦⣤⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⡋⠹⢿⣇⠹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣰⣿⡄⠰⣶⡄⠀⠀⢸⣟⣴⣿⣦⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢴⣶⣶⣶⣿⣿⣿⣿⣶⣶⣿⣶⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣀⠢⢿⣿⣾⣿⠟⢁⣴⣿⣿⣦⣤⣼⣷⣿⣟⣏⣠⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠈⠛⠿⢿⡛⠛⢟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣷⣶⣿⣿⣿⠀⢼⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⢿⠛⣻⣿⣿⣿⣿⣿⣿⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⠀⣦⠀⠀⠀⠘⠛⠛⠻⠿⢆⣿⣿⢋⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠇⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠠⢿⣏⣿⣿⣿⣿⣿⣧⠈⠙⠿⢿⠿⠃⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢸⡿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠲⠶⣶⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⡿⣿⣿⣿⡷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⣿⡟⠁⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠘⠉⠁⢸⣿⠉⠃⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠠⠗⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣴⣿⣿⣿⣿⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠃⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠠⠤⠤⣀⠐⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠘⠿⣿⣿⣟⣻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠐⠂⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠻⠿⠫⠉⠁⠉⠉⠙⠻⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠅⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡰⣶⠖⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠶⠲⣶⠈⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠙⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠈⠋⠇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡿⣿⡿⠟⠭⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⢻⣿⠛⠁⠀⠀⢀⣀⢈⢃⣀⣳⡙⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠏⠀⣾⠋⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣷⡌⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣹⠉⠉⠉⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡟⠀⠀⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⢀⣤⣄⣄⣤⣴⣿⣧⣄⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⢘⠻⠿⠛⠛⣿⡟⠻⣿⣿⢸⣿⣿⣿⣿⣆⠀⠀⠀⠀⠈⠻⣿⡟⠋⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠂⠀⠀⠀⠀⠀⣿⣢⣤⣀⣠⣤⣿⣦⣀⣀⣹⠸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠉⠁⠀⣒⣾⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⡿⠻⠿⢿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⠉⣹⣿⡷⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣸⣦⠀⠀⠀⠀⠀⢀⡿⠶⠤⣾⣿⣿⠏⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢬⣽⣥⣝⣿⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠃⠀⣾⣿⣿⠇⠀⡤⠀⠀⠀⠀⢤⣤⣬⣿⠿⠁⠈⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⣽⣿⣿⣿⣿⣍⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⠀⠐⠻⠿⠀⠀⠀⢹⣧⣤⠀⠀⠀⠈⣿⡟⠀⠀⢸⣿⣿⡏⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠂⠀⠸⠿⣿⣿⣿⣿⣿⣆⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠀⠀⠀⠀⠙⠇⠀⠀⢸⣿⣿⣷⠀⣻⣷⣶⣶⣤⣦⣄⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣟⠁⠽⢿⠀⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠁⠀⠀⠐⣣⡄⠀⠀⢠⣾⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠠⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⣀⡀⠠⠀⣰⣿⠀⠀⣠⣾⣿⣷⣤⣤⡈⡋⠼⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠉⠻⠛⣍⡉⢛⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣾⣿⣿⠇⠀⠀⣿⣇⣠⣾⣿⣿⣿⣿⣿⣿⣧⠁⠀⠀⠀⢹⣿⣿⣿⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡏⣻⣿⢸⣿⣿⣿⣿⣿⣿⣿⣀⢸⡆⠀⠀⠀⠉⠉⠙⠛⠓⣼⣿⡏⣽⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠟⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣸⣿⣿⣿⡇⠈⠛⠿⠟⠋⠀⠸⢹⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⡿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣘⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⣿⣿⡿⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠨⠿⠿⡿⣿⡟⣿⣿⣿⡇⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣿⣿⡆⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠈⠀⠀⠀⠀⢸⠃⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠏⠇⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢰⣿⣿⣿⣿⣿⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠈⠀⣸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠠⠄⠤⠀⢙⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⣟⠀⠀⠈⠻⠿⣿⣿⣽⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠁⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠒⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠛⠛⠓⠀⠀⠀⠀⠈⠙⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡶⣶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠖⠲⣶⠀⠶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣾⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠙⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠉⠹⠏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢠⣤⣤⣤⣤⣤⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣟⡿⠟⠭⢿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⢻⣿⠛⠀⠀⠀⢀⣀⣈⣃⣘⣧⡹⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠏⢀⣿⠃⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⡜⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡏⠉⠉⠙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡟⠀⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣇⠀⠀⠀⠀⢰⣴⣤⣀⣤⣾⣿⣤⣄⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⠐⠙⠻⠯⠉⠛⣿⠛⠛⣿⣧⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠙⣿⣿⠛⠉⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⣿⣦⣀⣠⣤⣠⣿⣦⣀⣀⣿⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠉⠀⣐⣺⡿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿⠻⠿⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣈⣽⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣸⣦⠀⠀⠀⠀⢰⣽⡿⠶⠴⠾⣿⣿⠇⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⢀⣿⣿⡇⠀⠀⢀⣼⡿⠀⠬⣭⣥⣽⣿⠀⠠⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠃⠀⣾⣿⣿⠇⠀⠀⡏⠀⣷⠀⢤⣦⣴⣽⠿⠀⠉⢿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⣾⣿⣿⣿⣿⣷⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⠀⠈⠻⠟⠀⠀⠀⠀⠐⢸⡏⠀⠀⠀⣿⡟⠀⠀⡑⠘⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⠗⠀⠈⠟⠿⣿⣿⣿⣿⣷⡸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠙⠃⠀⣰⣿⠀⢹⣿⣿⣿⣷⣶⣢⣶⣶⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣍⠈⠿⣇⢹⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣾⠃⠀⠀⠐⣧⡀⠀⠀⠛⠋⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢲⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⣠⣠⣤⠈⠀⠁⠀⢀⣠⣾⣿⣷⣤⣤⠀⠂⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠙⠛⢻⣉⣉⣛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡿⠀⠀⢠⣠⣤⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⢰⣿⣿⣿⣿⣯⢻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡃⣿⡿⢸⣿⣿⣿⣿⣿⣿⣇⣐⣧⠀⠀⠀⠈⠉⠉⠙⠛⢲⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡏⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⣿⣿⣿⣿⣿⡆⠈⠛⠿⠋⠁⠀⠽⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠟⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢈⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣻⣿⣿⣿⣇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣾⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⣟⢻⣿⣿⣿⠀⠀⠀⠀⣾⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡯⠁⠈⠀⠀⠀⠀⡟⠺⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⢁⣀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠠⠤⠤⠈⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠟⠁⠉⠛⢿⣯⣽⡿⠿⠿⠟⠋⠉⠉⠉⠻⡇⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣂⡀⠀⠀⠀⠀⠂⢤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⡿⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡷⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⠷⠲⣶⠀⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣰⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠁⠻⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣠⣤⣤⣤⣤⣄⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⡿⠻⠭⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⢻⡿⠋⠀⠀⠀⢀⡀⡙⣀⣘⣆⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠏⢀⡿⠃⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⡝⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡉⠉⠉⢹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡏⠀⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡆⠀⠀⠀⠀⣤⣦⣄⣠⣴⣿⣷⣤⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠁⠀⠀⠀⠀⠘⠻⠍⠉⠛⣿⠛⠻⣿⡇⣸⣿⣿⣿⣷⡀⠀⠀⠀⠈⠹⣿⡟⠋⠙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⣶⣀⣄⣀⣤⣴⣿⣄⣀⣌⣷⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠉⠁⢀⣒⣛⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⠟⠿⢿⣿⣿⣿⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣉⣿⡿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣼⣦⠀⠀⠀⠀⣤⣼⠘⠷⠴⢿⣿⣿⣿⣇⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠉⠛⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⢀⣿⣿⡆⢠⣦⢀⣿⢁⠤⣬⣭⣤⣹⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠃⠀⣾⣿⢿⠁⢸⣿⡶⠀⠘⢠⠶⠤⣤⣿⠟⢹⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢰⣿⣿⣿⣿⣿⣌⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⠀⠈⠛⠛⠀⠀⠸⠻⢷⣄⣠⡏⠀⠀⣿⡇⠀⢘⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠃⠀⠙⠻⢿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠙⠂⠀⢼⣿⣿⠉⠉⣛⣷⣶⣦⣤⣴⣦⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣏⡀⠹⣷⡈⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠠⣤⠀⣀⠼⠃⠀⠀⣠⠀⠀⠀⠀⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⣀⣠⣾⣮⠄⠈⠀⢀⣤⣾⣿⣷⣦⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⢻⣿⢿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠙⠛⣏⣉⣩⣽⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣷⣿⣿⣿⣿⣿⠀⣀⣤⣾⣿⣿⣿⣿⣿⣦⠀⢿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡏⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣀⣸⡆⠀⠀⠀⠀⠈⢉⣙⠃⣾⣿⢃⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢿⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠉⠛⠟⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠸⠛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⠻⠛⠿⠙⣿⣿⠿⠇⠀⠀⠀⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⢸⠃⢹⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⠟⠋⠉⠻⠿⠿⠿⠀⢹⣿⣿⣿⣿⣿⣿⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⡠⠤⠤⣋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠋⠀⠈⠻⢫⠼⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠲⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣞⡻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠿⣶⠀⠶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣾⣿⣿⣿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠉⠇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⣀⣹⣯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⡿⠻⠭⢽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⢻⡿⠋⠀⠀⠀⢀⡀⢙⣀⣉⣌⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠏⢀⡿⠃⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣶⠙⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠉⠉⠉⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡏⠀⠀⠁⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠀⠀⠀⠀⠠⢦⣤⣤⣤⣾⣿⣦⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠁⠀⠀⠀⠀⠙⠿⠍⠉⠛⣿⠛⠻⣿⡇⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⢻⣿⡛⠉⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠰⣶⣠⣄⣀⣠⣴⣿⣄⣤⣬⣷⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠀⢀⣚⣛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣟⠉⠿⢿⣿⣿⡇⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⡗⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣸⣦⠀⢀⠀⠀⠸⣿⣟⢠⢦⢿⣿⣿⡇⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣿⣿⡄⢸⡆⣀⣠⠛⠁⠀⡀⠤⣿⣿⣿⣷⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠃⠀⣼⣿⠿⠁⢸⡿⢿⣿⣶⠇⣼⠀⠈⣿⣿⣿⠹⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣾⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⠀⠀⠙⠋⠀⠀⠘⠉⠀⠈⠻⣿⡏⠀⣾⣿⣿⣿⠀⠉⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠿⠗⠀⠈⠛⠿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣮⣾⡍⠀⠀⠈⢹⣿⣿⠀⠀⠈⠉⣟⣿⣾⣶⣴⣶⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣠⣼⣯⡀⢘⣻⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠉⠀⢀⡄⠀⠈⢿⣿⡆⣾⣷⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⣀⣠⣾⣿⣿⣿⠁⠀⣤⣾⣿⡄⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⡏⣿⡟⢿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠈⠙⢹⣄⣈⣭⣏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣷⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⡎⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠅⣿⡟⢸⣿⣿⣿⣿⣿⣿⣇⣀⣷⠀⠀⠀⠀⢀⣀⣉⣉⣸⣿⣏⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠻⣿⣿⣿⣿⣿⣿⣿⠁⢀⣸⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠛⠉⠀⠀⠨⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣸⣿⣿⣿⣿⣿⡏⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠛⠹⣿⡿⠿⠀⠀⠀⠀⣾⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⣴⣿⣿⣿⣿⣿⣿⣯⣽⠿⠿⠿⠿⠿⢿⡧⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠿⠘⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠏⠀⢉⡍⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⡤⠄⣬⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠏⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⣀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠇⠶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣴⣿⣿⣿⡟⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠙⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠈⠹⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢠⣤⣤⣤⣤⣤⣀⣈⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⡿⠻⠭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⣿⡿⠋⠀⠀⠀⢀⡀⢛⣀⣹⣌⢿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠇⢠⡿⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦⠹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⠉⠉⠙⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡏⠀⠈⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠂⣿⣿⣿⣇⠀⠀⠀⠀⠰⣾⣤⣤⣤⣾⣿⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠙⠯⠍⠉⢻⡿⠛⢻⣿⡆⣿⣿⣿⣿⣄⠀⠀⠀⠀⠈⢿⣿⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠰⣷⣤⣤⣄⣤⠘⣷⣶⣤⣬⡗⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣛⣛⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⠃⡈⢸⣿⣿⡇⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣸⣆⠀⠀⠀⠀⠈⣿⠿⡸⠉⣿⣿⣿⣇⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣿⣿⡆⢸⡄⣴⣶⣇⡨⠃⠀⣿⣿⣿⠏⢰⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣟⣛⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠋⠀⣼⣿⠻⠀⢸⠇⠋⠙⢿⣯⣼⠀⣿⣿⣿⠀⠙⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢰⣿⣿⣿⣿⣿⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⠀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣎⣹⠟⠸⢿⣿⣿⠀⠀⠙⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠿⠂⠀⠙⠙⢿⣿⣿⢿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠿⠀⠀⠘⣿⣿⠀⠀⠀⠈⢸⣿⣿⣿⣦⣶⣶⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⡀⢀⣀⣴⣿⣆⠀⣑⣿⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡋⠀⢀⠀⠀⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣀⣠⣠⣾⣿⣿⣿⡿⠁⢰⣿⣆⠰⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢹⣿⡿⣿⣿⣿⣿⣿⣿⣤⠀⢀⠀⠀⠈⠉⠦⣤⣴⣿⡝⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣷⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⢸⣿⠇⣿⣿⣿⣿⣿⣿⣿⣤⣼⡆⠀⠀⠀⠀⢀⣠⣬⣁⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠘⠻⣿⣿⣿⣿⣿⣿⡏⠀⠀⢹⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠰⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣿⣿⣿⣿⣿⣿⠁⠀⠀⣾⣿⣿⡇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠛⠁⢻⡿⠛⠇⠀⠀⠀⠀⡿⢽⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣨⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠛⠛⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠘⡁⠸⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⠇⠀⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⠄⠠⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠏⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⢀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⢷⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣾⣿⣿⡿⠛⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠁⠻⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣠⣤⣤⣤⣤⣤⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⡿⠛⠭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⢿⡿⠋⠀⠀⠀⢀⡀⢓⣈⣹⣌⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠏⢠⡿⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦⠹⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡌⠉⠉⢹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡏⠀⠈⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⠀⠀⠀⠀⢷⣷⣤⣴⣴⣿⣷⣦⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠉⠯⠍⠉⢹⡟⢛⡻⣿⡆⣿⣿⣿⣿⣄⠀⠀⠀⠀⠘⣿⡏⠉⠈⢉⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠸⢶⣤⣄⣤⣴⡀⠷⢨⣧⣬⡗⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣨⣿⣛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⢡⣤⣨⣿⣿⡇⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣄⣿⡿⢪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣸⣆⠀⠀⠀⠀⠀⠽⠟⡼⠀⣛⣿⣿⣧⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠉⠉⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣿⣿⡆⢀⠀⢾⣿⣿⣴⠁⠄⣿⣿⣿⠏⢰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⢻⣿⣟⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠏⠀⢰⣿⠻⠀⠸⠅⠀⢈⠙⢿⣾⣆⣿⣿⣿⠀⠹⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⣼⣿⣿⣿⣿⣷⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠀⠀⠉⠉⠀⠀⠀⠀⠀⠐⠨⣨⡛⠈⣿⣿⡟⠀⠀⢩⣿⣷⣆⣀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠟⠀⠀⠋⠻⢿⣿⡿⢿⣷⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣻⡟⠃⠀⠀⣿⡇⠀⠀⢀⠀⢺⣿⣿⣿⣶⣶⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣀⠀⣠⣼⣿⣄⢀⣺⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣯⠆⠀⠀⣰⣿⡇⠀⢀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣀⣀⡀⢠⣿⣿⣿⣿⡏⣸⣷⠀⢻⣿⣷⣴⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⡟⢹⣿⢻⣿⣿⣿⣿⣿⣷⡄⠀⡀⠀⠀⠉⠡⠄⢤⣵⣯⠹⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣷⣷⣿⢶⣿⣿⣿⣿⣿⠈⢹⣿⡆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⢿⣿⣿⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠇⢸⣿⢸⣿⣿⣿⣿⣿⣿⣷⣤⣿⡄⠀⠀⠀⠀⣠⣤⣌⣨⣿⣏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠙⠿⣷⣿⣿⣿⣿⣿⠃⠀⠀⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠁⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⠀⠀⢠⣿⣿⣿⣿⣿⡟⠀⠀⢴⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠃⣿⡟⠛⠃⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣇⣵⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠉⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⠀⢸⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⠃⠰⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⠃⠀⠴⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⢀⡄⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⢿⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣰⣿⣿⡿⠟⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠈⠙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠁⠇⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣠⣤⣤⣤⣤⣤⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⡿⠫⠭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⢿⡿⠋⠀⠀⠀⢀⡀⢛⣀⣫⣌⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠋⢠⡿⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠈⠉⠉⢽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡏⠀⠈⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡆⠀⠀⠀⠀⢶⣦⣤⣤⣾⣿⣷⣤⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠉⠯⠍⠉⢹⡟⢛⡻⣿⡀⣿⣿⣿⣷⣀⠀⠀⠀⠀⠙⣿⡋⠁⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⣆⣠⣄⣤⣴⡀⠲⢬⣶⣬⡗⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣹⣟⡋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⠥⠤⣼⣿⣿⡇⠸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣤⣠⣿⡗⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣸⣆⠀⠀⠀⠀⠀⠘⠎⡰⠀⢸⣿⣿⣧⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣿⣿⡆⠘⠀⠸⢿⣿⣤⡇⡀⢸⣿⣿⠃⣰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠟⢻⣿⣋⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠟⠀⢰⣿⠛⠀⠀⠆⠀⠀⠈⠻⣿⣇⣿⣿⣿⠀⠹⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠙⣹⡏⠀⠀⢹⣿⣶⣀⣀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠹⠟⠀⠈⠉⠻⣿⡿⠿⣿⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣺⡟⠃⠀⠀⣿⠁⠀⠀⠀⠀⣰⣟⣟⣿⣶⣶⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⣀⣀⣀⣤⣿⣧⣀⣀⣪⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠁⠀⠀⣼⣿⡀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⢿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⠀⣀⣠⣤⡤⢠⣾⣿⣿⣿⡏⣠⣧⠀⣻⣿⣧⣴⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⣿⣟⢿⣿⣿⣿⣿⣿⣷⡄⠀⡀⠀⠀⠉⠰⠠⢤⣾⣏⢻⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⢰⣶⣾⢰⣶⣾⣿⣯⣿⡿⣷⣮⢿⢰⣶⣾⣷⣿⢾⣾⣾⣿⣷⣿⣏⠹⢿⢿⣿⡿⠋⠻⢿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠃⣿⡏⢸⣿⣿⣿⣿⣿⣿⣧⣤⣷⠀⠀⠀⠀⠀⣤⣤⣄⣼⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡟⢸⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⠁⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⢸⣿⣇⢸⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⡿⠛⠹⠀⠀⠀⠀⣸⠨⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣼⣿⣿⢸⣿⣿⡟⣻⣿⣇⣿⣿⠀⣿⣿⡛⣿⣷⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣮⣿⣿⣾⣿⣿⣷⡇⠉⠍⠉⠁⠈⠉⠉⢷⣽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⢀⠠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡟⠀⠰⠂⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⡄⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣴⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠇⠰⠰⠶⠖⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠺⡿⢿⠏⠋⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠘⠇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⣀⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⡿⠫⠽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠿⣿⡿⠋⠀⠀⢀⣀⣀⣉⣤⣷⣜⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠏⢠⡟⠁⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣦⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠉⠉⠉⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡏⠀⠈⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡀⠀⠀⠀⠰⢶⣤⣤⣤⣾⣿⣦⣤⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠉⠋⠉⠉⢹⡟⢉⠻⣿⡀⣿⣿⣿⣧⣀⠀⠀⠀⠀⢛⣿⠉⠁⠉⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠐⣷⣤⣤⣤⣴⡀⠒⣼⣦⣼⡏⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣭⣿⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⢥⡤⣼⣿⣿⠇⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⣄⣼⣿⢏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣸⣆⠀⠀⠀⠀⠀⡸⠞⣲⠀⢸⣿⣿⡧⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣿⣿⡆⠘⠀⠸⢿⣿⣴⠃⡄⢸⣿⣿⠁⣸⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠛⣿⣿⣉⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠟⠀⢰⣿⠛⠀⠀⠄⠀⠀⠀⠻⣷⣆⣿⣿⡏⠀⠹⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣸⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⢀⡿⠀⠙⣹⡇⠀⠀⢹⣿⣶⣄⣀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠉⠉⠛⠃⠀⠉⠙⢿⣿⠿⠿⣿⡎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡿⡿⠃⠀⠀⣿⠀⠀⠀⠀⠀⢸⣯⣻⣿⣷⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣠⣼⣿⣦⣀⣈⣷⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠅⠀⠀⣼⣿⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠻⢿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠀⣀⣤⣤⡤⢠⣾⣿⣿⣿⡟⣠⣇⠈⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⢸⣿⡟⣿⣿⣿⣿⣿⣿⣶⠀⢀⠀⠀⠀⠁⠢⠤⢴⣾⡌⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⢰⣶⣾⢰⣶⣾⣿⢿⣿⡿⣷⣮⢿⢰⣶⣿⣷⣿⢾⣿⣿⣿⣷⣿⡇⠻⠿⣿⣿⠟⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡅⠸⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣦⣼⣇⠀⠀⠀⠀⠤⣤⣤⣤⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡏⢸⣿⣿⣿⣿⣿⡏⣿⣿⢸⢸⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⢿⣿⣿⣧⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠒⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣇⢸⣿⣿⣿⣿⣿⡇⣿⣿⢸⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠸⡏⠁⠉⠀⠀⠀⠀⡿⢺⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⢸⣿⣿⡟⣻⣿⣇⣿⣿⠀⣿⣿⡛⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠃⠈⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣽⣿⣾⣿⣿⣷⡗⠉⠉⠉⠁⠈⠉⠉⢷⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣠⡄⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣾⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠇⠠⠴⠶⠖⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢤⡿⠿⠿⠛⠁⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠉⠋⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠈⠹⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣤⣤⣤⣤⣤⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⠟⠭⠽⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠟⣿⠟⠁⠀⠀⢀⣀⣈⣩⣤⣶⡜⢿⣿⣿⣿⣯⠀⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⢰⠟⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠁⠉⠩⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣷⠀⠀⠀⠀⠐⢾⣦⣤⣴⣿⣿⣦⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⢸⣿⠃⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⢹⡏⡉⠻⣿⢸⣿⣿⣿⣦⡀⠀⠀⠀⠀⢛⣿⠉⠈⢉⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⢸⣿⠀⠀⠀⠀⠀⠘⣷⣦⣤⣤⣴⡀⠲⣿⣤⣼⡏⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢬⣭⣏⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣧⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⢡⢤⣿⣿⣿⠀⢹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢠⣤⣾⡿⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣼⣆⠀⠀⠀⠀⠀⡳⠙⡔⠀⣿⣿⣿⡆⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣿⣿⠀⠐⠀⠾⣿⣧⣜⢀⠀⣿⣿⡟⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⠻⣿⣏⣹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠋⠀⢰⡿⠛⠀⠈⠄⠀⠀⠙⠿⣿⢤⣿⣿⡇⠀⢻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⣼⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃
⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡏⠈⠏⣿⠃⠀⠀⠹⣷⣆⢀⣀⠀⠀⢀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠛⠁⠀⠉⠙⢿⡿⠿⢿⣷⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢨⡟⠁⠀⢸⣿⠀⠀⠀⠀⢀⢺⣽⣿⣷⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣀⣀⣀⣤⣿⣷⣄⣨⣽⣆⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣾⠀⠀⢠⣾⣿⠀⠀⣸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠻⣿⡿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠀⣀⣠⣤⣄⢀⣾⣿⣿⣿⡏⣰⡆⢙⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡏⢹⣿⢹⣿⣿⣿⣿⣿⣿⡆⠀⣀⠀⠀⠀⠐⠄⠤⢶⣧⠹⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⢰⣶⣾⢰⣶⣾⣿⢿⣿⡿⣷⣮⣧⢳⣶⣿⣷⣿⢾⣿⣿⣿⣷⣿⡇⠛⠿⣿⠿⠋⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠃⢸⡿⢸⣿⣿⣿⣿⣿⣿⣷⣴⣿⡄⠀⠀⠀⠠⠤⢶⣤⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡏⢸⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣇⢸⣿⣿⣿⣿⣿⡇⣿⣿⠸⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠈⠁⠀⠀⠀⢸⡇⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⢸⣿⣿⡟⣻⣿⣇⣿⣿⠀⣿⣿⡛⣿⣷⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⠀⠀⠀⠀⠘⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣽⣿⣾⣿⣿⣷⡇⠉⠉⠉⠁⠈⠉⠉⣷⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡟⠀⠐⠃⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣤⣠⡴⣫⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣴⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠇⠠⠰⠶⠖⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣸⢿⢿⠛⠋⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠁⠋⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣠⣤⣤⣤⣤⣤⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⠟⠭⠽⡿⠿⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠟⣿⠛⠁⠀⠀⢀⣀⣈⣩⣼⣦⡙⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⠿⣿⣿⢿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⠁⢸⠃⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠉⢽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣇⠀⠀⠀⠀⠲⣶⣦⣤⣶⣿⣷⣦⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⢸⣿⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠉⣿⢏⡙⢿⣇⢸⣿⣿⣿⣄⡀⠀⠀⠀⠈⠻⡏⠁⠈⣹⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⢸⡿⠀⠀⠀⠀⠀⢲⣶⣤⣤⣤⣖⠑⢶⣷⣤⣽⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⢭⣭⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣇⠀⠀⡀⠀⠀⠀⠈⠙⣻⣿⣿⣤⣼⣿⣿⣿⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣴⣿⠏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣷⠀⠀⣿⡄⠀⠀⠀⠀⠀⠂⠡⠇⢘⣿⣿⣿⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⢸⣿⠀⠀⣿⣿⠀⠀⠀⠶⣷⣄⡌⢠⢸⣿⣿⡏⢀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⠛⣻⣿⣭⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⢸⠃⠀⣾⡟⠃⠀⠠⠀⠀⠈⠛⢿⣷⣸⣿⣿⠁⠀⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⢠⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠙⠩⣿⠀⠀⠀⠽⠷⡠⣀⡀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠙⠃⠀⠈⠉⠛⣿⠛⠛⢿⣎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡴⠓⠀⠀⣾⡇⠀⠀⢀⣀⢀⣾⣸⣷⣷⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣄⣀⣠⣼⣿⣦⣠⣬⣽⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣶⠀⠀⣴⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⠻⡿⠏⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⠀⠀⣠⣤⠄⣰⣿⣿⣿⣿⠃⣼⠀⣹⣿⣿⣶⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⠁⣿⡇⢿⣿⣿⣿⣿⣿⣷⠀⢠⡀⠀⠀⠀⠐⠐⠶⠿⡌⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⢰⣶⣾⢰⣶⣾⣿⢯⣿⡿⣷⣮⡇⢷⣾⣿⣷⢿⢾⣿⣿⣿⣷⣿⠉⠹⢿⠿⠋⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣇⠈⠀⡿⠃⣾⣿⣿⣿⣿⣿⣿⣷⣾⣧⠀⠀⠀⠀⠰⠶⣶⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡟⢸⣿⣿⣿⣿⣿⡇⣿⣿⢀⢸⣿⢹⣿⣸⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⢸⣿⣧⢸⣿⣿⣿⣿⣿⡇⣿⣿⠸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠈⠀⠀⠀⠀⠟⠙⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⢸⣿⣿⡟⣻⣿⣇⣿⣿⠀⣿⣿⡛⣿⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⣿⣷⠇⠉⠉⠉⠁⠈⠉⠉⣷⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⠏⠀⠘⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⡼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣾⣿⣟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠘⡛⠩⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠈⠇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣤⣤⣤⣤⣤⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⠟⠭⠽⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠟⣿⠛⠁⠀⠀⢀⣀⣈⣉⣔⣦⡻⣿⣿⣿⣿⠆⠀⠀⠀⠀⠾⠿⠿⡿⢿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⠁⢸⠏⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣷⡜⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠃⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡆⠀⠀⠀⠐⠲⣶⣦⣶⣾⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁
⢸⣿⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠉⣿⢋⠙⢿⡇⢸⣿⣿⣷⣄⠀⠀⠀⠀⠈⢿⠍⠀⢈⣽⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⢸⡿⠀⠀⠀⠀⠀⢒⣦⣤⣤⣤⣆⠑⣾⣷⣤⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠤⢭⣭⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣇⠀⠀⡀⠀⠀⠀⠈⠙⣿⣿⣟⣤⣽⣿⣿⡟⠀⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢤⣼⣿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣷⠀⠀⣿⡄⠀⠀⠀⠀⠀⠊⢩⠆⢸⣿⣿⣿⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⢸⣿⠀⠠⣿⣿⠀⠀⠀⢾⣷⣤⡏⠀⢸⣿⣿⡇⢠⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⠋⣿⣿⣭⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀
⢸⠃⠀⣾⡟⠃⠀⠰⠀⠀⠉⠛⢷⣷⣸⣿⣿⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡋⠀⣸⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⡀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠛⢹⡟⠀⠀⠀⠽⠦⣄⣄⠀⠀⠀⡀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠁⠛⠁⠀⠉⠉⢻⣿⠛⠻⣿⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⣴⠏⠀⠀⣿⡇⠀⠀⢀⣀⣨⣯⣼⣿⣶⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣤⣤⣤⣴⣾⣿⣦⣤⣬⣧⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡧⠀⠀⣴⣿⡇⠀⢀⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⠿⠿⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠀⢤⣰⣶⠀⣰⣿⣿⣿⣿⢁⣶⢀⣽⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⢸⣿⡏⣿⣿⣿⣿⣿⣿⣷⠀⢠⠀⠀⠀⠐⠂⠒⠺⠿⢈⣿⣿⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢰⣶⣮⢰⣶⣾⣿⢿⣿⡿⣷⣮⠸⣷⣾⣿⣷⢻⢾⣿⣿⣿⣷⣿⠈⠻⢿⡟⠉⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⡆⠈⠸⡿⠃⣿⣿⣿⣿⣿⣿⣿⣶⣾⣇⠀⠀⠀⠀⠲⠶⣶⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡏⢸⣿⣿⣿⣿⣿⡇⣿⣿⠀⢸⣿⢹⣿⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⡿⢿⣿⣿⣧⠀⠀⠀⠀⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⢸⣿⣧⢸⣿⣿⣿⣿⣿⡇⣿⣿⠘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠁⠀⠀⠀⠀⠇⢙⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣼⣿⣿⢸⣿⣿⡟⣹⣿⣇⣿⣿⠀⣿⣿⡛⣿⣷⣿⣿⣿⣿⣿⠇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⣿⣷⠃⠉⠉⠉⠁⠈⠉⠉⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⠇⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣶⣤⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣰⣿⣿⠙⠛⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠙⠉⠉⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠈⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠈⠘⠊⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣤⣤⣤⣤⣤⣄⣠⣿⣼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⠟⠭⠽⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠟⣿⠋⠀⠀⠀⣀⣀⣘⣁⣀⣤⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠿⠿⠿⠿⢿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡟⠁⢸⠃⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⡝⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠨⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡀⠀⠀⠀⠘⠶⣶⣶⣶⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀
⢸⡿⠀⠀⠀⠀⠀⠀⠈⠹⠉⠉⠙⣿⢋⠻⢿⡇⣸⣿⣿⣷⣄⠀⠀⠀⠀⠉⠿⠀⠀⣉⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆
⢸⡗⠀⠀⠀⠀⠀⠳⣦⣤⣤⣴⡆⠛⣿⣦⣤⣿⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⠤⢭⣭⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⠀⡀⠀⠀⠀⠈⠛⣿⣿⣯⡤⣽⣿⣿⡏⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⢀⣿⡄⠀⠀⠀⠀⠘⠎⢹⠀⢸⣿⣿⡷⠀⢹⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃
⢸⡟⠀⢸⣿⡗⠀⠀⠰⠿⣷⣤⡁⡀⢸⣿⣿⠁⢠⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⠟⢩⣿⣯⣽⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄
⢸⠁⠀⠿⠏⠁⠀⠰⠀⠀⠈⠻⣿⡇⣾⣿⣿⠀⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⣿⣿⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠋⢹⡏⠀⠀⠀⠿⠣⣤⡄⡀⠀⢀⡀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠈⠋⠀⠀⠀⠈⣻⡟⠛⠻⣷⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⡌⠃⠀⢀⣿⠀⠀⠀⣀⣀⣸⣧⣽⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣤⣤⣤⣶⣿⣷⣦⣴⣾⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡆⠀⢀⣾⣿⡀⠀⢀⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠛⠻⠛⠙⠻⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⠀⢀⣰⣶⣠⣼⣿⣿⣿⣿⢠⣧⢀⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡏⢸⣿⢸⣿⣿⣿⣿⣿⣿⡇⠀⣄⠀⠀⠀⠀⠂⠚⠻⠷⣸⣿⡏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢰⣶⣾⢰⣶⣾⣿⢿⣿⡿⣷⣮⢸⣷⣿⣿⣶⢿⢾⣿⣿⣿⣷⣿⠈⠹⠿⠋⠈⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠸⠟⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⡄⠀⠀⠀⠀⠒⢻⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡟⢸⣿⣿⣿⣿⣿⡇⣿⣿⠀⢸⣿⢹⣿⡸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠻⠏⢿⣿⣿⡇⠀⠀⠀⢸⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣧⢸⣿⣿⣿⣿⣿⡇⣿⣿⠀⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠸⠁⢸⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⡟⣹⣿⣇⣿⣿⠀⣿⣿⡛⣿⣷⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠀⠀⠀⠀⠀⠈⠀⣸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⣿⡧⠁⢉⠉⠉⠁⠈⠉⠩⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⠃⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢀⣾⣿⣯⡭⠉⠋⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⢿⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠙⠁⠁⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠈⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠹⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢠⣤⣤⣤⣤⣤⣀⣸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⠟⠭⢽⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⢛⣿⠋⠀⠀⠀⣀⣀⢘⣁⣰⣎⠻⣿⣿⣿⡷⠀⠀⠀⠀⠰⠾⠿⠿⠿⢿⡿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡟⠀⠼⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⣿⣿⠀⠀⠀⠀⠘⢶⣶⣶⣞⢿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⠀
⢸⡿⠀⠀⠀⠀⠀⠀⠈⠹⠉⠉⠙⣿⢉⠻⣿⡇⣿⣿⣿⣧⡄⠀⠀⠀⠀⠹⠧⠀⢀⣨⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡆
⢸⡇⠀⠀⠀⠀⠐⢳⣶⣤⣤⣴⡆⠲⣿⣤⣤⡟⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠴⣿⣥⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⠀⡀⠀⠀⠀⠉⢛⣿⣿⣧⡬⣽⣿⣿⡇⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⢴⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⢠⣷⡄⠀⠀⠀⠀⠘⠈⡽⠀⢸⣿⣿⡷⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃
⢸⡇⠀⢸⣿⡇⠀⠀⠰⠿⣷⣠⠀⡄⣿⣿⣿⠀⢸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣽⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣤⡄
⠘⠀⠀⠿⠏⠁⠀⠐⠀⠀⠈⠻⣿⡆⣿⣿⡏⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢠⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣁⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠐⠉⣽⠇⠀⠀⠀⠟⠦⣤⣄⣀⠀⣀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠘⠁⠀⠀⠀⠉⣿⠛⠛⠿⡇⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠌⠁⠀⢸⣿⠀⠀⠀⣀⣀⣼⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢠⣦⣤⣴⣾⣿⣷⣤⣶⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⠄⠀⢠⣿⣿⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⡿⣿⡿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠙⠿⠋⠛⠛⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⠀⣤⣴⣶⢴⣾⣿⣿⣿⡿⢰⡇⢨⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⡇⣿⣷⢸⣿⣿⣿⣿⣿⣿⡆⠠⡆⠀⠀⠀⠈⠀⠛⠛⠇⣻⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢰⣶⣾⢰⣶⣾⣿⢯⣿⡿⣷⣮⢸⣷⣿⣿⣶⣿⢾⣿⣿⣿⣷⣷⠈⠻⠟⠋⠁⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠿⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢀⣛⣻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡟⢸⣿⣿⣿⣿⣿⡇⣿⣿⠸⢸⣿⢹⣿⣹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠻⣿⣿⢿⠀⠀⠀⠀⢸⣋⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣷⢸⣿⣿⣿⣿⣿⡇⣿⣿⠀⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠘⠈⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⡟⢹⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⣿⡇⠀⣉⠉⠉⠁⠈⠉⠩⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣿⣿⣿⠋⠀⠩⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⢷⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠈⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠈⠈⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠛⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣠⣶⣤⣤⣴⣦⣀⣼⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⠋⠭⢽⢿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⢻⡿⠋⠀⠀⠀⣀⣀⣘⣁⣰⣎⠻⣿⣿⣿⡇⠀⠀⠀⠀⠰⠿⠿⠿⠿⢿⢿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡏⠀⠼⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⡀⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣷⠀⠀⠀⠀⠙⢷⣶⣶⣟⢿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣈⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀
⢸⡟⠀⠀⠀⠀⠀⠀⠈⠩⠉⠉⠙⣿⣉⠻⣿⡇⣿⣿⣿⣧⡀⠀⠀⠀⠈⠹⠇⠀⣀⣸⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⡆
⢸⡇⠀⠀⠀⠀⠀⢱⣶⣤⣤⣴⡆⢲⣿⣤⣤⡇⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠶⣾⡅⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⠀⡄⠀⠀⠀⠉⢋⣿⣿⣧⠬⣿⣿⣿⡇⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠲⢴⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⢰⣷⡄⠀⠀⠀⠀⠘⠊⣝⠀⣹⣿⣿⡇⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁
⢸⡇⠀⢸⣿⡇⠀⠀⠰⠿⣷⣠⡁⡄⣿⣿⣿⠀⢼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡟⠉⣿⣿⣿⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣴⡆
⠘⠀⠀⠿⠋⠁⠀⠐⠀⠀⠈⠛⢷⣆⣷⣿⡇⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡁⠀⣸⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠉⣿⠃⠀⠀⠀⠻⠲⢤⡄⡀⠀⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠈⠁⠀⠀⠀⢹⣿⠉⠙⠿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠁⠀⢸⣟⠀⠀⠀⣤⣄⣺⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢰⣶⣶⣶⣾⣿⣷⣶⣶⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⠀⢠⣿⣷⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⢿⣿⡿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠈⠙⠛⠉⠙⠛⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠐⣤⣴⡐⣠⣿⣿⣿⣿⡟⢰⡆⢨⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠀⣿⡇⣿⣿⣿⣿⣿⣿⣿⠀⢰⡀⠀⠀⠀⠉⠉⠙⠛⠂⣿⡿⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢰⣶⣾⢰⣶⣾⣿⣯⣿⡿⣷⣮⢹⣷⣿⣿⣶⣿⢾⣿⣿⣿⣷⡇⠉⠻⠟⠋⠈⠈⠹⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢈⣛⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⡇⣿⣿⠘⢸⣿⢹⣿⣹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⣿⡿⣿⠀⠀⠀⠀⣿⢻⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣷⢸⣿⣿⣿⣿⣿⡇⣿⣿⠀⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡃⠈⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⡟⢹⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡂⠀⠀⠀⠀⠀⣁⣠⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⣿⡅⠀⣩⠉⠉⠁⠈⠉⢩⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣰⣿⣿⣷⠆⠂⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠷⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠈⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠁⠃⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣴⣶⣶⣦⣶⣤⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⠫⠽⠶⠿⢿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⢻⡟⠉⠀⠀⠀⣀⣀⣉⣥⣰⣎⠻⣿⣿⣿⡇⠀⠀⠀⠀⠸⠿⠿⠿⠿⣿⠿⢿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡏⠀⡞⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣧⠀⠀⠀⠀⠛⣿⣶⣾⡿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠁⠀⠀
⢸⡟⠀⠀⠀⠀⠀⠀⠈⠙⠊⠉⢙⡿⣉⠹⢿⡀⣿⣿⣿⣦⡀⠀⠀⠀⠈⠻⠆⠀⣀⣼⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⡆
⢸⡇⠀⠀⠀⠀⠀⠻⣶⣶⣦⣶⡅⠒⣿⣤⣶⡇⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⠲⣶⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⠀⡀⠀⠀⠀⠈⢩⣿⢿⣣⠤⣽⣿⣿⡃⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠲⠾⠿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⢸⣿⡀⠀⠀⠀⠀⠘⠈⡽⠀⣿⣿⣿⠇⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠁
⢸⡇⠀⣸⣿⡇⠀⠀⠘⠻⣿⣤⠀⠀⣿⣿⡿⠀⢼⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠟⢀⣿⣿⣾⣿⣏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣴⡆
⠈⠀⠀⠿⠁⠀⠀⠘⠀⠀⠈⠛⢿⢤⣿⣿⡇⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⡀⠀⣾⢿⣿⣿⣿⣿⣆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢘⠉⣿⠁⠀⠀⠐⠛⢧⣤⣄⣀⣀⣄⢀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠉⠀⠀⠀⠀⣹⣏⠉⠙⢿⠌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠰⠈⠀⠀⣠⡇⠀⠀⠠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣶⣶⣶⣾⣿⣿⣷⣶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠀⠀⢰⣿⣧⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢻⣿⡿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠛⠋⠈⠙⣛⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⠐⣦⣶⣿⣦⣿⣿⣿⣿⡇⢲⡆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠹⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⠀⣲⡀⠀⠀⠀⠁⠉⠙⠛⢨⣿⡏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢰⣶⣾⢰⣶⣾⣿⣯⣿⡿⣷⣦⢻⣷⣿⣿⣶⣿⢾⣿⣿⣿⣷⡇⠀⠛⠛⠁⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡏⢸⣿⣿⣿⣿⣿⡇⣿⣿⠸⢹⣿⢹⣿⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠛⢻⣿⠿⠟⠀⠀⠀⠀⡿⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠁⠸⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⡟⢹⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⣿⠅⠀⡭⠉⠉⠁⠈⠉⢩⣷⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⢀⡀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣴⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠸⢿⡿⠏⠉⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⠷⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠈⢙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠃⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣶⣶⣶⣶⣶⣦⣤⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⠿⠋⠵⠶⠾⢿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠟⢻⡟⠉⠀⠀⢀⣀⣀⣉⣥⣴⣎⠻⣿⣿⣿⠇⠀⠀⠀⠀⠻⠛⠻⠟⠻⡿⠿⠿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠟⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣧⠀⠀⠀⠀⠛⢿⣿⣿⠿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠀⠀⠀
⢸⡏⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢹⡯⡉⠹⢿⡀⣿⣿⣿⣦⠀⠀⠀⠀⠈⠻⠂⠀⣀⣾⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⡆
⢸⡇⠀⠀⠀⠀⠈⠿⣷⣶⣶⣶⡅⢻⣿⣤⣾⡇⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠒⢲⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⠀⡄⠀⠀⠀⠈⠹⠿⢿⣳⠦⣿⣿⣿⠁⢘⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠲⠾⠟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⢸⣿⡄⠀⠀⠀⢀⠘⠈⡝⠀⣿⣿⣿⠃⢨⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠁
⢸⠇⠀⣸⣿⡇⠀⠀⠘⠻⣷⣤⢀⠀⣿⣿⡏⠀⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⠋⣰⣿⣿⣾⣿⡍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣶⡆
⠈⠀⠘⠿⠁⠀⠀⠉⠀⠀⠈⠛⢿⢠⣿⣿⠃⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⣯⠀⠀⡿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣠⣤⣌⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠨⠀⡿⠀⠀⠀⠈⠙⢱⣆⣠⣄⣤⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠁⠀⠀⠀⠀⣹⣏⠉⠙⢻⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣐⠘⠀⠀⣠⡇⠀⠀⢠⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠀⠀⣴⣿⣧⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⢹⣿⢻⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠈⠛⢋⠉⢙⣹⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⠘⢤⣶⣞⣶⣿⣿⣿⣿⠇⢸⡆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠹⢸⣿⠈⣿⣿⣿⣿⣿⣿⣷⣀⣺⡀⠀⠀⠀⠀⢉⣉⡙⢺⣿⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢰⣶⣾⣿⣿⣿⡿⣷⣦⢻⣷⣿⣿⣶⣿⢶⣿⣿⣿⣷⡇⠁⠋⠉⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣏⢸⣿⣿⣿⣿⣿⡇⣿⣿⠸⢸⣿⢹⣿⣸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠟⢻⣿⠿⡇⠀⠀⠀⠰⡏⢿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠁⢘⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⡟⢹⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⣿⠁⠀⠭⠉⠉⠁⠈⠉⢩⣷⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⣀⡀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣾⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢺⡿⡿⠓⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⠷⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠈⢉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠃⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣴⣶⣶⣶⣶⣤⣤⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⠟⠩⠶⠖⠾⢿⢿⡿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠟⢹⡟⠁⠀⠀⢀⣀⣄⣩⣥⣴⣎⠻⣿⣿⣿⠇⠀⠀⠀⠀⠺⠛⠻⠟⠻⡿⠿⠿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠟⠁⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣇⠀⠀⠀⠀⠛⢿⣿⢿⠿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⠀⠀⠀
⢸⡏⠀⠀⠀⠀⠀⠀⠀⠓⠂⠀⢹⡏⡉⠹⢿⣠⣿⣿⣿⣦⠀⠀⠀⠀⠈⠻⠂⠀⣀⣾⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⡇
⢸⡃⠀⠀⠀⠀⠀⠳⣷⣶⣶⣾⡁⢻⣿⣶⣾⡇⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠒⢲⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡆⠀⢀⡄⠀⠀⠀⠈⠱⠿⢿⣱⠢⣿⣿⣿⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠲⠿⠟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⢸⣿⡀⠀⠀⠀⢀⠀⠉⠈⠀⣿⣿⣿⠃⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠁
⢸⠇⠀⣼⣿⡇⠀⠀⠘⠻⣷⣬⢠⠀⣿⣿⡇⠀⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡿⠋⢠⣿⣿⣿⣿⡍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⢠⣶⡆
⠈⠀⠘⠛⠀⠀⠀⠁⠀⠀⠈⠛⢿⢰⣿⣿⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⣧⠀⠀⠿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⣄⣌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠈⠀⡟⠀⠀⠀⠈⠙⣢⡤⣤⣠⣤⣄⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠀⠀⠀⣽⣅⠈⠙⢻⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠊⠈⠀⠀⣤⡇⠀⠀⢠⣷⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣶⣶⣶⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠀⠀⣶⣿⣧⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡿⢹⣿⢿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠈⠙⢁⡉⢉⣹⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⠘⣠⣶⢞⣴⣿⣿⣿⣿⠃⢺⡄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠇⢸⣿⠈⣿⣿⣿⣿⣿⣿⣧⣀⣶⠀⠀⠀⠀⠀⢉⣉⡙⣼⣿⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢰⣶⣾⣿⣿⣷⡿⣷⣦⢻⣷⣿⣿⣶⣿⢶⣿⣿⣿⣷⡇⠀⠋⠉⠁⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡆⠀⠘⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣏⢸⣿⣿⣿⣿⣿⡇⣿⣿⢸⢹⣿⢹⣿⣸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⢻⠟⠛⠇⠀⠀⠀⢸⠇⢹⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢈⠀⢸⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⡟⢸⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⣿⠁⠀⠍⠉⠉⠁⠈⠉⢩⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⣀⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢠⣾⣿⣿⠟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠿⠿⠋⠉⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⠷⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠈⢩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠂⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣶⣶⣶⣶⣶⣦⣤⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⠟⠑⠒⠲⠾⡿⢿⡿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠛⣹⡟⠁⠀⠀⢀⣤⣤⣩⣤⣴⣎⠻⣿⣿⣿⠇⠀⠀⠀⠀⠛⠛⠛⠟⠿⡿⠿⠿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠃⠐⠟⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣧⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡇
⢸⣿⠀⠂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣇⠀⠀⠀⠀⠙⣿⣿⠿⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⣏⡍⠹⢿⣰⣿⣿⣿⣦⠀⠀⠀⠀⠀⠛⠀⠀⢤⣿⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⡆
⢸⠁⠀⠀⠀⠀⠀⠷⣷⣶⣶⣮⡈⢻⣿⣶⣾⠃⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠒⢻⣶⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡆⠀⢠⡄⠀⠀⠀⠈⠹⠿⣿⣴⠲⣿⣿⣿⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠓⠿⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⢸⣿⠀⠀⠀⢀⣀⡈⢁⠈⠀⣿⣿⡿⠁⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠁
⢸⠃⢀⣼⣿⠀⠀⠀⠚⠻⢷⣾⣠⠀⣿⣿⡇⠀⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠿⠃⣼⣿⣿⣿⣿⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⣴⣿⡆
⠀⠀⠘⠛⠀⠀⠀⠁⠀⠀⠈⠙⠿⢸⣿⣿⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢟⣧⠀⠰⢿⢿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣤⣤⣌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠐⣀⡏⠀⠀⠀⠈⠉⢦⢤⣤⣤⣤⣄⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠀⠀⠀⣿⣁⠈⠙⢷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣆⡂⠈⠀⠀⣴⡇⠀⠀⢰⣶⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⣿⣶⣶⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡟⢀⠀⣾⣿⣧⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡿⢹⣿⢻⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠈⠙⢁⣉⣉⣹⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⠘⣤⣾⡝⣾⣿⣿⣿⣿⠃⢸⡄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠇⢸⣿⢸⣿⣿⣿⣿⣿⣿⣧⣀⣷⠀⠀⠀⠀⠀⣈⣉⡑⣿⣿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢰⣶⣾⣿⣿⣷⡿⣷⣦⢻⣷⣿⣿⣶⣿⢾⣿⣿⣿⣷⡃⠀⠛⠋⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣏⢸⣿⣿⣿⣿⣿⡇⣿⣿⢸⢹⣿⢹⣿⣸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⢻⠟⠛⠃⠀⠀⠀⢸⡇⢹⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⣿⢿⣿⡇⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢨⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⡟⢸⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⣯⠁⠀⠏⠉⠉⠁⠈⠉⢭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⢀⣀⣀⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣰⣿⣿⣟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡘⠿⠟⠓⠉⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⠷⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠈⢩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣶⣶⣶⣶⣶⣦⣤⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⠟⠑⠒⠲⠿⡿⠿⡿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠛⣹⡟⠁⠀⠀⢀⣤⣄⣭⣤⣼⣌⠻⣿⣿⣿⠃⠀⠀⠀⠀⠚⠛⠛⠛⠻⡿⠿⠿⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠃⠐⠋⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡇
⢸⣿⠀⠂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⢠⣿⣿⣇⠀⠀⠀⠀⠙⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⡀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⡏⡌⠛⢿⣸⣿⣿⣿⣦⠀⠀⠀⠀⠀⠛⠀⠀⢴⣿⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡆
⢸⠁⠀⠀⠀⠀⠀⠷⣶⣶⣶⣯⡈⢻⣷⣶⣾⠁⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⠒⢺⣶⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⢠⡄⠀⠀⠀⠈⠹⡿⣿⡖⠲⣿⣿⣿⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠓⠿⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⢸⣿⠀⠀⠀⢀⣀⠘⢀⠃⠀⣿⣿⡿⠁⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠉⠁
⢸⠃⢀⣼⣿⠁⠀⡀⠛⠻⢷⣤⣀⢀⣿⣿⡇⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⠁⣼⣿⣿⣿⣿⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣴⣿⡆
⠀⠀⠘⠛⠀⠀⠀⠁⠀⠀⠈⠙⠿⢼⢿⣿⠀⠀⠘⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢛⣧⠀⢠⢿⢿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⣤⣌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢐⡏⠀⠀⠀⠈⠉⢔⠤⣄⣤⣤⣄⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠀⠀⠀⣿⣄⠈⠙⢧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⡀⠀⠀⢀⣼⡇⠀⠀⢰⣶⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠐⣿⣾⡶⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡗⠀⠀⣿⣿⣧⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡏⣿⣿⢻⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠈⠉⢁⣀⣉⣽⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⠀⢤⡶⠍⣾⣿⣿⣿⣿⠁⢸⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠇⢹⣿⢸⣿⣿⣿⣿⣿⣿⣧⣀⣷⠀⠀⠀⠀⠀⢈⣉⡁⣿⣿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢰⣶⣾⣿⣿⣷⡿⣷⣦⢻⣷⣿⣷⣶⣿⢶⣾⣿⣿⣷⠃⠀⠙⠉⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣇⢸⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⢹⣿⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⢻⠟⠛⠃⠀⠀⠀⢸⠀⢹⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠉⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⣿⢿⣿⡇⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠨⠀⢸⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⡟⢸⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⣯⠁⠀⠏⠉⠉⠁⠈⠉⢩⣷⣿⣿⣿⣿⣿⣿⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⢀⣀⣠⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢀⣼⣿⣿⡿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠚⢿⠟⠛⠁⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢛⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠈⠀⠈⢩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣶⣶⣶⣶⣶⣤⣴⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡿⠛⠑⠒⠲⠿⡿⢿⡿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠛⣹⠋⠀⠀⠀⢠⣤⣤⣥⣤⣾⣌⢻⣿⣿⣿⠀⠀⠀⠀⠀⠛⠛⠛⠛⠻⡿⠿⠿⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠁⠀⠋⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⣰⣧⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡇
⢸⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⡆⠀⠀⠀⠈⠛⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀
⢸⠃⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⢸⣥⡌⠻⢿⢸⣿⣿⣿⣦⠀⠀⠀⠀⠙⠛⠀⠀⣴⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡇
⢸⠁⠀⠀⠀⠀⠀⢷⣶⣶⣶⣯⠈⢻⣷⣶⣾⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⠒⢲⣶⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠀⠀⢰⡀⠀⠀⠀⠉⠺⡿⣿⡖⢺⣿⣿⣿⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠓⠿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠀⠀⣾⣷⠀⠀⠀⢀⣀⠊⢱⠃⢨⣿⣿⡿⠀⣸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠉⠁
⠸⠀⢀⣿⣿⠀⠀⡀⠋⠻⢷⣆⡀⢸⣿⣿⠃⠐⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠿⢁⣼⣿⣿⣿⣿⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣴⣿⡆
⠀⠀⠘⠛⠀⠀⠀⠁⠀⠀⠈⠙⡟⣼⣿⣿⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⣥⠄⠸⢿⣿⣿⣿⣿⣷⡬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣴⠂⠁⢰⠇⠀⠀⠀⠈⠻⣶⢤⣤⣤⣴⣄⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠀⠀⢀⣿⡁⠉⠛⠇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣸⣤⡂⠀⠀⢀⣼⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠰⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⡀⠀⣴⣿⣿⣿⡇⠀⠀⣿⣿⣇⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡏⣿⣿⢿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠈⠛⢁⣀⣉⣽⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣤⣿⣏⣾⣿⣿⣿⣿⠁⢺⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠇⣿⡿⢸⣿⣿⣿⣿⣿⣿⣧⣀⣷⠀⠀⠀⠀⠁⠈⠉⣳⣿⣿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢰⣶⣾⣿⣿⣷⡿⣷⣦⢿⣷⣿⣷⣶⣿⢾⣿⣿⣿⣷⠃⠀⠙⠉⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣧⢸⣿⣿⣿⣿⣿⡇⣿⣿⢸⢹⣿⢹⣿⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⢻⠟⠛⠃⠀⠀⠀⢼⠈⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⣿⢻⣿⡇⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠉⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⡏⢸⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠠⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⡯⠁⠀⠏⠉⠉⠁⠈⠉⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⣀⣠⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⢀⣾⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⢿⠟⠛⠁⠀⠀⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠟⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠈⠽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠘⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢰⣶⣶⣶⣶⣶⣤⣼⣷⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡿⠛⠓⠒⠶⢿⡿⢿⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⠋⣼⠋⠀⠀⠀⣠⣤⣌⣥⣬⣷⡝⢿⣿⣿⡿⠀⠀⠀⠀⠀⠛⠛⠛⠛⢿⠿⠿⠿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡿⠁⠨⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡎⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡇
⢸⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡄⠀⠀⠀⠘⠻⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⢀⠀⠀
⢸⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣿⣡⠉⠻⣇⢸⣿⣿⣷⡄⠀⠀⠀⠀⠘⠓⠀⢀⣴⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣾⣿⡆
⢸⠀⠀⠀⠀⠀⠈⢿⣷⣶⣶⣧⠈⣾⣷⣶⣿⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠒⠒⣲⣦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠀⠀⢰⠀⠀⠀⠀⠉⢿⢿⣯⡖⢺⣿⣿⡇⠀⣻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠘⠺⠿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠀⠀⣿⣧⠀⠀⠀⢀⣀⠉⡘⠁⢸⣿⣿⠟⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠃
⠘⠀⢠⣿⠿⠀⠀⠀⠛⠿⣧⣇⡄⢸⣿⣿⠀⠸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⢅⣾⣿⣿⣿⣷⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢶⣶⡆
⠀⠀⠘⠋⠀⠀⠈⠀⠀⠀⠉⠻⠧⣿⣿⡇⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⣤⠀⢼⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⣤⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⢸⠃⠀⠀⠀⠉⠙⡤⣠⣤⣤⣤⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⢠⣯⡈⠉⠛⠇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣠⣄⠀⠁⠀⢠⣾⠀⠀⠀⣰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠲⣿⣷⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⡀⢀⣼⣿⣿⣿⠆⡀⠰⣿⣿⣄⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⡏⣿⡟⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠈⠋⣀⣈⣩⣽⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣥⣿⣇⣾⣿⣿⣿⡿⠀⢷⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠃⣿⡇⢸⣿⣿⣿⣿⣿⣿⣇⣀⣆⠀⠀⠀⠀⠁⠉⠙⣣⣿⣟⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢰⣾⣾⣿⢯⣶⡿⣷⣮⢿⣷⣿⣷⣶⢿⢾⣿⣿⣿⣷⠀⠈⠉⠉⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢈⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⢸⢻⣿⢹⣿⣸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠙⠉⣿⠟⠛⠀⠀⠀⠀⣿⠈⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⣿⢻⣿⡇⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠇⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⡇⢸⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⡏⠁⠰⠉⠉⠉⠁⠈⠉⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⣠⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣾⣿⡿⠿⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠿⡿⡟⠃⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠏⠶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠂⠀⢀⡀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢻⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠈⠀⠉⡽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠙⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢰⣶⣶⣶⣶⣦⣤⣼⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠿⠋⠓⠒⠾⢿⠿⣿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⢋⡾⠉⠀⠀⠀⣤⣤⣬⣥⣬⣧⡙⣿⣿⣿⡿⠀⠀⠀⠀⠐⠛⠛⠛⠛⢿⠿⠿⠿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡟⠀⠘⠁⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣇⠀⠀⠀⠀⢀⠀⠀⠀⠀⣸⡆⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡇
⢸⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡅⣼⣿⣿⡄⠀⠀⠀⠈⠻⣿⡿⠽⠿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠀⢀⠀⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢀⣿⣠⠉⢿⡇⣿⣿⣿⣷⡆⠀⠀⠀⠀⠐⠓⠀⢠⣴⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⡆
⠈⠀⠀⠀⠀⠀⠐⣾⣶⣶⣾⡅⠙⢿⣶⣶⡟⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠒⠒⣶⡦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⠀⠀⣠⠀⠀⠀⠀⠉⢿⢿⣷⠒⣿⣿⣿⡇⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠘⠷⠿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⠀⠀⣿⣇⠀⠀⠀⣀⡈⠉⡞⠀⣹⣿⣿⠇⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠃
⠈⠀⣠⣿⡿⠀⠀⠈⠛⠿⣦⡄⡂⣹⣿⣿⠀⢸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⢠⣿⣿⣿⣿⣧⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠠⣶⣶⡆
⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠉⠻⢷⣿⣿⡇⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢋⣤⠀⣾⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣤⣤⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠠⠀⣾⠁⠀⠀⠀⠉⢁⣤⣠⣠⣤⣤⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡈⠉⠻⡆⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⣠⣿⠀⠀⠀⣶⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⣀⡀⠀⢀⣼⣿⣿⣿⠂⡀⢸⣿⣿⣄⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⠛⣿⡟⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠈⢛⣌⣈⣩⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣯⣭⢷⣿⣿⣿⣿⡏⠀⡧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠁⣿⡇⢻⣿⣿⣿⣿⣿⣿⣆⣐⡆⠀⠀⠀⠀⠀⠉⠙⣿⣿⡏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢰⣾⣾⣿⢯⣶⡿⣷⣮⢿⣷⣿⣷⣶⢿⢶⣿⣿⣿⣷⠀⠉⠋⠁⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠁⠁⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠐⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⢸⢻⣿⢹⣿⣸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⣿⠛⠛⠀⠀⠀⠀⡿⠈⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢨⢸⣿⣿⢸⣿⣿⣿⢹⣿⡇⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠃⠀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⡅⢸⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠄⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⡏⠁⠐⠉⠉⠉⠁⠈⠉⣽⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣀⣀⣄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⡏⠃⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠏⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣴⣿⣿⡇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠙⢿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠈⠀⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢴⣶⣶⣶⣶⣦⣤⣼⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠟⠓⠒⠛⠿⣻⡻⢿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠟⢡⡟⠁⠀⠀⢀⣤⣤⣬⣤⣬⣧⡙⣿⣿⣿⡟⠀⠀⠀⠀⠘⠛⠛⠛⠻⢿⠿⠿⠿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡏⠀⠘⠁⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡄⠀⢀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡇
⢸⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡀⠀⠀⠀⠈⠻⣿⡯⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⢀⠀⠁
⠘⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⢸⢏⣄⠹⢿⡄⣿⣿⣿⣷⡄⠀⠀⠀⠀⠘⠃⠀⢠⣼⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⡆
⠈⠀⠀⠀⠀⠀⠰⣾⣶⣶⣾⡄⢙⣿⣶⣾⡇⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠒⠒⣶⡦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣤⠀⠀⠀⠀⠙⠿⢿⣷⠓⣿⣿⣿⡇⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠾⠟⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⠀⢰⣿⡆⠀⠀⢀⣀⡘⠁⠟⠀⣿⣿⣿⠃⢀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠃
⠈⠀⣼⡿⡇⠀⠀⠈⠙⢷⣴⣠⠀⣿⣿⡗⠀⢺⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡿⠟⣰⣿⣿⣿⣿⣆⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠠⣶⣶⡆
⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠉⢻⢱⠿⣿⠇⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣩⡦⠀⣿⣿⣿⣿⣿⣿⣆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠆⠠⠀⡞⠀⠀⠀⠀⠉⢡⣤⣤⣤⣤⣦⣀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠈⠀⠀⠀⠀⣼⣇⠈⠉⠻⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠉⠀⠀⣴⡇⠀⠀⠀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⣀⣀⠀⣠⣾⣿⣿⡷⢀⠀⢺⣿⣷⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⠛⣿⡟⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠉⢹⣀⣈⣭⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣷⣿⣴⣿⣿⣿⣿⠇⠘⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠀⣿⡇⣿⣿⣿⣿⣿⣿⣿⣄⣰⡄⠀⠀⠀⠀⠈⠉⠙⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢰⣾⣾⣿⢯⣶⡿⣷⣮⢿⣷⣿⣶⣶⣿⢾⣿⣿⣿⣷⠀⠉⠉⠁⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠋⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⣿⣿⢿⣿⡇⣿⣿⢸⢻⣿⢹⣿⣹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⣿⠛⠛⠀⠀⠀⠀⣏⠸⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠈⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢈⢸⣿⣿⢸⣿⣿⡟⢸⣿⡇⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢁⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠸⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⢸⣿⣿⢸⣿⣿⡅⢸⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⠍⠁⠐⠉⠉⠉⠀⠈⠉⣽⣿⣿⣿⣿⣿⣿⣷⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣠⡄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⡏⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠏⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⢿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠠⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠃⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣴⣶⣶⣶⣶⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡿⠛⠑⠚⠟⠛⣿⠻⠿⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠟⢱⡏⠀⠀⠀⢠⣤⣤⣤⣦⣼⣦⡹⣿⣿⣿⡇⠀⠀⠀⠀⠘⠛⠛⠛⠛⢿⠿⠿⠿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠃⠀⠊⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⢀⣾⣄⠀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡇
⢸⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠀⠀⠀⠀⠉⠻⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠸⡇⡄⠙⢿⡐⣿⣿⣿⣷⡄⠀⠀⠀⠀⠘⠃⠀⢠⢼⡯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠢⣿⣶⣶⣯⠄⢙⣿⣶⣿⠇⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠚⣷⡆⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⡄⠀⠀⠀⠀⠘⡟⣿⣾⠒⣿⣿⣿⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠺⠛⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⡄⠀⠀⢀⣀⠈⢡⠃⠀⣿⣿⡿⠁⢠⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⢿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠙⠃
⠀⠀⣼⡿⠇⠀⠀⠈⠙⢧⣤⣰⠀⣿⣿⡇⠀⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⠿⠃⣼⣿⣿⣿⣿⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠠⢾⣶⡆
⠀⠀⠛⠁⠀⠀⠀⠀⠀⠈⠙⠿⢼⠿⣿⠀⠀⠈⢻⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠛⣡⠄⢰⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣦⣤⣬⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠄⠀⡏⠀⠀⠀⠈⠉⡥⠆⣠⣠⣤⣤⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⣿⣅⠉⠙⢻⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⢀⣴⡇⠀⠀⢐⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠰⢿⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⣀⡀⠀⣰⣿⣿⣿⡟⢀⠀⣿⣿⣧⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⢹⣿⡟⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠙⣁⣀⣉⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢺⣯⡳⣼⣿⣿⣿⣿⠁⠘⡄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠸⣿⡇⣿⣿⣿⣿⣿⣿⣷⣀⣲⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣦⢰⣿⣾⣿⢯⣶⡿⣷⣮⣿⣷⣿⣶⣶⣿⢶⣿⣿⣿⣶⠀⠈⠉⠁⠀⠀⠈⡿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠁⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠒⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⣿⣿⢸⣿⡇⣿⣿⢹⢿⣿⢻⣿⣹⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠸⡿⠙⠁⠀⠀⠀⢰⡇⠸⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⢸⣿⣿⡏⢸⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⢸⣿⣿⢸⣿⣿⡄⢸⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⠉⠁⠂⠉⠉⠉⠀⠈⢩⣽⣿⣿⣿⣿⣿⣿⣧⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣠⣤⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣼⣿⣿⣿⡯⠀⠁⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠃⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠩⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣶⣶⣶⣶⣶⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡿⠋⠑⠚⠟⢟⣟⠿⡿⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠋⣱⠋⠀⠀⠀⢠⣤⣤⣵⣤⣵⣌⠻⣿⣿⣿⡇⠀⠀⠀⠀⠘⠛⠛⠛⠛⢿⠿⠿⠿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠁⠀⠋⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⡆⠀⠀⠀⠀⣀⠀⠀⠀⢀⣿⡀⠀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡇
⢘⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣷⠀⠀⠀⠀⠉⠻⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⢀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠸⠣⡄⠛⢿⠸⣿⣿⣿⣷⡄⠀⠀⠀⠀⠘⠃⠀⢠⣾⠏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⡆
⠀⠀⠀⠀⠀⠈⠰⣿⣶⣾⣯⠈⢻⣷⣾⣿⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⢚⣷⡦⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⡄⠀⠀⠀⠈⠸⣟⣿⡞⢺⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠺⠟⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⡀⠀⠀⣀⣀⠈⠡⠃⢸⣿⣿⡟⠀⢸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠙⠃
⠀⢀⣼⣿⠃⠀⠀⠉⠻⣧⣤⣔⢨⣿⣿⠇⠐⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⠿⢃⣾⣿⣿⣿⣷⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠠⢾⣿⡆
⠀⠈⠛⠀⠀⠀⠁⠀⠀⠈⠙⡿⢼⠿⣿⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢛⣡⠀⢸⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣦⣤⣬⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠄⢀⡏⠀⠀⠀⠈⢉⡴⡄⣀⣤⣤⣦⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠀⠀⢨⣯⡈⠙⠻⠇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⢀⣾⡇⠀⠀⢐⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠸⢿⣿⣾⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⣀⡀⠀⣴⣿⣿⣿⡟⢀⠀⣿⣿⣧⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⢹⣿⡟⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠈⠋⣁⣉⣉⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢺⣧⠞⣼⣿⣿⣿⣿⠁⠸⡄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡇⠘⢸⣿⠇⣿⣿⣿⣿⣿⣿⣧⣀⣆⠀⠀⠀⠈⠉⠉⠙⢳⣿⣟⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣦⢰⣿⣾⣿⢯⣶⡿⣷⣮⣿⣷⣿⣶⣶⣿⢾⣿⣿⣿⣶⠀⠈⠙⠁⠀⠀⠈⡿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⣿⣿⢸⣿⡇⣿⣿⢹⢿⣿⢹⣿⣻⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠸⡿⠛⠋⠀⠀⠀⢸⠧⢸⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⢸⣿⣿⠇⢸⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⣤⣼⣿⣿⣿⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⢸⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢠⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⠉⠁⠂⠉⠉⠉⠁⠈⢩⣽⣿⣿⣿⣿⣿⣿⣧⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⣤⣤⣤⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣾⣿⣿⣿⡏⠀⠙⣿⣿⠟⠉⠙⠛⠁⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠁⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣼⣿⣿⣿⣿⡇⠀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠻⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠩⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠃⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣶⣶⣶⣶⣶⣦⣤⣿⣾⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡿⠋⠐⠚⠟⢟⣟⠿⡿⢿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡿⠋⣼⠋⠀⠀⠀⢠⣤⣤⣥⣤⣽⣌⠻⣿⣿⣿⡇⠀⠀⠀⠀⠚⠛⠛⠛⠛⢿⠿⠿⠿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠁⠀⠋⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⡆⠀⠀⠀⠀⢀⠀⠀⠀⢠⣿⡀⠀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⠀⠀⠀⠀⠉⠿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠠⠀⠀⠉⠀⢀⠾⢡⡀⠛⣷⢸⣿⣿⣿⣷⡄⠀⠀⠀⠀⠘⠂⠀⢠⣾⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠺⣿⣶⣾⣧⠈⢿⣷⣾⣿⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⢚⣷⡦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢠⡄⠀⠀⠀⠀⠹⣿⣿⡞⢺⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠛⠛⠛⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣾⣿⠀⠀⠀⣀⣀⠉⠸⠃⢸⣿⣿⡟⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠈⠙⠃
⠀⢀⣾⣿⠀⠀⠀⠉⠻⣧⣅⡄⢸⣿⣿⠇⠐⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣰⣾⣿⣿⣿⣏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠠⢾⣿⡆
⠀⠘⠛⠀⠀⠀⠁⠀⠀⠈⠙⡟⣾⢿⣿⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠋⣤⠀⣾⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣨⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠁⢸⠇⠀⠀⠀⠈⠉⡴⡆⢀⣠⣤⣤⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⠀⠁⣨⣏⠉⠛⠿⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣠⣴⣤⡀⠀⠀⢠⣾⠀⠀⠀⢰⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢶⣶⣶⣶⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⣀⡀⠀⣴⣿⣿⣿⠇⡀⠐⣿⣿⣧⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⢹⣿⡟⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠘⢛⡈⠉⣙⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣴⣾⣿⣿⣿⣿⠀⠻⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠸⢸⣿⠇⣿⣿⣿⣿⣿⣿⣇⣐⡄⠀⠀⠀⠉⠉⠙⠛⣿⣿⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢰⣿⣾⣿⢧⣶⡿⣷⣮⣿⣷⣷⣶⣶⣿⢾⣿⣿⣿⣶⠀⠉⠋⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠰⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⣿⣿⢸⣿⡇⣿⣿⢹⢿⣿⢹⣿⣻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠘⡿⠉⠋⠀⠀⠀⢰⠇⢼⣿⣿⣿⣿⣿⠿⢻⡆⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⢸⣿⣿⠇⢸⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⡇⠀⣠⣷⡀⢲⡇⡄⠘⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣸⣿⣿⢸⣿⣯⡄⢺⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡆⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠋⠀⠻⡿⠃⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⡯⠉⠁⠂⠉⠉⠉⠀⠈⢩⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣽⣿⣿⣿⡏⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿⣿⣿⡇⢸⣿⠟⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠀⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣼⢿⣅⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⠹⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⢨⢻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠃⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣶⣶⣶⣶⣶⣦⣤⣿⣾⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⣿⠟⠋⠒⠛⠛⢛⡟⢿⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡿⠉⣼⠁⠀⠀⠀⣤⣤⣤⣶⣶⣷⡈⢿⣿⣿⣿⡇⠀⠀⠀⠀⠘⠛⠛⠛⠛⣿⠿⠿⠿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⠁⠀⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣧⠀⠀⠀⠀⠙⠻⣿⡿⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣁⠀⢀⠈⠁
⠀⠀⠀⠀⠀⢀⠀⠈⠁⠀⠀⢿⢤⠈⠻⣇⢸⣿⣿⣿⣷⡄⠀⠀⠀⠀⠘⠂⠀⠤⣾⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⡆
⠀⠀⠀⠀⠀⠘⢿⣿⣶⣾⡥⠘⢻⣷⣾⣿⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⢚⣷⠆⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢠⡀⠀⠀⠀⠀⢻⢻⣷⡟⢺⣿⣿⣧⠀⢹⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠛⠻⠛⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⠀⠀⠀⣀⣠⠁⡜⠀⢸⣿⣿⠏⠀⣸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠈⠙⠃
⠀⢠⣿⢿⠀⠀⠀⠉⠻⣦⣥⡆⢸⣿⣿⠂⠘⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠿⠟⣼⣿⣿⣿⣿⡍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠠⢾⣿⡆
⠀⠘⠋⠀⠀⠀⠀⠀⠀⠈⢻⠇⡿⢿⡇⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⢁⡄⢀⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣤⣄⣼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠠⠁⢸⠁⠀⠀⠀⠉⢉⡵⡀⢂⣠⣤⣦⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⠀⠀⠀⠀⣽⡉⠉⠛⠷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣠⣤⣠⡀⠀⠀⢠⣿⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠠⣶⣶⣶⣾⣿⣿⣶⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⠀⢀⣼⣿⣿⣿⠃⡀⠰⣿⣿⣆⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢻⣿⡿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠙⢉⠉⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣡⣿⣿⣿⣿⡿⠀⠳⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⡆⠘⢸⣿⠃⣿⣿⣿⣿⣿⣿⣤⣰⣠⡄⠀⠈⠉⠉⣻⢷⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢰⣿⣾⣿⢣⣶⡿⣷⣮⣿⣷⣷⣶⣷⣿⢾⣿⣿⣿⣶⠀⠉⠛⠀⠀⠀⠈⡿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⠉⣿⣤⣶⢾⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⣿⡟⢸⣿⡇⣿⣿⢹⢿⣿⢹⣿⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠹⡿⠛⠋⠀⠀⠀⠀⠇⢜⣿⣿⣿⣿⡿⠿⠾⢿⣿⣇⠙⠉⠁⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢸⣿⣿⢸⣿⣿⠃⢸⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣴⣶⣾⣿⣿⣿⣯⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣼⣿⣿⢸⣿⣧⡄⢺⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡆⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⡏⠉⠁⠀⠉⠉⠉⠀⠈⢭⣿⣿⣿⣿⣿⣿⣿⡅⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣀⣀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⣿⣿⣿⣷⠈⣿⣿⣿⣿⣶⣤⣠⣺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣷⠀⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠈⠹⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢨⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠃⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣷⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠠⣶⣶⣶⣶⣶⣦⣤⣿⣾⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠟⠉⠒⠛⠛⢻⡟⢿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡟⢉⡾⠁⠀⠀⠀⣤⣤⣤⣶⣶⣧⡈⢿⣿⣿⣿⠇⠀⠀⠀⠀⠘⠛⠛⠛⠻⡿⠿⠿⠿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠀⠘⠃⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⡄⠀⠀⠀⠀⡀⠀⠀⢀⢠⣿⡀⠀⢌⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠸⣿⠿⣿⢿⣿⣿⣿⣿⡇⢻⣿⣿⣧⠀⠀⠀⠀⠙⠿⣿⠿⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⣀⠈⠃
⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⡀⢟⢤⠈⠻⣇⢾⣿⣿⣿⣶⡀⠀⠀⠀⠀⠚⠂⠀⠤⣿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⡆
⠀⠀⠀⠀⠀⠙⢾⣿⣾⣿⡥⠙⣿⣷⣿⡟⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣷⠦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢠⡀⠀⠀⠀⠁⢻⢻⣷⠓⣻⣿⣿⡇⠀⢹⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠛⠿⠛⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣧⠀⠀⢀⣀⡼⠁⡟⠀⣾⣿⣿⠏⠀⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠈⠙⠃
⠀⢠⣿⠿⠀⠀⠈⠉⠻⣶⣤⡂⣿⣿⡿⠀⠸⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⠿⢃⣾⣿⣿⣿⣯⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠠⢾⣿⡆
⠀⠙⠋⠀⠀⠀⠀⠀⠀⠈⢻⠷⡿⢿⡇⠀⠀⠙⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⣠⠄⢘⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣨⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠈⠀⣺⠀⠀⠀⠀⠉⣉⣦⢆⣤⣠⣴⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠉⠀⠀⠈⢈⣿⡉⠙⠛⠇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣤⣦⣄⠈⠀⠀⣰⣿⠀⠀⠀⣸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢰⣶⣶⣶⣾⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⠀⣠⣾⣿⣿⣿⠂⡀⢸⣿⣿⣆⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢻⣿⠻⣿⣿⣿⣿⣷⡄⠀⠀⠀⢼⡝⣃⢉⣉⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⢷⣿⣿⣿⣿⡏⠀⠳⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⢸⣿⠁⣿⣿⣿⣿⣿⣷⣤⣷⠀⢈⣡⣾⡿⣿⣿⡿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣷⣾⣿⢡⣶⡿⣷⣮⣿⣷⣷⣶⣷⣿⢾⣿⣿⣷⣶⠀⠉⠉⠀⠀⠀⠙⡿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠁⠀⡿⣿⣿⣿⣿⣿⣿⡟⠾⠋⣻⣿⣿⠟⡹⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⣿⡏⢸⣿⡏⣿⣿⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠸⡏⠉⠃⠀⠀⠀⠘⠃⢸⣿⣿⣿⣿⠿⠁⠀⠀⠀⠉⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢸⣿⣿⢸⣿⡿⠁⢸⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢸⣿⣧⡔⢸⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⠍⠉⠁⠀⠉⠉⠉⠁⠈⣭⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⣧⢘⣿⣿⣿⣿⣿⣏⣸⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⣷⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠻⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⢸⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡷⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢠⣶⣶⣶⣶⣶⣤⣴⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢿⡿⠛⠑⠊⠛⠛⣻⡻⠿⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠟⢡⡿⠁⠀⠀⢀⣤⣤⣤⣶⣾⣧⡘⢿⣿⣿⣿⠇⠀⠀⠀⠀⠛⠛⠛⠛⠛⡿⠿⠿⠿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⠀⠘⠁⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⡀⠀⠀⠀⠀⣀⠀⠀⣀⣰⣷⡀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠼⡿⠿⡿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣧⠀⠀⠀⠀⠙⠿⡿⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⠀⣀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡸⡇⣄⠘⢻⡆⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠛⠀⠠⠤⣿⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡆
⠀⠀⠀⠀⠀⠰⢿⣷⣾⣿⡄⠙⣿⣾⣿⡇⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢻⣷⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣤⠀⠀⠀⠀⠐⢿⣿⣵⠓⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢠⣿⡇⠀⠀⢀⣀⡌⢀⠍⠀⣿⣿⣿⠃⢀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠈⠙⠃
⠀⣰⡿⠏⠀⠀⠈⠙⢿⣦⣠⠀⣿⣿⡿⠀⠺⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⠟⢠⣿⣿⣿⣿⣏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠰⢿⣿⡆
⠀⠙⠃⠀⠀⠀⠀⠀⠀⠉⢻⢲⠿⢿⠇⠀⠀⠙⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⣠⠀⣸⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣦⣤⣬⡄
⠀⠀⠀⠀⠀⠀⠀⡀⢀⢠⠇⠘⠀⡾⠀⠀⠀⢈⠉⣩⣠⣆⣤⣤⣤⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠁⠀⠀⠀⢨⣯⡉⠙⠻⠇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⣼⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢴⣶⣶⣶⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⠀⣠⣾⣿⣿⡿⢀⠀⢸⣿⣿⣄⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢻⣿⢻⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠙⠁⣉⣩⣿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⡟⣿⣿⣿⣿⣿⠇⠈⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⢿⣿⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⢸⣿⠀⣿⣿⣿⣿⣿⣧⣤⣧⢠⣴⢶⣿⣏⣡⡶⢿⣯⣼⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⣾⣿⢠⣶⡿⣷⣮⣿⣷⣶⣶⣷⣿⣾⣿⣿⣷⣶⠀⠉⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⢀⡿⣿⣿⣿⣿⣿⣿⡟⠈⠉⠈⠛⢿⣯⡶⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⢸⣿⣿⠇⢸⣿⡏⣿⣿⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠸⡟⠉⠁⠀⠀⠀⠸⠁⣼⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠈⠉⠘⢩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢈⢸⣿⣿⢸⣿⡟⠀⢸⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣇⣴⣶⣆⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣽⣿⣿⢸⣿⣧⡔⢸⣿⣇⣿⣿⠈⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⠉⠉⠁⠀⠉⠉⠉⠁⠈⣽⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢹⣿⣿⣿⣇⠹⣿⣿⣿⣿⣿⣿⠁⣀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣼⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⡟⠀⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⣶⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠻⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⢨⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢰⣶⣶⣶⣶⣶⣦⣴⣿⣾⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢿⡿⠋⠑⠚⠛⠛⣻⠻⠿⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠏⢱⡟⠀⠀⠀⢠⣤⣤⣤⣶⣾⣦⡙⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⠛⠛⠛⠻⡟⠿⠿⠿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠚⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⠀⠀⠀⠀⠀⣀⠀⠀⡀⣰⣧⡀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠾⡿⢿⡿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣇⠀⠀⠀⠀⠙⢿⡿⠽⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⡀⠈⠃
⠀⠀⠀⠀⠀⣀⠀⠉⠀⢀⠸⡣⡄⠘⢻⡄⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠛⠀⠠⠤⢿⠎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⡆
⠀⠀⠀⠀⠀⠑⢿⣿⣿⣿⡄⠹⣿⣾⣿⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢻⣷⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣆⠀⠀⠀⠀⠐⢟⣿⣾⠓⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣿⡇⠀⠀⢀⣠⡌⢨⠁⠠⣿⣿⣿⠃⢀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠙⠃
⠀⣼⡿⡇⠀⠀⠈⠙⢿⣷⣴⢀⣿⣿⡟⠀⢹⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⡿⠟⢡⣿⣿⣿⣿⣧⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠴⢿⣷⡆
⠀⠙⠃⠀⠀⠀⠀⠀⠀⠙⡻⢾⠿⢿⠂⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⣀⠀⢘⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⡏⠀⠀⠀⢀⠉⣠⣠⣠⣤⣤⣴⣦⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠁⠀⠀⠁⢠⣯⡈⠉⠛⠇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⢀⣾⡇⠀⠀⠀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠶⢶⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⠀⣠⣿⣿⣿⡟⢀⠀⢾⣿⣷⣄⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⢻⣿⢻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠨⢃⣈⣩⣿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠠⣽⡿⣿⣿⣿⣿⣿⠇⠈⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠁⢸⢿⢀⣿⣿⣿⣿⣿⣧⣤⣧⢠⣶⠞⣿⣯⣵⠿⣻⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢰⣾⣾⡿⢠⣶⡿⣷⣯⣿⣷⣶⣾⣷⣿⢾⣿⣿⣷⣶⠀⠈⠉⠀⠀⠀⠙⡿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⢸⡿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⣿⠃⢸⣿⡟⣿⣿⢿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠏⠉⠁⠀⠀⠀⢸⣇⣸⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⢸⣿⣿⢸⣿⡟⠀⢸⣿⡇⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⢀⣴⣾⣷⣀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣹⣿⣿⢸⣿⣧⡔⢸⣿⣇⣿⣿⠈⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣮⠉⠉⠁⠀⠉⠉⠉⠁⠨⣽⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢹⣿⣿⣿⣷⡘⢻⣿⣿⣿⣿⣿⣇⣀⡀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠿⣶⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠹⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠁⠀⢩⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢠⣶⣶⣶⣶⣶⣦⣴⣿⣾⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⠋⠑⠛⠛⠛⣻⡻⠟⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠋⣱⠏⠀⠀⠀⢠⣤⣤⣴⣶⣾⣦⡙⣿⣿⣿⣿⠄⠀⠀⠀⠀⠛⠛⠛⠛⠻⡟⠻⠿⠿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠋⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⠀⠀⠀⠀⠀⣀⡀⠀⣀⣰⣧⡀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⡾⣿⣿⡿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣆⠀⠀⠀⠀⠙⢿⣿⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⣀⠀⠁
⠀⠀⠀⠀⢀⡀⠀⠉⠀⠀⠸⡣⡄⠘⢻⡄⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠛⠀⠠⠤⢿⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠒⢷⣷⣿⣿⡄⢹⣿⣾⣿⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢻⣷⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣄⠀⠀⠀⠀⠘⣟⣿⡟⢻⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡇⠀⠀⢀⣀⠏⢸⠁⢸⣿⣿⡿⠁⢠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⠙⠃
⠀⣼⡿⡇⠀⡀⠈⠹⢷⣧⣼⢰⣿⣿⠏⠀⢻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡞⠟⢣⣿⣿⣿⣿⣷⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠴⢿⣿⡆
⠀⠙⠃⠀⠀⠀⠀⠀⠀⠉⡿⢾⠿⣿⠀⠀⠀⠙⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⢠⡄⠠⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣰⡁
⠀⠀⠀⠀⠀⠀⠀⠠⠠⣼⠃⠚⢀⡏⠀⠀⠀⠀⢉⣪⣻⣦⣤⣤⣴⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠉⠀⠀⠀⡀⣾⣄⠈⣙⣃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣼⣤⡄⠀⠀⢀⣿⡇⠀⠀⠀⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠶⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⠀⣠⣿⣿⣿⡟⢀⠀⢾⣿⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⢹⣿⢻⣿⣿⣿⣿⣧⡀⠀⡀⠀⠀⠀⢃⣠⣬⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠠⣿⡿⣽⣿⣿⣿⣿⠃⠘⠆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠁⢸⣿⢀⣿⣿⣿⣿⣿⣷⣤⣿⠀⣶⡟⢿⣿⣵⡾⢟⣿⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⣾⡟⢠⣶⡿⣷⣯⣿⣷⣶⣾⣶⣿⣾⣿⣿⣷⣶⠀⠉⠉⠁⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⢰⡿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠉⠈⠙⣿⣾⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⢸⣿⣿⠁⢸⣿⡟⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⠟⠉⠁⠀⠀⠀⢸⣃⣼⣿⣿⣿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠛⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣸⣿⣿⢸⣿⡏⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣄⣴⣿⣿⣧⡄⠀⠀⠀⠀⠘⠻⠿⣿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢸⣿⣧⡔⢸⣿⣇⣿⣿⡈⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢠⣤⡄⣤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡃⠀⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣮⠉⠉⠁⠀⠉⠉⠉⠁⢩⣽⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⣇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⠀⡠⠇⠻⢞⣜⣚⣿⣿⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠶⠷⢶⣿⣿⢷⢾⣿⣛⣿⣟⣛⢫⢿⣳⡿⣯⢭⣯⡍⣽⡯⡏⡏⣯⢹⢱⣩⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡷⢸⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⢇⠿⠻⣹⣿⣿⣿⡇
⢸⣿⠿⣶⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⢃⣛⣫⣟⣷⣬⣿⣥⣥⣥⣮⣭⣮⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠹⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠉⠈⢽⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡿⠷⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢠⣶⣶⣶⣶⣶⣦⣴⣿⣾⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠿⠋⠐⠙⠋⠛⣟⠻⡟⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⠋⣸⠇⠀⠀⠀⢠⣤⣤⣴⣶⣾⣆⡹⣿⣿⣿⣿⠅⠀⠀⠀⠀⠛⠛⠛⠛⠻⡟⠻⠿⠿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠋⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⠀⠀⠀⠀⠀⣠⡀⠀⠀⣰⣧⡀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⢿⣿⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣆⠀⠀⠀⠀⠙⣿⡿⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⣀⠈⠃
⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀⢼⣡⡀⠙⢿⡄⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠛⠀⠠⠤⢿⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠈⠒⣿⣶⣿⣿⠈⢹⣿⣾⣿⠇⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠘⢻⣷⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⣆⠀⠀⠀⠀⠚⣟⣿⡿⢹⣿⣿⣿⡀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡇⠀⠀⢠⣤⡎⣸⠁⢸⣿⣿⡿⠀⣰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⢿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠙⠃
⠀⣼⡿⡇⠀⡀⠈⠹⢷⣷⣼⢸⣿⣿⠇⠀⢻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡾⠛⠃⣾⣿⣿⣿⣿⣄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠴⢿⣿⡆
⠀⠙⠁⠀⠀⠀⠀⠀⠀⠉⡿⣾⠿⣿⠀⠀⠀⢙⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⢀⡔⠠⣿⠿⣿⣿⣿⣿⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⢐⡇⠀⠀⠀⠀⠨⣼⣎⣦⣴⣶⣴⣆⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈⠀⠀⠀⡀⣾⣦⡀⣈⣁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣴⣤⡄⠀⠀⢀⣮⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠾⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⡀⠀⣴⣿⣿⣿⡇⢀⠀⣿⣿⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢹⣿⢻⣿⣿⣿⣿⣧⡀⠀⡀⠀⠀⠀⢘⣠⣤⡾⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⣿⡇⣼⣿⣿⣿⣿⠁⠘⠆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⡿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠁⢸⣿⢀⣿⣿⣿⣿⣿⣧⣬⣿⡄⣴⡿⢻⣿⣷⡾⢟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⣾⡏⢠⣶⡿⣷⣯⣿⣷⣶⣾⣶⣿⢾⣿⣿⣷⣶⠀⠉⠉⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠉⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⣿⠁⢸⣿⡗⣿⣿⣿⣿⣿⢹⣿⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⠟⠋⠁⠀⠀⠀⢸⣇⣼⣿⣿⣿⠿⠟⠋⢀⠀⠀⠀⠀⠀⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⢹⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣀⣴⣿⣿⣧⣀⠀⠀⠀⠀⠘⠹⠿⣿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢸⣿⣧⡔⢸⣿⣇⣿⣿⡈⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢠⣤⡄⣤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⠀⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣮⠉⠉⠁⠀⠉⠉⠉⠁⢩⣽⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣰⣠⣇⠻⢜⣜⣚⣿⣿⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠰⠷⢶⣿⣿⢷⢾⣿⣛⣿⣟⣛⢣⢽⣻⡿⣯⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡷⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⢇⠿⠻⣹⣿⣿⣿⡇
⢸⣿⠿⣶⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⢃⣛⣪⣟⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠙⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠈⢬⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣶⣶⣶⣶⣶⣦⣴⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠟⠋⠐⠙⠛⢛⡟⠿⠟⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⠋⣼⠇⠀⠀⠀⣠⣤⣤⣴⣶⣿⣆⠹⣿⣿⣿⣿⠁⠀⠀⠀⠀⠛⠛⠛⠛⠛⡟⠛⠿⠿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠋⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⠀⠀⠀⠀⢀⣠⠀⠀⡀⣰⣧⡀⠀⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣇⠀⠀⠀⠀⠉⠿⡿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⠀⣀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⢞⢡⡀⠙⢿⠘⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠛⠀⠠⠤⢿⠎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠲⢿⣶⣿⣯⠈⢹⣷⣿⣿⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⣻⣷⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⣄⠀⠀⠀⠀⠚⣿⣿⡏⢻⣿⣿⣿⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡆⠀⠀⣠⣤⠋⠼⠁⢸⣿⣿⡟⠀⣰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⢿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠙⠃
⢀⣾⡿⠇⠀⡀⠉⠻⣿⣧⡆⢸⣿⣿⠇⠀⢻⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⠛⠇⣾⣿⣿⣿⣿⣆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠴⢿⣿⡆
⠀⠙⠁⠀⠀⠀⠀⠀⠀⠙⠟⡿⠿⣿⠀⠀⠀⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⢠⡖⠠⡿⠿⣿⣿⣿⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠁⢠⡇⠀⠀⠀⠈⠉⢄⣴⣦⣴⣦⣶⣦⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠀⠀⠀⢀⣾⣦⡀⣈⣉⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣶⣤⡄⠀⠀⢀⣿⡇⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠾⠿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣄⡀⠀⣴⣿⣿⣿⡏⢀⠀⣿⣿⣷⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⢹⣿⢹⣿⣿⣿⣿⣧⠀⠀⡀⠀⠀⠀⢈⣠⣤⡾⣿⣿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⣽⡗⣼⣿⣿⣿⣿⠀⠸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡄⠁⢸⣿⢀⣿⣿⣿⣿⣿⣧⣬⣿⡄⣴⡿⢻⣿⣷⣾⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⣾⡏⢠⣶⡿⣷⣯⣿⣷⣶⣾⣶⣿⢾⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⣿⠀⢸⣿⡗⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠟⠉⠁⠀⠀⠀⢸⣗⣸⣿⣿⣿⡿⠟⠋⢀⡀⠀⠀⠀⠀⠙⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⢹⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣀⣴⣿⣿⣿⣄⡀⠀⠀⠀⠘⠩⠿⢿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢸⣿⣧⡆⢸⣿⣇⣿⣿⡈⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢠⣤⡄⣤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⠁⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⡮⠉⠉⠁⠀⠉⠉⠉⠁⢫⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⣇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣸⣠⣇⡻⢜⣜⣚⣿⣿⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠰⠷⢶⣿⣿⢿⢾⣿⣛⣿⣟⣛⢣⢽⣻⡾⣯⣭⣯⡍⣽⡯⡏⡏⣯⢹⢱⣩⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡷⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣹⣿⣿⣿⡇
⢸⣿⠿⣶⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⣛⣪⣟⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠹⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⢨⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢰⣾⣷⣶⣶⣶⣦⣶⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠟⠉⠐⠉⠙⢛⣟⠿⠟⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⠉⣼⠃⠀⠀⠀⣠⣤⣤⣴⣶⣿⣆⠹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠛⠛⠛⠛⠛⡟⠛⠿⠿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠃⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡀⠀⠀⠀⢀⣀⡀⠀⡀⣰⣧⡀⠀⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⠀⠂⠀⠀⠀⠀⢿⣿⣿⢿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣇⠀⠀⠀⠀⠙⢿⡿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⣀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢞⢠⠀⠙⢿⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠛⠀⠠⠤⠿⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠲⢿⣾⣾⣧⢈⢻⣷⣿⣿⠀⢻⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠙⣻⣷⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⣄⠀⠀⠀⠀⠛⣻⣿⡏⢻⣿⣿⣿⠀⠨⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡆⠀⠀⣠⣤⡋⠈⠁⢺⣿⣿⡟⠀⣰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⢿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠙⠃
⠀⣾⡿⠇⠀⡀⠉⠻⣿⣧⡆⢸⣿⣿⠇⠀⢻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⡾⠛⠃⣾⣿⣿⣿⣿⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠴⠿⣿⡇
⠀⠙⠁⠀⠀⠀⠀⠀⠀⢙⠟⡿⠿⡿⠀⠀⠀⢹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠛⢀⡖⠀⢿⡿⣿⡿⢿⣿⣆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⣤⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠁⣰⠇⠀⠀⠀⢀⠈⢩⣶⣶⣴⣶⣴⣦⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠈⠀⠀⠀⡀⣾⣦⡀⣈⣉⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢠⣥⣤⡀⠀⠀⢠⣿⡇⠀⠀⢈⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠻⠿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⢀⣴⣿⣿⣿⠇⢀⠀⣿⣿⣷⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢻⣿⢹⣿⣿⣿⣿⣷⠀⠀⡀⠀⠀⠀⢈⣤⣤⣾⣿⣿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣽⡟⣾⣿⣿⣿⣿⠀⠸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⢿⣿⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠁⢸⣿⠀⣿⣿⣿⣿⣿⣧⣬⣿⡄⢶⣟⢻⣿⣷⣾⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⣾⡇⢠⣶⡿⣷⣯⣿⣷⣶⣶⣶⣿⢾⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⢀⣿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⢸⣿⣿⠀⢸⣿⡗⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠟⠉⠁⠀⠀⠀⢸⣟⣘⣿⣿⣿⡿⠟⠋⢀⡀⠀⠀⠀⠀⠘⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⢹⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡄⣴⣿⣿⣿⣤⡀⠀⠀⠀⠘⠹⠿⣿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢿⣿⣿⢸⣿⣧⡆⢸⣿⣇⣿⣿⡊⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢠⣤⡄⣤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⠇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⡮⠉⠉⠁⠀⠉⠉⠉⠁⢫⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣸⣠⣇⡻⢞⣜⣚⣿⣿⣧⣷⣽⣯⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠰⠷⢶⣿⣿⢿⢖⣟⣛⣿⣟⣛⢻⢬⣻⡿⣯⣭⣯⡍⣽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡷⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⣿⠿⣶⠀⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⣛⣪⣟⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠙⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠉⢨⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣷⣶⣶⣶⣦⣶⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠟⠉⠈⠉⠙⢛⣟⠿⠟⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠉⣼⠃⠀⠀⠀⣠⣤⣤⣴⣶⣿⣄⠹⣿⣿⣿⣿⠇⠀⠀⠀⠀⠛⠛⠛⠛⠛⡟⠛⠿⠿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠈⠃⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡀⠀⠀⠀⢀⣠⡀⠀⡀⣰⣧⣀⢀⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⠀⠀⠀⠀⠀⠰⣿⢿⣿⢿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣇⠀⠀⠀⠀⠈⠿⡿⠿⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⣀⡀⠃
⠀⠀⠀⠀⢀⠀⠈⠁⠀⡀⢟⢠⠀⠙⣿⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠛⠀⠠⠴⠿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠰⢿⣿⣾⣧⠨⢹⣷⣿⣿⠀⢻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠙⣻⣷⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢠⣄⠀⠀⠀⠀⠻⣻⣿⡏⢻⣿⣿⣿⠀⢨⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡆⠀⠀⣠⣤⠁⡝⠀⢺⣿⣿⡏⠀⣼⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⢿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠉⠃
⢠⣾⡿⠇⠀⡀⠉⠻⣿⣧⡆⢸⣿⣿⠇⠀⢻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⠛⠣⣾⣿⣿⣿⣿⣆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠴⠿⣿⡇
⠀⠙⠁⠀⠀⠀⠀⠀⠀⢙⠟⡿⠿⡿⠀⠀⠀⢹⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠋⢀⡦⠀⢿⠿⣿⡿⢿⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣦⣤⣬⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠁⣸⠃⠀⠀⠀⢀⠉⢫⣷⡶⣴⣶⣶⣦⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⢀⣾⣦⣀⣈⣉⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣠⣿⣥⡄⠀⠀⢠⣾⡀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠻⠿⢿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⢀⣴⣿⣿⣿⠇⣀⠀⣿⣿⣷⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢹⣿⠹⣿⣿⣿⣿⣷⡄⠀⡀⠀⠀⠀⢈⣤⣴⣾⣿⣿⡿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣽⡟⣾⣿⣿⣿⣿⠀⠸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⢿⣿⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⡿⠀⣿⣿⣿⣿⣿⣧⣤⣿⡆⢾⣿⣻⣿⣷⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⣾⡇⢠⣶⡿⣷⣯⣿⣷⣶⣶⣶⣿⢾⣿⣿⣷⣶⠀⠀⠁⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⢸⣿⡿⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠸⠟⠉⠁⠀⠀⠀⢸⣏⣘⣿⣿⣿⡿⠟⠋⢀⡀⠀⠀⠀⠀⠘⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣺⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣻⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠀⣴⣿⣿⣿⣤⡀⠀⠀⠀⠐⠩⠿⣿⠿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣺⣿⣿⢸⣿⣧⡆⢸⣿⣇⣿⣿⣈⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢠⣤⡄⣤⣍⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⡎⠉⠉⠁⠀⠉⠉⠉⠁⢫⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⣇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⣿⣸⣡⣇⡻⣜⣜⣚⣿⣻⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠰⠷⢶⣿⣿⢿⢖⣟⣛⣿⣟⣻⢻⢽⣻⡿⣯⢭⣯⡍⣽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡷⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⣿⠷⣶⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⣛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠁⠀⠙⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠠⢻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠿⠿⠷⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠠⣾⣿⣾⣶⣿⣶⣶⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠟⠉⠈⠉⠙⢛⡟⠿⠟⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⢉⣼⠃⠀⠀⠀⣤⣤⣤⣶⣶⣷⣄⠻⣿⣿⣿⣿⠇⠀⠀⠀⠀⠛⠛⠛⠛⠛⡟⠛⠻⠿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠘⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡀⠀⠀⠀⢀⣠⣀⠀⣀⣸⣷⣀⢀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⠀⠀⠀⠀⠀⠰⢿⢿⣿⢿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣇⠀⠀⠀⠀⠉⠻⣿⠻⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⢀⡈⠃
⠀⠀⠀⠀⢀⡀⠈⠁⠀⡀⣟⢤⠀⠛⣧⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠛⠀⠠⠴⠿⠎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠰⢿⣾⣿⣧⠨⢻⣷⣿⣿⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⣻⣿⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢠⣄⠀⠀⠀⠀⢻⣻⣿⡏⣻⣿⣿⣿⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠛⠛⠋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡆⠀⠀⣠⣬⠉⡟⠀⣾⣿⣿⡏⠀⣼⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⢿⣿⣙⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠃
⢠⣾⡿⠇⠀⠀⠉⠻⣿⣧⡇⢸⣿⣿⠃⠀⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⠛⠃⣾⣿⣿⣿⣿⣆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠰⠿⣿⡇
⠀⠙⠁⠀⠀⠀⠀⠀⠈⢙⠗⡿⢿⡟⠀⠀⠀⣹⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠛⢀⡶⠀⠿⠿⢿⡿⢿⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⠀⠀⣸⠁⠀⠀⠀⢀⠈⢻⣷⣶⣤⣦⣶⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⣀⣼⣧⣀⣈⣉⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣠⣴⣥⡀⠀⠀⢰⣾⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠻⠿⢿⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⡀⢀⣼⣿⣿⣿⠃⡀⠐⣿⣿⣷⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⢻⣿⡙⣿⣿⣿⣿⣿⡄⠀⣀⠀⠀⠀⢈⣤⣴⣾⣿⣿⡿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⢧⣾⣿⣿⣿⣿⠀⠸⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠙⢿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢸⣿⠃⣿⣿⣿⣿⣿⣷⣤⣽⡆⠴⣿⣻⣿⣷⣿⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⣾⡇⢠⣶⡿⣷⣯⣿⣷⣶⣾⣶⣿⢾⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⢸⣿⡿⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠘⡏⠉⠃⠀⠀⠀⢰⣏⣈⣿⣿⣿⡿⠟⠋⢁⣀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⢻⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡇⢠⣾⣿⣿⣥⡀⠀⠀⠀⠀⠋⠿⢿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢸⣿⣧⡇⢸⣿⣇⣿⣿⡊⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢠⣤⡄⣤⣍⢭⢩⢹⡟⡍⢲⢂⡎⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⡎⠉⠉⠁⠀⠉⠉⠉⠁⢫⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣸⣣⣇⡻⣜⣜⣚⣿⣻⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠉⠀⠀⠐⠷⢶⣿⣿⢿⢗⣟⣛⣿⣟⣻⢻⢭⣻⡿⢿⣭⣯⡍⣽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡷⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⣿⠷⣶⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⣛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠘⣿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠨⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠰⣾⣿⣾⣶⣿⣶⣶⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠟⠁⠉⠉⠙⢻⠛⠻⠛⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⢁⡾⠁⠀⠀⠀⣤⣤⣤⣶⣶⣧⣌⠻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠛⠛⠛⠛⠛⡛⠛⠛⠿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠘⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⡀⠀⠀⠀⢀⣀⡀⢀⡀⣰⣷⣀⢀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⠀⠀⠀⠀⠀⠰⣿⠿⢿⢿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣇⠀⠀⠀⠀⠙⠻⡿⠳⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⡠⣛⢤⠀⠛⣧⠘⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠛⠀⠠⠤⠿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠰⢾⣶⣿⡇⠈⢿⣷⣿⣿⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⣻⣿⠔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣄⠀⠀⠀⠀⠻⣻⣿⠋⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠛⠛⠋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣾⣿⡆⠀⠀⣤⣬⠁⡏⠀⣾⣿⣿⡇⠀⣼⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⢿⣿⣙⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⠃
⢠⣿⡿⠃⠀⠀⠉⠻⣿⣧⡇⣼⣿⡿⠃⠀⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⠙⠏⣾⣿⣿⣿⣿⣆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠰⠿⣿⠇
⠈⠙⠀⠀⠀⠀⠀⠀⠀⢙⠗⡿⢿⡗⠀⠀⠀⣹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠛⢀⣶⠀⠽⠿⢿⡿⢿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣦⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣸⠁⠀⠀⠀⢀⠈⢿⣷⣖⣴⣶⣶⣦⣄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣀⣈⣙⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣠⣥⣄⡀⠀⠀⢰⣾⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠺⠟⢿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣄⡀⢀⣼⣿⣿⣿⠇⣀⠘⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⢺⣿⠙⣿⣿⣿⣿⣿⣄⠀⢀⠀⠀⠀⢈⣤⣴⣾⣿⣿⡿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣽⢀⣾⣿⣿⣿⡟⠀⠸⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠿⢿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢸⡿⠃⣿⣿⣿⣿⣿⣿⣤⣼⡆⠴⣿⣹⣿⣷⣿⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⣾⠇⢠⣶⡿⣷⣿⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⢸⣿⡟⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡏⠀⠁⠀⠀⠀⢰⣏⣈⣿⣿⣿⡿⠟⠋⠁⡀⠀⠀⠀⠀⠈⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⢼⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⢿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⢠⣾⣿⣿⣤⡀⠀⠀⠀⠀⠛⠿⢿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣻⣿⣿⢸⣿⣧⡇⢸⣿⣇⣿⣿⣈⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⣤⡄⣤⣌⢭⢩⢹⡟⡍⢲⢂⡄⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⡎⠉⠉⠁⠀⠉⠉⠉⠁⢩⣽⣿⣿⣿⣿⣿⣿⣯⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⣿⣸⣧⣇⡻⣜⣜⣚⣿⣻⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢗⣟⣛⣿⣟⣻⢻⢽⣫⡿⢿⣭⣯⡍⣽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡷⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⣿⠷⣶⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠘⢿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠨⢿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢠⣾⣿⣾⣶⣿⣶⣶⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠋⠀⠉⠉⠛⢻⠛⠻⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢡⡟⠀⠀⠀⢀⣤⣤⣤⣶⣶⣷⣌⠻⣿⣿⣿⣿⠇⠀⠀⠀⠀⠛⠛⠛⠛⠛⡛⠛⠻⠿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠘⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⠀⣀⣸⣷⣀⢀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⠀⠀⠀⠀⠀⠸⣿⡿⡿⢿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣇⠀⠀⠀⠀⠘⠿⡿⠿⠚⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⡰⣣⣆⠈⠻⣧⠸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠛⠀⠠⠴⠿⠎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠲⢷⣶⣿⡆⡉⣿⣷⣿⡿⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⣻⣿⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣰⣄⠀⠀⠀⠘⢻⣿⣿⠋⣿⣿⣿⡗⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠛⠛⠋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⡄⠀⢀⣠⣌⢁⡏⠀⣿⣿⣿⡇⢀⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⢿⣟⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⠃
⢠⣿⠿⠁⠀⠈⠙⢻⣿⣤⡃⣿⣿⡿⠁⠈⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⠹⠟⣾⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠴⠿⣿⠇
⠈⠉⠀⠀⠀⠀⠀⠀⠈⣹⢳⡿⢿⡇⠀⠀⠀⣽⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠋⢀⣶⠀⠽⠿⢿⡿⢿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣦⣤⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠈⠀⣺⠀⠀⠀⠀⣀⠉⢲⣿⡖⣴⣦⣶⣦⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣼⣦⣀⣈⣹⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣰⣭⣄⠀⠀⠀⣼⣿⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠺⠿⢿⠯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣄⡀⢀⣼⣿⣿⣿⠃⡀⠸⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⢹⣿⠙⣿⣿⣿⣿⣿⣄⠀⢀⠀⠀⠀⢈⣤⣶⣾⣿⣿⡿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⢰⣿⣿⣿⣿⡟⠀⠑⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢸⣿⠃⣿⣿⣿⣿⣿⣿⣤⣼⡆⠴⣿⣻⣿⣷⣿⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⣾⠃⢠⣶⡿⣷⣯⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⢸⣿⡏⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⡟⠉⠃⠀⠀⠀⢸⣇⣼⣿⣿⣿⡿⠟⠋⢀⣀⠀⠀⠀⠀⠈⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⢠⣾⣿⣿⣦⡀⠀⠀⠀⠀⠋⠿⢿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢸⣿⣧⡇⢸⣿⣇⣿⣿⣙⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢠⣤⡄⣤⣌⢭⢩⢹⡟⡍⢲⢂⡎⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢼⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⡌⠉⠉⠁⠀⠉⠉⠉⠁⢫⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣼⣧⣇⡻⣜⣜⣚⣿⣿⣧⣷⣽⣯⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢇⣟⣛⣿⣟⣻⢻⢽⣻⡿⢿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡷⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡷⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⡿⠳⣶⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠙⢿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠨⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢰⣿⣿⣿⣾⣷⣶⣾⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠋⠀⠉⠉⠛⣿⠛⠿⠻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢰⡏⠀⠀⠀⢠⣤⣤⣴⣶⣾⣦⡈⢻⣿⣿⣿⣿⠃⠀⠀⠀⠐⠛⠛⠛⠙⠛⡛⠛⠛⠿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠛⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⡀⢀⢀⣸⣧⣀⢀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⠀⠀⠀⠀⠀⠿⣿⣿⡿⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠙⠿⡿⠗⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⣀⡀⠃
⠀⠀⠀⠀⠀⠀⠉⠀⢀⠸⡣⡆⠈⢻⡆⢻⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠋⠀⠠⠼⠿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠐⠳⢷⣾⣿⡄⡙⣿⣾⣿⡇⠈⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⠉⢻⣿⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣠⡀⠀⠀⠀⠘⣛⣿⣿⢙⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⠀⠀⢠⣤⣌⢰⠁⠰⣿⣿⣿⠁⢠⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⢿⣟⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠁
⢰⣿⢿⠀⠀⠈⠙⢿⣿⣴⠀⣿⣿⡟⠀⠘⢿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⠹⠟⣾⣿⣿⣿⣿⣏⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠴⠿⣿⡇
⠈⠉⠀⠀⠀⠀⠀⠀⠉⠻⢸⠿⣿⠇⠀⠀⠀⣿⣷⣧⢀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠋⢀⡶⠀⠽⠿⢿⡿⢿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣦⣤⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠘⢀⣿⠀⠀⠀⠀⡀⠈⢵⣾⣶⣴⣶⣶⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣼⣦⣀⣈⣙⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣴⣯⣄⠈⠀⠀⣼⣿⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠺⠿⢿⠏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⣄⠀⣠⣾⣿⣿⣿⠀⡀⢸⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⠹⣿⣿⣿⣿⣷⡄⠀⢀⠀⠀⠀⢈⣤⣶⣾⣿⣿⡿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠿⢰⣿⣿⣿⣿⡇⠀⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠿⣿⣿⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⢸⢿⠀⣿⣿⣿⣿⣿⣿⣤⣽⡆⠴⣿⣻⣿⣷⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢰⣶⣾⢸⣿⣾⠁⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢸⡏⠉⠁⠀⠀⠀⢸⣏⣺⣿⣿⣿⡿⠟⠋⢁⣀⠀⠀⠀⠀⠘⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡆⢠⣾⣿⣿⣥⡀⠀⠀⠀⠀⠻⠿⣿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣻⣿⣿⢸⣿⣷⡄⢸⣿⣇⣿⣿⣙⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢠⣤⡄⣤⣍⢭⢩⢹⡟⡍⢲⢂⡎⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⠌⠉⠉⠁⠀⠉⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣸⣧⣇⣻⣜⣜⣚⣿⣿⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢇⣟⣛⣿⣟⣻⢻⢽⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡷⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⡿⠳⣶⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢹⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠘⢿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠨⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢰⣿⣿⣿⣾⣿⣶⣶⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠿⠋⠈⠉⠉⠛⡿⠛⠟⠻⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢰⠏⠀⠀⠀⢠⣤⣤⣴⣶⣾⣦⡈⢻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠛⠛⠛⠙⠛⡛⠛⠛⢿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠛⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⠀⣀⣸⣧⣀⢀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢿⡇
⠀⠀⠀⠀⠀⠾⣿⠿⠿⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⣿⠿⠗⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⠀⣀⡈⠃
⠀⠀⠀⠀⠀⠀⠉⠀⢀⢸⣣⡆⠈⢻⡆⢻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠋⠀⠠⠼⠿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠐⠻⢿⣿⣿⡄⡽⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠉⣻⣿⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣤⡀⠀⠀⠀⠘⢻⣿⣿⢹⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠛⠛⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⠀⠀⢠⣤⣍⢰⠃⠰⣿⣿⣿⠁⢠⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣿⣿⢿⣿⣹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁
⢰⣿⠿⠀⠀⠈⠙⢿⣿⣼⢀⣿⣿⡟⠀⠘⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⠙⠛⣾⣿⣿⣿⣿⣧⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠰⠿⢿⡇
⠘⠋⠀⠀⠀⠀⠀⠀⠉⠻⢺⠿⣿⠇⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠋⢀⡶⠀⠿⠿⢿⡿⢿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣦⣤⡅
⠀⠀⠀⠀⠀⠀⡀⠀⣼⠇⠘⢀⡿⠀⠀⠀⠀⣀⡉⢽⣾⣶⣶⣶⣶⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⡀⣀⣼⣧⣄⣀⣭⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣴⣤⣄⠈⠀⠀⣾⣿⠀⠀⠀⣹⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠺⠟⢿⠯⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⣄⠀⣠⣾⣿⣿⡿⠀⡀⢸⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⠙⣿⣿⣿⣿⣷⡄⠀⢀⠀⠀⣀⣈⣤⣶⣾⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠽⢰⣿⣿⣿⣿⡇⠀⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠿⣿⣿⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⢸⢿⠀⣿⣿⣿⣿⣿⣿⣤⣿⡆⠾⣿⣹⣿⣿⣿⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢰⣶⣾⢸⣿⣾⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡏⠉⠁⠀⠀⠀⢸⣷⣼⣿⣿⣿⡿⠟⠋⣁⣀⠀⠀⠀⠀⠘⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡆⢀⣾⣿⣿⣧⡄⠀⠀⠀⠐⠫⠿⢿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢽⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢠⣤⡄⣤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⣧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢼⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⠌⠉⠉⠁⠀⠉⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣸⣧⣇⣻⣜⣜⣚⣿⣿⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢇⣟⣛⣿⣟⣻⢻⢽⣫⡿⢿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⠸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⡿⠳⣶⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢻⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠘⢿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠊⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠿⡿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢰⣿⣿⣿⣿⣿⣶⣾⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡿⣿⠟⠉⠈⠉⠉⠋⢿⠙⠛⠻⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⣰⠏⠀⠀⠀⢠⣶⣤⣶⣶⣾⣦⡈⢻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠙⠉⠉⠙⠛⡋⠛⠛⢻⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠋⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣀⡀⡀⣸⣧⣀⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢿⡇
⠀⠀⠀⠀⠀⠾⠿⠿⠿⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⠿⠿⠓⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⠀⣀⣀⠁
⠀⠀⠀⠀⠀⠀⠉⠀⢀⢸⣳⡆⠈⢻⡆⢻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠉⠀⠀⠾⠿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇
⠀⠀⠀⠀⠐⠻⢿⣿⣿⢄⡼⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⢈⠉⣹⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣤⡀⠀⠀⠀⠘⢿⣿⣿⢩⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠛⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⠀⠀⢠⣤⣌⢠⠃⠠⣿⣿⣿⠁⢠⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⢿⣿⣭⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⠁
⢰⣿⠿⠀⠀⠈⠙⢻⣿⣼⢀⣿⣿⡟⠀⠘⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡞⠙⠋⣾⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠰⠿⢿⡇
⠘⠋⠀⠀⠀⠀⠀⠀⠉⠻⢸⠟⣿⠇⠀⠀⠀⣿⣿⣧⢀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠋⠀⡶⠀⠿⠿⢿⡿⠿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⠀⢠⡿⠀⠀⠀⢀⣄⡈⣼⣿⣶⣴⣶⣶⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣀⣀⣼⣧⣄⣠⣬⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⢀⣾⣏⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠺⠟⢿⠯⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⣄⠀⣠⣿⣿⣿⡿⠀⡀⢸⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⠸⣿⣿⣿⣿⣷⡤⠀⣀⠀⠀⣀⣈⣴⣶⣾⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠿⢶⣿⣿⣿⣿⡇⠀⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠿⢿⡿⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⠿⠀⣿⣿⣿⣿⣿⣷⣤⣿⡆⠾⣿⣙⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢰⣶⣾⢸⣿⣾⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⢾⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⡏⠉⠁⠀⠀⠀⢸⣿⣾⣿⣿⣿⡿⠟⠋⣀⣀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡆⢠⣾⣿⣿⣧⡄⠀⠀⠀⠀⠫⠿⣿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢸⣿⣯⡅⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⢠⣤⡄⣤⣍⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⠌⠉⠉⠁⠀⠉⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣸⣧⣇⡻⣜⣜⣚⣿⣻⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢇⣟⣛⣿⣟⣻⢻⢭⣫⡿⢿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⠸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⡿⠲⣶⠈⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠼⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⡟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣶⣾⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠟⠁⠈⠉⠉⠫⠯⠛⡛⠻⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣸⠃⠀⠀⠀⣠⣶⣴⣶⣶⣾⣦⡈⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠛⠉⠉⠉⠙⡋⠛⠛⣻⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠃⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣀⣀⣀⣼⣷⣄⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⡇
⠀⠀⠀⠀⠀⠿⠿⠿⠿⢿⡿⢿⣿⣿⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠉⢻⣿⠛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⣀⡀⠁
⠀⠀⠀⠀⢀⠀⠁⠀⢀⢞⣲⡄⠈⣻⡆⢹⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠉⠀⠀⣺⡿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠻⢿⣿⣷⢄⢼⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢈⡉⣹⣿⢆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣤⡀⠀⠀⠀⠘⣟⣿⡏⢹⣿⣿⣿⡃⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⠀⣿⣿⠀⠀⢠⣤⣍⠸⠁⢸⣿⣿⣿⠀⢰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⢿⣯⣽⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢈⠁
⢸⣿⠿⠀⠀⠈⠙⢿⣷⣬⢸⣿⣿⠟⠀⠘⢿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠟⠙⠛⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠐⠻⠿⠇
⠘⠃⠀⠀⠀⠀⠀⠀⠉⡿⢺⠟⣿⠁⠀⠀⠀⣿⣿⣧⠄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⠋⠠⡷⠀⠻⠿⢿⠿⠿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣴⡄
⠀⠀⠀⠀⠀⠀⡄⠀⢸⠃⠘⢀⡏⠀⠀⠀⣀⣄⣠⣮⣷⣿⣶⣷⣶⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⣀⣾⣷⣄⣤⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣼⣤⣆⠀⠀⢀⣷⣇⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠛⠛⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣄⠀⣠⣿⣿⣿⡟⠀⡀⢻⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⠘⣿⣿⣿⣿⣷⡄⠀⣀⠀⠀⣀⣨⣴⡶⣿⣿⣿⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⠙⢶⣿⣿⣿⣿⠃⠀⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠿⣿⡿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠿⠀⣿⣿⣿⣿⣿⣷⣤⣿⡆⠾⣿⣹⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡾⠀⢠⣶⡿⣷⣿⣿⣷⣶⣶⣶⣿⢾⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠈⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠈⠁⠀⠀⠀⢸⣻⣼⣿⣿⣿⡿⠛⢋⣁⣀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡄⢠⣾⣿⣿⣧⡄⠀⠀⠀⠀⠩⠿⣿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣤⡄⣤⣍⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⣧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⠈⠉⠉⠁⠀⠉⠉⠉⠁⣯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⣿⣺⣧⣇⡻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢇⣟⣛⣿⣟⣻⢻⢭⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⡿⠲⣶⠀⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠿⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠈⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢿⡟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣶⣾⣿⣷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠟⠁⠈⠉⠉⠫⡯⠛⡋⠻⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣸⠃⠀⠀⠀⣠⣶⣴⣶⣶⣿⣤⡘⢿⣿⣿⣿⣿⠃⠀⠀⠀⠈⠉⠉⠉⠉⠙⡋⠛⠛⢻⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠃⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡗⠈⣿⣿⣿⣿⡀⠀⠀⠀⢀⣠⣀⣀⣀⣼⣷⣄⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠿⠿⠿⠿⣿⡿⢿⣿⣷⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⢿⣟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⣀⣀⡃
⠀⠀⠀⠀⠀⠀⠁⠀⢀⢚⣲⡄⠈⣻⡄⢻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠉⠀⠀⣺⡿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠻⢿⣿⣷⢀⢼⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢈⣉⣹⣿⢆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣤⡀⠀⠀⠀⠘⣟⢿⡏⢹⣿⣿⣿⠃⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⠐⣿⣿⠀⠀⢠⣤⡀⡸⠁⢸⣿⣿⣿⠀⣰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⢿⣯⣭⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⢈⠁
⢸⣿⠟⠀⠀⠈⠙⢿⣧⣬⢸⣿⣿⠛⠀⠘⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠟⠙⠛⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠐⠿⢿⡇
⠘⠃⠀⠀⠀⠀⠀⠀⠈⡛⢻⠛⣿⠀⠀⠀⠠⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⠋⠠⡶⠀⠻⠿⢿⠿⠿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠃⠀⢠⡏⠀⠀⠀⣀⣀⣀⣼⣿⣾⣶⣶⣶⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⣄⣾⣷⣄⣤⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣴⣦⣄⠀⠀⢀⣿⣇⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠻⠛⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⣤⠀⣠⣿⣿⣿⡟⢠⡀⢻⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⢸⣿⠹⣿⣿⣿⣿⣷⡄⠀⣀⠀⠀⣀⣨⣴⡶⣿⣿⣿⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⠉⢶⣿⣿⣿⣿⠃⠀⠃⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠿⣿⡿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠿⠀⣿⣿⣿⣿⣿⣷⣤⣿⡆⠾⣿⣹⣿⣿⣟⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡾⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⢾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⢠⡟⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⡏⠀⠁⠀⠀⠀⢸⣿⣼⣿⣿⣿⡿⠛⠋⣁⣀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢺⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠀⢠⣾⣿⣿⣷⡄⠀⠀⠀⠀⠩⠿⢿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢿⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⢠⣤⡄⣤⣌⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣾⣧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⠈⠉⠉⠁⠀⠉⠉⠉⠁⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⣿⣸⣧⣇⡻⣜⣜⣚⣿⣻⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢇⣟⣛⣿⣟⣻⢻⢭⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⡟⠲⣶⠀⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠻⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠞⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠈⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠿⠟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢿⣿⠟⠁⠉⠉⠉⠫⠯⠛⡋⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣼⠁⠀⠀⠀⣰⣶⣴⣶⣶⣿⣤⡘⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠉⠉⠉⠉⢙⡉⠛⠛⣻⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠃⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⠀⠀⠀⠀⢀⣠⣀⣀⣀⣼⣧⣄⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠿⠿⠿⠿⣿⡿⢿⣿⣷⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠉⠿⣿⠛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⣀⣀⡁
⠀⠀⠀⠀⠀⠀⠁⠀⣀⢚⣲⡀⠉⣻⡆⢻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠉⠀⠀⣺⡿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠻⢿⣿⣷⢠⢽⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣉⣽⣿⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣤⡀⠀⠀⠀⠛⣿⢿⡏⢹⣿⣿⣿⠁⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠛⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⢸⣿⣿⠀⠀⣠⣤⡄⡼⠀⢸⣿⣿⣿⠀⣰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⢿⣯⣽⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠁
⢸⡿⠏⠀⠀⠉⠙⢷⣧⣦⢸⣿⣿⠋⠀⠘⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠟⠙⠙⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠐⠻⠿⡇
⠘⠃⠀⠀⠀⠀⠀⠀⠉⡟⢿⠛⣿⠀⠀⠀⠀⣿⣿⣧⠄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠙⠋⢠⡿⠀⠻⠟⢿⠟⠿⢿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢸⡇⠀⠀⠀⣀⣀⣀⣾⣾⣿⣷⣶⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣀⣀⣄⣿⣷⣤⣤⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣾⣤⣄⠀⠀⢀⣿⣇⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠛⠛⢿⠯⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⣄⠀⣰⣿⣿⣿⡟⢠⡀⢻⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⠸⣿⣿⣿⣿⣷⡄⠀⣀⠀⠀⣄⣨⣶⡶⣿⣿⣿⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠰⡅⣾⣿⣿⣿⣿⠃⠀⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠻⠿⣿⠟⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠸⠿⠀⣿⣿⣿⣿⣿⣷⣤⣿⡆⠾⣿⢹⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⢰⣶⣾⢸⣿⡞⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠈⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⢠⡟⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠈⠁⠀⠀⠀⢸⣿⣼⣿⣿⣿⠿⠛⢉⣀⣀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢾⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣷⡄⠀⠀⠀⠀⠩⠿⣿⠿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢠⣤⡄⣤⣌⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⠈⠉⠉⠁⠀⠉⠉⠉⠁⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⣿⣺⣧⣇⡻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢗⣟⣛⣿⣟⣻⢻⢭⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⢻⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠜⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠈⢻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⠟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣾⣿⣷⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢿⣿⠟⠁⠉⠉⠉⠫⠯⠛⡋⠻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣼⠁⠀⠀⠀⣰⣶⣤⣶⣶⣿⣤⡘⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠉⠉⠉⠉⢙⡉⠛⠛⣻⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠃⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⠀⠀⠀⠀⢀⣠⣀⣀⣀⣼⣧⣄⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠿⠿⠿⠿⣿⡿⢿⣿⣧⢀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠉⠿⣟⠛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⣀⣀⡁
⠀⠀⠀⠀⠀⠀⠁⠀⣀⢾⣲⡀⠉⣿⡂⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠀⠐⣚⡟⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠻⢿⣿⣷⢀⢹⣿⣿⣿⠁⠘⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⣉⣽⣿⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣤⡀⠀⠀⠀⠚⣿⢿⡏⢹⣿⣿⣿⠁⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠛⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⠘⣿⣷⠀⠀⣠⣤⡁⡼⠀⢸⣿⣿⣿⠀⣸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⢻⣿⣽⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⢀⡈⠁
⢸⡿⠏⠀⠀⠉⠙⢿⣧⣆⢸⣿⣿⠃⠀⠘⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠟⠙⠋⣿⣿⣿⣿⣿⣧⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠐⠻⢿⡇
⠘⠃⠀⠀⠀⠀⠀⠀⢉⡟⡿⠛⣿⠀⠀⠀⠠⣿⣿⡧⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠛⠁⢠⡷⠀⠻⠟⢿⠟⠿⢿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢸⡇⠀⠀⠀⣐⣀⣠⢼⣿⣿⣶⣶⣾⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣀⣀⣀⣤⣿⣷⣤⣤⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢠⣾⣦⣄⠀⠀⢠⣿⣇⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠻⠛⢿⠫⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢄⠀⣰⣿⣿⣿⡏⢠⠀⢻⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⠸⣿⣿⣿⣿⣷⡄⠀⣀⠀⠀⣀⣠⣶⡾⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠖⣾⣿⣿⣿⣿⠁⠀⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠛⠿⠿⠛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⠿⠀⣿⣿⣿⣿⣿⣷⣤⣿⡆⠾⣯⣽⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⢰⣶⣾⢸⣿⡞⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⢾⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣿⡇⠀⠀⠀⢠⡿⢻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠁⠀⠀⠀⢸⣿⣼⣿⣿⣿⠿⠛⢉⣀⣀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡁⢰⣿⣿⣿⣷⡄⠀⠀⠀⠀⠹⠿⡿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣤⡄⣤⣌⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⠈⠉⠉⠁⠀⠉⠉⠉⠑⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⣿⣺⣣⣇⡻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢗⣟⣛⣿⣟⣻⢻⢭⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠈⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠻⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠊⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠈⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣾⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢿⡿⠋⠁⠉⠙⠙⠹⠋⠛⡙⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡾⠁⠀⠀⠀⣴⣦⣴⣶⣶⣷⣤⡙⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠉⠉⢙⡉⠛⠛⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠃⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠠⣤⣀⣀⢀⣼⣧⣄⣐⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠿⠿⠿⠿⣿⡿⣿⣿⣇⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⠿⡟⠛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⡀⢻⣲⠀⢉⣿⠂⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠀⠐⣚⡟⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠻⢿⣿⣷⢀⢿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣉⣽⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⣤⡀⠀⠀⠀⠻⣿⣿⠏⢹⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠛⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡇
⠸⣿⣧⠀⠀⣤⣴⡀⡛⠀⢾⣿⣿⣷⠀⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣯⣽⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⠈⠁
⢸⡿⠇⠀⠀⠉⠛⣿⣧⡇⣸⣿⣿⠃⠀⠘⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠏⡝⠙⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠒⠿⠿⠇
⠘⠁⠀⠀⠀⠀⠀⠀⢈⠇⡿⢻⡿⠀⠀⠀⠰⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠛⠁⠰⠟⠀⠻⠿⢿⠟⠿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠁⢸⡇⠀⠀⢀⣀⣀⡀⢼⣿⣷⣦⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣀⣀⣤⣿⣷⣤⣤⣬⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣶⣦⣄⠀⠀⣰⣿⡇⠀⠀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠛⠛⢿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡀⠀⣴⣿⣿⣿⡏⢠⠀⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢹⣿⠸⣿⣿⣿⣿⣷⡄⠀⣀⠀⢀⣀⣡⣶⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⠸⣿⣿⣿⣿⣿⠀⠈⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⠻⠿⠿⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡆⠁⢸⠿⠀⣿⣿⣿⣿⣿⣧⣤⣿⡆⠿⠯⡽⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⢰⣶⣾⢸⣿⡎⠀⢠⣶⣿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠉⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⢠⡿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠁⠀⠀⠀⣸⣷⣾⣿⣿⣿⠟⠛⢉⣀⣀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣼⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣠⢰⣿⣿⣿⣶⡄⠀⠀⠀⠀⠱⠿⢿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣤⡄⣤⣜⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⣿⣺⣧⣇⡻⣜⣜⣚⣿⣿⣧⣷⣽⣯⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢗⣟⣛⣿⣟⣛⢻⢭⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠈⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢻⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠻⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠊⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠈⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣾⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢿⡿⠋⠁⠉⠙⠙⠹⠋⢛⡛⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡾⠁⠀⠀⠀⣴⣦⣴⣶⣶⣷⣤⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠉⠉⢙⡉⠛⠛⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠃⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠠⣤⣀⣀⢀⣾⣧⣄⣐⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⡇
⠀⠀⠀⠀⠰⠿⠿⠿⠿⣿⠿⣿⣿⡇⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⠿⡟⠛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣠⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣛⣲⠀⢙⣷⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠁⠀⢐⣚⡟⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠿⣿⣿⡧⣀⢿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣉⣽⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⣤⡀⠀⠀⠀⠻⡻⣿⠏⢿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠛⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⠸⣿⡇⠀⠀⣤⣴⠀⡛⠀⢿⣿⣿⣷⠀⣼⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⡿⣿⣯⣽⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⡈⠁
⢸⡿⠇⠀⠀⠉⠛⢿⣧⡇⣸⣿⣿⠃⠀⠘⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡙⠙⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠘⠻⢿⠇
⠘⠁⠀⠀⠀⠀⠀⠀⢈⠇⡿⢛⡿⠀⠀⠀⠸⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠙⠁⠰⠗⠐⠛⠿⣿⠟⠿⢿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢸⡇⠀⠀⢀⣀⣀⣀⢼⣿⣶⣶⣶⣶⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣀⣀⣤⣿⣷⣤⣤⣬⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣾⣦⡄⠀⠀⣰⣿⡇⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠛⠛⢿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣴⣿⣿⣿⠇⢠⠀⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡿⢸⣿⠸⣿⣿⣿⣿⣷⡄⠀⡀⠀⢀⣀⣡⣶⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⠪⣾⣿⣿⣿⣿⠀⠈⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠙⠻⢿⡿⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⠿⠀⣿⣿⣿⣿⣿⣷⣤⣿⡄⠿⡯⢽⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⢰⣶⣾⢸⣷⡎⠀⢠⣶⣿⣿⣿⣿⣷⣶⣶⣶⣿⢾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⡿⣿⣿⣿⡇⠀⠀⠀⢰⣿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠁⠀⠀⠀⣸⣷⣾⣿⣿⣿⠿⠛⢉⣀⣀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣼⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠁⢰⣿⣿⣿⣶⡄⠀⠀⠀⠀⠹⠿⣿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣤⡄⣤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣺⣣⣇⣻⣜⣜⣚⣿⣿⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢖⣟⣛⣿⣟⣛⢻⢽⣻⡿⣿⣭⣯⡍⡭⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠻⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠚⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠈⢻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢿⡿⠋⠀⠉⠉⠙⠹⠉⢛⡛⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡾⠀⠀⠀⠀⣴⣶⣴⣶⣶⣷⣦⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠉⠉⢙⡉⠙⠛⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠃⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠠⣤⣄⣀⢤⣾⣧⣄⣰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⡇
⠀⠀⠀⠀⠸⠿⠿⠿⠿⣿⠿⣿⣿⡇⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠹⢿⡟⠛⠙⢛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⣀⣀⡁
⠀⠀⠀⠀⠀⠈⠀⠀⡀⣟⣶⠀⢙⣷⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⢀⣐⣚⡛⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠙⠿⣿⣿⡧⣀⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣈⣽⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⡀⠀⠀⠀⠻⣿⣿⠋⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⢸⣿⡇⠀⠀⣤⣤⠀⡛⠀⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣯⣽⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⣀⣈⠁
⢸⡿⠇⠀⠀⠉⠛⣿⣧⡇⣾⣿⣿⠃⠀⢹⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠹⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠘⠻⠿⡇
⠘⠁⠀⠀⠀⠀⠀⠀⢉⠃⡿⢻⡟⠀⠀⠀⠸⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠙⠁⢰⠗⠐⠛⠟⣿⠛⠿⢿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣾⡆
⠀⠀⠀⠀⠀⠀⡀⠀⡾⠀⠁⣸⡇⠀⠀⢀⣐⣀⣀⢽⣿⣿⣦⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣀⣀⣀⣤⣿⣷⣤⣤⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣾⣦⡄⠀⠀⣸⣿⡇⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠛⠛⢿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣴⣿⣿⣿⠇⢠⠈⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡟⢹⣿⠸⣿⣿⣿⣿⣷⡄⠀⡀⠀⢀⣀⣡⣶⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠭⣿⣿⣿⣿⣿⠀⠘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠙⠛⢿⡿⠟⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⠿⠐⣿⣿⣿⣿⣿⣧⣬⣿⡄⠿⡯⢽⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢰⣶⣾⢸⣿⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⡿⣿⣿⣿⡇⠀⠀⠀⢰⡿⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡟⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠁⠀⠀⠀⣸⣵⣼⣿⣿⣿⠟⠛⢉⣀⣄⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣠⢴⣿⣿⣿⣶⡄⠀⠀⠀⠀⠽⠿⣿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢾⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢠⣤⡄⣤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⣿⣺⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠉⠀⠀⠐⠷⢶⣿⣿⢿⢖⣟⣛⣿⣟⣻⢻⢭⣻⡿⣿⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⠸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⢻⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠚⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⡈⠈⢻⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣛⠛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡿⠋⠀⠉⠉⠉⠽⠝⢛⠙⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡿⠀⠀⠀⢀⣴⣶⣶⣶⣾⣷⣤⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠉⠉⢹⡉⠉⠙⢻⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠃⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⠀⠀⠀⠀⠠⣤⣄⣠⣠⣾⣧⣄⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠻⡇
⠀⠀⠀⠀⠸⠿⠿⠿⠿⣿⠿⢿⣿⡇⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⠟⡟⠉⠙⢛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⣠⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⡰⣓⣦⠈⢙⣷⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣐⣚⡛⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠘⠿⣿⣿⡆⣀⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣽⣿⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⡀⠀⠀⠀⢻⡻⣽⠉⣿⣿⣿⣟⠀⢀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⢸⣿⡇⠀⠀⣤⣴⠀⡏⠀⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣹⣿⡿⣿⣯⣽⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣈⠁
⢸⡿⠇⠀⠀⠉⠛⣿⣧⡇⣿⣿⣿⠁⠀⠙⢿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠟⢻⣿⣿⣿⣿⣿⣆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠘⠛⢿⠇
⠘⠁⠀⠀⠀⠀⠀⠀⢉⠃⡟⢻⡟⠀⠀⠀⠸⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠛⠁⢰⠟⠐⠛⠛⣿⠛⠿⣿⡎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⡀⠀⡾⠀⢁⣾⠁⠀⠀⢀⣠⣄⣤⢾⣿⣷⣶⣶⣶⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣀⣀⣠⣴⣿⣶⣤⣤⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣾⣦⡄⠀⠀⣸⣿⡄⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠛⠛⡟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡄⢀⣼⣿⣿⣿⠇⢠⠘⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡏⢸⣿⢸⣿⣿⣿⣿⣷⠄⢀⡀⠀⢀⣀⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠡⣿⣿⣿⣿⡿⠀⠘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠛⢿⠿⠋⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⠿⢸⣿⣿⣿⣿⣿⣧⣬⣿⡔⢿⠯⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢰⣶⣾⢸⣿⡆⠀⢠⣶⣿⣿⣿⣿⣷⣶⣶⣷⣿⣾⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⡿⣿⣿⣿⡇⠀⠀⠀⢸⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣸⣿⣿⢸⣿⡇⠀⢸⣿⡏⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠁⠀⠀⠀⣸⣥⣼⣿⣿⣿⠟⠛⢉⣀⡄⠀⠀⠀⠀⠈⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣽⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣀⣴⣿⣿⣿⣶⡄⠀⠀⠀⠀⠽⠿⣿⠿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢿⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢠⣤⡄⣤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡃⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢼⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⣿⣺⣣⣇⣻⣞⣜⣚⣿⣿⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠉⠀⠀⠰⠷⢶⣿⣿⢿⢖⣟⣻⣿⣟⣻⢻⢼⣻⡿⣿⣭⣯⡍⡭⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠇⠲⣶⠀⢶⠄⠰⠲⠶⠆⠀⠀⠀⠀⣻⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⣛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⢻⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠊⢯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⣀⣀⡀⢀⡀⠈⢻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣛⠛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡿⠋⠀⠉⠉⠙⠽⠝⢛⡙⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡿⠀⠀⠀⢀⣴⣶⣶⣶⣾⣷⣄⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠉⠉⢹⡉⠉⠙⢻⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠃⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⠀⠀⠀⠀⠠⣤⣄⣀⣠⣿⣧⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢻⡇
⠀⠀⠀⠀⠸⠿⠿⠿⠿⣿⠿⢿⣿⡇⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⠛⠋⠉⠙⢛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⣓⣶⠀⣙⣷⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣐⣛⡛⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠿⣿⣿⣆⡀⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣈⣽⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⡀⠀⠀⠀⢻⡻⣿⠉⣿⣿⣿⣟⠀⢘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⢸⣿⡇⠀⠀⣤⣤⢀⡏⠀⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣹⣿⡿⣿⣧⣼⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣈⠁
⢸⡿⠇⠀⠀⠀⠛⣿⣧⡇⣿⣿⣿⠁⠀⠙⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠏⢻⣿⣿⣿⣿⣿⣆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠘⠻⢿⠇
⠘⠁⠀⠀⠀⠀⠀⠀⢙⠃⡟⢻⡟⠀⠀⠀⠸⢿⣿⣷⠄⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠁⢰⠟⠀⠛⠛⣿⠛⠿⣿⡞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠁⢾⠁⠀⠀⢀⣠⣀⣀⢼⣻⣿⣶⣶⣶⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⣠⣴⣿⣶⣤⣤⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣷⣦⡀⠀⠀⣸⣿⡄⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⠛⡟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡀⢀⣴⣿⣿⣿⠇⢠⠈⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡏⢸⣿⢸⣿⣿⣿⣿⣷⠀⢀⡄⠀⢀⣀⣥⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⣿⣿⣿⣿⡿⠀⠘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠛⠻⠿⠏⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⠻⢸⣿⣿⣿⣿⣿⣧⣬⣿⡐⠿⡯⠿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢰⣶⣾⢸⣿⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⢾⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠘⠛⠻⢿⡿⣿⣿⣿⡇⠀⠀⠀⢸⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡟⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣸⣤⣼⣿⣿⣿⠟⠛⢉⣀⣄⠀⠀⠀⠀⠈⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣏⡀⣴⣿⣿⣿⣶⡀⠀⠀⠀⠀⠼⠿⣿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢿⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣟⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢠⣤⡄⣤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡃⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣺⣣⣇⣻⣞⣜⣚⣿⣿⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠉⠀⠀⠠⠷⢶⣿⣿⢿⢖⣟⣛⣿⣟⣻⢻⢽⣻⡿⣿⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠇⠲⣶⠀⠶⠄⠰⠲⠶⠆⠀⠀⠀⠀⢿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⣛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⢻⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⡤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠊⢯⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣀⣀⣀⣀⡀⠈⢻⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡛⠛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡿⠋⠀⠉⠉⠙⠽⠝⢛⡙⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡿⠀⠀⠀⢀⣴⣦⣶⣶⣾⣿⣤⠹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠉⠉⢹⡉⠉⠙⢻⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⠀⠀⠀⠀⠠⣤⣤⣀⡠⣾⣷⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠻⡇
⠀⠀⠀⠀⠸⠿⠿⠿⠿⣿⠿⢿⣿⡇⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⠛⣋⠉⠉⠛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⣠⣀⡁
⠀⠀⠀⠀⠀⠈⠀⠀⡐⢓⣦⠀⣙⣷⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣐⣚⣋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠿⣿⣿⣇⣈⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣽⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⡀⠀⠀⠀⢻⡹⣽⠁⣿⣿⣿⣟⠀⢘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⢸⣿⡇⠀⠀⣤⣴⠀⡏⠀⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣹⣿⡿⣿⣧⣼⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣈⠁
⢸⡟⠇⠀⠀⠀⠛⣿⣧⡇⣾⣿⡿⠁⠀⠙⢿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠏⢻⣿⣿⣿⣿⣿⣆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠘⠛⢿⠇
⠘⠁⠀⠀⠀⠀⠀⠀⢉⠃⡟⢛⡟⠀⠀⠀⠸⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠋⠁⢰⠗⠀⠛⠛⣿⠛⠿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠁⣸⠃⠀⠀⢀⣤⣄⣀⢾⣿⣷⣤⣶⣶⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣠⣤⣤⣿⣦⣤⣤⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣶⣤⡀⠀⠀⣸⣿⡀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠛⠛⡟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡀⢀⣴⣿⣿⣿⠇⢠⠈⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡟⢸⣿⠸⣿⣿⣿⣿⣧⠀⢀⡄⠀⢀⣄⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠑⣿⣿⣿⣿⡿⠀⠘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠛⠻⠿⠋⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⠛⢰⣿⣿⣿⣿⣿⣧⣬⣿⡔⠿⠯⠿⣿⣿⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠠⢰⣶⣾⢸⣷⡆⠀⢠⣶⣿⣿⣿⣿⣷⣶⣶⣶⣿⢾⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⡿⣿⣿⣿⡇⠀⠀⠀⢸⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡟⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣸⣤⣾⣿⣿⣿⠟⠋⢉⣀⣀⠀⠀⠀⠀⠈⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣯⣀⣰⣿⣿⣿⣶⡄⠀⠀⠀⠀⠼⠿⣿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣟⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢠⣤⡄⣤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⠃⡇⣷⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣺⣣⣇⣻⣞⣜⣚⣿⣿⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢔⣟⣛⣿⣟⣻⢻⢭⣻⡿⣿⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠇⠲⣶⠀⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢻⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⢻⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠊⢿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣀⣀⣀⣀⡀⠈⢻⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣛⠛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡿⠋⠀⠁⠉⠙⢽⠍⢛⡙⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⢀⣶⣦⣶⣶⣾⣿⣄⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠀⠈⢩⡉⠉⠉⢻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⣤⣤⣤⣠⣾⣷⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢻⡇
⠀⠀⠀⠀⠸⠿⠿⠿⠿⣿⠿⢿⣿⡇⢸⣿⣿⣿⣿⣇⡀⠀⠀⠀⠙⠋⡉⠉⠉⢛⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠀⣠⣀⡁
⠀⠀⠀⠀⠀⠈⠀⢀⡐⣓⣦⠀⣙⣷⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣛⣋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠘⠿⣿⣿⣆⣈⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣄⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⡀⠀⠀⠀⢻⡽⣿⠁⣿⣿⣿⣟⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⢸⣿⡇⠀⠀⣤⣤⢀⡏⠀⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣹⣿⡿⣿⣧⣾⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣈⡁
⢸⡟⠇⠀⠀⠀⠛⢿⣷⡇⣿⣿⣿⠁⠀⠙⢿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠟⢻⣿⣿⣿⣿⣿⣆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠘⠛⢿⡇
⠘⠁⠀⠀⠀⠀⠀⠀⢙⠓⠟⢻⡟⠀⠀⠀⠸⡿⢿⣷⡄⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠁⢰⠟⠜⠛⠛⣿⠛⠿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠁⢸⠃⠀⠀⢀⣤⣀⣄⣮⣷⣿⣶⣶⣶⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⣤⣴⣿⣶⣦⣤⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣷⣦⣀⠀⠀⣸⣿⡄⠀⢀⣠⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⠛⡟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡀⢀⣴⣿⣿⣿⠃⢠⠈⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡟⢸⣿⢸⣿⣿⣿⣿⣷⠀⢀⡀⠀⢀⣄⣥⣶⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⣿⣿⣿⣿⡿⠀⠘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠛⠻⠿⠋⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⠿⢸⣿⣿⣿⣿⣿⣧⣬⣿⡐⢿⣯⣿⣿⣿⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢰⣶⣾⢸⣿⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣷⣿⣾⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⡿⣿⣿⣿⡇⠀⠀⠀⢸⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡟⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⠀⠀⠀⠀⣸⣤⣾⣿⣿⣿⠟⠋⢁⣀⡀⠀⠀⠀⠀⠈⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣀⣰⣿⣿⣿⣶⡄⠀⠀⠀⠀⠼⠿⣿⠿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢻⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣟⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⢠⣤⡄⣤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣾⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡟⠈⠉⠉⠁⠀⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣺⣣⣇⣻⣞⣜⣚⣿⣿⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠠⠷⢶⣿⣿⢿⢔⣟⣛⣿⣟⣻⢻⢽⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⣗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠇⠲⣶⠀⠶⠄⠰⠲⠶⠆⠀⠀⠀⠀⢿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠻⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠠⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠂⢿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣀⣀⣀⣀⣀⠀⢹⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣟⣛⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡿⠋⠀⠁⠙⠘⠽⠍⢛⡙⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⢀⣶⣶⣶⣶⣿⣿⣤⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠁⠀⠈⢹⡍⠉⠉⢻⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⠀⠀⠀⠀⠠⣦⣤⣤⠀⣾⣷⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠻⡇
⠀⠀⠀⠀⠸⢿⠿⠿⠿⣿⠿⢿⣿⡇⢸⣿⣿⣿⣿⣇⡀⠀⠀⠀⠈⠉⠉⠉⠉⢛⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⣤⣀⡁
⠀⠀⠀⠀⠀⠀⠀⢀⠐⢓⣦⠀⢙⣷⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣉⣋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠿⣿⣿⣇⣜⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣄⣿⡿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⡀⠀⠀⠀⢹⡽⣽⠁⣿⣿⣿⣟⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⢸⣿⡇⠀⠀⣤⣤⢀⡏⠀⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⡿⣿⣧⣼⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣀⡁
⢸⡟⠇⠀⠀⠀⠛⢿⣷⡇⣼⣿⣿⠁⠀⠙⢻⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠏⢻⣿⣿⣿⣿⣿⣆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠘⠛⢿⡇
⠘⠁⠀⠀⠀⠀⠀⠀⢙⠃⡟⢻⡟⠀⠀⠀⠸⠿⢿⣷⡄⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠋⠀⢰⠏⠀⠛⠛⡿⠛⠿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡇
⠀⠀⠀⠀⠀⢀⠀⠀⡟⠀⠀⢼⠁⠀⠀⢀⣠⣠⣄⢦⣎⣟⣾⣶⣶⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⣤⣴⣿⣶⣤⣤⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣷⣆⡀⠀⠀⣸⣿⡄⠀⢀⣠⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠛⠻⡟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⠃⢠⠈⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⢸⣿⠘⣿⣿⣿⣿⣷⠀⢀⡀⠀⢀⣀⣥⣶⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⡿⠀⠘⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠛⠻⠿⠋⠋⠛⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠸⠛⢐⣿⣿⣿⣿⣿⣦⣼⣿⡐⢿⣯⣿⣿⣿⣯⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠠⢰⣶⣾⢸⣷⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⣿⢿⣿⣿⡇⠀⠀⠀⢸⡟⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡟⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣸⣤⣾⣿⣿⣿⠟⠋⢁⣀⣄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢺⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢀⣰⣿⣿⣿⣶⡄⠀⠀⠀⠀⠼⠿⣿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢼⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢠⣤⡄⣤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠱⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣺⣣⣇⣻⣜⣜⣚⣿⣿⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢀⣟⣛⣿⣟⣻⢻⢯⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠇⠲⣶⠀⠶⠄⠰⠲⠶⠆⠀⠀⠀⠈⢽⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠻⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠄⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠁⠻⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⢀⣀⣀⣀⣀⣀⠀⣻⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡛⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡿⠋⠀⠁⠙⠉⠽⠍⢛⡙⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⢀⣶⣦⣶⣶⣿⣿⣤⠙⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢩⡍⠉⠉⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠴⣦⣤⣤⣤⣿⣷⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠙⠻⡇
⠀⠀⠀⠀⠸⢿⠿⠿⠿⣿⠿⢿⣿⡇⢸⣿⣿⣿⣿⣧⡀⠀⠀⠀⠈⠉⠁⠉⠉⢙⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⣤⣀⡀
⠀⠀⠀⠠⠀⠀⠀⢀⠐⣗⣦⠀⣙⣷⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣨⣭⣭⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠿⣿⣿⣇⣘⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣤⣿⡿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⡀⠀⠀⠀⢹⡽⣽⠁⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⢸⣿⡇⠀⠀⣤⣴⢀⡏⠀⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⡿⣻⣯⣾⣿⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣀⠁
⢸⡟⠇⠀⠀⠈⠛⣿⣷⡇⣿⣿⣿⠁⠀⠙⢻⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠛⢻⣿⣿⣿⣿⣿⣆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠘⠛⠿⡇
⠈⠁⠀⠀⠀⠀⠀⠀⢙⠛⡟⢻⡏⠀⠀⠀⠸⡿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠋⠉⠀⢰⠟⠨⠛⠻⣿⠛⠿⣿⡞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣼⠁⠀⠀⢀⣠⣀⣄⣾⣅⣿⣷⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣀⣀⣠⣴⣿⣦⣤⣤⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣴⣦⡀⠀⠀⣸⣿⣄⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠛⠻⡟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡀⢀⣼⣿⣿⣿⠃⢠⠈⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠿⢸⣿⠘⣿⣿⣿⣿⣷⠀⢠⡄⠀⢀⣀⣥⣶⢿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠐⣾⣿⣿⣿⡿⠀⠘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠈⠛⠻⠿⠋⠊⠛⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⠛⠀⣿⣿⣿⣿⣿⣦⣾⣿⡰⠿⡯⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠠⢰⣶⣾⢸⣷⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⡿⢿⣿⣿⡇⠀⠀⠀⢠⡟⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣸⣿⣿⢸⣿⡇⠀⢸⣿⡟⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⣸⣤⣾⣿⣿⣿⠟⠋⢉⣀⣄⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⣰⣿⣿⣿⣷⡄⠀⠀⠀⠈⠼⠿⣿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢺⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣟⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢠⣤⡄⣤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣧⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡟⠈⠉⠉⠁⠀⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣺⣣⣇⣻⣞⣜⣚⣿⣿⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢄⣟⣛⣿⣟⣻⢻⢿⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠇⠲⣶⠀⠶⠄⠰⠶⠶⠆⠀⠀⠀⠈⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡋⠀⠀⠈⠻⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠄⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠁⠻⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⢀⣀⣀⣀⣀⣄⣀⣹⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡛⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡿⠋⠀⠁⠙⠉⠽⠍⢛⡙⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⢀⣶⣶⣶⣶⣿⣿⣤⠙⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡍⠉⠉⢽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡅⢸⣿⣿⣿⣿⡀⠀⠀⠀⠴⣦⣤⣤⣤⣿⣷⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠙⢻⡇
⠀⠀⠀⠀⠸⢿⠿⠿⠿⣿⠿⢿⣿⡆⢸⣿⣿⣿⣿⣧⡀⠀⠀⠀⠈⠉⠁⠉⠈⠙⣟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠐⢗⣦⠀⣙⣷⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣬⣭⣭⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠁⠿⣿⣿⣇⣘⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣤⣾⡿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⡀⠀⠀⠀⢹⠽⣹⠁⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⢸⣿⡇⠀⠀⣤⣴⠀⡏⠀⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⡿⣻⣯⣼⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣀⡁
⢸⡟⠃⠀⠀⠀⠛⣿⣷⡇⣾⣿⣿⠁⠀⠙⢻⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⢚⣶⣾⣯⣛⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠃⠛⢻⣿⣿⣿⣿⣿⣄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠘⠛⢿⡇
⠈⠁⠀⠀⠀⠀⠀⠀⢙⠛⡟⢻⡏⠀⠀⠀⠸⡿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢾⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠀⢰⠟⠘⠛⠛⡿⠛⠿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⢀⣼⠁⠀⠀⢀⣠⣀⢄⣐⠑⣵⢶⠷⢿⣷⣶⣾⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⢟⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣀⣀⣠⣴⣿⣦⣤⣤⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣰⣵⣦⡀⠀⠀⣸⣿⣄⠀⢀⣠⣿⣿⣹⣿⣸⣿⢈⣿⣿⡇⣶⢻⣯⢻⣿⣽⣿⣿⣿⣟⣛⡿⣸⠿⠻⣿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠛⠻⡟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡀⢀⣼⣿⣿⣿⠃⢠⠈⣿⣿⣿⣷⣾⣿⣿⣿⣿⢸⣏⣿⢸⣧⣿⢸⡟⣿⠋⣿⣸⡟⣿⢀⡛⢹⣏⡃⣿⡇⣾⡟⣸⣗⡊⣾⢻⡇⢤⣤⡄⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠐⣾⣿⣿⣿⡿⠀⠘⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⠉⠁⠉⠘⠣⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⣼⡿⣾⣿⢺⣇⣿⡐⢿⡯⣿⣿⣿⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣷⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⡿⢷⣶⣶⡇⠉⠈⠁⢛⡛⢘⣣⣿⣸⡼⢿⣿⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡟⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⣸⣵⣾⣿⣿⣿⠛⠋⢁⣀⣄⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢼⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⣰⣿⣿⣿⣷⡄⠀⠀⠀⠈⠾⠿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢠⣤⡄⡤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡟⠈⠉⠉⠁⠀⠉⠉⠉⠱⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢼⣇⠧⢟⢿⣺⣣⣇⣻⣞⣜⣚⣿⣿⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢀⣛⣛⣿⣟⣻⢻⢽⣻⡿⣿⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠇⠲⣶⠀⠶⠄⠰⠲⠶⠆⠀⠀⠀⠀⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡃⠀⠀⠈⠻⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠄⠀⠠⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠁⠻⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⢀⣀⣀⣀⣠⣄⣀⣹⣫⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡛⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢻⠿⠋⠀⠁⠉⠉⠽⠍⢛⡉⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡏⠀⠀⠀⢀⣶⣶⣶⣾⣿⣿⣤⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡍⠉⠉⢽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠠⣦⣤⣤⣠⣾⣷⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠙⢻⡇
⠀⠀⠀⠀⠸⢿⠿⠿⠿⣿⠿⢿⣿⡆⢸⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠉⠀⠉⠈⠉⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠐⢕⣦⠀⣙⣷⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⣬⣭⣥⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠁⠿⣿⣿⣇⣘⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣤⣿⡿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣤⠀⠀⠀⠀⢻⡹⣹⠁⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⢸⣿⡇⠀⠀⣤⣴⠀⡇⠀⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⡿⣿⣯⣼⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣀⡁
⢸⡟⠇⠀⠀⠀⠛⢿⣷⡆⣿⣿⡟⠁⠀⠙⢻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⢚⣶⡾⣯⣛⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠙⢳⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠘⠛⢿⡇
⠈⠀⠀⠀⠀⠀⠀⠀⢉⠛⠟⢻⡇⠀⠀⠀⠘⠿⢿⢷⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢾⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠀⢰⠟⠈⠛⠻⠿⠻⠿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⢀⣼⠁⠀⠀⢀⣠⣀⢄⣀⠉⣴⢶⠷⢾⣷⣶⣾⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⢟⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣀⣀⣀⣴⣷⣦⣠⣤⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣴⣄⠀⠀⠀⣸⣿⣄⠀⢀⣠⣿⣿⣹⣿⣸⣿⢈⣿⣿⡇⣶⢳⣯⢹⣿⣽⣻⣿⡿⣟⣛⡿⣸⠿⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⠻⡟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⠃⢤⠈⣿⣿⣿⣷⣿⣿⣿⣿⣿⢸⣇⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡻⢸⣏⡃⣿⡇⣾⡟⣸⣗⡊⣾⢻⡇⢤⣤⡄⠀⢀⣐⣡⣶⣾⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⡟⠀⠘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⠉⠁⠉⠸⠃⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⢿⢸⣇⣿⠐⠿⢯⣿⣿⣿⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠠⢰⣶⣾⢸⣷⡆⠀⢠⣶⣿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⡿⢶⣶⣶⡇⠉⠈⠁⢛⡛⢘⣣⣿⣸⡼⢿⣿⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡟⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⣸⣥⣼⣿⣿⣿⠛⠋⢁⣀⡀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⢰⣾⣿⣿⣦⡀⠀⠀⠀⠉⠾⠿⢿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢻⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣟⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⢠⣤⡄⡤⣍⢭⢩⢹⡟⡍⢲⠂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡟⠈⠉⠉⠁⠀⠉⠉⠉⠱⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇⡅⣿⣿⢸⣸⠄⡏⡆⢸⢴⣇⠧⢟⢿⣺⣧⣇⢻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢀⣛⣛⣿⣟⣻⢻⢽⣻⡿⣿⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠇⠲⣶⠀⠶⠄⠰⠲⠶⠆⠀⠀⠀⠀⢻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡃⠀⠀⠈⠻⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠁⠻⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣤⣠⣠⣤⣤⣀⣹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡛⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢻⠿⠋⠀⠁⠉⠉⠽⠍⢛⡉⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⢀⣶⣶⣶⣶⣿⣿⣤⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡍⠉⠉⢽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⡀⠀⠀⠀⠠⣶⣤⣤⣠⣿⣷⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠙⠻⡇
⠀⠀⠀⠀⠸⢿⠿⠿⠿⣿⠿⢿⣿⡆⢸⣿⣿⣿⣿⣧⡀⠀⠀⠀⠈⠉⠀⠉⠈⠉⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⣠⣀⡁
⠀⠀⠀⠀⠀⠀⠀⢀⠐⢕⣦⠀⣙⣷⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⣬⣭⣥⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠿⣿⣿⣇⣘⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣤⣿⡿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣤⠀⠀⠀⠀⢻⡽⢻⠁⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⢸⣿⡇⠀⠀⣤⣴⠀⡇⠀⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⡟⣻⣯⣽⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣀⡁
⢸⡟⠇⠀⠀⠀⠛⢿⣷⡇⣿⣿⡟⠁⠀⠙⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⢚⣶⡾⣯⣛⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠃⠙⢻⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠘⠛⢿⡇
⠈⠀⠀⠀⠀⠀⠀⠀⢉⠋⠟⢻⡏⠀⠀⠀⠘⠿⢿⢷⡄⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢾⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠀⢰⠇⠀⠿⠿⡿⠿⢿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣼⠁⠀⠀⢀⣠⣀⢀⣐⠑⣳⢲⠷⢾⣷⣶⣾⣿⣿⣯⣿⣧⣟⣻⣿⣻⠷⢟⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣀⣀⣠⣰⣷⣤⣠⣬⣥⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣰⣶⣤⡀⠀⠀⣸⣿⣄⠀⢀⣠⣿⣿⣹⣿⣸⣿⢈⣿⣿⡇⣶⢻⣏⢹⣿⣽⣿⣿⡿⣟⣛⡿⣸⠿⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⠻⡟⠽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⠃⢤⠈⣿⣿⣿⣷⣿⣿⣿⣿⣿⢸⣏⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡻⢸⣏⡃⣿⡇⣾⡟⣸⣗⡊⣾⢻⡇⢤⣤⡄⠀⢀⣐⣡⣶⣾⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⡟⠀⠘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⠉⠁⠉⠸⠃⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢸⡿⣾⣿⢾⣇⣿⠠⢿⣯⣿⣿⣿⣫⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡆⠀⢠⣶⣿⣿⣿⣿⣷⣶⣶⣷⣿⣾⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⡿⣶⣶⣶⡇⠉⠈⠁⢛⡛⢘⣣⣿⣸⣼⢿⣿⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡟⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡃⠀⠀⠀⠀⠀⣸⣷⣼⣿⣿⣿⠛⠋⠁⡀⡀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⢰⣾⣿⣿⣦⡀⠀⠀⠀⠉⠾⠿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢺⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣟⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢠⣤⡄⡤⣍⢭⢩⢹⡟⡍⢲⠂⡏⡆⣎⣶⡧⡇⡇⣿⢿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡟⠈⠉⠉⠁⠀⠉⠉⠉⠑⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢰⣇⠧⢟⢿⣸⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢀⣚⣛⣿⣟⣻⢻⢿⣻⡿⣿⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣩⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⣗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠇⠲⣶⠀⠶⠄⠰⠰⠶⠆⠀⠀⠀⠀⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡃⠀⠀⠈⠻⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠁⠻⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣟⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣤⣤⣤⣤⣤⣀⣹⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡛⢛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⣻⠿⠋⠀⠁⠉⠉⠽⠉⢙⡉⢻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡏⠀⠀⠀⢀⣶⣶⣶⣾⣿⣿⣦⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡍⠉⠉⠽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡀⠀⠀⠀⠠⣶⣤⣤⣤⣿⣷⣦⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠻⠇
⠀⠀⠀⠀⠸⢿⠿⠿⠿⣿⠿⢿⣿⡇⢸⣿⣿⣿⣿⣧⣀⠀⠀⠀⠈⠉⠀⠉⠈⢉⣯⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠐⢿⣦⡀⣉⣷⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠤⣤⣭⣥⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠟⣿⣿⣆⣘⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢠⣤⣾⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⠀⠀⠀⠀⢹⠽⣻⠁⣿⣿⣿⡏⠀⢨⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⢸⣿⡇⠀⠀⣤⣼⠠⠃⡀⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⡿⣿⣯⣽⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣀⡀
⢸⡟⠇⠀⠀⠀⠙⢿⣷⡇⣿⣿⡿⠁⠀⠙⢻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⢚⣶⡶⣯⣛⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠃⠛⢳⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠘⠛⠿⡇
⠈⠀⠀⠀⠀⠀⠀⠀⢹⠓⠟⢻⡇⠀⠀⠀⠘⠿⢿⣿⡆⠀⠀⠀⠀⢀⠀⢠⣴⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢾⣿⣿⣿⣿⣿⣿⡿⠉⠉⠋⠀⢰⠆⠈⠿⠻⡿⠿⢿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠎⠈⢀⣸⠁⠀⠀⢀⣀⣠⢀⣐⠈⣑⢶⠷⢾⣿⣶⣾⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⢟⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣀⣀⣀⣰⣷⣤⣠⣬⣥⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣴⣤⡄⠀⠀⣸⣿⣆⠀⢀⣠⣿⣿⣹⣿⣸⣿⢈⣿⣿⡇⣶⢳⣏⢻⣿⣽⣻⣿⡿⣟⣛⡿⣈⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⠻⡟⠽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⠃⢠⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⢸⣇⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣸⣗⡊⣾⢻⡇⢤⣤⡄⠀⢀⣀⣡⣶⣾⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠐⣾⣿⣿⣿⡿⠀⠘⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⠉⠁⠉⠸⠣⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢸⡿⣾⢿⢺⣇⣿⡀⢿⡏⣿⣿⣿⣫⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣷⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢶⣶⣶⡧⠉⠈⠁⢛⡛⢘⣣⣿⣸⡼⢿⣿⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡟⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣸⣧⣴⣿⣿⣿⠟⠉⠁⣀⠀⠀⠀⠀⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣯⠀⢠⣾⣿⣷⣦⡀⠀⠀⠀⠈⠾⠿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣟⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⡄⡤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⡎⣶⡧⡇⡇⣿⢿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠑⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡅⣿⣿⢸⣸⠄⡏⡆⢸⢄⣇⠧⢟⣿⣸⣧⣇⢻⣞⣜⣚⣿⣿⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢀⣚⣛⣿⣟⣻⢻⢽⣻⡿⣿⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠗⠲⣶⠀⠶⠄⠰⠲⠶⠆⠀⠀⠀⠀⢹⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡃⠀⠀⠈⠹⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠀⠠⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠻⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣤⣤⣤⣤⣦⣄⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡛⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⣻⠿⠉⠀⠁⠁⠈⠭⠍⠛⡉⢻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡏⠀⠀⠀⢀⣶⣶⣶⣾⣿⣿⣦⠙⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⠀⠈⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡄⠀⠀⠀⠰⣶⣶⣴⣶⣿⣿⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠻⡇
⠀⠀⠀⠀⠘⠿⠿⠿⠿⣿⠿⢿⣿⡇⢸⣿⣿⣿⣿⣧⣀⠀⠀⠀⠈⠉⠀⠉⠈⢉⣿⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢯⣶⡀⣉⣷⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠤⢤⣿⣥⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠑⠿⣿⣿⣇⣘⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣤⣾⡿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣤⡀⠀⠀⠀⠹⠽⣻⠁⣿⣿⣿⡯⠀⢀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⢸⣿⡇⠀⠀⣤⣴⣀⡏⡀⢿⣿⣿⡇⠀⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⡿⣿⣟⣽⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⣀⡀
⢸⡟⠇⠀⠀⠀⠙⢿⣷⡇⣾⣿⣿⠁⠀⠘⢻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⢛⣵⡶⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠋⠛⢳⣿⣿⣿⣿⣷⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠘⠛⢿⡇
⠈⠀⠀⠀⠀⠀⠀⠀⢈⠃⠟⢻⡟⠀⠀⠀⠘⠿⠿⣿⡆⠀⠀⠀⠀⣀⠀⢀⣴⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢺⣿⣿⣿⣿⣿⣿⣿⠉⠉⠋⠀⢰⠆⠈⠻⠻⡿⠿⢿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢀⣸⡇⠀⠀⢀⣤⣀⢄⣀⠃⣱⢷⠷⢿⣿⣶⣾⣿⣿⣯⣿⣧⣟⣻⣿⣻⠷⢟⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣀⣀⣀⣰⣷⣄⣠⣬⣥⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣰⣶⣤⣄⠀⠀⣸⣿⣇⠀⢀⣠⣿⣿⣹⣿⣸⣿⢈⣿⣿⡇⣶⢻⣯⢻⣿⣽⣻⣿⡿⣟⣻⡿⣈⠿⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⠻⡏⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⠃⢠⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡏⢤⣤⡄⠀⢀⣐⣡⣶⣾⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣾⣿⣿⣿⣿⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⠍⠁⠉⠸⠣⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⣿⢿⣇⣿⠰⢿⣏⣿⣿⣿⣻⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣷⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⡿⢶⣶⢶⡷⠉⠈⠁⢛⡛⢘⣣⣿⣸⣼⢿⣿⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡟⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣠⣷⣼⣿⣿⣿⠟⠋⠁⣀⡀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⢠⣾⣿⣷⣦⡄⠀⠀⠀⠉⠾⠿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢺⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⡄⡤⣍⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡇⡇⣿⢿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠑⣯⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢜⣇⠧⢟⣿⣺⣧⣇⢻⣞⣜⣚⣿⣿⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢄⣚⣛⣿⣟⣻⢻⢽⣻⡿⣿⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠗⠲⣶⠀⠶⠄⠰⠰⠶⠆⠀⠀⠀⠀⣻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠹⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠄⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠙⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣤⣤⣴⣶⣶⣤⣼⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡛⢉⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢻⠿⠉⠀⠀⠀⠈⠩⠍⠙⡉⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡏⠀⠀⠀⢀⣶⣶⣶⣾⣿⣿⣦⡙⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⡆⠀⠀⠹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡄⠀⠀⠀⠐⢶⣶⡶⣶⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠻⡇
⠀⠀⠀⠀⠐⠿⠿⠿⠿⣿⠿⢿⣿⡇⢸⣿⣿⣿⣿⣧⣀⠀⠀⠀⠈⠁⠂⠀⢀⣉⣿⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢯⣶⡀⣉⣿⠀⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠦⢶⣶⣶⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠑⠿⣻⣿⣇⣈⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣤⣾⡿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣦⡀⠀⠀⠀⠹⠽⢻⠁⢿⣿⣿⡯⠀⢀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⢸⣿⡇⠀⠀⣤⣶⠀⡏⡀⢿⣿⣿⡇⠀⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⡿⢿⣟⣹⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⣄⡀
⢸⡟⠇⠀⠀⠀⠉⠿⣷⡇⣼⣿⣿⠁⠀⠈⢻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⢛⣵⡶⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠋⠛⢣⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠘⠛⠻⡇
⠈⠁⠀⠀⠀⠀⠀⠀⢈⠃⡟⢻⡟⠀⠀⠀⠘⠻⠿⠿⣆⠀⠀⠀⢀⣀⠀⢀⣾⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢺⣿⣿⣿⣿⣿⣿⣿⠋⠉⠛⠁⢰⠆⠀⠹⠻⡿⠿⢿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⣸⡇⠀⠀⠠⣤⣄⣄⣀⠄⣀⢶⠿⢿⣿⣶⣷⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⢟⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⣀⢠⣷⣤⣀⣬⣥⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣰⣷⣶⡄⠀⠀⣸⣿⣇⠀⢀⣠⣾⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢻⣯⢻⣿⣽⣻⣿⡿⣟⣛⡿⣁⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⠻⡋⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⠇⢠⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣟⡊⣾⢻⡏⢤⣤⡄⠀⢀⣀⣠⣶⣾⣿⣿⡿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠐⣾⣿⣿⣿⣿⠀⠈⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡯⠁⠉⠘⠃⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢸⡿⣾⣿⢿⣇⣿⡠⣿⣏⣿⣿⣿⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢶⣶⣶⣷⠉⠈⠁⠛⡛⢘⣣⣿⣺⡼⢿⣿⠁⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣠⣯⣼⣿⣿⡿⠛⠉⠀⣀⡀⠀⠀⠀⠀⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢼⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣷⠀⢠⣾⣿⣿⣦⡄⠀⠀⠀⠉⠾⠿⢿⠿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⡄⡤⣌⢭⢩⢹⡟⡍⢲⠂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠁⣯⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢤⣇⠧⢟⣿⣺⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢆⣘⣛⣿⣟⣻⢻⢼⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⠶⠄⠰⠲⠶⠆⠀⠀⠀⠀⢻⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠙⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠄⠀⠀⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠙⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢠⣤⣤⣴⣶⣶⣤⣼⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡛⢉⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⣻⡿⠋⠀⠀⠀⠈⠨⠍⠩⡉⠻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⠿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⢀⣶⣶⣶⣾⣿⣿⣦⠘⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⠀⠀⠻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⢶⣶⡶⣶⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠻⡇
⠀⠀⠀⠀⠀⠿⠿⠿⠿⣿⠿⠿⣿⡇⢸⣿⣿⣿⣿⣷⣀⠀⠀⠀⠈⠁⠂⠀⢀⣉⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠄⢭⣻⡀⣉⣿⠀⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠠⠶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠑⠿⣻⣿⣇⣘⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⣤⣾⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣦⡀⠀⠀⠀⠹⠽⣻⠃⢿⣿⣿⣯⠀⢀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⢸⣿⡇⠀⠀⢤⣴⠀⡏⡀⢿⣿⣿⡇⠀⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⡿⢿⣟⣻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⣀⡀
⢸⡟⠇⠀⠀⠀⠉⠿⣷⡇⣾⣿⣿⠁⠀⠈⢻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⢛⣵⡶⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠋⠛⢡⣽⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠈⠙⠻⡇
⠈⠁⠀⠀⠀⠀⠀⠀⢈⠃⠟⢻⡟⠀⠀⠀⠘⠿⠿⠿⡂⠀⠀⠀⢀⣀⠀⢀⣾⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⣿⠉⠉⠛⠁⢠⠄⠀⠹⠿⣿⠿⢿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⣸⡇⠀⠀⠠⣤⣄⣄⣐⠠⣊⢿⠿⢾⣿⣾⣿⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣀⠀⢠⣷⣄⣀⣬⣅⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣶⣶⡄⠀⠀⣰⣿⣇⠀⢀⣠⣾⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢻⣯⢻⣿⣽⣻⣿⡿⣟⣻⡿⣁⠿⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⢻⡋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⠇⢠⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡏⢤⣤⡄⠀⠀⣐⣡⣴⣶⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠐⣾⣿⣿⣿⣿⠀⠈⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠸⠣⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⣸⡿⣾⣿⢿⣇⣿⡀⣿⣏⣿⣿⣿⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣷⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢶⣶⣶⣷⠉⠈⠁⠛⣛⢘⣣⣿⣸⣼⢿⣿⠀⠀⠀⠀⠘⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⣧⣼⣿⣿⡿⠛⠉⠀⡀⡀⠀⠀⠀⠀⠉⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⢠⣾⣿⣿⣦⡀⠀⠀⠀⠉⠾⠿⢿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⣤⡄⡤⣌⢭⢩⢹⡟⡍⢲⠂⡏⡆⣎⣶⡧⡇⡇⣿⢿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠁⣯⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢜⣇⠧⢟⣿⣺⣧⣇⣻⣞⣜⣚⣿⣿⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢆⣚⣛⣿⣟⣻⢻⢽⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⠶⠄⠰⠰⠶⠆⠀⠀⠀⠀⢹⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⠛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠛⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠙⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢠⣤⣴⣶⣶⣶⣤⣼⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡛⢉⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢻⠿⠋⠀⠀⠀⠈⠨⠍⠉⡉⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢾⢿⢿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡏⠀⠀⠀⢀⣶⣶⣶⣾⣿⣿⣦⡘⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡅⠀⠀⠻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡆⠀⠀⠀⠐⢶⣶⡶⣶⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⡇
⠀⠀⠀⠀⠐⠿⠿⠿⠟⣿⠿⠿⣿⡇⢸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠈⠁⠀⠀⢀⣉⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠭⣻⡀⢉⣿⠀⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠶⢶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠑⠛⣻⣿⣇⣸⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣴⣿⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣦⡀⠀⠀⠀⠉⠽⢻⠃⢿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⡇
⢸⣿⡇⠀⠀⣤⣴⢀⠇⡀⢿⣿⣿⡷⠀⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⡿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣤⡀
⢸⡟⠇⠀⠀⠀⠉⠿⣷⡇⣾⣿⣿⠁⠀⠈⢻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⢛⣵⡶⣯⢟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⠋⠻⢡⣽⣿⣿⣿⣧⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠈⠙⠻⠇
⠈⠁⠀⠀⠀⠀⠀⠀⢈⠃⡟⢻⡟⠀⠀⠀⠘⠻⠿⡿⡷⠀⠀⠀⠀⣀⠀⠀⣾⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢺⣿⣿⣿⣿⣿⣿⡿⠛⠉⠛⠁⢠⠆⠈⠻⠿⣿⠿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠁⣸⡇⠀⠀⠠⣤⣤⣄⣀⠔⣕⢶⠿⢾⣿⣶⣿⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣀⢀⢠⣶⣄⣀⣉⣅⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣶⣴⡅⠀⠀⣰⣿⣇⡀⢀⣠⣾⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢳⣯⢻⣿⣽⣻⣿⡿⣟⣻⡿⣅⠿⠿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠻⢻⡋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⠇⢰⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣇⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡏⢤⣤⡄⠀⢀⣐⣡⣴⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠐⣾⣿⣿⣿⣿⠀⠈⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠸⠣⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢸⡿⣾⣿⢻⣇⣿⡀⣾⣟⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢶⣶⢶⣷⠉⠈⠁⠛⣛⠘⣣⣿⣹⣼⢿⣿⠀⠀⠀⠀⠘⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⣧⣼⣿⣿⣿⠛⠉⠀⣀⣀⠀⠀⠀⠀⠉⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢼⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣏⠀⢠⣾⣿⣿⣦⡀⠀⠀⠀⠩⠾⠿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢺⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⣤⡄⣤⣌⢭⢩⢹⡟⡍⢲⠂⡏⡆⣎⣾⡧⡇⡇⣷⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠁⣯⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢜⣇⠧⢟⣿⣺⣧⣇⣻⣞⣜⣚⣿⣿⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢆⣚⣛⣿⣟⣻⢻⢽⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⢶⠄⠰⠲⠶⠆⠀⠀⠀⠀⢹⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣷⣿⣿⣿⣿⣇⠀⠀⠀⠹⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠙⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢠⣤⣴⣶⣶⣶⣦⣼⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡋⢉⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢻⠿⠋⠀⠀⠀⠈⠨⠍⠉⡉⠻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣾⣿⢿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⢀⣶⣶⣶⣾⣿⣿⣦⡘⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡅⠀⠀⠻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡄⠀⠀⠀⠐⢶⣶⡶⣶⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠇
⠀⠀⠀⠀⠀⠿⠿⠿⠻⣿⠿⠿⣿⡇⢸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⢀⣉⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡔⢭⣻⡀⢉⣿⠀⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠶⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠱⠟⣻⣿⣇⣰⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣦⣿⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣦⡀⠀⠀⠀⠉⠽⢻⠃⢿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⡇
⢸⣿⡇⠀⠀⣤⣴⢀⠇⡀⢿⣿⣿⡧⠀⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⢿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣄⡀
⢸⡟⠇⠀⠀⠀⠉⠿⣷⡇⣼⣿⣿⠁⠀⠈⢻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⢛⣵⡾⣯⢟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠋⠻⢅⣽⣿⣿⣿⣧⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠈⠙⠻⡇
⠈⠁⠀⠀⠀⠀⠀⠀⢈⠃⡛⢻⡟⠀⠀⠀⠘⠻⠿⣿⡷⠄⠀⠀⢀⣀⠀⠀⣾⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢺⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠁⢠⠄⠀⠻⠿⣿⠿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠁⣸⡇⠀⠀⠠⣴⣤⣄⣐⠖⣇⢶⠿⢾⣿⣶⣿⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄⣀⣉⣁⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣶⣶⡥⠀⠀⣰⣿⣇⡀⢀⣠⣾⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢳⣯⢻⣿⣽⣿⣿⡿⣟⣻⡿⣁⠿⠿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠻⢿⡛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⠇⢰⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡏⢤⣤⡄⠀⠀⠀⣁⣤⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⠀⠈⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠘⠣⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢸⡿⣾⣿⢻⣇⣷⡀⣾⣟⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢶⣶⢶⣷⠉⠈⠁⠛⣛⠘⣣⣿⣸⣼⢿⣿⠀⠈⠁⠁⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⣧⣼⣿⣿⣿⠛⠉⠀⠀⢀⠀⠀⠀⠀⠉⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢼⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⢠⣾⣿⣿⣦⡀⠀⠀⠀⡩⠾⠿⢿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⡄⡤⣜⢭⢩⢹⡟⡍⢲⠂⡎⡆⡎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠁⣯⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢤⣇⠧⢟⣿⣺⣧⣇⣻⣜⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢆⣘⣛⣿⣟⣻⢻⢽⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢹⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣷⣿⣿⣿⣿⣇⠀⠀⠀⠛⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠠⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣤⣶⣶⣶⣶⣦⣼⣥⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡛⢍⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⣻⠿⠋⠀⠀⠀⠈⠨⠍⠉⡉⠻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢾⣿⠿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡏⠀⠀⠀⢀⣴⣶⣶⣾⣿⣿⣦⠘⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⠀⠀⠻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣬⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡆⠀⠀⠀⠐⢶⣶⢶⣶⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⡇
⠀⠀⠀⠀⠐⠛⠿⠿⠻⣿⠿⠿⣿⡇⢸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⢀⣉⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠄⢭⣿⡀⣉⣿⠀⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠠⢶⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠑⠟⣻⣿⣇⣐⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣴⣿⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣦⡀⠀⠀⠀⠉⡙⢻⠃⣿⣿⣿⣯⠀⢀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠉⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⢸⣿⡇⠀⠀⣤⣴⣀⠆⡀⢿⣿⣿⡧⠀⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⡿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣄⡀
⢸⡟⠇⠀⠀⠀⠉⠿⣷⡇⣭⣿⣿⠁⠀⠈⢻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⢛⣵⡾⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠏⠻⢅⣿⣿⣿⣿⣦⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠛⢻⡇
⠈⠁⠀⠀⠀⠀⠀⠀⢀⠃⡟⢻⡟⠀⠀⠀⠈⠻⠿⠿⡳⠀⠀⠀⠀⣀⠀⠠⣾⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠁⢰⠄⠈⠻⢿⣿⢿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠞⠀⠁⣼⡇⠀⠀⠠⣤⣤⣄⣐⠢⣀⢾⠿⢾⣿⣾⣿⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣀⣀⣉⣁⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣶⣶⡤⠀⠀⣴⣿⣇⡀⢀⣠⣾⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢳⣯⢹⣿⣽⣿⣿⡿⣟⣛⡿⣁⠿⠿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠟⢿⡛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⡇⢰⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣇⣿⢸⣧⣿⢸⡟⣿⠋⣿⣸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡏⢤⣤⡄⠀⠀⠀⣁⣤⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡀⣾⣿⣿⣿⣿⠀⠈⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠸⠣⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢸⡿⣾⣿⢿⣇⣷⡠⣾⣟⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣷⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢶⣶⠶⢷⠉⠈⠁⠛⡛⢘⣣⣿⣹⣼⢿⣿⠀⠈⠁⠁⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⣯⣼⣿⣿⣿⠛⠉⠀⡀⣀⠀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢾⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠀⢀⣾⣿⣿⣦⡀⠀⠀⠀⡨⠾⠿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢽⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⡄⡤⣜⢭⢩⢹⡟⡍⢲⠂⡎⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠁⣯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢼⣇⠧⢟⣿⣺⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢆⣚⣛⣿⣟⣻⢻⢼⣻⡿⣿⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⠶⠄⠰⠴⠶⠆⠀⠀⠀⠀⢻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣷⣿⣿⣿⣿⣇⠀⠀⠈⠙⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣴⣶⣶⣶⣶⣦⣾⣥⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡋⣉⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⣻⠿⠃⠀⠀⠀⠈⠨⠍⠉⡉⠻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠾⠿⠿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡏⠀⠀⠀⢀⣴⣶⣶⣾⣿⣿⣦⡘⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⡻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⢶⣶⢶⣶⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⡇
⠀⠀⠀⠀⠀⠛⠿⠿⠻⣿⠿⠿⣿⡇⢸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠂⠀⢀⣉⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⣠⣤⡀
⠀⠀⠀⢀⠀⠀⠀⢀⠄⢭⣻⡀⣉⣿⠀⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠠⢶⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠙⠟⣻⣿⣇⣰⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣶⣿⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣦⡀⠀⠀⠀⠉⠽⢻⠁⢿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⡇
⢸⣿⡇⠀⠀⡤⣴⡀⡆⡀⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⡿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣄⡀
⢸⡟⠇⠀⠀⠀⠉⠿⣷⡇⣯⣿⣿⠁⠀⠈⢻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⢛⣵⡶⣯⢟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠋⠛⢅⣾⣿⣿⣿⣦⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠈⠛⢻⡇
⠈⠁⠀⠀⠀⠀⠀⠀⢀⠃⡛⢻⡟⠀⠀⠀⠈⠿⠿⠿⡢⠀⠀⠀⢀⣀⠀⠀⣾⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⡏⠋⠉⠛⠁⢠⠄⠈⠻⢿⣿⢿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠁⣼⡇⠀⠀⠠⣤⣤⣄⣐⠶⣀⢶⠷⢾⣿⣾⣿⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⢟⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣉⣁⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣴⣶⣶⡤⠀⠀⣴⣿⣇⡀⢀⣠⣾⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢳⣯⢻⣿⣽⣿⣿⡿⣟⣛⡿⣅⠿⠿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠻⢿⡛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⢀⣾⣿⣿⣿⠇⢰⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣇⣿⢸⣧⣿⢸⡟⣿⠋⣿⣸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡇⢤⣤⡄⠀⠀⠀⣁⣤⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⠀⠈⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠸⠣⠛⠘⠏⠹⢇⢿⠼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⣿⢿⣇⣧⡠⣾⣟⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢶⣶⣶⣷⠉⠈⠁⠛⡛⢘⣣⣿⣹⣼⢿⣿⠀⠈⠁⠁⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣠⣯⣼⣿⣿⣿⠛⠉⠀⡀⡀⠀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢼⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠀⢀⣾⣿⣿⣦⡀⠀⠀⠀⡠⠾⠿⢿⠿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⡄⡤⣍⢭⢩⢹⡟⡍⢲⠂⡏⡆⣎⣶⡧⡇⡇⣷⢿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠁⣯⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡅⣿⣿⢸⣸⠄⡏⡆⢸⢸⣇⠧⢟⣿⣺⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢄⣚⣛⣿⣟⣻⢻⢽⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠗⠲⣶⠀⠶⠄⠰⠴⠶⠆⠀⠀⠀⠀⢹⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣷⣿⣿⣿⣿⣅⠀⠀⠀⠹⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣤⣶⣶⣶⣶⣶⣾⣴⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡛⣉⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⣻⠿⠋⠀⠀⠀⠈⠨⠍⠉⡉⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⠾⠿⠿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⢀⣴⣶⣶⣾⣿⣿⣦⡘⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡆⠀⢀⡺⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⢶⣶⠶⣒⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠇
⠀⠀⠀⠀⠀⠛⠿⠿⠛⣿⠿⠿⣿⡇⢸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⢀⣉⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠄⢭⣷⡀⣈⣿⠀⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠤⢶⣶⣶⣦⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠑⠛⣿⣿⣇⣰⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢴⣾⣿⣿⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣦⡄⠀⠀⠀⠉⡙⣻⠁⢿⣿⣿⡿⠀⢀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠉⠉⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⡇
⢸⣿⡇⠀⠀⡤⣦⢀⠇⡀⢿⣿⣿⡗⠀⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⡿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⣄⡀
⢸⡟⠃⠀⠀⠀⠉⠿⣷⣇⣼⣿⣿⠁⠀⠈⢻⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⢛⣵⡾⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠏⠻⢅⣾⣿⣿⣿⣦⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠈⠛⢻⡇
⠀⠁⠀⠀⠀⠀⠀⠀⢀⠃⡟⢻⡟⠀⠀⠀⠘⠻⠿⠿⣷⠀⠀⠀⢀⣀⠀⠀⣾⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢺⣿⣿⣿⣿⣿⣿⡏⠋⠉⠛⠁⢠⠀⠀⠻⠿⣿⠿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠾⠀⠁⣸⡇⠀⠀⠠⣤⣄⣄⣁⠶⣀⢾⠿⢾⣿⣶⣿⣿⣿⣯⣿⣧⣟⣻⣿⣻⠷⢟⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀⣀⣉⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣾⣶⡦⠀⠀⣰⣿⣇⡀⢀⣠⣾⣿⣹⣿⣸⣿⢈⣿⣿⡇⣶⢳⣯⢻⣿⣽⣻⣿⡿⣟⣛⡿⣇⠿⠻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠻⢿⡙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⠇⢰⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡇⢤⣬⡄⠀⠀⠀⣡⣤⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⠀⠈⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠸⠣⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⣿⢿⣇⣷⣀⣾⣟⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣷⡎⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⢾⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢶⣶⣶⡷⠉⠈⠁⠛⣛⢘⣣⣿⣹⡼⢿⣿⠁⠀⠉⠁⠹⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⣧⣼⣿⣿⣿⠛⠉⠀⡀⡀⠀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⢠⣾⣿⣿⣦⡀⠀⠀⠀⡠⠾⠿⣿⠿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢼⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⡄⡤⣍⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣾⡧⡇⡇⣷⢿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠁⣯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡅⣿⣿⢸⣸⠄⡏⡆⢸⢼⣇⠧⢟⣿⣺⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢆⣘⣛⣿⣟⣻⢻⢽⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⠶⠄⠰⠰⠶⠆⠀⠀⠀⠀⢹⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣷⣿⣿⣿⣿⣅⠀⠀⠀⠹⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠉⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣴⣶⣶⣶⣶⣶⣾⣴⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡛⢍⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⠿⠋⠀⠀⠀⠈⠨⠍⠉⡉⠛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⢾⠿⠿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⢀⣴⣶⣶⣾⣿⣿⣦⡘⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⣇⠀⢀⡚⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⡆⠀⠀⠀⠐⢷⣶⠶⣲⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠇
⠀⠀⠀⠀⠀⠿⠿⠿⠛⣿⠿⠿⣿⣧⠰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⢀⣉⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠭⣿⡀⣈⣿⠀⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠤⣶⣶⣶⣦⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠛⣻⣿⣗⣴⣻⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣦⡀⠀⠀⠀⠉⡝⣻⠇⢺⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠉⠉⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⡇
⢸⣿⡇⠀⠀⡤⣶⣀⡋⡀⢻⣿⣿⡿⠀⢾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⡿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣤⡀
⢸⡟⠃⠀⠀⠀⠉⠿⣷⣇⣸⣿⣿⠁⠀⠈⠻⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣿⢛⣵⡾⣯⢟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠇⠛⠅⣼⣿⣿⣿⣧⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠈⠋⠻⡇
⠀⠁⠀⠀⠀⠀⠀⠀⢀⠃⡟⢻⡿⠀⠀⠀⠈⠻⠿⠿⢗⡀⠀⠀⠀⣀⠀⠀⣼⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠁⢠⠄⠀⠻⠿⣿⠿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠁⣼⡇⠀⠀⠀⣤⣄⣄⣁⠢⣂⢾⠿⢾⣿⣶⣿⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣀⣀⣉⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣰⣾⣶⣦⠀⠀⣰⣿⣇⡀⢀⣠⣾⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢻⣯⢻⣿⣽⣿⣿⡿⣟⣛⡿⣇⠿⠿⣿⡿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠻⢿⡋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⡇⢰⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢹⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡇⢤⣬⡄⠀⠀⠀⣡⣤⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⠀⠀⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠸⠣⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢸⡿⣾⣿⢿⣇⣷⣀⣾⣟⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡎⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢶⣶⠶⠷⠉⠈⠁⠛⣛⢘⣣⣿⣺⣼⢿⣿⠀⠀⠁⠁⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣀⣷⣬⣿⣿⣿⠛⠉⠀⡀⠀⠀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⢠⣾⣿⣿⣦⡀⠀⠀⠀⡠⠾⠿⣿⠿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢼⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⡄⡤⣍⢭⢩⢹⡟⡍⢲⠂⡏⡆⣎⣶⡧⡇⡇⣷⢿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠁⣯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡅⣿⣿⢸⣸⠄⡏⡆⢸⢼⣇⠧⢟⢿⣺⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠷⢶⣿⣿⢿⢆⣘⣛⣿⣟⣻⢻⢽⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠙⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠠⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠉⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣴⣶⣶⣶⣶⣶⣾⣶⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⣛⢏⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡾⠋⠀⠀⠀⠈⠨⠍⠹⡉⠛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠾⠿⠿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣦⡈⢻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡚⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢘⣿⣿⣿⣿⡆⠀⠀⠀⠀⢶⣶⠶⣲⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠇
⠀⠀⠀⠀⠐⠟⠿⠿⠟⣿⠿⠿⣿⣧⠸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⠀⣉⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠽⣻⡀⢈⣿⠀⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢤⣶⣶⣶⣦⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠚⣻⣿⣗⣼⣻⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣬⣿⣿⣿⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣦⡀⠀⠀⠀⠉⠽⣻⠇⢺⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠉⠉⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⡇
⢸⣿⡇⠀⠀⡤⣦⣀⡊⡀⢻⣿⣿⡿⠀⢾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⡿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣀⡀
⢸⡟⠃⠀⠀⠀⠉⠿⣷⣇⣸⣿⣿⠁⠀⠈⢻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⢛⣵⡾⣯⢟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠇⠛⢅⣾⣿⣿⣿⣧⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠈⠛⠻⠇
⠈⠁⠀⠀⠀⠀⠀⠀⢀⠃⣟⢻⡿⠀⠀⠀⠘⠻⠿⠿⢦⠀⠀⠀⢀⣀⠀⠀⣴⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢹⣿⣿⣿⣿⣿⣿⡏⠋⠉⠛⠁⢠⠄⠀⠹⠿⣿⠿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠑⣼⡇⠀⠀⠀⣤⣤⣄⣀⠰⣀⢶⠿⢾⣿⣶⣿⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⣀⣉⣤⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣰⣾⣶⣧⠀⠀⣰⣿⣇⡀⠀⣠⣾⣿⣹⣿⣸⣿⢈⣿⣿⡇⣶⢻⣯⢻⣿⣽⣿⣿⡿⣟⣛⡿⣇⠿⠿⣿⡿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠻⢿⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⡇⢰⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡇⢤⣬⡄⠀⠀⠀⣡⣴⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣾⣿⣿⣿⣿⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠘⠣⠛⠘⠏⠹⢇⢿⠼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⣿⢻⣇⣷⡀⣾⣟⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡎⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢲⣶⠶⢷⠉⠈⠁⠛⣛⢘⣣⣿⣺⣼⢿⣿⠁⠀⠁⠁⠸⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⣧⣬⣿⣿⣿⠛⠉⠀⣀⠀⠀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⢠⣾⣿⣿⣦⡀⠀⠀⠀⡠⠾⠿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣋⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⡄⡤⣝⢭⢩⢹⡟⡍⢲⠂⡏⡆⡎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢼⣇⠧⢟⣿⣼⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠉⠀⠀⠀⠷⢶⣿⣿⢿⢆⣘⣛⣿⣟⣻⢻⢽⣻⡿⣿⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⠴⠄⠰⠲⠶⠆⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣷⣿⣿⣿⣿⣅⠀⠀⠀⠙⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣴⣶⣶⣶⣶⣶⣾⣴⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⣛⢏⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡿⠋⠀⠀⠀⠈⠨⠍⠩⡉⠟⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠷⠿⠿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣦⡈⢻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢀⣚⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢘⣿⣿⣿⣿⡆⠀⠀⠀⠀⢶⣶⠶⣒⣻⣿⡶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠇
⠀⠀⠀⠀⠀⠻⠿⠿⠛⣿⠿⠿⣿⣇⠰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⠀⣈⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡄⢽⣻⡀⢈⣿⠀⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣤⣶⣶⣶⣦⡆⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠑⠞⣻⣿⣗⣰⣻⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣦⡀⠀⠀⠀⠉⡙⣻⠇⢸⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠉⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⡇
⢸⣿⡇⠀⠀⢤⣦⡀⡊⡀⢻⣿⣿⡿⠀⢾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⡿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣀⡀
⢸⡟⠃⠀⠀⠀⠉⠿⣷⣇⣼⣿⣿⠁⠀⠈⢻⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⢛⣵⡾⣯⢟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠃⠛⢅⣼⣿⣿⣿⣧⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠈⠙⠛⡇
⠈⠁⠀⠀⠀⠀⠀⠀⢀⠃⠟⢻⡿⠀⠀⠀⠘⠻⠿⠿⠇⠀⠀⠀⠀⣀⠀⠀⣼⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢹⣿⣿⣿⣿⣿⣿⡯⠉⠉⠛⠁⢠⠄⠀⠻⠿⣿⠿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠁⣼⡇⠀⠀⠀⣄⣦⢄⣀⠢⣐⢴⠿⢾⣿⣶⣶⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⣀⣉⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣾⣶⣦⠀⠀⣰⣿⣇⡀⠀⣠⣾⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢳⣯⢻⣿⣽⣿⣿⡿⣟⣛⡿⣇⠿⠿⣿⡿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠹⢻⡉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣴⣿⣿⣿⡇⢰⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣇⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡇⢤⣬⡄⠀⠀⢀⣡⣴⣶⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡯⠁⠉⠘⠃⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢸⡿⣾⢿⢻⣇⣷⡠⣾⣛⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡎⠀⢠⣶⡿⣷⣿⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢲⡶⠶⠷⠉⠈⠁⠛⡛⢘⣣⣿⣸⣼⢿⣿⠁⠈⠁⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣠⣧⣬⣿⣿⣿⠋⠉⠀⡀⡀⠀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣗⠀⢠⣾⣿⣿⣦⡀⠀⠀⠀⡠⠾⠿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢺⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣊⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⡄⡤⣍⢭⢩⢹⡟⡍⢲⢂⡎⡆⣎⣶⡧⡇⡇⣷⢿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡅⣷⣿⢸⣸⠄⡏⡆⢸⢴⣇⠧⢟⢿⣺⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢄⣚⣛⣿⣟⣻⢻⢽⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⠶⠄⠰⠲⠶⠆⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠻⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢠⣤⣶⣶⣶⣶⣶⣾⣴⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⣛⢋⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡿⠋⠀⠀⠀⠈⠨⠍⠩⡉⠙⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⠷⠿⠿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣦⡈⢻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢀⡚⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠐⣿⣿⣿⣿⡆⠀⠀⠀⠀⢶⣶⠶⣒⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠇
⠀⠀⠀⠀⠀⠻⠿⠿⠛⣿⠿⠿⣿⣧⠰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⠀⣈⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠽⣻⡀⢈⣿⡁⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣶⣶⣾⣢⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠐⠛⣻⣿⣗⣼⣻⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣽⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣦⡄⠀⠀⠀⠉⡹⢻⠃⢸⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠉⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⡇
⢸⣿⡇⠀⠀⢤⣦⡠⡃⡀⢻⣿⣿⡿⠀⢾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⢹⣿⡿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣤⡀
⢸⡟⠃⠀⠀⠀⠙⠿⣷⣇⣼⣿⣿⠁⠀⠈⢻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣿⢛⣵⡾⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⠃⠛⢁⣾⣿⣿⣿⣧⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠈⠉⠛⡇
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠇⠟⢻⡿⠀⠀⠀⠈⠻⠿⠿⣇⠀⠀⠀⠀⣀⠀⢀⣾⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⡿⠉⠉⠛⠁⢠⠀⠀⠹⠿⣿⠿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠐⣸⡇⠀⠀⠀⣬⣤⣄⣀⠢⣐⢳⠿⢾⣿⣶⣾⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⣀⣉⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣾⣷⣤⠀⠀⣰⣿⣇⡀⠀⣠⣾⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢳⣯⢻⣿⣽⣻⣿⡿⣟⣛⡿⣇⠿⠿⣿⡿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠻⢻⡉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣴⣿⣿⣿⡇⢰⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢹⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡏⢤⣤⡄⠀⠀⢀⣣⣴⣶⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡯⠁⠉⠘⠃⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⣿⢿⣇⣷⡀⣾⣛⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡎⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠿⠲⣶⠶⢷⠉⠈⠁⠛⣛⠘⣣⣿⣹⣼⢿⣿⠀⠘⠁⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣠⣯⣬⣿⣿⣿⠋⠉⠀⣀⠀⠀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡧⠀⢠⣾⣿⣿⣦⡀⠀⠀⠀⡠⠾⠿⣿⠿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣚⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢢⣤⡄⡤⣜⢭⢩⢹⡟⡍⢲⠂⡌⡆⣎⣶⡧⡇⡇⣷⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡇⡅⣿⣿⢸⣸⠄⡏⡆⢸⠼⣇⠧⢟⢿⣺⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠉⠀⠀⠀⠷⢶⣿⣿⢿⢄⣛⣛⣿⣟⣻⢻⢽⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⠴⠄⠰⠶⠶⠆⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠹⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠀⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠃⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣴⣶⣶⣶⣶⣶⣾⣴⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⣛⢉⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡿⠋⠀⠀⠀⠈⠨⠍⠉⡉⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠿⠿⠿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡞⠀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣦⡈⢻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⢀⡺⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⢀⣜⣿⣿⣿⣿⣿⣿⣿⡇⠰⣿⣿⣿⣿⡆⠀⠀⠀⠀⢶⣶⠖⣒⣿⣿⡶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠇
⠀⠀⠀⠀⠀⢻⡿⠿⠛⣿⠿⠿⣿⣧⠰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⢀⣉⡿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⣀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠽⣻⡀⢈⣿⡁⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣶⣶⣶⣦⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠙⠟⣻⣿⣗⣼⣻⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣽⣿⣿⣿⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣦⡄⠀⠀⠀⠉⠙⢻⠃⢸⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⠉⠉⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⠇
⢸⣿⡇⠀⠀⢤⣤⡀⡂⡀⢻⣿⣿⡿⠀⢾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⡿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣠⡀
⢸⡟⠃⠀⠀⠀⠉⠿⣷⣇⣨⣿⣿⠁⠀⠈⢻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⢛⣵⡶⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⠃⠛⢅⣼⣿⣿⣿⣧⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠈⠙⢛⡇
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠇⠟⢛⡿⠀⠀⠀⠀⠻⠿⠿⡦⠀⠀⠀⠀⢀⠀⢀⣾⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⡯⠉⠉⠛⠁⢠⠀⠀⠹⠿⣿⠿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠑⣸⡇⠀⠀⠀⣌⣢⣄⣀⠦⣔⢾⠾⢾⣿⣾⣾⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⣀⣉⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣶⣶⡤⠀⠀⣰⣿⣇⡀⠀⣠⣾⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢳⣯⢹⣿⣽⣻⣿⡿⣟⣛⡿⣇⠿⠿⣿⡿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠻⢻⡋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠠⢀⣴⣿⣿⣿⡇⢰⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣇⣿⢸⣧⣿⢸⡟⣿⠋⣿⣸⡟⣿⢀⡛⢹⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡇⢤⣤⡄⠀⠀⢀⣣⣴⣶⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠸⠃⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⢿⢿⣇⣧⠠⣾⣛⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡎⠀⢠⣶⡿⣷⣯⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟⢲⡶⠶⢷⠉⠈⠁⠛⣛⠘⣣⣿⣸⣼⢿⣿⠀⠘⠁⠁⠹⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣠⣧⣬⣿⣿⣿⠋⠉⢀⣠⡀⠀⠀⠀⠀⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢼⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⢠⣾⣿⣿⣦⡀⠀⠀⠀⡠⠿⠿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣚⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢢⣤⡄⡤⣝⢭⢩⢹⡟⡍⢲⠂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠈⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢼⣇⠧⢟⢿⣺⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠉⠀⠀⠀⠷⢶⣿⣿⢿⢀⣛⣛⣿⣟⣻⢻⢽⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⢹⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣅⠀⠀⠈⠹⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠃⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣤⣶⣶⣶⣶⣶⣾⣶⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⣛⢍⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡿⠋⠀⠀⠀⠈⠨⠍⠩⡉⠛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⠿⠿⠿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣦⡈⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠐⡺⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠐⣿⣿⣿⣿⡆⠀⠀⠀⠀⢶⣶⠖⣒⣿⣿⡶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠃
⠀⠀⠀⠀⠀⢿⠿⠿⠟⣿⠿⠿⣿⣧⠰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⢀⣉⣷⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣠⣦⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠯⣻⡀⢉⣿⡁⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣶⣶⣶⣢⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠐⠞⣻⣿⣗⣼⣻⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣽⣿⣿⣿⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣦⡄⠀⠀⠀⠉⡹⢻⠇⢸⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⠇
⢸⣿⡇⠀⠀⢤⣤⡠⡃⡀⢻⣿⣿⡿⠀⢾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣄⡀
⢸⡟⠃⠀⠀⠀⠙⠿⣷⣇⣨⣿⣿⠁⠀⠈⢻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣿⢛⣵⡾⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⠃⠻⢅⣾⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠉⠛⠇
⠈⠁⠀⠀⠀⠀⠀⠀⢀⠇⠟⢻⡿⠀⠀⠀⠈⠻⠿⢿⣇⠀⠀⠀⠀⣀⠀⠀⣾⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⡯⠉⠉⠛⠁⢠⠀⠀⠻⠿⣿⢿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⣸⡇⠀⠀⠠⣌⣢⣄⣀⠤⣄⢾⠿⢷⣿⣶⣾⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⣀⣉⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣶⣶⣤⠀⠀⣰⣿⣇⡀⠀⣠⣾⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢳⣯⢻⣿⣽⣻⣿⡿⣟⣛⡿⣇⠿⠿⣿⡿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠿⢿⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣴⣿⣿⣿⡇⢰⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢸⣧⣿⢸⡟⣿⠋⣿⣸⡟⣿⢀⡛⢹⣏⡃⣿⡇⣿⡟⣼⣗⡊⣿⢻⡇⢤⣤⡄⠀⠀⢀⣡⣴⣶⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠘⠃⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⣿⢻⣇⣧⡠⣾⣛⣿⣿⣿⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡎⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢲⡶⠶⡷⠉⠈⠁⠛⡛⠘⣣⣿⣸⡼⢿⣿⠀⠘⠁⠁⠹⢿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣠⣯⣴⣿⣿⣟⠛⠉⠀⣀⡀⠀⠀⠀⠀⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣼⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣯⠀⢠⣾⣿⣿⣦⡄⠀⠀⠀⡠⠿⠿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣋⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢢⣤⡄⡤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⠈⠉⠉⠁⠀⠉⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢼⣇⠧⢟⢿⣾⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠉⠀⠀⠀⠷⢶⣿⣿⢿⢄⣚⣛⣿⣟⣻⢻⢽⣻⡿⣯⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⢶⠄⠰⠰⠶⠆⠀⠀⠀⠀⢹⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣷⣿⣿⣿⣿⣁⠀⠀⠈⠻⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠀⡠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠃⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣤⣶⣶⣶⣶⣶⣿⣤⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⣛⢉⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡿⠋⠀⠀⠀⠈⠨⠍⠉⡉⠟⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢿⠿⠿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣦⡈⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠐⡺⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠐⣿⣿⣿⣿⡄⠀⠀⠀⠀⢶⣶⠖⣒⣿⣿⡶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠃
⠀⠀⠀⠀⠀⠿⡿⠿⠟⣿⠿⠿⣿⣧⠰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⢀⣉⡷⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠯⣻⡀⢉⣿⡁⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣶⣶⣶⣠⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠟⢻⣿⣗⣼⣻⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣽⣿⣿⣿⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣦⡄⠀⠀⠀⠉⡹⢻⠃⣸⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⠇
⢸⣿⡇⠀⠀⡤⣤⡀⡇⡀⢻⣿⣿⡿⠀⢾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⡿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⢀⣤⡀
⢸⡟⠃⠀⠀⠀⠉⠿⣷⣇⣨⣿⣿⠁⠀⠈⠻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣿⢛⣵⡾⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⠃⠛⠅⣼⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠉⢻⠇
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠃⠟⢻⡿⠀⠀⠀⠀⠻⢿⢿⣄⠀⠀⠀⠀⢀⠀⠀⣼⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⡿⠉⠉⠛⠁⢠⡄⠀⠻⠿⣿⢿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠑⣸⡇⠀⠀⠠⣄⣢⣄⣐⠠⣄⢻⠷⢶⣿⣾⣷⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⣀⣉⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣶⣶⣦⠀⠀⣰⣿⣇⡀⠀⣠⣾⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢳⣯⢻⣿⣽⣻⣿⡿⣟⣛⡿⣇⠿⠿⣿⡿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠿⢿⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠠⢀⣴⣿⣿⣿⡇⢰⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡇⢤⣤⡄⠀⠀⢀⣡⣴⣶⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠘⠃⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⣿⢿⣇⣧⡠⣾⣛⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡎⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠞⢲⡶⠶⠷⠉⠈⠁⠛⡛⠘⣣⣿⣹⡼⢿⣿⠀⠘⠁⠁⠹⢿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣠⣧⣤⣿⣿⣿⠛⠉⢀⣀⡀⠀⠀⠀⠀⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢾⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⢠⣾⣿⣿⣦⠀⠀⠀⠀⡠⠿⠿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢿⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢢⣤⡄⡤⣝⢭⢩⢹⡟⡍⢲⠂⡏⡆⣎⣶⡧⠃⡇⣷⢿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠑⢯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡇⡅⣿⣿⢸⣸⠄⡏⡆⢸⢼⣇⠧⢟⣿⣺⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠉⠀⠀⠀⠷⢶⣿⣿⢿⢀⣛⣛⣿⣟⣻⢻⢽⣻⡿⣯⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣨⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡟⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⢶⠄⠰⠲⠶⠆⠀⠀⠀⠀⢸⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣷⣿⣿⣿⣿⣁⠀⠀⠈⠹⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠄⠄⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠃⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣤⣶⣶⣶⣶⣶⣾⣤⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡛⢉⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⠿⠋⠀⠀⠀⠈⠹⠅⠩⡉⠛⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⢿⠿⠿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣦⡈⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠐⡺⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣜⣿⣿⣿⣿⣿⣿⣿⡇⠰⣿⣿⣿⣿⡄⠀⠀⠀⠀⢶⣶⠖⣒⣿⣿⡶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠃
⠀⠀⠀⠀⠀⠻⡿⠿⠛⣿⠿⠿⣿⣧⠰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣉⡷⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠿⣻⡀⢈⣿⠁⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣀⣶⣶⣶⣠⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠿⣫⣿⣗⣸⣻⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⣽⣿⣿⣿⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣦⡄⠀⠀⠀⠉⠝⢿⠃⢼⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠇
⢸⣿⡇⠀⠀⠠⣤⡀⡋⡀⢻⣿⣿⡿⠀⢾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⡿⢿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣤⡀
⢸⡟⠃⠀⠀⠀⠈⠿⣷⣇⣨⣿⣿⠁⠀⠈⠻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣿⢛⣵⡶⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⠃⠛⢅⣼⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠉⠻⠇
⠈⠁⠀⠀⠀⠀⠀⠀⢀⠇⡟⢛⡿⠀⠀⠀⠀⠿⢿⢿⠠⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⡏⠉⠉⠛⠁⢠⡄⠀⠹⠿⣿⢿⣿⣦⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠐⣸⡇⠀⠀⠠⣄⣠⢄⣀⠀⣜⢿⠷⢶⣷⣶⣾⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣾⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠈⠀⠀⠀⢠⣦⡀⣀⣉⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣶⣶⣄⠀⠀⣰⣿⣇⡀⠀⣠⣾⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢳⣏⢻⣿⣽⣻⣿⡿⣟⣛⡿⣇⠿⠿⣿⡿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠿⢿⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠠⢀⣴⣿⣿⣿⡇⢰⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣇⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡇⢤⣤⡄⠀⠀⢀⣡⣴⣶⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡯⠁⠉⠘⠣⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⢿⢿⣇⣧⢠⣾⣛⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡎⠀⢠⣶⡿⣷⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢲⡶⠶⠷⠉⠈⠁⠛⡛⠘⣣⣿⣻⡼⢿⣿⠀⠸⠁⠀⠹⢿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣠⣧⣴⣿⣿⣟⠛⠉⢀⡀⡀⠀⠀⠀⠀⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢼⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣇⠀⣠⣾⣿⣿⣤⠀⠀⠀⠀⡠⠿⠿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣚⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢢⣤⡄⡤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⠃⡇⣷⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⡇⡅⣿⣿⢸⣸⠄⡏⡆⢸⢼⣇⠧⢟⢿⣺⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠉⠀⠀⠀⠷⢶⣿⣿⢿⢀⣛⣛⣿⣟⣻⢻⢽⣻⡿⣯⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⢶⠄⠰⠲⠶⠆⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣁⠀⠀⠈⠻⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠀⡠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠃⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣤⣶⣶⣶⣶⣶⣾⣤⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡛⢉⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⠿⠋⠀⠀⠀⠈⠹⠅⠩⡉⠙⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠠⢿⠿⠿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣧⡈⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠐⡺⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠐⣿⣿⣿⣿⡆⠀⠀⠀⠀⢶⣶⠖⣒⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠃
⠀⠀⠀⠀⠀⢻⡿⠿⠛⣿⠿⠿⣿⣧⠰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⢀⣉⡷⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠿⣻⡀⣈⣿⡁⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣶⣶⣶⣠⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠾⣻⣿⣗⣸⣻⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⢇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣦⡄⠀⠀⠀⠉⡹⣿⠃⢼⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⠇
⢸⣿⣇⠀⠀⢠⣤⡀⡂⡀⢻⣿⣿⡿⠀⢾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣤⡀
⢸⡟⠃⠀⠀⠀⠈⠿⣷⡇⣸⣿⣿⠁⠀⠈⠻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⢛⣵⡾⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⠃⠛⠅⣾⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠉⠻⠇
⠈⠁⠀⠀⠀⠀⠀⠀⢀⠇⡟⢻⡟⠀⠀⠀⠀⠻⠿⢿⡦⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⡏⠉⠉⠛⠁⢠⡆⠀⠹⠿⣿⢿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠁⣸⡇⠀⠀⠠⣄⣠⢄⣀⠠⣄⢼⠿⢶⣿⣶⣾⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣾⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠈⠀⠀⠀⢠⣦⡀⣀⣉⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣶⣶⣦⠀⠀⣰⣿⣇⡀⠀⣠⣼⣿⣹⣿⣸⣿⢈⣿⣿⡇⣶⢳⣏⢻⣿⣽⣻⣿⡿⣟⣛⡿⣇⠿⠿⣿⡿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠿⢿⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠠⠀⣴⣿⣿⣿⡏⢰⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣇⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡇⢤⣤⡄⠀⠀⢀⣡⣴⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⠁⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠸⠃⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⢿⢻⣇⣦⣠⣾⣛⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣷⡞⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢲⡶⠶⣷⠉⠈⠁⠛⡛⠘⣣⣿⣹⣼⢿⣿⠀⠘⠁⠀⠹⢿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣠⣧⣤⣿⣿⣟⠋⠉⠀⡐⡀⠀⠀⠀⠀⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⠀⣠⣾⣿⣿⣦⡀⠀⠀⠀⡠⠿⠿⣿⠿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢢⣤⡄⡤⣝⢭⢩⢹⡟⡍⢲⠂⡏⡆⣎⣶⡧⠃⡇⣷⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢼⣇⠧⢟⢿⣼⣧⣇⣻⣞⣜⣚⣿⣿⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠉⠀⠀⠀⠷⢶⣿⣿⢿⢄⣛⣛⣿⣟⣻⢻⢿⣻⡿⣯⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⢴⠄⠰⠲⠶⠆⠀⠀⠀⠀⢸⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡁⠀⠀⠈⠻⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠃⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣤⣶⣶⣶⣶⣶⣾⣤⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡋⢉⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⠿⠋⠀⠀⠀⠈⠹⠅⠩⡉⠙⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠠⢿⢿⢿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣧⡈⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠐⣿⣿⣿⣿⡄⠀⠀⠀⠐⢶⣶⠶⣒⣿⣿⡶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠃
⠀⠀⠀⠀⠀⠿⡿⠿⠛⣿⠿⠿⣿⣧⠰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣉⡷⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠯⣻⡀⢈⣿⡁⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣶⣶⣶⣀⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠺⢻⣿⣗⣼⣻⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⣽⣿⣿⣿⢇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣦⡄⠀⠀⠀⠉⡹⢿⡇⢸⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡇
⢸⣿⣷⠀⠀⢠⣤⡄⡞⠀⢸⣿⣿⡿⠀⢾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣄⡀
⢸⡿⠃⠀⠀⠀⠘⠿⣷⣇⣸⣿⣿⠁⠀⠈⠻⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣿⢛⣵⡾⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⠃⠻⠅⣾⣿⣿⣿⣦⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠙⢛⠇
⠀⠁⠀⠀⠀⠀⠀⠀⢀⡇⣟⢻⡿⠀⠀⠀⠀⠻⠿⢿⡆⠀⠀⠀⠀⢀⠀⢀⣶⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⡏⠉⠉⠛⠁⢠⡆⠀⠻⠿⣿⢿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠓⣸⡇⠀⠀⠠⣌⣦⣄⣀⠀⣀⢿⠷⢶⣿⣾⣾⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⢟⣾⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠈⠁⠀⠀⢠⣦⡀⣀⣉⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣶⣶⣤⠀⠀⣰⣿⣧⣀⠀⣠⣼⣿⣹⣿⣸⣿⢈⣿⣿⡇⣶⢳⣯⢻⣿⣽⣻⣿⡿⣟⣛⡿⣇⠿⠿⣿⡿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠻⢿⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠠⠀⣴⣿⣿⣿⡏⢰⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢺⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡇⢤⣤⡄⠀⠀⢀⣡⣴⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⠁⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡯⠁⠉⠘⠃⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⢿⢿⣇⣆⢠⣾⣛⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡞⠀⢠⣶⡿⣷⣿⣿⣷⣶⣶⣶⣿⢾⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠾⢲⣶⠶⢷⠉⠈⠁⠛⣛⠘⣣⣿⣸⣼⢿⣿⠀⠙⠋⠉⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣠⣧⣴⣿⣿⣟⠋⠉⠀⡐⡀⠀⠀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡷⠀⣠⣾⣿⣿⣦⡀⠀⠀⠀⡠⠿⠿⣿⠿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢻⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣚⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⣤⡄⡤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⡎⣾⡧⠃⡇⣷⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⠈⠉⠉⠁⠀⠉⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢴⣇⠧⢟⢿⣺⣧⣇⣻⣞⣜⣚⣿⣿⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠉⠀⠀⠠⠷⢶⣿⣿⢿⢄⣚⣛⣿⣟⣻⢻⢽⣻⡿⣯⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⣧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⠶⠄⠰⠲⠶⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡁⠀⠀⠈⠻⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠃⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣤⣶⣶⣶⣶⣶⣾⣤⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡫⢉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⠿⠋⠀⠀⠀⠈⠰⠁⠩⡁⠙⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⢿⢿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⢀⣴⣶⣶⣿⣿⣿⣷⡌⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⠻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣮⣿⣿⣿⣿⣿⣿⣿⡇⢐⣿⣿⣿⣿⡄⠀⠀⠀⠀⢶⣶⠶⣒⣿⣿⡶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠃
⠀⠀⠀⠀⠀⠛⡟⠛⠛⣿⠿⠿⣿⣧⠰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⢈⣉⡷⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡄⢿⣻⡀⣈⣿⡁⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣶⣶⣶⣀⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠁⠾⢻⣿⣷⣼⣻⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⣿⣿⣿⣿⢇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣦⡄⠀⠀⠀⠈⡽⢿⡇⢸⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡇
⢸⣿⣷⠀⠀⢠⣤⡄⡞⠀⢺⣿⣿⡿⠀⢾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣄⡀
⢸⡿⠃⠀⠀⠀⠘⠿⣷⣇⣸⣿⣿⠁⠀⠈⠻⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⢛⣵⡾⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⠃⠻⠅⣾⣿⣿⣿⣦⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠙⢛⠇
⠀⠁⠀⠀⠀⠀⠀⠀⢈⡇⣿⢻⡟⠀⠀⠀⠀⠻⠿⣿⡢⠄⠀⠀⠀⣀⠀⠀⣶⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⡟⠉⠉⠛⠁⢠⡆⠀⠻⠿⣿⢿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠒⣼⡇⠀⠀⠀⣌⣤⣄⣀⠤⣬⢻⠷⢶⣿⣶⣷⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⢟⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⢠⣦⡀⣈⣉⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣶⣶⣤⠀⠀⣠⣿⣧⣀⠀⣠⣼⣿⣹⣿⣸⣿⢈⣿⣿⡇⣶⢳⣯⢻⣿⣽⣻⣿⡿⣟⣛⡿⣇⠿⠿⣿⡿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠿⢿⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣴⣿⣿⣿⡏⠠⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢺⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡇⢤⣤⡄⠀⠀⢀⣡⣴⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣸⣿⣿⣿⣿⠁⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡯⠁⠉⠘⠃⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⣿⢿⣇⣆⢠⣾⣻⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡞⠀⢠⣶⡿⣷⣿⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠾⢲⡶⠶⡷⠉⠈⠁⠛⣛⠘⣣⣿⣹⣼⢿⣿⠀⠹⠋⠉⠹⢿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣠⣧⣴⣿⣿⣟⠛⠉⢀⣐⡄⠀⠀⠀⠀⠉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⠀⣠⣾⣿⣿⣦⡀⠀⠀⠀⡠⠿⠿⣿⠿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢼⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣋⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢢⣤⡄⡤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⠃⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⠈⠉⠉⠁⠀⠉⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣸⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠉⠀⠀⠰⠷⢶⣿⣿⢿⢀⣛⣛⣿⣟⣻⢻⢽⣻⡿⣯⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⣧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡁⠀⠀⠈⠻⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠀⣠⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠃⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣤⣶⣶⣶⣶⣶⣾⣦⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡫⣉⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢻⠟⠁⠀⠀⠀⠀⠐⠂⢩⣀⠙⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢾⢿⢿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⢀⣾⣷⣶⣿⣿⣿⣶⡌⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡅⠀⢐⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠠⣮⣿⣿⣿⣿⣿⣿⣿⡇⠐⣿⣿⣿⣿⡄⠀⠀⠀⠐⢶⣶⠖⣒⣿⣿⡶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠃
⠀⠀⠀⠀⠀⠛⡛⠛⠛⣿⠛⠻⣿⣧⠰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⢀⣉⡷⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣀⣦⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡄⢿⣹⣀⣈⣿⠅⢹⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣶⣶⣶⣀⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠺⢻⣿⣷⣼⣻⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⢇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣶⡄⠀⠀⠀⠈⡭⢿⡇⢸⣿⣿⣯⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⠇
⢸⣿⣿⠀⠀⢀⣤⣄⡞⠀⢸⣿⣿⡿⠀⢾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣤⡀
⢸⡿⠋⠀⠀⠀⠈⠿⣷⣇⣸⣿⣿⠁⠀⠈⠹⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣿⢛⣵⡾⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⠁⠛⠁⣼⣿⣿⣿⣦⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠙⢻⠃
⠈⠁⠀⠀⠀⠀⠀⠀⢀⡏⣿⢻⡟⠀⠀⠀⠀⠻⠻⣿⣧⢀⠀⠀⠀⣀⠀⠀⣼⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⠟⠙⠉⠛⠁⠠⣆⠀⠻⠿⣿⢿⣿⣦⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠓⣼⡇⠀⠀⠀⣬⣤⣀⣀⠀⣄⢼⠶⢶⣿⣶⣾⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢁⠀⠀⢠⣦⡀⣈⣉⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢠⣾⣦⣤⠀⠀⣠⣿⣧⣀⠀⣠⣼⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢳⣏⢻⣿⣽⣿⣿⡿⣟⣻⡿⣇⠿⠿⣿⡿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠿⢿⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠠⢄⣠⣿⣿⣿⡏⠠⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢺⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡇⢤⣤⡄⠀⠀⢐⣠⣴⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⠁⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠸⠃⠛⠘⠏⠹⢇⢿⠼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⣿⢻⣇⣦⢠⣾⣻⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡞⠀⢠⣶⡿⣷⣿⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠶⣶⠶⡷⠉⠈⠁⠛⣛⠘⣣⣿⣸⡼⢿⣿⠀⠙⠉⠉⠹⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⣠⣧⣬⣿⣿⡟⠋⠉⢀⣐⡀⠀⠀⠀⠀⠉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡅⠀⣰⣾⣿⣿⣦⠀⠀⠀⠀⡠⠿⠿⣿⠿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢼⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣚⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⣤⡄⡤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⠃⡇⣿⢿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⠈⠉⠉⠁⠀⠉⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢼⣇⠧⢟⢿⣺⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠉⠀⠀⠰⠷⢶⣿⣿⢿⢀⣛⣛⣿⣟⣻⢻⢿⣿⡿⣯⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣨⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⣧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⠻⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠃⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣤⣶⣶⣶⣶⣶⣾⣴⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡫⣉⣭⣭⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢻⠟⠉⠀⠀⠀⠀⠰⠂⢩⣄⠛⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠠⢾⠿⢿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⢀⣾⣷⣶⣿⣿⣿⣶⡌⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⡅⠀⢀⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣮⣿⣿⣿⣿⣿⣿⣿⡇⠐⣿⣿⣿⣿⡄⠀⠀⠀⠀⢲⣶⠖⣒⣿⣿⡶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠙⠃
⠀⠀⠀⠀⠀⠛⡛⠛⠛⣿⠛⠻⣿⣧⠰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣉⡧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡄⢿⣹⣀⣠⣿⡁⢹⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣶⣶⣶⣀⡄⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠚⢻⣿⣷⣴⣻⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⢇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣶⡄⠀⠀⠀⠈⠽⢿⠇⢼⣿⣿⣯⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⡇
⢸⣿⣷⠀⠀⢠⣤⣄⡊⡀⢺⣿⣿⡿⠀⢾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣹⣿⣿⣿⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣤⡀
⢸⡿⠋⠀⠀⠀⠈⠿⣷⣇⣸⣿⣿⠀⠀⠈⠙⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣿⢛⣵⡾⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡴⠃⠻⢁⣼⣿⣿⣿⣆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⡉⠛⠃
⠈⠁⠀⠀⠀⠀⠀⠀⢀⡇⣿⢻⡟⠀⠀⠀⠀⠻⠿⣿⣢⡀⢀⠀⠀⠀⠀⢀⣾⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢺⣿⣿⣿⣿⣿⣿⠟⠉⠉⠛⠁⠠⡦⠈⠿⠿⣿⢿⣿⣦⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠉⣼⡇⠀⠀⠀⣤⣦⣀⣀⠠⣔⢾⠿⢶⣿⣶⣾⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⢟⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⣠⣦⣀⣈⣩⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢠⣶⣦⣤⠀⠀⣰⣿⣧⣀⠀⣠⣼⣿⣹⣿⣸⣿⢈⣿⣿⡇⣶⢳⣯⢻⣿⣽⣿⣿⡿⣟⣛⡿⣇⠿⠿⣿⡿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠿⢿⠉⢻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠠⠀⣴⣿⣿⣿⡏⠠⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢺⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢹⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡇⢤⣤⡄⠀⠀⢘⣠⣴⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣸⣿⣿⣿⣿⠃⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠸⠃⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⢿⢿⣇⣆⢠⣾⣻⣿⣿⣿⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡞⠀⢠⣶⡿⣷⣿⣿⣷⣶⣶⣶⣿⢾⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠲⣶⠶⡷⠉⠈⠁⠛⣛⠘⣣⣿⣹⡼⢿⡿⠀⠘⠋⠉⠹⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⣠⣧⣤⣿⣿⡟⠋⠁⢀⣐⡀⠀⠀⠀⠈⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⣰⣾⣿⣿⣦⠀⠀⠀⠀⡴⠿⠿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣊⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⣤⡄⡤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡖⡎⣾⡧⠀⡇⣿⢿⡸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⠈⠉⠉⠁⠀⠉⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⡇⡅⣿⣿⢸⣸⠄⡏⡆⢸⢼⣇⠧⢟⢿⣸⣦⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠉⠀⠀⠐⠷⢶⣿⣿⢿⢀⣛⣛⣿⣟⣻⢻⢿⣿⡿⣯⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⠶⠄⠰⠲⠶⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠘⢻⣿⣿⣿⣿⡇
[26A⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠠⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠃⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣤⣶⣶⣶⣶⣶⣾⣤⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡻⣉⣩⣭⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢻⠞⠁⠀⠀⠀⠈⠰⠂⢩⣄⠙⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠠⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⢀⣾⣷⣶⣿⣿⣿⣶⡌⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡍⠀⠀⡻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣮⣿⣿⣿⣿⣿⣿⣿⡇⢐⣿⣿⣿⣿⡄⠀⠀⠀⠀⢶⣶⠖⣒⣿⣿⡶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠙⠃
⠀⠀⠀⠀⠀⠛⡛⠛⠛⣿⠛⠻⣿⣧⠰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣉⡧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⣀⣦⡀
⠀⠀⠀⠀⠀⢀⣀⢀⡄⢿⣹⣀⣠⣿⡁⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣶⣶⣶⣀⡀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠚⢻⣿⣷⣸⣻⣿⣿⣿⡂⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⢇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⣦⡄⠀⠀⠀⠈⡽⢿⠇⢼⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠇
⢸⣿⣷⠀⠀⢠⣴⣄⡊⠀⢸⣿⣿⡿⠀⢾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣹⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣤⡀
⢸⡿⠋⠀⠀⠀⠈⠿⣷⣇⣸⣿⣿⠁⠀⠈⠙⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣿⢛⣵⡾⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣯⡴⠁⠿⢅⣾⣿⣿⣿⣄⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠉⢛⠃
⠈⠁⠀⠀⠀⠀⠀⠀⢀⡏⡿⢻⡿⠀⠀⠀⠀⠻⠿⣿⣦⠀⢀⠀⠀⣀⠀⢀⣶⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⠟⠉⠙⠛⠁⢠⡄⠈⠿⢿⣿⢿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠃⣸⡇⠀⠀⠀⣄⣀⣀⣀⠀⣄⢽⠿⢶⣿⣶⣾⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠁⠀⠀⣠⣧⡀⣈⣁⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣼⣶⣦⠀⠀⢠⣿⣧⣀⠀⣠⣼⣿⣹⣿⣸⣿⢈⣿⣿⡇⣶⢳⣏⢻⣿⣽⣿⣿⡿⣟⣛⡿⣇⠿⠿⣿⡿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠻⢿⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣠⣿⣿⣿⡟⠀⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢺⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣟⡊⣿⢻⡇⢤⣤⡄⠀⠀⢐⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣸⣿⣿⣿⣿⠇⠀⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡯⡁⠉⠸⠃⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⢿⢿⣇⣆⢠⣾⣻⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡾⠀⢠⣶⡿⣷⣿⣿⣷⣶⣶⣶⣿⢾⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠻⠶⡶⠶⠷⠉⠈⠁⠛⣛⠘⣣⣿⣹⣼⢿⡿⠀⠹⠋⠉⠽⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢀⣠⣧⣬⣿⣿⡿⠛⠉⢀⣀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⣠⣾⣿⣿⣦⠀⠀⠀⠀⡰⠿⠿⣿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣺⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⡊⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⣤⡄⡤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⠀⡇⣿⣿⡸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⠈⠉⠉⠁⠀⠉⠉⠉⠁⢫⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣸⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠐⠷⢶⣿⣿⢿⢀⣛⣛⣿⣟⣻⢻⢿⣻⡿⣯⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⣧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢨⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠘⢻⣿⣿⣿⣿⡇
䷩ 𝚕𝚒𝚗𝚎 2409
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
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Gemini version at gemini://gemini.techrights.org/2022/07/16/epo-iac-kangaroo-tribunal/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.16.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ [Meme]_The_EPO’s_Kangaroo_Tribunals_Explained⠀✐
Posted in Europe, Patents at 10:20 am by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇EPO_IAC_-_Kangaroo_Tribunal⦈_
Summary: Chairman Sir Paul Mahoney (OBE) explains the workings of the EPO‘s
Internal Appeals Committee to a new member
⣿⢼⠧⡧⢼⠤⡧⢼⠬⡧⣿⢼⡧⣿⢼⡧⣿⢼⡭⡯⣽⢽⡧⣿⢽⡯⣿⢽⡯⣯⣽⣭⣯⣿⣽⣯⣿⢽⡯⣯⣽⣭⣯⣽⣽⣯⣿⣽⣯⣯⣽⣭⣯⣽⣽⣯⣿⣽⣯⣿⣽⣭⣯⣽⣽⣯⣿⣽⣯⣯⣽⣭⣯⣿⣽⣯⣿⣽
⣿⣺⣗⣟⣺⣓⣗⣻⣚⣗⣿⣺⣗⣿⢺⡗⣿⣺⣛⣗⣿⢺⡗⣿⢺⡗⣿⢺⡗⣷⣾⢶⡷⣿⢺⡗⣿⢺⡗⣷⢺⠶⡷⣾⢺⡗⣿⢺⡗⣷⢾⠶⡷⢾⢾⡷⣿⢺⡷⣿⢾⠶⡷⣾⢾⡷⣿⢾⡷⣿⢾⠶⡷⣿⢾⡷⣿⢾
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠋⠋⠙⠉⠋⠙⠉⠋⠙⠙⠋⠛⠙⠋⠛⠙⠋⠋⠙⠙⠋⠛⠙⠋⠛⠙⠋⠛⠙⠛⠋⠛⠙⠋⠛⠙⠋⠛⠙⠛⠛⠛⠙⠋⠛⠙⠋⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠛⠛
⢸⣿⣿⣿⣿⣿⡇⠤⠶⠴⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠯⠭⠭⠍⠀⠀
⢸⣿⣿⣿⣿⣿⡇⠭⠭⠿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣷⢸⡏⣶⠱⢸⡿⢺⣿⣷⣾⣷⣸⡇⠀⡼⣿⡄⣿⢹⣾⡏⣷⣾⢳⣲⣷⣾⡇⡾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠛⠛⠙⠒⠀⠀
⠸⠿⠿⠿⠿⠿⠇⠋⠃⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠀⠉⠈⠁⠈⠁⠈⠉⠉⠈⠈⠈⠁⠈⠁⠉⠉⠛⠉⠘⠋⠁⠈⠁⠈⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠇⠛⠙⠛⠋⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠰⢆⣀⡀⣀⣀⣀⣀⣀⣀⣀⢐⡆⣴⣀⣆⢀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤⠸⠿⠇⠿⠿⠼⠿⠿⠿⠿⠼⠇⠿⠜⠧⠻⠭⠻⠯⠃⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⡄⠀⠀⠀⠀⢀⣠⣴⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠻⠒⠠⣶⣤⠈⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠾⣯⣥⣤⣽⢡⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠈⠽⢓⣶⣿⢲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⢠⣿⣿⣏⠙⢘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠠⣶⣆⣚⠟⠋⠀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⠈⢷⣶⣆⠀⢂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⡷⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠇⢸⣿⣿⣿⣷⠶⠿⢿⣤⠀⠘⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠟⠉⠉⠀⠉⠉⠉⠁⠠⡀⠀⠉⠁⠀⠀⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⣿⣻⣟⣿⣿⣿⣿⣿⡿⠟⠋⠉⠁⢸⢇⠀⠈⢿⣿⣿⣑⠘⠘⠀⢙⠂⠤⠑⠒⢿⣿⣿⣿⣿⣿⣟⣿⣻⣟⣿⣻⣿⡟⠁⠀⠀⠀⣀⡤⠊⠀⠀⢠⣹⣦⣤⣦⠀⠀⠀⠀⠴⣿⣿⣿⠟⠁⢻⣟⣿⣻⣿⣿⣿⣿⣟⣿⣻
⣿⣿⣯⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠘⢿⣧⣄⢂⡢⢹⠟⠋⠀⠀⠀⠀⢢⡄⠀⠈⣿⣿⣿⣿⣿⣯⠿⠙⠋⠛⠛⠛⠁⠀⣀⣴⣾⢋⡀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⢻⣿⣽⣿⣿⣿⣿⣯⣿⣽
⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠞⠃⠀⠀⠀⠀⠀⠀⠀⢩⣌⢮⣿⣿⣿⣿⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⣿⣿⣿⣿⡇⣿⣽⣧⣧⣿⣾⣼⣾⣿⣿⣮⣬⣄⣅⣍⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⣿⢾⡷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⣿⡇⣿⣿⢙⡟⢿⣿⢿⣿⡏⣿⣿⡻⢻⣿⣻⢿⡟⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢿⡿⢷⣿⢾
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⣿⣽⣠⣤⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⢽⣿⣶⣾⣶⣿⣾⣷⣷⣿⣾⣷⣿⣿⣾⣿⣿⣶⣴⣶⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢽⣿⢧⣿⣽
⣿⣿⡟⣛⣏⡅⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢀⣀⡀⠀⠘⣿⣿⣿⣿⣿⣿⢺⣿⣴⣽⣽⣯⣯⣿⣟⣯⣽⣼⣿⣭⣿⣭⣿⣽⣿⣯⣿⣿⡇⢰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣦⡌⢻⣿
⠛⠛⢣⠩⢨⡂⠈⠉⠉⠁⠁⠀⠀⠀⠀⠀⠈⠉⠉⠀⢿⣿⣛⡛⠛⠁⠀⠀⠀⣿⣿⣿⣿⣿⡅⣿⣹⣻⣟⣟⣿⣙⣹⣻⣿⣍⣛⣟⣻⣿⣛⣿⣿⣿⣿⣿⡇⠐⢚⣷⣒⣶⣦⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⡿⢿⣿⢸⣿
⠀⠀⢸⣧⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣒⡆⣿⡿⢿⢻⠻⠿⠿⣿⣿⣟⣿⠿⣿⡟⠿⡿⠿⣿⡿⣿⡟⡇⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⡶⣼⣶⣶⡿⠟⢛
⠀⠀⠘⣿⣀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⢷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠉⠭⠟⠋⠁⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠸⠃⠈⢻⢻⣿⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣭⣭⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⢿⠟⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠀⠐⠾⠿⠿⠿⠿⠿⠟⠓⠚⠛⠛⢀⠀⠀⢀⣠⣠⣤⣩⣽⡿⢀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁⠒⠅⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀
䷩ 𝚕𝚒𝚗𝚎 2463
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
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✐ IRC_Proceedings:_Friday,_July_15,_2022⠀✐
Posted in IRC_Logs at 2:22 am by Needs Sunlight
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䷩ 𝚕𝚒𝚗𝚎 2590
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✐ Microsoft_Cuts_Off_Free_and_Open_Source_Software_From_Using_the_Windows_Store
for_Donations⠀✐
Posted in Free/Libre_Software, Microsoft at 12:29 am by Guest Editorial Team
Guest post by Ryan, reprinted with permission from the_original
M
icrosoft has made a change to the Windows Store rules prohibiting the sale of
Free and Open Source Software unless the program’s author has the policy of
billing everyone who receives a copy of the software outside the store.
The Windows Store already makes it impossible to comply with Copyleft Free
Software licenses, such as the GPL.
The GPL and many copyleft licenses require that the user is guaranteed to be
able to run as many copies as they care to for whatever reason they want to use
the program, and to make more copies to share, and to have access to the source
code to modify, run, and share with others on the same, or perhaps at their
option, later terms of the same license.
Microsoft says their new policy of de-funding Free and Open Source Software is
designed to solve a problem that really does exist and is out of control in the
Windows store, that there are many obviously fake and exploitative applications
that charge money, and none of it actually goes to the project.
For example, people have come along and put LibreOffice into an AppX package
and then dumped it into the Windows store, failed to keep it up to date, and
then sat back and started taking money from users who didn’t know any better.
I complained about Microsoft allowing things like this to happen, but this is
not a legitimate way to handle that. It’s probably, however, for the best, for
other reasons.
You can sell copies of Free and Open Source Software. In fact, it wouldn’t be
FOSS if you couldn’t. Even Richard Stallman encourages you to sell software,
copying services, and usage manuals, professional services, etc.
As long as the software itself remains Free (as in Freedom), the Free Software
proponents certainly don’t wish that nobody made money off of it. In fact, Free
Software is very big business.
But there are only so many ways you can do that, and one of them is not Digital
Restrictions Malware, or DRM.
Enforcing DRM implicitly makes software non-Free, because there is no way to
copy, modify, and share a useful version of the software at that point, and if
you told anyone how it worked, it would be useless, so you can’t share the
source code if you expect it to hold up.
There’s a thought-provoking mental exercise. It’s a simple question.
How many angels can dance on the head of a pin? The answer: As many as want to.
How many users may have a copy of a Free Software program? As many as want to.
So, DRM cannot be “Free Software”, yet the Windows Store is a form of DRM, like
the Apple Store is.
The Windows Store is designed to be anti-competitive.
In addition to imposing DRM that forces you to be a jerk when your friend asks
for a copy and you can’t give it to them, it’s designed as an attack on Wine (a
Free Software program that allows GNU/Linux and *BSD users to run Windows
programs, without Windows) because there’s no way to move the program out of
the Windows Store and install the package into Wine.
Nothing published in the Windows Store is Free Software because of this. It
deprives the user of his or her Freedom by the intended method of its
operation.
To maintain the Freedom for your users, you have to reject the Windows Store
entirely. Yes, it’s possible to publish Free and Open Source Software on
Windows.
Using Windows is a bad idea, and it’s very foolhardy, but the underlying
platform being problematic has no bearing on whether a program the user is
running is Free or not unless that platform is getting in the way of the user
enjoying their Freedom as it pertains to that program.
This means, you would have to install software for Windows the traditional way,
by including it in a NSIS installer or something, so that the platform doesn’t
constrain the user.
Some projects that don’t care that they violate and internally conflict with
their own license, or use some pushover license that is Free until they put it
in the Windows Store, but doesn’t do anything to make sure it stays Free, and
becomes Non-Free do publish in the Windows Store, and that is very unfortunate.
On my Android phone, I run into this problem too. Because the Google Play store
has pretty much all of the same problems as the Windows Store (except that it’s
not 9 fake apps per 1 real one, approximately).
I absolutely never install Free and Open Source applications from the Play
Store because then I don’t have much control over them and Google has shoved
them full of nasty things even if the author objects.
I use the F-Droid store.
Some projects and software authors say that you are using a “trial” copy of
their program in the Windows Store, but the trial works exactly the same as the
paid version and never expires, so you would only buy it to “make a donation”.
Unfortunately, when you do this, at least when it was allowed, Microsoft takes
20% of your money for not doing much at all.
There’s a better way to ask your users for money than having them fund
Microsoft, such as including a donation link, or a place they could send you a
money order.
In the 1990s, before Nullsoft was purchased by AOL, Justin Frankel said that
enough users found his program useful that just asking for $10 in the mail to a
PO Box was enough to live comfortably and run the company.
There’s nothing wrong with asking your user to make a donation if they found
your software helpful. That isn’t DRM, (done tastefully) it doesn’t make you a
pest, and you shouldn’t devalue your efforts by feeling you can’t ask them for
help developing the software.
Doing it the right way doesn’t poison their rights to use and share the
program, and it doesn’t involve funding the Archenemy of the Free World.
The Windows Store is not an “ecosystem” and Microsoft is not a “community”. If
you make it super convenient to use the Windows Store, you help them to attack
all computer users.
This is another of those times we have to stop and consider the kind of world
we want to build and live in.
The Windows Store has been sitting there as a joke, overflowing with malware
and fake apps, getting little attention from legitimate software publishers or
users for a decade.
The way I understand it, the “LTSC” version of Windows doesn’t even have the
Store.
Let’s let it die and make it another failed dirty trick that Microsoft spent a
lot of money on.
When I was a teenager, I found a man who had a Web site where he listed “free”
software, but in the way he used the term, it meant free of cost, not “freedom”
to do whatever you wanted to with it. His name was Graham Pockett and I don’t
know if he’s still around.
He said he was a software pirate who used to have get togethers with other
computer users in Australia to copy programs for one another that cost a lot of
money to buy in the store. You’d bring diskettes and other people would too,
and you’d all see what each other had and what you could use.
He then converted to Christianity and then changed his mind to “copying
software without permission is stealing”. It may be a copyright violation. You
might be civilly liable for it, but copying software gratis to help others is a
fundamentally social activity. In comparison, hoarding is being a jerk.
Proprietary software licenses force you to be a jerk and to be at odds with
social behavior, therefore they force you to behave in an anti-social way to
obey the wording of a license.
A person of conscience should simply walk away and refuse to play this anti-
social game of being a jerk because some software company says they have to be
one if they use that program.
Most software companies are not hurting for money. That’s just the plain and
simple truth of it.
They have a product that costs money one time to produce and then costs them
essentially nothing to produce from there on out.
They use DRM as a way of keeping prices high.
In some ways, it’s like grocery stores who buy food that had to be grown or
raised and then pour bleach all over it in front of hungry people before
tossing it in a dumpster because it would reach its sell by date.
You could feed every hungry person in the city twice with half of what Walmart,
Aldi, Kroger, and Albertson’s bleach and throw away.
They would rather ruin it and force people who cannot afford it to go without,
and throw it away right in front of them, than adjust production or lower
prices.
The copyright industry knows that when they have pirates, most of them don’t
actually have money (kids, third world country, dead end job, etc…), and if
they do, it’s not enough disposable income that they would buy a copy of that
software. But when it comes time to tell the government how much “piracy” is
allegedly hurting them, they claim every single pirate copy was a lost sale.
Hollywood goes even further and starts talking about how jobs will be lost
because of the corn that wasn’t used to sell you a $30 bucket of popcorn at the
movies.
The truth is that they’re trying to muddy the waters.
When Microsoft started to lose a lot of money to GNU/Linux and other Free
Software, they started to call it a cancer and a stolen product.
They made the same claim against it that the MPEG-LA patent troll did about
media codecs. “It’s impossible to make or use anything without paying us.”.
So even if you don’t pirate anything and go use something they didn’t even
contribute to, they complain and argue that laws should be changed to put an
end to it.
Again, why do we even put up with these people? Much less make excuses and new
channels of revenue for them? █
䷩ 𝚕𝚒𝚗𝚎 2866
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/16/patent-microcosm-collusion/#comments
Gemini version at gemini://gemini.techrights.org/2022/07/16/patent-microcosm-collusion/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.16.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
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✐ Illegally_Monetising_an_Attack_on_the_European_Patent_Convention_(or_How
National_Delegates_Participate_in_a_Coordinated_Patent_Collusion,_a_Form_of
Organised_Crime)⠀✐
Posted in Europe, Law, Patents at 2:35 am by Dr. Roy Schestowitz
Video_download_link | md5sum 652c8ad54777128b03dad22911b6c763
Abusing Granting Authority at EPO
Creative Commons Attribution-No Derivative Works 4.0
http://techrights.org/videos/selling-illegal-patent-grants.webm
Summary: A sort of “patent racket” based around Germany* is threatening Europe;
to make matters worse, it’s creating a financial calamity, but few actors
profit from this calamity and coordinate the agenda
THE above video concerns the latest_part in a series [1, 2, 3, 4] about an
imploding bubble at the EPO. Crime seems to be the last resort now; the only
way the EPO can sustain its existence, given the severe damage done over the
past decade, is deliberate violation of laws, constitutions, and treaties. The
general idea is, misuse the granting authority to grant hundreds of thousands
if not millions of illegal patents. Who benefits? NPOs**. It is all connected.
“Of course the corporate media is never mentioning any of that!”Just before
recording the above video I opened the front page of the EPO’s Web site (a
source of endless lies) and later I noticed that a couple of days ago, this
page had been updated to congratulate António_Campinos, who merely continues
the illegal plans of Benoît_Battistelli, aiming to bring an illegal kangaroo
court to authorise fake European Patents, including European_software_patents
that should never have been granted in the first place.
If the EPO plans to attack the law (EPC) and then celebrate its 50th
anniversary (adding insult to injury next_year), then citizens of Europe should
at least be fully aware, properly informed. The same people who staged a coup
at the EPO (turning a patent office into a bank) are now staging a coup against
patent courts all across the EU, seeking to replace them with plaintiff-
friendly kangaroo courts, presuming validity of patents granted by de facto
bankers. Today’s EPO is run by managers with no grasp of patents. It’s all
nepotism and destruction for personal gain. Patent examiners are rightly unset
and the uproar results in industrial actions and strikes. Of course the
corporate media is never mentioning any of that! █
to-day basis by Germany for German interests. Except when it’s kowtowing to
American interests.” This is what's_happening_in_EPO_for_sure, never mind the
EU.
survey as well as prior surveys.
🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇EPO_AC_trust_level⦈_
Slide from the_EPO_Staff_Survey which ended a couple of months ago
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䷩ 𝚕𝚒𝚗𝚎 2973
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Gemini_version_available_♊︎
✐ Links_16/07/2022:_Recycling_Old_PCs_With_GNU/Linux,_GNU_Rush_2.3⠀✐
Posted in News_Roundup at 3:10 pm by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈
§ Contents⠀➾
* GNU/Linux
o Desktop/Laptop
o Kernel_Space
o Graphics_Stack
o Instructionals/Technical
* Distributions_and_Operating_Systems
o EasyOS
o PCLinuxOS/Mageia/Mandriva/OpenMandriva_Family
o Open_Hardware/Modding
o Mobile_Systems/Mobile_Applications
* Free,_Libre,_and_Open_Source_Software
o Programming/Development
# Rust
* Leftovers
o Science
* Gemini*_and_Gopher
o Personal
o Technical
* § GNU/Linux⠀➾
o § Desktop/Laptop⠀➾
# ⚓ OMG Ubuntu ☛ Breath_Lets_You_Run_Regular_Ubuntu_on_Modern
Intel_Chromebooks_–_OMG!_Ubuntu!⠀⇛
This post is not a tutorial or a walkthrough or
comprehensive introduction or anything else that
would probably be beneficial or helpful to those
you reading it.
Instead, it’s a bit of a waffle.
I’ve just spent a few hours playing with something
very cool on my over-powered and under-used Acer
Chromebook Spin 13. I’ve scratched an itch I’ve had
for the longest time and it’s so satisfying. So, a
bit like when I resurrected an ancient Chromebook,
I want to tell someone about it — but this time
without any weird spooky gifs
# ⚓ South Africa ☛ Best_Linux_distributions_to_revive_an
ancient_laptop⠀⇛
A Linux distribution (distro) is an operating
system based on the Linux kernel.
Operating systems require many programs other than
the kernel to be functional, and Linux
distributions typically rely on tools released by
the GNU Project.
GNU founder Richard Stallman has long contended
that Linux distros should be referred to as GNU/
Linux systems.
However, his suggestion never caught on, and
“Linux” remains the widely-used shorthand for these
operating systems.
Linux distros are attractive because they are free
to use, open-source, and often have lower hardware
requirements.
Many Linux distros also allow users to preview the
operating system by booting it from a USB drive
before committing to installing it.
Here are some of the most lightweight Linux
distributions that could breathe life into even
some of the oldest laptops.
# ⚓ AppleInsider ☛ ChromeOS_Flex_now_available_to_run_on_aging
Macs_and_PCs⠀⇛
Google is rolling out ChromeOS Flex as an
enterprise option to replace operating systems on
old Macs and PCs, letting users turn their aging
hardware into Chromebooks.
[....]
With ChromeOS Flex, Google hopes to help businesses
keep older computers around for longer. The
lightweight operating system is designed to work
well on older hardware to extend the life of a
product, which can lead to reduced e-waste.
The OS can be quickly deployed via a USB stick or
over a network connection. Systems running ChromeOS
Flex can be managed via a Chrome Enterprise Upgrade
using the Google Admin Console.
Google has approved 295 devices so far for ChromeOS
Flex. However, it can be installed on other
hardware, but non-certified hardware may run into
performance issues.
# ⚓ Ubuntu Pit ☛ 30_Essential_Chromebook_Keyboard_Shortcuts_|
The_Ultimate_Guide⠀⇛
People are looking for shortcuts in aspects of
life, and there is no exception while operating
computers. Shortcuts are usually applied by the
keyboard, which saves more time for inputting
commands in another way. We are familiar with
keyboard shortcuts for Windows and Mac computers
that help our everyday tasks easier and faster.
Similarly, you can use keyboard shortcuts on Chrome
OS. A few Windows reliable keyboard shortcuts can
work on Chrome OS, but there some many commands set
differently here. We have listed 30 essential
Chromebook keyboard shortcuts to navigate better
and operate Chrome OS.
Learn about Chrome OS keyboard shortcuts for text
editing, taking a screenshot, faster lock screen,
web browsing, and more to produce your work more
quickly. So bookmark this keyboard shortcut
ultimate guide to decreasing cumbersome tasks of
moving the mouse and increasing your productivity.
o § Kernel Space⠀➾
# ⚓ WCCF Tech ☛ Intel_Meteor_Lake_Integrated_Graphics_Gets
Initial_Support_Within_Linux_5.20⠀⇛
The company reported earlier this month that it is
working on patches for the Meteor Lake graphics
driver inside the unreleased Linux 5.20 kernel.
Readers will remember that Meteor Lake is the
successor to Raptor Lake, which will be released
later this year.
o § Graphics Stack⠀➾
# ⚓ WCCF Tech ☛ AMD_RDNA_3_GPUs_Get_SubVP_Feature_In_AMDGPU_For
Linux_5.20⠀⇛
AMD is reported to publish the last feature updates
planned for the AMDGPU and AMDKFD drivers to the
DRM-Next for Linux 5.20 to prepare for RDNA 3′s
release. The merge window will open later this
month, so companies such as AMD and the recently
reported Intel additions are being finalized to
prepare new generations of graphics for the two
tech giants.
[...]
The Linux AMD pull updates also saw the integration
of DisplayPort Multi-Stream Transport (DP MST),
numerous audio patches, and the modification of the
GART size on recent APUs to add Scatter and Gather
display support. Finally, AMD also integrated the
querying of the GFXOFF status for VanGogh series
APUs, enhanced buffer object domain pinning, and a
few AMDKFD modifications.
o § Instructionals/Technical⠀➾
# ⚓ DebugPoint ☛ 4_Ways_to_Fix_the_Laptop_Brightness_Problem_In
Ubuntu⠀⇛
This article features four quick ways to fix the
everlasting Laptop brightness problem in Ubuntu.
Ubuntu plus most of the Linux distributions always
had issues with Laptop brightness. The default
hardware controllers never in the Laptop keyboard
worked most of the time after a fresh install.
# ⚓ ID Root ☛ How_To_Install_Nginx_on_Rocky_Linux_9_–_idroot⠀⇛
In this tutorial, we will show you how to install
Nginx Web Server on Rocky Linux 9. For those of you
who didn’t know, Nginx (short for Engine X) is a
free and open-source web server that serves as a
reverse proxy, HTTP load balancer, and email proxy
for IMAP, POP3, and SMTP. Thanks to its ability to
handle massive numbers of connections, it is the
preferred web server of many websites that deal
with high traffic.
This article assumes you have at least basic
knowledge of Linux, know how to use the shell, and
most importantly, you host your site on your own
VPS. The installation is quite simple and assumes
you are running in the root account, if not you may
need to add ‘sudo‘ to the commands to get root
privileges. I will show you the step-by-step
installation of the Nginx web server on Rocky
Linux. 9.
# ⚓ AddictiveTips ☛ How_To_Install_and_configure_Samba_on
Debian_11_Bullseye⠀⇛
Samba is a fantastic tool; with it, Linux desktops,
laptops, and servers can host Windows/Mac OS
compatible file shares. This guide will show you
how to install and configure Samba on Debian 11
Bullseye.
Note: this guide assumes you are using Debian 11.
However, the instructions should be the same if you
use Debian 10 or older. Feel free to follow along.
# ⚓ Ubuntu Handbook ☛ How_to_Fix_No_Sound_Issue_in_Ubuntu_22.04
with_ESSX8336_Sound_Card_|_UbuntuHandbook⠀⇛
Sound does not work in your Ubuntu 22.04, and
happen to have Everest ESSX8336 sound card in your
machine? This tutorial may help!
ESSX8336 is one of the common used chips in recent
laptops and tablets, such as Huawei Matebook
D14~16, Gemini Lake laptop, and Chuwi Hi10X tablet.
But, the current Linux Kernel does not support this
sound card, though there seems to have patches
(here and here) for it.
Until Linux Kernel officially adds the device
support, you may build Kernel manually with the
patch. Or use yangxiaohua’s custom kernel files to
fix the issue.
# ⚓ ByteXD ☛ Installing_Cinnamon_Desktop_Environment_on_Debian
11⠀⇛
Cinnamon is a desktop environment for the Linux
operating system that offers advanced features and
a traditional user interface. It is available for
download from the Cinnamon website. It is based on
the GNOME desktop environment and includes a number
of features that make it more user–friendly and
customizable than other desktop environments.
A desktop environment’s importance is tuning an OS
to suit a user’s needs. From accessing the menu,
managing applications, selecting folders,
performing a search, and opening and closing a
program.
So, an environment helps to efficiently manage our
files and apps, keeping our desktop organized and
enabling the user to incorporate less effort and
time to navigate the desktop.
This article will look at how we can install the
Cinnamon environment on a Debian 11 OS. There are
three ways we can install a Cinnamon desktop
environment on Debian.
# ⚓ Tech Times ☛ Should_You_Use_Another_IP_Address?_Here’s_How
to_Add_One_to_Your_Linux_Server_|_Tech_Times⠀⇛
Getting another IP address has many advantages. If
you have many IP addresses, you can operate
multiple apps in just a single port. Running apps
can sometimes be conflicting, especially if they
are tied to one IP address. This way, you can avoid
this hassle and access them with ease.
If you’re having problems with web content servers,
you might want to address this through a reverse
proxy. This particular server places the content in
other locations under one port.
# ⚓ Install_Logstash_8_on_Ubuntu/Debian_–_kifarunix.com⠀⇛
This guide is about how to install and configure
Logstash 8 on Ubuntu/Debian as a continuation of
our guide on how to setup Elastic Stack 8. We have
already covered the installation of Elasticsearch
and Kibana.
# ⚓ Linux Capable ☛ How_to_Install_PHP_8.1_on_Rocky_Linux_9⠀⇛
# ⚓ ID Root ☛ How_To_Install_Emacs_Text_Editor_on_Ubuntu_22.04
LTS_–_idroot⠀⇛
In this tutorial, we will show you how to install
Emacs Text Editor on Ubuntu 22.04 LTS. For those of
you who didn’t know, GNU Emacs is a programmable
text editor. It is a very comprehensive and
platform-independent editor that can be expanded
with its own Lisp dialect (Emacs Lisp). At its core
is an interpreter for Emacs Lisp, a dialect of the
Lisp programming language with extensions to
support text editing. This makes Emacs highly
extensible and users can add new functionality by
writing their own Emacs Lisp code or installing
packages that add new features.
This article assumes you have at least basic
knowledge of Linux, know how to use the shell, and
most importantly, you host your site on your own
VPS. The installation is quite simple and assumes
you are running in the root account, if not you may
need to add ‘sudo‘ to the commands to get root
privileges. I will show you the step-by-step
installation of Emacs Text Editor on Ubuntu 22.04
(Jammy Jellyfish). You can follow the same
instructions for Ubuntu 22.04 and any other Debian-
based distribution like Linux Mint, Elementary OS,
Pop!_OS, and more as well.
# ⚓ How_to_Create_a_Bastion_Host_in_AWS_[Tutorial]_|_strongDM⠀⇛
Want to secure remote access to a private network?
In this series of technical posts, we will share
step-by-step instructions to create a Linux bastion
host and create an audit trail by logging SSH
commands.
* § Distributions and Operating Systems⠀➾
o ⚓ DebugPoint ☛ Pop_OS_22.04_LTS_–_New_Features_and_Release
Updates⠀⇛
System76 released the Pop OS 22.04 LTS on April 25, 2022.
We unwrap the new features and updates in this post.
System76’s POP OS is based on Ubuntu releases, and the
Ubuntu 22.04 LTS release is just released. Following the
release schedule, the Pop OS 22.04 is now available for
download and upgrade. You can now do some hands-on and
find out the new features.
o § EasyOS⠀➾
# ⚓ Barry Kauler ☛ Automatic_save_at_shutdown_fixed⠀⇛
o § PCLinuxOS/Mageia/Mandriva/OpenMandriva Family⠀➾
# ⚓ PC Linux ☛ The_Graphics_Special_Edition,_Volume_3_of_the
PCLinuxOS_Magazine⠀⇛
o § Open Hardware/Modding⠀➾
# ⚓ Arduino ☛ This_smart_lock_uses_voice_recognition_to_control
access_|_Arduino_Blog [Ed: Amazon’s Alexa is wiretapping;
better aim for something that processes data locally, if at
all]⠀⇛
Smart locks are a highly convenient way to secure a
house, and they can have their number of
connectivity options expanded even further by
connecting them to an IoT home assistant service
such as Google Assistant or Amazon Alexa.
Jithin Sanal’s project uses Amazon’s Alexa skill to
automatically secure a custom door locking
mechanism without the need for Bluetooth or a
fingerprint. It is based around a Nano RP2040
Connect, and due to its onboard connectivity suite,
can talk with the Arduino Cloud. Other than the
Nano, Sanal designed a simple PCB with pads for a
buzzer, voltage regulator, and several LEDs for
monitoring its current status. The circuit also
includes a relay that applies power to a solenoid
which acts as a deadbolt when power is applied.
o § Mobile Systems/Mobile Applications⠀➾
# ⚓ CNX Software ☛ CANDuino_v3_–_A_Microchip_ATmega168PA_board
with_CAN_bus,_Arduino_Nano_form_factor_–_CNX_Software⠀⇛
CANduino v3 is the third revision of
MassiveButDynamic’s CAN bus board with Arduino Nano
form factor based on Microchip ATmega168PA 8-bit
AVR microcontroller, Microchip MCP2515 CAN
controller with an SPI interface, and Microchip
MCP2551 CAN transceiver suitable for 12V and 24V
systems.
The CANDuino v3 board is now slightly narrower in
order to give access to two rows on each side when
installed on a breadboard, comes with a USB Type-
C port to reduce the number of cables needed, and
the CAN bus function can be deactivated via a
jumper in order to use the CANduino as a normal
Arduino Nano.
# ⚓ CNET ☛ Clean_Out_Your_Android_Phone’s_Cookies_and_Cache_to
Get_Rid_of_Excess_Junk_Files_–_CNET⠀⇛
# ⚓ How_to_Update_Android_Apps⠀⇛
# ⚓ HowTo Geek ☛ How_to_Make_Your_Android_Phone_as_Private_as
Possible⠀⇛
# ⚓ Hindustan Times ☛ Xiaomi_11i_HyperCharge,_Xiaomi_11i
FINALLY_get_Android_12:_Better_than_Nothing_now?_|_Mobile
News⠀⇛
# ⚓ PC Mag ☛ Google_Is_Taking_Android_Devs_at_Their_Word_When
It_Comes_to_Data_Usage_|_PCMag⠀⇛
# ⚓ Giz China ☛ Google_removes_a_lot_of_Fuchsia_codes_from
Android_–_Gizchina.com⠀⇛
# ⚓ [Reposted] 9to5Google ☛ Android_removes_much_of_Fuchsia-
related_code_as_Starnix_project_progresses⠀⇛
A big chunk of Fuchsia-related code has been
removed from the Android Open Source Project (AOSP)
this week, but Google’s two operating systems are
still set to have an intertwining relationship.
In its most public form, Google’s in-house
operating system, Fuchsia, powers two of the
company’s smart displays, the Nest Hub and Nest Hub
Max. But having watched it develop over the last
few years, we know that Google has much larger
ambitions for the Fuchsia project.
Easily the most ambitious of these is a clear
intention for some Fuchsia devices to be able to
run apps from other operating systems like Android
and Linux. This could — in theory! — allow a
Fuchsia-powered device to seamlessly replace a
Chromebook or Android phone, keeping older apps
running as normal.
There are a few ways to achieve that goal, one of
Google’s earliest attempts was to run a full
instance of the Android operating system in a
virtual machine. This is how Chrome OS and Google
Play Games for PC bring support for Android apps,
but it comes with some potential performance
drawbacks.
* § Free, Libre, and Open Source Software⠀➾
o § Programming/Development⠀➾
# ⚓ GNU ☛ GNU_rush_version_2.3⠀⇛
GNU rush version 2.3 is available for download.
This is a bug-fixing release.
# ⚓ Russ_Allbery:_INN_2.7.0⠀⇛
This is the first major release of the INN news
server package since 2015. It incorporates tons of
work on just about every part of INN, ranging from
a brand new overview backend contributed by Bo
Lindbergh through Cancel-Lock support contributed
by Julien ÉLIE to numerous smaller changes in
configuration files, protocol support, and overall
simplification.
# ⚓ Medium ☛ GSoC’22_Update_—_Coding_Phase_1._Some_time_has
passed_since_I_wrote_my…_|_by_Asmit_Malakannawar_|_Jul,_2022
|_Medium⠀⇛
Well GSoC’22 coding period actually started from
13th June, 2022, but at the same time my end
semester exams started too. What a time to give
exams ! Well because of that I had to take 2 weeks
of break from my project. During community bonding
period, I gathered resources and jot them down at
one place, so as soon as my exams were over, I
would get back to my project easily.
During community bonding period, I went through all
the content written on the site and made a rough
draft of FAQs section. I also checked out the
images which we are supposed to include in the
website to make the pages more relevant. Changed a
few CSS styles, updated outdated packages and fixed
a few accessibility errors.
Currently I am developing a form for the website
which allows users to easily create profiles and
add themselves to the website. Since the site is
based on Jekyll, a static site generator, the
challenge here was how to make it easier for the
newcomers to add themselves easily and save the
fuss of navigating through the file system, make
merge requests according to content formatting
standards, required fields and all sorts of stuff.
They might even need to spin-up the site locally,
to ensure the content looks right.
# ⚓ dgplug_mailing_list_has_a_new_home⠀⇛
We were using the mailman2 instance provided by
Dreamhost for many years as the mailing list for
dgplug. But, over the years many participants had
trouble with receiving emails. In the last few
years, most emails were landing in spam.
# § Rust⠀➾
# ⚓ Rust Blog ☛ 1.62.1_pre-release_testing_|_Inside_Rust
Blog⠀⇛
The 1.62.1 pre-release is ready for testing.
The release is scheduled for July 19. Release
notes can be found here.
# ⚓ Advice_for_the_next_dozen_Rust_GUIs_|_Raph_Levien’s
blog⠀⇛
A few times a week, someone asks on the #gui-
and-ui channel on the Rust Discord, “what is
the best UI toolkit for my application?”
Unfortunately there is still no clear answer
to this question. Generally the top
contenders are egui, Iced, and Druid, but
web-based approaches are in the running, and
of course there’s always the temptation to
just build a new one. And every couple or
months or so, a post appears with a new GUI
toolkit.
This post is something of a sequel to Rust
2020: GUI and community. I hope to offer a
clear-eyed survey of the current state of
affairs, and suggestions for how to improve
it. It also includes some lessons so far from
Druid.
# ⚓ Steinar H Gunderson ☛ Steinar_H._Gunderson:_Rust_GUI
advice⠀⇛
The piece is largely about Rust, but Raph
Levien’s blog post about Rust GUI toolkits
contains some of the most thoughtful writings
on GUI toolkits that I’ve seen in a while,
regardless of language. Recommended.
* § Leftovers⠀➾
o § Science⠀➾
# ⚓ Quanta Magazine ☛ The_Computer_Scientist_Who_Parlays
Failures_Into_Breakthroughs⠀⇛
Nestled among the impressive domes and spires of
Yale University is the simple office of Daniel
Spielman. His shelves are lined with tall black
notebooks, containing decades of handwritten notes,
and against a wall sits a large, comfortable couch
that looks particularly well used.
“I’m sort of built for sitting still and thinking,”
he admitted.
What he thinks about, amid the gothic grandeur of
the campus, is a slightly more modern topic:
computer science. And over his career, Spielman has
produced a slew of influential results, although as
he describes it, failure has been his most common
outcome. “The key point is you have to enjoy the
process of working,” he said. “As long as I enjoy
that process, then it’s OK — as long as there’s
success once in a while.”
# ⚓ New Scientist ☛ Robot_made_of_sticky_tape_and_metal_powder
could_crawl_on_your_organs_|_New_Scientist⠀⇛
Tiny robots made of metallic powder stuck to
plastic tape and controlled by magnetic fields
could one day crawl inside internal organs and
repair injuries
* § Gemini* and Gopher⠀➾
o § Personal⠀➾
# ⚓ SpellBinding:_ABILUSR_Wordo:_CORNU⠀⇛
# ⚓ Re:_Cash-ocalypse⠀⇛
Me not being a “real person” then, I couldn’t agree
more. 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇:)⦈
In my humble opinion paying cash is a nice puzzle
piece of resistance. I routinely pay cash for
almost everything, that I buy locally. I have
bought a number of fairly expensive things (for my
personal definition of fairly expensive, that is)
and payed several of them cash, e.g. a new
motorcycle, an old car, a vinyl turntable plus
amplifier and speakers. Fortunately none of those
vendors objected to cash. The point is: paying cash
does to my knowledge not neccesarily produce a
digital record of who pays how much for what to
whom and where. Even more so, if this is a second
hand deal from a private person. The authorities do
not need to know, whether I spend my cash on more
or rather less questionable things. The assumption
always seems to be “more questionable things”, like
weapons, hard drugs and child porn. Well, I don’t.
And I estimate more than 95% of folks don’t. But of
course, if you jail them all, the questionable 5%
will be with them. Don’t get caught by this flawed
reasoning!
o § Technical⠀➾
# ⚓ Decouple_your_application⠀⇛
Arduino libraries are particularly egregious when
it comes to coupling. The SPI code is mixed in with
the device logic. I’m also lukewarm to the
“abstract interfaces” approach. People tend to
overdo the C++-isms wrt classes, so you end up with
a lot of “onion skins” (you peel back one layer of
the onion only to reveal another, with the result
that you end up confused and crying. As some wag
put it: you can solve every problem in computing by
adding a layer of abstraction, except for the
problem of having too many layers of abstraction).
[...]
If you look at the standard C library, it is
remarkable that the libraries have little coupling.
That’s not 100% accurate, as under the hood print
functions might need memory allocations. What I do
when writing the equivalent functions for mcus I
try to not use any memory allocations at all. If
you use mallocs, then you are effectively saying
that my buffers might be of unbounded size. Well,
you don’t have unbounded memory. Figure out what is
reasonable, and use that. If you found that
assumption too narrow, then increase it. It may be
iffy in a general-purpose computing environment,
but you are likely to yield much greater simplicity
when writing for memory- or time- contrained
environments.
# ⚓ Some_Email_Idiocy⠀⇛
Stupid is as Stupid Does
I’ve been, stupidly, using an email account that
came with a free web page account. I figured – what
harm could it be, it’s free, it’s been around… Now
I want to get rid of it, but I am away from home,
and there are some accounts I can’t access to
update the email address… So I am stuck.
I’ve been using a webmail client, maybe roundcube
(why nonsensical names?). Somehow the interaction
of the webmail client with my browser causes
repeated logins with a wrong (or no) password.
Bahm, my account gets locked out by whatever
security software they run. I don’t know about it
until a few days later, when I can’t log in.
The recovery process involves going on Discord and
begging the disgruntled sysop to unban my IP
address. That usually takes a whole day, sometimes
two, and involves some groveling.
[...]
Top shows that, running in the background with
automatic email fetching shut off — in other words,
doing absolutely nothing — it eats up about 5% CPU
and 5% memory. That is a ridiculously large
fraction of my machine — for doing absolutely
nothing. I have 8GB RAM), so the sleeping beauty
needs 400 MB to do nothing. Is this a bad joke?
=> =============================================================================
World Wide Web but a lot lighter.
䷩ 𝚕𝚒𝚗𝚎 3800
╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.16.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Links_16/07/2022:_OpenBGPD_7.5_and_AYANEO_Adopts_GNU/Linux⠀✐
Posted in News_Roundup at 9:04 am by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈
§ Contents⠀➾
* GNU/Linux
o Desktop/Laptop
o Kernel_Space
o Applications
o Instructionals/Technical
o WINE_or_Emulation
o Games
o Desktop_Environments/WMs
# K_Desktop_Environment/KDE_SC/Qt
# GNOME_Desktop/GTK
* Distributions_and_Operating_Systems
o BSD
o Fedora_Family_/_IBM
o Devices/Embedded
o Open_Hardware/Modding
o Mobile_Systems/Mobile_Applications
* Free,_Libre,_and_Open_Source_Software
o SaaS/Back_End/Databases
o Content_Management_Systems_(CMS)
o Programming/Development
# Python
# Shell/Bash/Zsh/Ksh
* 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
# 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
o Digital_Restrictions_(DRM)
o Monopolies
# Copyrights
* Gemini*_and_Gopher
o Personal
o Politics
o Technical
# Science
# Internet/Gemini
# Programming
* § GNU/Linux⠀➾
o § Desktop/Laptop⠀➾
# ⚓ Bradley Taunt ☛ The_Linux_Desktop_is_Hard_to_Love⠀⇛
I want to love the “Linux Desktop”. I really do.
But I’ve come to the realization that what I love
is the idea of the Linux Desktop. The community.
The security and core focus on open source. The
customizable environments. Tweaking as much or as
little of the operating system as I please!
I just can’t stick with it. I always end up back on
macOS. And I’m starting to understand why.
o § Kernel Space⠀➾
# ⚓ uni Toronto ☛ ‘iptables_-L’_doesn’t_show_you_interface
matches_on_rules_by_default⠀⇛
Today I learned something that I could have noticed
if I’d paid enough attention, which is that the
default ‘iptables -L’ output doesn’t show you
interface matches that are part of rules. In order
to see this in ‘iptables -L’ you have to make it
verbose (with -v), which also shows you the volume
counters. There is a story here.
o § Applications⠀➾
# ⚓ OpenSource.com ☛ Listen_to_music_on_Linux_with_Rhythmbox_|
Opensource.com⠀⇛
It’s hard for me to work in total silence. I need
some kind of background noise, preferably some
familiar music. My music-listening needs are pretty
simple: I just need a music player that plays my
library of MP3 music and streams from a few
websites I like to listen to.
o § Instructionals/Technical⠀➾
# ⚓ uni Toronto ☛ IMAP_servers_can_have_significant_imbalances
between_disk_and_network_IO⠀⇛
IMAP is deliberately a high level protocol; it
gives you abstract access to your mailboxes. One of
the decisions in the protocol is that it should
avoid round-tripping data through the client as
much as possible. For example, to copy messages
from one IMAP folder to another, your client
doesn’t download them and then upload them to store
them in the new folder; instead, it issues a COPY
command that tells the IMAP server ‘copy these
messages to this folder’. If you’re telling the
server to copy (or MOVE) a bunch of messages, your
network traffic is low but the server’s IO traffic
is potentially high (if they’re big messages). The
IMAP protocol is full of commands where the client
asks the server to do a lot of work on its behalf.
Often this will result in a lot of server disk IO
for relatively little network traffic to and from
the client.
# ⚓ Trend Oceans ☛ How_to_Fix_Remote_Host_Identification_has
changed_while_SSH_–_TREND_OCEANS⠀⇛
While accessing your remote server from your host
machine, you may encounter an error that states:
“WARNING: REMOTE HOST IDENTIFICATION HAS CHANGED!”
with a long message like the attached screenshot.
# ⚓ Trend Oceans ☛ How_to_Install_Metasploit_Framework_on
Android_Using_Termux_Without_Root⠀⇛

Metasploit is one of the essential tools that every
penetration tester should have. It can help you to
perform various tasks, such as creating and testing
exploits on the target system.
It is officially available for Linux, macOS, and
Windows. However, beginners interested in security
may not have a PC. In that case, you can take the
help of your Android device by installing the
Termux terminal emulator.
# ⚓ HowTo Forge ☛ How_to_Setup_DNS_Server_with_BIND_on_Ubuntu
22.04⠀⇛
BIND or Berkeley Internet Name Domain is free and
open-source DNS Server software. It’s one of the
most popular DNS server software used by more than
70% of DNS on the Internet. This guide will teach
you how to install DNS Server with BIND on Ubuntu
22.04 server. This tutorial will show you how to
set up Master-Slave BIND DNS server installation
using two Ubuntu servers.
# ⚓ UNIX Cop ☛ How_to_Install_FreetuxTV_on_Ubuntu_20.04_|_22.04
LTS⠀⇛
In this guide, we will show you how to install
FreetuxTV on Ubuntu systems.
FreetuxTV is a VLC -based program for receiving
Internet TV and radio in various languages.
Recording of current programs and time-shift
viewing are some of the useful program features.
The program is still under development, but many
well-known radio and television stations can
already be used. The list continues to grow.
# ⚓ Splitting_the_irealpro_1400_|_Adam_Young’s_Web_Log⠀⇛
The irealpro player has become an indispensable
tool for practicing a tune. Since I play saxophone,
the fact that irealpro will give me a full rhythm
section to play against makes working on a tune far
more possible than it was for me in the past.
I recently got a new phone and went to reinstall
the set of songs that I use. They come from a
collection called the Jazz 1400. This snuck up
slightly in number from the last time I imported,
and it must have hit a threshold, because my phone
refuses to import it.
# ⚓ Linux Capable ☛ How_to_Install_RPM_Fusion_on_Rocky_Linux
9⠀⇛
RPM Fusion is a repository of add-on packages for
RHEL type distributions and EL+EPEL that a group of
community volunteers maintains.
# ⚓ Ubuntubuzz ☛ How_To_Install_Kubuntu_22.04_with_Dualboot,
UEFI_and_External_Disk_Method⠀⇛
This tutorial will explain in step by step how you
can install Kubuntu 22.04 LTS “Jammy Jellyfish”. It
will start with requirements, continuing with 10
steps to install, finished with restart and the
final result. Let’s install it!
# ⚓ UNIX Cop ☛ How_to_install_Glances_on_CentOS_9_Stream_—
System_Monitor_written_in_Python⠀⇛
Hello, friends. In this post, you will learn how to
install Glances on CentOS 9 Stream.
# ⚓ ID Root ☛ How_To_Speed_Up_DNF_Package_Manager_on_Rocky
Linux_9_–_idroot⠀⇛
In this tutorial, we will show you how to speed up
the DNF package manager on Rocky Linux 9. For those
of you who didn’t know, DNF is the default package
manager for Rocky Linux 9 and newer versions, RHEL
9 and its clone CentOS 9 Stream, AlmaLinux 9, and
Fedora 36. One of the benefits of using DNF is that
it can be used to download packages from multiple
repositories, including Rocky Linux’s official
repositories, third-party repositories, and your
own local repositories. However, some users may
find the download speed slow compared to other
distributions. This can be frustrating after you
download and install many packages. Most users do
not realize that some minor tweaks to some
configuration files can increase your download
speed immensely.
This article assumes you have at least basic
knowledge of Linux, know how to use the shell, and
most importantly, you host your site on your own
VPS. The installation is quite simple and assumes
you are running in the root account, if not you may
need to add ‘sudo‘ to the commands to get root
privileges. I will show you the step-by-step
increase DNF download speed on Rocky Linux. 9.
# ⚓ UNIX Cop ☛ How_to_Install_SMPlayer_on_Ubuntu_20.04_|_22.04
LTS⠀⇛
In this guide, we will show you how to install
SMPlayer in Ubuntu systems.
SMPlayer is a cross-platform graphical front-end
for MPlayer and mpv and forks of Mplayer using GUI
widgets offered by Qt.
SMPlayer is free and open-source software subject
to the terms of the GNU General Public License
version 2 or later.SMplayer has been localized in
more than 30 languages.
SMPlayer is built with Qt and is based on MPlayer.
This makes it quite portable, since MPlayer and Qt
are already available on all major operating
systems. On the operating systems on which SMPlayer
has not yet been ported to, it is likely possible
to run the application through binary compatibility
with another Unix or Linux.
# ⚓ UNIX Cop ☛ How_to_Install_PhotoQT_Image_Viewer_on_Ubuntu
20.04_|_22.04_LTS⠀⇛
In this article, we will show you how to install
PhotoQt on Ubuntu systems.
PhotoQt is a simple yet powerful and good looking
image viewer, based on Qt/QML, published as open-
source, and completely free.
It is an image viewer that relies on an interesting
operating concept inspired by smartphones. While
the motif is displayed full-screen, all edges
except the right one serve as a trigger (when
touched with the mouse pointer) for a control
implemented in other programs via menus and
toolbars. For example, the left edge is used to
display the metadata , while the lower edge shows a
bar with a preview of neighboring images. This
leaves plenty of space for the actual image. On the
other hand, if you prefer keyboard control, you can
use various pre-configured key shortcuts that can
be reassigned if necessary.
o § WINE or Emulation⠀➾
# ⚓ WINE Project (Official) ☛ WineHQ_–_Wine_Announcement_–_The
Wine_development_release_7.13_is_now_available.⠀⇛
The Wine development release 7.13 is now available.
What’s new in this release:
– Gecko engine updated to version 2.47.3.
– USB driver converted to PE.
– Some theming improvements.
– Various bug fixes.
The source is available at:
https://dl.winehq.org/wine/source/7.x/wine-
7.13.tar.xz
Binary packages for various distributions will be
available from:
https://www.winehq.org/download
You will find documentation on https://
www.winehq.org/documentation
You can also get the current source directly from
the git
repository. Check https://www.winehq.org/git for
details.
Wine is available thanks to the work of many
people. See the file
AUTHORS in the distribution for the complete list.
o § Games⠀➾
# ⚓ GamingOnLinux ☛ AYANEO_to_have_their_own_AYANEO_OS_based_on
Linux⠀⇛
Looks like Linux is truly becoming a gaming
platform for the masses now, as AYANEO are throwing
their hat in the ring with AYANEO OS on their
hardware with the AYANEO AIR. While their new
IndieGoGo crowdfunding campaign focuses on it being
a Windows handheld, they’re also developing their
own full Linux distribution for their hardware
which will be available to download “in the
future”.
o § Desktop Environments/WMs⠀➾
# § K Desktop Environment/KDE SC/Qt⠀➾
# ⚓ Nate Graham ☛ This_week_in_KDE:_some_nice
improvements!⠀⇛

Current number of bugs: 52, down from 53. 0
added and 1 resolved…
Dolphin, Gwenview, and Spectacle now use the
XDG Portals interface for dragged-and-dropped
files, which allows them to successfully drop
files into sandboxed apps without punching a
hole in the sandbox by giving it access to
your entire home folder or the system’s temp
folder (Harald Sitter, version 22.08 of these
apps)
# § GNOME Desktop/GTK⠀➾
# ⚓ Its FOSS ☛ 13_Ways_to_Tweak_Nautilus_File_Manager_in
Linux_to_Get_More_Out_of_it⠀⇛

Nautilus is GNOME’s default file manager
application, and you may have seen it in many
Linux distributions.
It’s a good file manager with plenty of
features. However, you can enhance your
experience by employing some tweaks and tips.
I am going to share such tips and tweaks in
this article. Some tweaks may require
installing additional Nautilus plugins, while
some are built-in but lesser-known features.
A few tips are purely cosmetic and just
change the look and feel.
# ⚓ Medium ☛ GSoC’22_@GNOME_–_Coding_Phase_1:_Evaluate,
Design,_Code_|_by_Pooja_Patel⠀⇛
GNOME HIG CSS Library project aims to design,
develop and publish a unified CSS library
incorporating the revised Human Interface and
Visual Identity Guidelines allowing
developers to update the existing GNOME
websites and create new ones with a congruent
visual identity.
* § Distributions and Operating Systems⠀➾
o ⚓ Matt Rickard ☛ The_Story_of_CP/M⠀⇛
CP/M was special because it separated the physical I/
O system (now called BIOS – Basic I/O System) from the
disk operating system (at the time, called the BDOS –
Basic Disk Operating System). CP/M was the start of
program portability: before CP/M, programs were required
to run on exactly the same underlying hardware.
o § BSD⠀➾
# ⚓ uni Toronto ☛ How_Unix_didn’t_used_to_support_‘#!’,_a_brief
history⠀⇛
Before I started my research for writing this
entry, I would have said that kernel support for
‘#!’ was added in 4.2 BSD. That’s certainly where
it first appeared and where it became well known,
but according to the history section of Wikipedia’s
page on #!, it was first introduced by Dennis
Ritchie in 1980, after V7, although it might have
been suggested to him by someone else. It didn’t
become known through later releases of Research
Unix because those were never very widely spread,
unlike V7.
# ⚓ Undeadly ☛ rpki-client_7.9_released⠀⇛
# ⚓ Mailing list ARChives ☛ OpenBGPD_7.5_released⠀⇛
OpenBGPD-portable is known to compile and run on
FreeBSD, and the Linux distributions Alpine,
Debian, Fedora, RHEL/CentOS and Ubuntu. It is our
hope that packagers take interest and help adapt
OpenBGPD-portable to more distributions.
o § Fedora Family / IBM⠀➾
# ⚓ IT Web ☛ Matt_Hicks_appointed_as_Red_Hat_CEO_amid
leadership_changes⠀⇛
In a statement, the IBM-owned company says Hicks,
who previously served as Red Hat’s executive vice-
president of products and technologies, succeeds
Paul Cormier, who will serve as chairman of Red
Hat.
# ⚓ Fedora Project ☛ Fedora_Community_Blog:_Friday’s_Fedora
Facts:_2022-28⠀⇛
Here’s your weekly Fedora report. Read what
happened this week and what’s coming up. Your
contributions are welcome (see the end of the
post)!
o § Devices/Embedded⠀➾
# ⚓ Linux Gizmos ☛ Debix_Model_A_packs_i.MX_8M_Plus_and_mirrors
RPI_form_factor⠀⇛

According to the product page, the Debix Model A
seems to support Android 11, Yocto, Ubuntu and
Debix OS.
The company is also offering an I/O expansion board
and a LoRa board compatible with the Debix Model A.
See the spec list and the images below for more
details.
Specifications listed for the Debix Model A Single
Board Computer include…
o § Open Hardware/Modding⠀➾
# ⚓ Björn Wärmedal ☛ I_Built_a_Video_Game_Console⠀⇛
That’s code for “I built a fancy case for my
Raspberry Pi (3B+)” if you didn’t know.
# ⚓ Hackaday ☛ Stratum_1_Grandmaster_Time_Server_On_A_Budget⠀⇛
[Jeff Geerling] has been following the various open
source time projects for some time now, and is
finally able to demonstrate a working and
affordable solution for nanoseconds-accurate
timekeeping in your local lab. The possibility of a
low-cost time server came about with the
introduction of the Raspberry Pi CM4 compute module
back in Oct 2020, whose Broadcom network chip
(BCM54210PE) supports PTP (Precision Time Protocol,
IEEE-1588) 1PPS output and hardware-based time
stamping. Despite the CM4 data sheet specifying PTP
support, it wasn’t available in the kernel. An
issue was raised in Feb last year, and Raspberry Pi
kernel support was finally released this month.
# ⚓ Jeff Geerling ☛ Making_Noctua_fans_work_(quietly)_with_a
Supermicro_motherboard⠀⇛
Typically one installs whiny siren-like server fans
that spin at 5000+ rpm, and don’t worry much about
noise. But I do.
# ⚓ Linux Gizmos ☛ Debix_Model_A_packs_i.MX_8M_Plus_and_mirrors
RPI_form_factor⠀⇛
The Debix Model A from Polyhex is a Single Board
Computer (SBC) built around the i.MX 8M Plus Quad-
core ARM Cortex-A53 CPU industrial-grade processor.
This SBC integrates a 2.3 TOPS Neural Processing
Unit and expandable storage to target industrial
automation, multimedia, and other IoT applications.
The Debix Model A was designed by Polyhex
Technology and it’s based on the NXP NPU i.MX 8M
Plus industrial processor with maximum frequency of
1.6GHz. By default, this device comes with 2GB of
LPDDR4 but can be upgraded to 4GB or 6GB. The
default storage interface provides support for an
SD Card but can also be customized to provide eMMC
support from 8GB up to 128GB.
o § Mobile Systems/Mobile Applications⠀➾
# ⚓ Phone Arena ☛ This_“iPad”_made_for_prison_is_“clearly”
running_an_old_Android_version;_Tech_prisoners_use_–
PhoneArena⠀⇛
# ⚓ India ☛ Bluetooth_LE_For_Headphones_And_Earbuds_Coming_To
Android_13:_What_It_Promises_For_You?⠀⇛
# ⚓ InfoQ ☛ Android_13_Final_Beta_Improves_Security_and
Privacy,_and_More⠀⇛
# ⚓ Giz China ☛ Ulefone_Rugged_Armor_X6_Pro_Debuted_With
Android_12_–_Gizchina.com⠀⇛
# ⚓ Phone Arena ☛ OnePlus_Nord_CE_2_gets_its_first_Android_12
beta_update,_here’s_what’s_new_–_PhoneArena⠀⇛
# ⚓ CNET ☛ Google_Pixel_6A_vs._Pixel_6:_What’s_Different_About
Google’s_Cheaper_Android_12_Flagship_–_CNET⠀⇛
# ⚓ 9to5Google ☛ Android_Auto_Wi-Fi_connection_might_be_tweaked
in_latest_update⠀⇛
# ⚓ GO Media ☛ Delete_These_Android_Apps_Infected_With
Autolycos_Malware⠀⇛
# ⚓ 9to5Google ☛ Android_removes_Fuchsia_code_as_Starnix
project_progresses_–_9to5Google⠀⇛
# ⚓ Make Use Of ☛ The_15_Most_Popular_Free_Apps_Everyone_Needs
on_Their_Android_Phone⠀⇛
# ⚓ Android Central ☛ Moto_G_Power_(2022)_vs._Moto_G_Power_
(2021)_|_Android_Central⠀⇛
* § Free, Libre, and Open Source Software⠀➾
o ⚓ Bryan Lunduke ☛ Watch_as_the_“Microsoft_+_Open_Source”_apologists
push_a_narrative⠀⇛
Say what, now? I won’t deny, that’s a good opening line…
but… *ahem*…
In the beginning… IBM was The Evil Empire. And, if Steven
is talking about the early days of Microsoft… they were
not the Evil Empire at that time. Not by a long-shot.
In fact, Microsoft was (in those early days) primarily a
maker of software and hardware for a variety of computer
platforms made by other companies. Commodore, Apple,
Tandy, and so many others.
o ⚓ Remy Van Elst ☛ What’s_coming_in_the_next_version_of_Leaf_Node
Monitoring?⠀⇛
Leaf Node Monitoring is my own open source (GPLv3), paid,
network monitoring program for Windows, Linux & Android.
Written in C++ & Qt 5. Perfect to run on your desktop and
monitor your servers. Simple setup, auto-detects running
services, runs checks concurrently, open port scanning
and alerting. I’ve recently released the first version,
and this post goes over the features that will come in
the next release.
o § SaaS/Back End/Databases⠀➾
# ⚓ Ruben Schade ☛ Making_interactive_sqlite3_more_useful⠀⇛
sqlite3 is a fantastic embedded database for rapid
prototyping and resource-constrained environments,
given its lack of dependencies or a server. You
open one file with a CLI tool, and that’s it. You
probably interacted with several today without
realising it.
# ⚓ Evan Hahn ☛ The_difference_between_“=”_and_“IS”_in_SQLite⠀⇛
SQLite has two equality operators: = and IS (= can
also be written as ==). They’re very similar,
except when NULL is involved.
o § Content Management Systems (CMS)⠀➾
# ⚓ Linux Links ☛ 6_Best_Free_and_Open_Source_JavaScript-Based
Web_Content_Management_Systems⠀⇛

To provide an insight into the quality of software
that is available, we have compiled a list of 6
high quality free JavaScript-based Linux WCMS.
Hopefully, there will be something of interest for
anyone who wishes to manage a website.
Here’s our verdict. All the software featured here
is published under an open source license.
o § Programming/Development⠀➾
# ⚓ To_build_successful_software,_don’t_make_the_plan_better.
Make_it_shorter.⠀⇛
Consequently, to make up for these delays, teams
are pressured to deliver the next feature in less
time than they originally estimated.
When that happens, teams face two choices: cut
scope or cut corners. Because the all-knowing long-
term plan deems scope immutable, engineers will cut
corners, leading to more bugs and creating a
vicious cycle of delivering broken features.
This cascade of broken features will eventually
bring the team to a halt because they’ll be too
busy draining the flood to actually fix the leak
that’s causing it.
A further problem with the assumption that nothing
will go wrong is that it implies there will be no
mistakes to learn from. Therefore, teams will
continue operating with broken, costly, inefficient
processes.
# ⚓ glandium.org_»_Blog_Archive_»_Announcing_git-cinnabar
0.5.9⠀⇛
Git-cinnabar is a git remote helper to interact
with mercurial repositories. It allows to clone,
pull and push from/to mercurial remote
repositories, using git.
# § Python⠀➾
# ⚓ Buttondown ☛ Sneak_Peek:_Crimes_with_Python’s_Pattern
Matching⠀⇛
The pattern matching feature is, on the
whole, pretty reasonably designed, and people
will expect it to behave in reasonable ways.
Whereas __subclasshook__ is extremely dark
magic. This kind of chicanery might have a
place in the dark beating heart of a complex
library, certainly not for any code your
coworkers will have to deal with.
# § Shell/Bash/Zsh/Ksh⠀➾
# ⚓ Idiomdrottning ☛ zshbrev⠀⇛
zshbrev allows you to mix zsh code and brev
code. Not for polished li’l “eggs” but for
your own duct tape and chewing gum hacking
and automation. Quick and dirty♥.
* § Leftovers⠀➾
o ⚓ The Nation ☛ Richard_Seymour’s_World_Is_Full_of_Wonder⠀⇛
In 2015, Richard Seymour’s entire world was in flux. The
London-based author, editor of Salvage, a socialist
magazine that covers art and politics, and contributor to
the New Left Review had recently left the Socialist
Workers Party; his long-term relationship had fallen
apart; and then, on Christmas Day, he noticed how eerily
warm the weather was where it should have been crisply
cold. As Seymour explained, all this contributed to a
“deep crisis” in which he rethought everything from his
“tough-minded militant” persona (the “political ego
ideal,” he says) to actual politics, specifically where
the overlapping crises of the climate and environment fit
into his decidedly class-focused worldview. During this
period, Seymour came to understand the climate as “the
problem of problems” because, as he says, “the biosphere
is the precondition for everything else.”
o ⚓ Counter Punch ☛ The_Comic’s_Kosky⠀⇛
This solemn field spreads itself literally at the center
of Germany—its historical consciousness, its politics,
its culture, its crimes. The Nazi Chancellery was here
and Hitler’s bunker nearby, though the exact location is
not marked and therefore not available as a site of
pilgrimage for Fascists.
The sprawling American embassy is across the street from
the memorial, and just beyond it the Brandenburg Gate.
With its cool beige stone, glass and steel, the embassy’s
neo-Art-Deco-ism seems an ironic nod to the Good Old Days
of the Cold War, when America’s power was ascendant. I
think of the building as a diplomatic diner serving up
Marshall Plan burgers, NATO fries washed down with the
chocolate shake of Mutually Assured Destruction.
o ⚓ Data Swamp ☛ Storing_information_on_paper_using_the_Pen_To_Paper
protocol⠀⇛
Here is a draft for a protocol named PTPDT, an acronym
standing for Pen To Paper Data Transfer. It comes with
its companion specification Paper To Brain.
The protocol describes how a pen can be used to write
data on a sheet of paper. Maybe it would be better named
as Brain To Paper Protocol.
o ⚓ Tedium ☛ What_Brits_Know_About_Class_That_Americans_Don’t⠀⇛
Americans have a really hard time talking about so many
topics. Given the ubiquity of social media, you might
think I’m being deliberately obtuse. I don’t think I am;
race, gender, LGTBQ+, politics, among others are widely
discussed but anyone that’s spent any time online knows
that almost all those conversations happen in echo
chambers or they quickly fall into chaos. Admittedly,
trying to have a “reasonable” conversation with someone
who believes you have fewer rights over your body
(whether reproductive or simply the right not to have
your teeth kicked in by law enforcement) is all but
impossible. However, one topic that almost all Americans,
regardless of political persuasion, are loath to discuss
is the subject of class. Today’s Tedium is looking at one
of the most iconic sketches in the history of British
comedy to understand the lack of discussion around class
in America and what it says about even the most “cynical”
of Americans.
o ⚓ Hackaday ☛ Got_A_Cardboard_Box?_Get_Into_Food_Smoking!⠀⇛
We appreciate a good kitchen hack, and we have always
liked TV personality and chef [Alton Brown]’s McGuyver-
ish approach to these things. So for anyone who hasn’t
seen it, let’s take a moment to highlight how to make
(and use) Alton Brown’s Cardboard Box Smoker.
o ⚓ The Nation ☛ There_Are_Still_Things_to_Love_About_America⠀⇛
It’s hot and hazy as July rolls around. Growing up in the
Baltimore swamplands, we used to say, “It’s not the heat,
it’s the humidity.” Meaning that the humidity was harder
to deal with than the feverish temperatures. At some
point in my family, the phrase morphed into: “It’s not
the heat, it’s the stupidity.” At the time, we meant the
antics of people when it gets hot, including public
drunkenness, mishaps with fireworks, and fights over
slights. (These days, sadly enough, you’d have to add to
that list slaughtering people at a July 4th celebration
with an AR-15-style rifle.)
o ⚓ Hackaday ☛ Collaborative_Effort_Gets_Laser_Galvos_Talking_G-
Code⠀⇛
Everyone should know by now that we love to follow up on
projects when they make progress. It’s great to be able
to celebrate accomplishments and see how a project has
changed over time. But it’s especially great to highlight
a project that not only progresses, but also gives back a
little to the community.
o § Science⠀➾
# ⚓ Matt Rickard ☛ Hotelling’s_Law_and_Differentiation⠀⇛
The resulting observation is called Hotelling’s law
– that rational producers will tend to make their
products as similar as possible. You can think of
this as the opposite of product differentiation.
Through the lens of game theory, both A and B have
reached Nash Equilibrium by situating themselves in
the middle of the beach.
o § Education⠀➾
# ⚓ Teachers_often_work_a_second_job_outside_of_the_classroom⠀⇛
In a 2021 national survey of 1,200 classroom
teachers conducted by the Teacher Salary Project, a
nonpartisan organization, 82% of respondents said
they either currently or previously had taken on
multiple jobs to make ends meet. Of those, 53% said
they were currently working multiple jobs,
including 17% who held jobs unrelated to teaching.
o § Hardware⠀➾
# ⚓ Hackaday ☛ A_Simple_Web-Based_Wiring_Harness_Tool⠀⇛
When building electronic assemblies there is quite
often the need to construct custom cables to hook
things up. It’s all very well if you’re prototyping
by hand, or just building one or two of a thing,
but if you’re cranking them out using outside help,
then you’re going to want to ensure that cable is
described very accurately. [Christian Nimako-
Boateng Jr.] presents for us the first version of
wirely, a wiring harness tool. This is a web-based
tool that allows one to describe the cable ends and
connectivity between them, producing a handy
graphic and exports to excel in a format that
should be easy to follow.
# ⚓ Hackaday ☛ Helping_Secure_Amateur_Radio’s_Digital_Future⠀⇛
The average person’s perception of a ham radio
operator, assuming they even know what that means,
is more than likely some graybeard huddled over the
knobs of a war-surplus transmitter in the wee small
hours of the morning. It’s a mental image that,
admittedly, isn’t entirely off the mark in some
cases. But it’s also a gross over-simplification,
and a generalization that isn’t doing the hobby any
favors when it comes to bringing in new blood.
# ⚓ Hackaday ☛ Hackaday_Podcast_177:_Microscopes,_Telescopes,
Telephonoscopes,_And_A_Keyboardoscope?⠀⇛
This week, Editor-in-Chief Elliot Williams and
Assignments Editor Kristina Panos stood around
talking like they weren’t thousands of miles apart.
And we mean that literally: Kristina just got an
up/down desk, and it turns out that Elliot’s had
the exact same one for years.
o § Health/Nutrition/Agriculture⠀➾
# ⚓ ABC ☛ California_social_media_addiction_bill_drops_parent
lawsuits⠀⇛
A first-of-its-kind proposal in the California
Legislature aimed at holding social media companies
responsible for harming children who have become
addicted to their products would no longer let
parents sue popular platforms like Instagram and
TikTok.
The revised proposal would still make social media
companies liable for damages of up to $250,000 per
violation for using features they know can cause
children to become addicted. But it would only let
prosecutors, not parents, file the lawsuits against
social media companies. The legislation was amended
last month, CalMatters reported Thursday.
# ⚓ Orac ☛ AAPS_joins_the_legal_thuggery_against_medical
standards⠀⇛
I’ve written about the Association of American
Physicians and Surgeons (AAPS) on a number of
occasions, dating all the way back to 2006. The
first time I discovered AAPS, I described the
organization as a “medical John Birch Society” in
that it is in reality a political organization
disguised as a legitimate medical professional
society. More than that, AAPS is a crank medical
organization every bit as much a bunch of far right
conspiracy theorists as the John Birch Society ever
was and has been around a long time, having been
founded in 1943. This makes unsurprising to me that
earlier this week AAPS announced that it was suing
three medical specialty boards that had announced
measures to strip physicians promoting COVID-19
misinformation and other health misinformation of
their board certifications.
o § Proprietary⠀➾
# ⚓ The Verge ☛ It’s_ChromeOS_now,_not_Chrome_OS⠀⇛
Chrome OS, Google’s Linux-based operating system
for its Chromebook devices, has been around for
more than a decade, but the company has made a
small but notable branding change: it’s now called
ChromeOS, with no space in between. James Croom,
Google’s senior director of marketing for ChromeOS,
confirmed the change to The Verge.
# ⚓ Tim Bray ☛ Living_With_Models⠀⇛
More people, more often, are finding themselves
dealing with the output of Machine-Learning (ML)
software. With even a little practice you can spot
when it’s happening. It makes me wonder what the
future of human/ML interaction looks like. Herewith
a few personal experiences.
# ⚓ Linux Capable ☛ How_to_Install_Visual_Studio_Code_on_Rocky
Linux_9 [Ed: Why promote proprietary malware of Microsoft,
which spies on users and their systems, in a system that
deleted itself from Microsoft GitHub and is providing an
alternative to increasingly evil IBM?]⠀⇛
# ⚓ Linux Capable ☛ How_to_Install_VSCodium_on_Rocky_Linux_9
[Ed: This one is not proprietary, it does not let Microsoft
spy on users, but it helps Microsoft's proprietary malware/
spyware (VS Code) gain foothold]⠀⇛
o § Security⠀➾
# ⚓ Why_Open_Source_is_ESG [Ed: When lawyers write about Free
software, or people who used to work for Microsoft, they
don't have much positive to say]⠀⇛
# ⚓ The Hill ☛ DHS_review_board_says_it_could_take_years_to_fix
government_software_vulnerability [Ed: Using Log4j to
distract from actual back doors in proprietary software]⠀⇛
The recommendations are categorized into four main
focuses — addressing the continued risks of Log4j,
adopting industry-accepted practices for managing
vulnerabilities, building a more proactive model of
vulnerability management and making investments for
the country’s digital security in the future.
# § Privacy/Surveillance⠀➾
# ⚓ Internet Freedom Foundation ☛ #Privacyofthepeople:_91
problems_but_this_ain’t_one⠀⇛
Delhi Police issued a notice to Razorpay
under Section 91 of the Criminal Procedure
Code, 1973 (“Section 91”) while it was
investigating Mr Mohammad Zubair, a fact-
checker and founder of Alt-News. In
compliance with the notice, Razorpay shared
the personal information of donors of Alt-
News without informing Alt-News or the
donors. In this #Privacyofthepeople post, we
explain the scope of Section 91 notices, how
they may impact your right to privacy and
what remedies you have under law. Since IFF
uses Razorpay to receive donations, we also
explain the steps we are taking to protect
donor privacy.
# ⚓ Wired ☛ A_New_Attack_Can_Unmask_Anonymous_Users_on
Any_Major_Browser⠀⇛
The findings, which NJIT researchers will
present at the Usenix Security Symposium in
Boston next month, show how an attacker who
tricks someone into loading a malicious
website can determine whether that visitor
controls a particular public identifier, like
an email address or social media account,
thus linking the visitor to a piece of
potentially personal data.
When you visit a website, the page can
capture your IP address, but this doesn’t
necessarily give the site owner enough
information to individually identify you.
Instead, the hack analyzes subtle features of
a potential target’s browser activity to
determine whether they are logged into an
account for an array of services, from
YouTube and Dropbox to Twitter, Facebook,
TikTok, and more. Plus the attacks work
against every major browser, including the
anonymity-focused Tor Browser.
# ⚓ Bruce Schneier ☛ San_Francisco_Police_Want_Real-Time
Access_to_Private_Surveillance_Cameras⠀⇛
If approved, the draft ordinance would also
allow SFPD to collect historical video
footage to help conduct criminal
investigations and those related to officer
misconduct. The draft law currently stands as
the following, which indicates the cops can
broadly ask for and/or get access to live
real-time video streams: [...]
# ⚓ Techdirt ☛ Would_Meta_Really_Shut_Down_Facebook_And
Instagram_In_The_EU_Over_Data_Transfer_Rules?⠀⇛
Just a few weeks back we talked about how the
US’s unwillingness to fix the way the NSA
collects internet data could basically mean
that most of the big US internet services
cannot work in the EU. That article was about
Google, and it goes through the background
and history of the various US/EU privacy data
sharing agreements, and how each one has been
tossed out by EU courts in large part because
of the NSA surveillance techniques brought to
light by Edward Snowden. But much less
attention has been paid to what this all
means at a practical level.
# ⚓ Computer World ☛ UK_government_ministers_urged_to_not
conduct_business_using_WhatsApp⠀⇛
A newly published report marks the conclusion
of a yearlong investigation launched in 2021
by then-Information Commissioner Elizabeth
Denham. The inquiry was initiated after
concerns were raised into the use of the
messaging service WhatsApp and private email
accounts by former health secretary Matt
Hancock and his deputy, James Bethell, at the
Department of Health and Social Care (DHSC)
during the height of the pandemic.
The report found that official information
had been shared through 29 WhatsApp accounts,
17 private text messaging accounts, eight
private email accounts and one LinkedIn
account.
# ⚓ The Verge ☛ Facebook’s_new_test_allows_people_to_have
up_to_five_profiles⠀⇛
As part of the test, some Facebook users will
have the ability to create up to four
additional profiles tied to their original
account. The idea is that additional profiles
can be used for different purposes, like one
for friends, one for co-workers, and others
for interacting with interest groups and
influencers. Users will still have one
account but be able to switch between
profiles with a few clicks.
# ⚓ EFF ☛ Ring_Reveals_They_Give_Videos_to_Police_Without
User_Consent_or_a_Warrant⠀⇛
The company has provided videos to law
enforcement, without a warrant or device
owner consent, 11 times already this year.
This admission comes in response to a series
of critical letters from Senator Ed Markey
(D-MA). Markey chastised the company over
many of the same privacy problems that EFF
has brought up, including the far-reaching
audio capabilities of Ring devices, and the
company’s refusal to commit to not
incorporate facial recognition technology
into their cameras.
Amazon must consider the danger these
products pose to the public by creating a
growing web of surveillance systems that are
owned by individuals, but are de-facto
operated by law enforcement.
Police are not the customers for Ring; the
people who buy the devices are the customers.
But Amazon’s long-standing relationships with
police blur that line. For example, in the
past Amazon has given coaching to police to
tell residents to install the Ring app and
purchase cameras for their homes—an
arrangement that made salespeople out of the
police force. The LAPD launched an
investigation into how Ring provided free
devices to officers when people used their
discount codes to purchase cameras.
# ⚓ Techdirt ☛ Arizona_Makes_It_Illegal_To_Record_Cops
From_Less_Than_Eight_Feet_Away⠀⇛
Courts (with the rare exception) are in
agreement: there’s a First Amendment right to
film cops. With every citizen carrying a
camera these days, there’s a lot more filming
happening. And those recordings have often
proven key when cops face criminal charges
for violating rights or, you know, murdering
people.
o § Defence/Aggression⠀➾
# ⚓ Eesti Rahvusringhääling ☛ Russian,_Belarusian_citizens_will
not_be_allowed_to_own_firearms_in_Estonia⠀⇛
The coalition agreement of the Reform Party, Isamaa
and the Social Democratic Party (SDE) aims to
prohibit citizens of Russia and Belarus from owning
guns in Estonia. Incoming interior minister Lauri
Läänemets said the change will take months to
implement and that repealing the weapons permits of
other unfriendly people should also be considered.
# ⚓ NPR ☛ Secret_Service_erased_texts_from_two-day_period
spanning_Jan._6_attack,_watchdog_says⠀⇛
A watchdog says the U.S. Secret Service deleted
many of the text messages sent during a two-day
period surrounding the Jan. 6 attack on the
Capitol.
The inspector general for the Department of
Homeland Security, which oversees the agency, told
Congress the messages were deleted after his office
asked for them.
The discovery was made as part of the watchdog’s
investigation into the deadly siege last year and
will likely play into the probe being led by the
House select committee investigating the attack.
# ⚓ TruthOut ☛ Secret_Service_Texts_From_January_6_Were_Deleted
After_Watchdog_Requested_Them⠀⇛
# ⚓ Common Dreams ☛ ‘Looks…_Pretty_Bad’:_Secret_Service_Erased
Jan._6_Texts_After_Being_Asked_for_Them⠀⇛
Thursday reporting by The Intercept that the Secret
Service deleted text messages from January 5 and 6,
2021 “shortly after oversight officials requested
the agency’s electronic communications” has
elicited many questions and concerns about what
evidence regarding last year’s deadly assault on
the U.S. Capitol was destroyed.
The Secret Service claims that the messages were
erased as “part of a device-replacement program.”
# ⚓ The Gray Zone ☛ US_intel_officer_targeted_by_John_Bolton
reacts_to_coup-plot_confession⠀⇛
# ⚓ TruthOut ☛ Noam_Chomsky:_Biden’s_Middle_East_Trip_Contains
Echoes_of_Trump’s_Policies⠀⇛
# ⚓ Scheerpost ☛ Ukrainian_Failed_Counterattack,_Weak_Defense
Lines,_and_Oversight-Free_Weapon_Deliveries⠀⇛
There is no oversight over where the ‘western’
weapon deliveries to the Ukraine go to…We can only
guess where those weapons will end up.
# ⚓ The Nation ☛ It_Can_Happen_Here:_A_White_Supremacist_Coup
That_Succeeded⠀⇛
Cedric Harrison is a tall man with a long view. He
leads heritage tours in Wilmington, N.C., the site
of the nation’s only successful white supremacist
coup.
# ⚓ Krebs On Security ☛ Why_8kun_Went_Offline_During_the
January_6_Hearings⠀⇛
The latest Jan. 6 committee hearing on Tuesday
examined the role of conspiracy theory communities
like 8kun[.]top and TheDonald[.]win in helping to
organize and galvanize supporters who responded to
former President Trump’s invitation to “be wild” in
Washington, D.C. on that chaotic day. At the same
time the committee was hearing video testimony from
8kun founder Jim Watkins, 8kun and a slew of
similar websites were suddenly yanked offline.
Watkins suggested the outage was somehow related to
the work of the committee, but the truth is
KrebsOnSecurity was responsible and the timing was
pure coincidence.
# ⚓ The Nation ☛ Reality_Bites_but_Gen_X_Can_Still_Fight_Back⠀⇛
Maybe it was seeing the former Oath Keeper wearing
a Descendents T-shirt when testifying before the
January 6 committee, but I think it’s past time we
reckoned with Generation X. The backbone of
Trumpist alt-right support comes from my
generation. Learning that polls show people born
between 1965 and 1980 are the foot soldiers and
ideological minders of the new fascism has been
jarring, because I’ve always considered Gen X
underrated. There has been much ink spilled about
the culture wars between boomers and millennials,
skipping right over us. It seemed unfair. After
all, we were the generation of grunge, some of the
best hip-hop ever made (defined by the
revolutionary sounds of Public Enemy), and the last
generation to read newspapers (that matters to me,
for some reason). We should be recognized. We
launched movements and challenged the two-party
duopoly.
# ⚓ Meduza ☛ ‘A_special_operation_against_city_preservation
advocates’_How_commercial_interests_in_St._Petersburg_are
using_the_‘political_situation’_to_demolish_historic
buildings_—_Meduza⠀⇛
On July 13, Live City, a movement dedicated to
preserving St. Petersburg’s cultural heritage,
published a letter from film director Alexander
Sokurov to city governor Alexander Beglov. In it,
Sokurov accuses the city authorities of taking
advantage of the “difficult military and political
situation” to dismantle the movement to preserve
St. Petersburg’s historic buildings. According to
the St. Petersburg news outlet Bumaga, the
government has spent the months since the start of
the war reorganizing and eliminating the city’s
oldest preservation advocacy groups, demolishing
monuments, and changing laws to benefit commercial
developers. With Bumaga’s permission, Meduza is
publishing an abridged translation of the
investigation.
# ⚓ Meduza ☛ Dying_to_kill_The_Russian_neo-Nazis_fighting
Vladimir_Putin’s_war_to_‘denazify’_Ukraine_—_Meduza⠀⇛
When announcing the February invasion of Ukraine,
Vladimir Putin said that one of Russia’s aims was
to “denazify” the country. In the months since,
Kremlin propaganda has continuously pushed the
notion that Russian troops are “destroying” and
capturing “nationalists,” “Banderities,” and “neo-
Nazis” in Ukraine — painting all Ukrainian soldiers
as far-right radicals and eliding the fact that
thousands of innocent civilians have died as a
result of the invasion. What the Kremlin’s
propagandists have conveniently ignored, however,
is the fact that several avowed ultra-right
nationalists are actually fighting on Moscow’s
side. Meduza tells the story of how Russian neo-
Nazis were drawn into Vladimir Putin’s war to
“denazify” Ukraine.
# ⚓ TruthOut ☛ Bernie_Sanders_Unveils_Resolution_to_End_US
Support_for_Saudi-Led_War_in_Yemen⠀⇛
# ⚓ Common Dreams ☛ Human_Rights_Watch_to_US:_Stop_Selling
Weapons_to_Saudis⠀⇛
As U.S. President Joe Biden met with Saudi Crown
Prince Mohammed bin Salman Friday, a top official
at Human Rights Watch implored the American leader
to not lift a ban on the sale of certain weapons to
the repressive monarchy as it continues waging an
atrocity-laden war in Yemen.
Responding to reports that the Biden administration
is considering ending its vague proscription
against the transfer of “offensive” weaponry to
Saudi Arabia, Michael Page, Human Rights Watch’s
(HRW) Middle East and North Africa deputy director,
warned that such a policy reversal “could lead to
fresh rights violations in Yemen.”
# ⚓ Common Dreams ☛ From_‘Bone_Saw’_to_‘Pariah’_to_‘Fist_Bump’:
Outrage_as_Biden_Greets_Murderous_Saudi_Prince⠀⇛
Making a mockery of his own campaign vow to treat
the repressive Saudi kingdom as a “pariah,” U.S.
President Joe Biden on Friday greeted Saudi Crown
Prince Mohammed bin Salman—who intelligence
agencies believe approved the murder of journalist
Jamal Khashoggi—with an amiable fist bump as he
arrived at the royal palace in Jeddah.
Already furious over the president’s decision to
meet with the crown prince despite his role in the
brutal 2018 murder of Khashoggi and subsequent
cover-up attempt, human rights defenders responded
with outrage to the greeting, which the Saudi
regime swiftly blasted out on social media.
# ⚓ Scheerpost ☛ JOHN_KIRIAKOU:_With_President_Biden_in_Saudi
Arabia⠀⇛
The truth is that Biden is arriving in Jeddah with
hat in hand to ask the Saudis to increase oil
production. That, of course, would lower oil prices
and help the Administration to get a hold on
inflation. But the Saudis (and the Emiratis and the
Kuwaitis) already have said that their oil
industries are operating near maximum capacity.
# ⚓ Scheerpost ☛ Chris_Hedges:_War_with_Iran⠀⇛
The United States, Israel and Saudi Arabia are
plotting a war with Iran. The 2015 Iranian nuclear
arms accord, or Joint Comprehensive Plan of Action
(JCPOA), which Donald Trump sabotaged, does not
look like it will be revived. U.S. Central Command
(CENTCOM) is reviewing options to attack if Teheran
looks poised to obtain a nuclear weapon and Israel,
which opposes U.S.-Iran nuclear negotiations,
carries out military strikes.
o § Transparency/Investigative Reporting⠀➾
# ⚓ Rolling Stone ☛ Secret_Service_Deleted_Jan._6_Texts_After
Oversight_Request_…_For_Some_Reason⠀⇛
The revelation came in a letter obtained by the
Jan. 6 committee that was sent by Department of
Homeland Security Office of Inspector General —
which oversees the Secret Service — to the House
and Senate homeland security committees. The letter
notes that the DHS IG’s office requested the Secret
Service’s electronic communications from Jan. 5 and
Jan. 6 before being informed that the
communications had been erased. The letter
reportedly notes that the erasure took place after
the request was made. Secret Service has claimed
the communications were deleted as part of a
“device-replacement program.”
# ⚓ NBC ☛ Secret_Service_erased_text_messages_from_Jan._6_and
the_day_before,_the_Homeland_Security_watchdog_says⠀⇛
The Secret Service erased text messages from both
Jan. 6 and the day before the attack on the Capitol
after the Department of Homeland Security’s
internal watchdog requested records of electronic
communications tied to the insurrection, according
to a letter sent to congressional committees that
was obtained by NBC News.
o § Environment⠀➾
# ⚓ The Nation ☛ SCOTUS_Limits_the_Environmental_Protection
Agency⠀⇛
# ⚓ Common Dreams ☛ ‘Europe_Is_Cooking’:_Records_Smashed_as
Historic_Heat_Alert_Issued⠀⇛
Several countries across Europe are enduring the
dangerous hot conditions that climate scientists
have longed warned of and meteorologists project
the brutal heatwave could last in some areas
through next month.
Spain and Portugal have faced high temperatures
since last Friday. According to CNN, at least three
Spanish cities set records this week: Ourense at
43.2°C (109.76°F); Soria at 38.7°C (101.66°F); and
Zamora at 41.1°C (105.98°F).
# ⚓ Common Dreams ☛ ‘Nothing_Short_of_a_Death_Sentence’:_Fury
as_Manchin_Tanks_Climate_Spending⠀⇛
Sen. Joe Manchin of West Virginia informed
Democratic leaders Thursday that he will not
support any new climate spending or tax increases
targeting the wealthy and large corporations,
sinking his party’s revived push for renewable
energy investments and further undercutting the
country’s ability to rein in carbon emissions.
While Manchin’s refusal to endorse green energy
funding may have been entirely foreseeable given
his close ties to the fossil fuel industry and his
role in tanking the Build Back Better package just
months earlier, climate advocates nevertheless
voiced dismay at the power one individual has been
able to exert over a process with implications for
billions of people across the planet.
# § Energy⠀➾
# ⚓ TruthOut ☛ Coal_Baron_Manchin_Kills_What_Could_Be
Nation’s_Last_Best_Chance_on_Climate⠀⇛
# ⚓ Common Dreams ☛ Biden_Urged_to_Respond_to_Manchin_by
Killing_West_Virginia_Fracked_Gas_Pipeline⠀⇛
President Joe Biden on Friday faced calls to
respond forcefully to Sen. Joe Manchin’s
latest climate obstruction by canceling a
fracked gas pipeline in the right-wing
Democrat’s home state of West Virginia, a
move that would prevent around 90 million
metric tons of new greenhouse gas emissions
from being spewed into the atmosphere each
year.
“West Virginians would be better served by
pursuing clean energy projects than climate-
polluting pipelines.”
# § Wildlife/Nature⠀➾
# ⚓ Telex (Hungary) ☛ Hungary,_the_dog_breeding
superpower⠀⇛
Due to the existing huge demand all across
Europe, illegal breeders have been
overbreeding dogs in Hungary. These animals
then grow up amidst poor conditions and are
not given proper medical care. Once they are
sold, many of them get sick with serious
illnesses, and a large percentage of them die
young. Our documentary traces the system of
dog trade in Hungary, and shows how it has
been built up over the last decades, as well
as some of those who are taking part in this
illegal business.
# ⚓ The Revelator ☛ WTO_Agreement_Boosts_Efforts_for_a
Sustainable_Ocean⠀⇛
o § Finance⠀➾
# ⚓ Common Dreams ☛ Opinion_|_Confronting_“Policy_Murder”_and
the_Rising_Violence_of_the_Right⠀⇛
On Juneteenth weekend, tens of thousands of people
walked up Pennsylvania Avenue toward the U.S.
Capitol as part of the epically titled Poor
People’s and Low-Wage Workers’ Assembly and Moral
March on Washington and to the Polls. (Priti Gulati
Cox and I traveled via Amtrak from Kansas to join
in.) Although we were following the footsteps of a
mob that had stormed the Capitol seventeen months
earlier, this march embodied the polar opposite
worldview. At the rally ending the march, Poor
People’s Campaign co-chair Rev. William J. Barber
II made that clear, saying that the event was not a
violent insurrection but rather “a resurrection” of
people power against violence.
# ⚓ Common Dreams ☛ Opinion_|_Behold:_The_Big_Business_Plot_to
Overthrow_Democratic_Rule⠀⇛
“[T]he monopoly which our manufacturers have
obtained against us … like an overgrown standing
army, has become formidable to the government, and
upon many occasions intimidate the
legislature.”—Adam Smith, The Wealth of Nations,
1776
o § AstroTurf/Lobbying/Politics⠀➾
# ⚓ Lee Yingtong Li ☛ Later-no-harm_and_the_‘Wright’_method_of
single_transferable_vote⠀⇛
Later-no-harm is a criterion for preferential
voting methods which provides that ‘Adding a later
preference to a ballot should not harm any
candidate already listed’ [1]. The most well-known
voting systems which comply with later-no-harm are
the single transferable vote (STV), and its single-
winner variant, instant runoff voting.
# ⚓ Lee Yingtong Li ☛ Curiosities_in_drafting_for_the_weighted
inclusive_Gregory_method_of_STV⠀⇛
In Australia, 2 jurisdictions make use of the
weighted inclusive Gregory method of the single
transferable vote (STV). The weighted inclusive
Gregory method of STV is one of 2 systems
recommended by the Proportional Representation
Society of Australia as part of a gold standard
electoral system.
Each of the 2 jurisdictions, however, has
interesting quirks in the drafting of the
legislation giving the specifications for the
weighted inclusive Gregory method, which are worth
exploring.
# ⚓ Eesti Rahvusringhääling ☛ Outgoing_IT_minister_announces
details_of_third_and_final_5G_auction⠀⇛
The auction, of the 694-790 MHz frequency range, is
set to take place in autumn, following the
conclusion of the current, ongoing auction
involving Telia, Tele2 and Bite.
Two telecoms firms will be eligible to bid.
# ⚓ Salon ☛ So_where_did_all_this_right-wing_religious_nuttery
come_from?⠀⇛
The Reagan presidency was their first major
victory; in eight short years he cut union
membership in America almost in half, dropped the
taxes on billionaires from a top 74% bracket down
to 27%, and slashed thousands of protective
regulations, particularly around guns and the
environment.
Over the 40 years of the Reagan revolution, we’ve
gone from having about the same gun-ownership
density as Canada (around 15 guns per 100 people)
to the most in the world (over 120 guns per 100
people). We’re now drenched in blood: Guns kill
more American children than drunk drivers or any
other cause.
# ⚓ TruthOut ☛ If_Trump_Jumps_Into_Presidential_Race_Before
Midterms,_All_Bets_Are_Off⠀⇛
# ⚓ Techdirt ☛ OAN_Starts_Attacking_Verizon,_The_Last_Cable
Giant_Willing_To_Platform_Its_Conspiratorial_Gibberish⠀⇛
When last we checked in with right-wing propaganda
network One America News (OAN), it was suffering
some kind of embolism for being kicked off of
DirecTV. Despite a lot of attention, not that many
people actually watch the channel, so DirecTV
finally kicked it aside. This was distorted by OAN
and numerous key Republicans into a claim that the
conspiracy theory floating outlet was being
“unfairly censored.”
# ⚓ Techdirt ☛ Why_The_GOP_Wants_To_Break_Your_Spam_Filter:_GOP
Candidate_Tricked_Gullible_Voters_Into_Funding_Him_With
Misleading_Spam_Emails⠀⇛
Over the last few months we’ve been covering this
bizarre story of how Republican politicians, pushed
by their preferred spamming provider (which
misrepresented a study on how email providers treat
political spam), have been falsely claiming that
Google is “censoring” their political emails.
They’ve also been pushing a law that would require
email providers not to label politician emails as
spam. In response, Google caved a bit and proposed
a new offering that would whitelist political
campaigns, keeping them out of the spam filter (but
including a button at the top asking the recipient
if they want to unsubscribe from that mailing).
Google asked the Federal Election Commission (FEC),
to bless this idea (and specifically to note it
wouldn’t be deemed to violate any campaign finance
laws).
# ⚓ The Nation ☛ Big_Corporate_Money_Wants_to_Kick_Andy_Levin
Out_of_Congress⠀⇛
When workers at Michigan’s SKLD Bloomfield Hills
Nursing Home launched a strike for improved working
conditions last Monday, they did not stand alone.
Their represen, Andy Levin, was right there with
them. And it wasn’t just a quick stop on the picket
line for Levin. He came to march, wearing his
“Unions For All” T-shirt and jeans. He raised a
clenched fist, jumped in behind the Service
Employees International Union’s “Respect Us!
Protect Us! Pay Us!” banner, and joined the chant
of “Ain’t no party like a union party, ’cause the
union party don’t stop.” Finally, he told the
crowd, “The whole community stands with these of
workers in the name of dignity, respect, and good
patient care.”
# ⚓ The Nation ☛ Ohio_Man⠀⇛
# ⚓ Scheerpost ☛ Neo-Cons:_Genesis_to_Ascendency⠀⇛
The adherents of the neo-conservative movement now
dominate positions of rank within the Executive
branch, and exercise intellectual hegemony among
members of the foreign policy community more
generally.
# ⚓ Common Dreams ☛ Opinion_|_NY_Times_Polls_on_Biden_and
Trump’s_Low_Popularity_Don’t_Provide_Enough_Context_for
Americans’_Foul_Mood⠀⇛
A new New York Times/Siena College poll is
generating a lot of attention. It showed that 64%
of Democratic voters say they would prefer another
Democratic candidate in the 2024 presidential
campaign. One-third (33%) of Democrats say that
their biggest concern is that Biden, who is 79, is
too old to run for re-election. Another one-third
(32%) say that his “job performance” hasn’t been
good enough to warrant another run for the White
House.
# ⚓ Common Dreams ☛ Opinion_|_How_To_Get_the_War_Out_of
America⠀⇛
Today I spoke with the foreign policy aide of a
United States Senator in a scheduled lobbying call
for our antiwar organization. Rather than use the
standard lobbying points about wasteful Pentagon
spending, I asked for a frank discussion regarding
ways our organization might find a successful
strategy to cut the Pentagon budget. I wanted the
perspective of somebody working on the Hill for a
conservative senator.
# ⚓ Common Dreams ☛ Opinion_|_President_Biden:_End_the_War_in
Yemen⠀⇛
The United Nations has called the Saudi Arabia-led
war in Yemen the “world’s worst humanitarian
crisis.” Yet even that designation hardly captures
the full extent of misery endured by its people
over seven years of violence and unrelenting war.
# ⚓ Common Dreams ☛ Opinion_|_Worsening_Chaos:_Israel’s
Political_Instability_Is_Now_the_Norm⠀⇛
The collapse of the short-lived Israeli government
of Naftali Bennett and Yair Lapid validates the
argument that the political crisis in Israel was
not entirely instigated and sustained by former
Israeli Prime Minister, Benjamin Netanyahu.
# ⚓ Common Dreams ☛ Progressives_Release_Blueprint_for_Federal
Action_on_Reproductive_Freedom⠀⇛
The Congressional Progressive Caucus on Friday
released a blueprint for legislative and executive
actions to protect reproductive freedom in the wake
of the U.S. Supreme Court’s decision that
eliminated the constitutional right to abortion and
endangers other civil rights.
“These concrete steps constitute a whole-of-
government response to expand access to essential
healthcare.”
# ⚓ Common Dreams ☛ 99%_of_House_GOP_Just_Showed_They_Support
Forcing_Children_to_Birth_‘Their_Rapist’s_Child’:_Pascrell⠀⇛
While reproductive rights advocates and many
Democrats on Friday welcomed the U.S. House of
Representatives’ passage of a bill protecting the
right to travel for abortion care, Congressman Bill
Pascrell Jr. called out GOP lawmakers who opposed
the legislation.
“Today 99% of House Republicans made clear they
support forcing raped children to give birth to
their rapist’s child,” declared the New Jersey
Democrat after the House approved the Ensuring
Access to Abortion Act in a 223-205 vote.
# ⚓ Common Dreams ☛ Jayapal_Says_‘Systemic_Reform’_Needed_to
Thwart_Manchin’s_Obstruction⠀⇛
As some campaigners urged activists to intensify
their organizing to counter U.S. Sen. Joe Manchin’s
latest act of climate obstruction, a leading
congressional progressive on Friday called for
“institutional, systemic reform” to ensure one
lawmaker can’t hold their party’s priorities
hostage.
“Progressives have fought tooth and nail for the
president’s and the Democratic Party’s agenda.
Unfortunately, the senator from West Virginia has
consistently worked to undermine it, blocking
action on a number of priorities from child care,
to housing, and now climate change,” Congressional
Progressive Caucus (CPC) Chair Pramila Jayapal (D-
Wash.) said after Manchin (D-W.Va.) revealed he
would not currently support any new climate
spending or tax increases targeting the wealthy and
corporations.
o § Censorship/Free Speech⠀➾
# ⚓ Mexico News Daily ☛ From_sex_in_the_Sumidero_to_sex_in_the
park:_porn_producer_under_fire_again⠀⇛
Marín’s “sex in the sumidero” video also went viral
and as a result caught the eye of the federal
government’s National Commission of Natural
Protected Areas, which denounced the improper use
of the national park. It said that the filming of
pornographic content in the park damaged “the image
of an icon that represents the pride of Chiapas”
and exceeded “moral limits.”
# ⚓ RFERL ☛ ‘I_Crossed_Some_Red_Lines’:_What_It’s_Like_To_Work
As_A_Journalist_In_Central_Asia⠀⇛
For decades, Central Asian governments have kept a
tight grip over information. State media dominate
and serve as government mouthpieces rather than the
public. The few independent outlets face growing
financial pressures and efforts to stifle their
reporting through a variety of means — assaults,
threats, arrests, and prosecution. Self-censorship
is pervasive among journalists and bloggers.
Even in Kyrgyzstan, which boasts a vibrant and
pluralistic media environment compared to its
neighbors, press freedom has been on the decline.
Independent journalists have been detained or
harassed by trolls on social media. The ongoing
trial of investigative journalist Bolot Temirov on
drug charges bears the signs of political
persecution, according to his colleagues.
As social media increasingly becomes the main
source of news [sic] for citizens — especially
young people — the governments seek to gain more
control over those outlets, too. Internet shutdowns
and website blocking are widespread, particularly
during anti-government protests.
# ⚓ Creative Commons ☛ CC_still_opposes_mandatory_filtering_and
so_should_you⠀⇛
As part of Creative Commons’ key strategic goal of
Better Sharing, we have taken a firm stance against
mandatory content filtering on the internet. In new
proposed legislation, the U.S. Congress is now
raising mandatory content filtering again as a tool
to eliminate infringement of copyrighted works. For
those who are new to the discussion, mandatory
filtering would require that all information
providers enable software that prevents the
distribution of materials claimed by rightsholders.
If you’ve ever uploaded videos to YouTube, you’ve
seen content filters at work: videos are scanned
for copyrighted audio like popular music before
they are published, and sometimes videos are
blocked even when they are legal to share. Policy
that forces every digital publisher, platform, and
service provider to adopt similar filters would
make this broken model universal. CC has long
stated that the effects of mandatory filtering are
devastating to free speech, as well as the sharing
of culture and knowledge. CC has also spoken out
against filtering mandates and opposed their
introduction in the European Union.
o § Freedom of Information / Freedom of the Press⠀➾
# ⚓ The Hill ☛ State-backed_[crackers]_targeted_US-based
journalists_in_widespread_spy_campaigns:_report⠀⇛
State-sponsored [crackers] from China, North Korea,
Iran and Turkey have been regularly spying on and
impersonating journalists from various media
outlets in an effort to infiltrate their networks
and gain access to sensitive information, according
to a report released on Thursday by cybersecurity
firm Proofpoint.
The report reveals that government-backed
[crackers] used various tools to target
journalists, including sending phishing emails to
gain access to reporters’ work emails, social media
accounts and networks.
# ⚓ Above_the_Fold_and_in_Your_Inbox:_Tracing_State-Aligned
Activity_Targeting_Journalists,_Media⠀⇛
Proofpoint data since early 2021 shows a sustained
effort by APT actors worldwide attempting to target
or leverage journalists and media personas in a
variety of campaigns, including those well-timed to
sensitive political events in the United States.
Some campaigns have targeted the media for a
competitive intelligence edge while others have
targeted journalists immediately following their
coverage painting a regime in a poor light or as a
means to spread disinformation or propaganda. For
the purposes of this report, we focus on the
activities of a handful of APT actors assessed to
be aligned with the state interests of China, North
Korea, Iran, and Turkey.
o § Civil Rights/Policing⠀➾
# ⚓ RTL ☛ Petition_calling_for_two_home_office_days_per_week
reaches_threshold⠀⇛
A petition arguing in favour of two home-office
days per week for any employee in Luxembourg
gathered the necessary 4,500 signatures in the span
of just a few hours, meaning that it will be
discussed in the Chamber of Deputies.
Eight new petitions were published on Wednesday
morning. If a proposal gathers a minimum of 4,500
signatures, it must be debated by MPs in the
Chamber of Deputies.
The most popular petition by far argues in favour
of two weekly home office days, specifically for
cross-border workers. On Thursday morning it had
already garnered over 7,500 signatures.
# ⚓ [Repeat] DaemonFC (Ryan Farmer) ☛ Participation_in_Facebook
and_Twitter_can_and_will_be_used_against_you._You_have_no
right_to_remain_silent_after_you’ve_already_spoken._If_you
need_an_attorney,_good_luck_with_that.⠀⇛
In one recent post, I linked to an archived Nitter
mirror showing that a company called FAMA doxxed a
man’s Twitter account for “bad language”, “risky
likes”, etc, and sent his employer a 350+ page
printout.
[...]
Many lawyers advise their Social Security clients
to either delete Facebook and Twitter, or at least
make their profiles “Friends Only”, so the
government can’t go combing through them.
The problem with the “Friends Only” advice is that
the government is the government, and if Facebook
or Twitter have information on you, the government
is going to get it. It’s only a matter of time.
# ⚓ Scheerpost ☛ Michelle_Wilde_Anderson:_Saving_Broke_and
Broken_America,_One_Town_at_a_Time⠀⇛
On this week’s “Scheer Intelligence,” Michelle
Wilde Anderson speaks to Robert Scheer about how
four working class towns struggling with poverty
and broke governments still managed to progress.
# ⚓ TruthOut ☛ Republicans_Block_Bill_Protecting_Right_to
Travel_for_Abortion⠀⇛
# ⚓ TruthOut ☛ Texas_AG_Sues_to_Block_Biden_Order_Guaranteeing
Emergency_Abortion_Access⠀⇛
# ⚓ TruthOut ☛ A_Woman’s_Ex-Husband_Is_Suing_the_Clinic_That
Provided_Her_Abortion_4_Years_Ago⠀⇛
# ⚓ FAIR ☛ Jessica_Mason_Pieklo_on_Abortion_Rights,_Preston
Mitchum_on_Reproductive_Justice⠀⇛
This week on CounterSpin: The Supreme Court’s
reversal on abortion rights is so actually and
potentially devastating that it’s hard to know
where to look. It’s worth tracing things
back—Katherine Stewart in the Guardian, among
others, walks us through how, at a time when most
Protestant Republicans, including the Southern
Baptist Convention, hailed the liberalization of
abortion law represented by Roe, Christian
nationalists, motivated by a desire to protect
school segregation and tax exemptions for Christian
schools, selected abortion as a way to united
conservatives across denominational barriers, by
providing a “focal point for anxieties about social
change.” Phyllis Schlafly wrote a whole book (How
the Republican Party Became Pro-Life) about the
work involved in forcing the Republican party to
center abortion as a cause—which then became the
longer term effort to reframe “religious liberty”
as exemption from law. The names Paul “I don’t want
everybody to vote” Weyrich and Bob Jones Sr.—who
called segregation “God’s established order”—may
also mean something to you.
# ⚓ Techdirt ☛ Student_Expelled_Over_Off-Campus_Nazi_Joke_Can
Continue_To_Sue_The_School,_Says_Appeals_Court⠀⇛
Another school has learned it can’t discipline
students for off-campus behavior, especially in
light of the Supreme Court’s “fuck cheer” decision.
# ⚓ Pro Publica ☛ Who_Will_Replace_Judge_Donna_Scott
Davenport?⠀⇛
For two decades, Judge Donna Scott Davenport
oversaw the illegal arrests and detentions of more
than a thousand children in her Rutherford County
courtroom.
Her decisions eventually caught up with her: The
county settled a multimillion-dollar lawsuit, and
an investigation by Nashville Public Radio and
ProPublica brought to light what had been happening
for years, unchecked. Tennessee lawmakers called
for her ousting, the governor asked for a review,
and Middle Tennessee State University cut ties with
the judge, who taught criminal justice at the
school. There were nationwide calls for reform.
# ⚓ Democracy Now ☛ James_Webb’s_Role_in_Purge_of_LGBTQ+_NASA
Workers_Prompts_Push_to_Name_Telescope_After_Harriet_Tubman⠀⇛
The release of the first images from NASA’s new
flagship James Webb Space Telescope brought renewed
attention to the controversy over naming the
telescope after James Webb, who led NASA ahead of
the Apollo moon landings in the 1960s. He also
played a key role in purging LGBTQ+ people from
NASA in what was known as the “lavender scare,” and
before that at the State Department under President
Truman. We speak with Lucianne Walkowicz, one of
four astronomers who led a petition to rename the
telescope. Although the petitioners value the
insights the telescope contributes, “the way that
NASA has dug in its heels about naming the
telescope after James Webb has really cast a pall
over that,” says Walkowicz. They are also the co-
founder of the JustSpace Alliance, which made a new
documentary about the push to rename the telescope.
We feature an extended excerpt from “Behind the
Name: James Webb Space Telescope,” which also
examines the push to name the telescope after
Harriet Tubman, who “observed the night sky and
used the stars for celestial navigation in the
service of … people’s freedom.”
# ⚓ Common Dreams ☛ Calling_On_Russia_to_Free_Brittney_Griner,
Bishop_Barber_Seeks_‘Humanitarian_Visit’⠀⇛
Bishop William J. Barber II on Friday reiterated
his support for Brittney Griner while calling on
Russian and U.S. authorities to allow faith leaders
to visit the jailed U.S. Olympian and Women’s
National Basketball Association superstar in Russia
to help secure her release.
“We are asking the U.S. government and the U.S. and
Russian embassies to allow faith leaders to travel
to Russia as part of a humanitarian effort to gain
her release.”
# ⚓ Common Dreams ☛ House_Progressives_Cite_Clarence_Thomas_to
Argue_SCOTUS_Should_Lose_Jurisdiction_Over_Abortion⠀⇛
Reps. Alexandria Ocasio-Cortez and Mondaire Jones
on Thursday led a group of progressive lawmakers in
sending a letter to Democratic leaders urging them
to support restricting the Supreme Court’s
appellate jurisdiction over statutes codifying
abortion and other civil rights imperiled by the
court’s reactionary majority.
“Congress must use its powers to restrain the court
and protect our fundamental rights—once and for
all.”
o § Internet Policy/Net Neutrality⠀➾
# ⚓ Techdirt ☛ Microsoft_Mapped_Broadband_Affordability_Gaps
Because_The_U.S._Government_Couldn’t_Be_Bothered_To⠀⇛
We’ve long noted how U.S. broadband maps are a bit
of a dumpster fire. U.S. taxpayers have spent more
than $350 million for FCC broadband maps that
overstate broadband availability and speeds,
downplay widespread monopolization and
consolidation, and can’t even be bothered to
measure affordability, one of the biggest obstacles
to widespread adoption.
o § Digital Restrictions (DRM)⠀➾
# ⚓ [Repeat] DaemonFC (Ryan Farmer) ☛ Netflix_thinks_that_the
solution_to_its_financial_woes_is_a_deal_with_Microsoft_to
put_ads_into_your_TV_shows.⠀⇛
Netflix is in major financial crisis. They’re doing
huge layoffs. They’ve spent years mismanaging the
platform and have only themselves to blame.
Even though the DRM is malicious, and encourages
people to be jerks who can’t share with their
friends, it’s not the cause of their financial
problems.
Back when it wasn’t so expensive and had shows that
people wanted to watch, people would pay the money
to subscribe and then keep paying, usually even if
there wasn’t anything on that they wanted to watch
that month.
o § Monopolies⠀➾
# ⚓ Common Dreams ☛ Opinion_|_Why_Food_Prices_Are_Rising_Even
More⠀⇛
Monopolies are slowly killing rural America—and
driving up the price you pay for food.
# § Copyrights⠀➾
# ⚓ Torrent Freak ☛ Google_Delists_Hundreds_of_Pirate_Bay
Domains_From_UK_Search_Results⠀⇛
Google began to delist pirate sites from
local search results last year. The search
engine voluntarily complies with court orders
targeted at third-party Internet providers.
This is also true in the UK, where The Pirate
Bay initially remained unblocked. A recent
wave of removal requests corrected this
initial oversight and hundreds of Pirate Bay
domains have since been removed.
# ⚓ Torrent Freak ☛ VNest_IPTV_Faces_US_Piracy_Lawsuit
After_Failing_to_Cease-and-Desist⠀⇛
A Las Vegas company and its owner have been
named in a DISH Network lawsuit targeting
pirate IPTV service VNest TV. DISH says the
service offered more than 5,000 channels
including some obtained from its satellite
feeds and others from Sling TV’s online
broadcasts. DISH believes VNest TV obtained
channels from Nitro TV, a service recently
hit with a $100m+ judgment.
# ⚓ Techdirt ☛ More_Issues_With_Copyright_Enforcement_At
Scale:_YouTube_Reinstates_Videos_After_False_Claims⠀⇛
It’s no secret that Techdirt believes
YouTube’s copyright enforcement program is an
absolute mess. On the one hand, it’s
difficult to be too hard on the company.
After all, it is trying to figure out how to
enforce draconian copyright laws in countries
like America at a scale that is absolutely
absurd. On the other hand, the way it works
today is so wide open for fraud and abuse,
that it’s literally a challenge to pick out
which of a ton of stories I want to link to
in order to show the history of fraud,
mistakes, and nefarious copyright claims
taken for reasons that fall completely
outside of any interest in copyright law or
protection.
* § Gemini* and Gopher⠀➾
o § Personal⠀➾
# ⚓ Online_Negativity_Is_A_Form_of_Virus⠀⇛
As the victim of a three-year-long harassment
campaign, during which my name has been slandered,
attacked, and dragged through the mud, I’ve come to
understand a few vital points on the nature of just
how effectively the Internet can be used to spread
disinformation and hatred. I believe comparing
smear campaigns to viruses or pathogens is apt-
like any disease, negativity is more appealing to
the human psyche than positivity, and has a
tendency to become more widely recognized and
discussed.
[...]
Reddit, I’m convinced, is one of the worst websites
ever created, and for the past three years of pure
Hell it has been used by these people in order to
blackmail me, harass me, rile up mobs against me,
and threaten my life and family. Reddit does not
only allow this harassment to continue, they
endorse it, banning anyone who goes against the
narrative these bad actors wish to present. It is a
farce, a kangaroo court, a crime against everything
the Internet should represent.
Reddit is doing this, I’m sure, to save face, as
they are currently one of the most disliked
websites of all time. They are known for having
hosted vile and reprehensible material on their
website throughout much of the early 2010s-
potentially illegal material, even- all under the
guise of “free speech,” and now in the later 2010s
and early 2020s have done a complete 180 to save
face and now ban and censor the least offensive
content imaginable without a second thought or any
form of justification. I arrived on the site at an
interesting period in its history- during the
transitional phase, when it went from a no-holds-
barred anarchist chaos arena to an authoritarian
police state. As such, I was able to witness,
firsthand, in a microcosm, the transformation of
the Internet.
I predicted, in 2019, that the public’s opinion
toward the site would soon shift and Reddit would
be viewed for what it has become- an outright
circus. At the time, the general public’s opinion
was mostly positive. However, as the years went on,
my prediction came to fruition. Reddit became
embroiled in multiple scandals which would put the
follies of Facebook to shame- for instance, the
debacle during which they knowingly hired a sex
offender and then banned anyone who dared post
about it. They are now one of the most censorship-
heavy websites on the Internet, deleting a huge
fraction of all content submitted. Programmers have
wasted hours trying to create facsimiles of the
website without censorship, such as “Removeddit,”
all to no avail.
The case of Reddit is a good example of just how
quickly negativity can spread. What exists on
Reddit today is a false sort of toxic positivity to
counteract the outright negativity which persists
in groups such as the one which has targeted me.
Reddit has become nothing more than 90% pictures of
adorable cats with no substance and 10% hate groups
which masquerade as righteous causes while spewing
ableist and racist rhetoric. The people who attack
me do so with no checks, no balances, no restraint,
and they are, for no reason whatsoever, hellbent on
seeing my failure, to a compulsive, even
sociopathic, degree.
# ⚓ Glad_to_see_OCD_stereotypes_being_broken_up⠀⇛
The first response is right on point: OCD is, by
definition, not rational.
I can relate with the OP’s son in that I have
contamination obsessions and wash my hands probably
more than the average person, and definitely way
more than necessary. These obsessions aren’t as bad
as they used to be, but they’re still there. Yet I
can go days without showering.
One possible explanation I’ve had, and which might
be the case for others, is that some instances of
contamination obsessions are–for lack of a better
term–self-serving. What I mean is that it’s about
keeping yourself quarantined from anything
external, and you’re not /quite/ as keen about not
contaminating others. (I’ve personally been making
an effort to be more considerate about this.) Since
I’m mostly reclusive, not showering isn’t putting
up any “contamination!” red flags in my brain, at
least not until I start to feel and smell gross
enough.
# ⚓ #_walking⠀⇛
So because of Ingress, and because my brain was
probably not functioning, I’ve walked the most in a
day yesterday.
[...]
Underestimating yourself is good in the sense that
you’re not trying to act like a higher up, but that
doesn’t mean to not make commitments. In fact, the
fact that we always “suck” means that we should
also have the mentality of “suck less”, so that we
can have the mindset for improving yourself.
It’s also worth noting that I’ve done all this
stuff because of outward forces, so for someone
like me who just can’t do commitments for self, try
finding people or events that drives you to
actually do some stuff. Even if the person you’re
looking for ended up being “bad”, at the end of the
day all the improvementd you’ve been trying to make
are going to benefit you, and looking back at it,
you’ll realise it’s worth it.
# ⚓ Ko_kongresu!⠀⇛
So a little while back, I applied for and was
accepted to a conference about youth work!
# ⚓ Advertising_Is_Psychological_Warfare⠀⇛
This is actually a great description. I consider
advertising to be a kind of psychological warfare.
It feels like an aggressive attack. I also blame it
for the sharp rise in attention deficit issues over
the last several decades.
We gave up cable TV in 2012, mainly because we
moved out of a place where we had free cable.
Paying money to be subjected to all that
advertising was just ludicrous. Now, whenever I’m
around a television, I feel like I’m in some kind
of distorted reality a la The Twilight Zone. I
really noticed it when I was in the hospital
recuperating last year.
It’s not just the advertising. It’s also the “news”
media, some of which is itself just a thinly veiled
form of promotion. They talk and talk and talk,
saying much and conveying little. Both advertising
and news seem to be targeting our most primitive
and strongest instincts: the instincts to fight,
flee, and accumulate. It plays to fear, be it the
fear of missing out on the latest product from
Apple or the fear of the terrorist.
# ⚓ Check_Out_My_Recommendations⠀⇛
In my circles there’s been an increasing interest
in “Links” pages as a way to help people discover
interesting content by looking at what people you
like like. For a long time I’ve had a
“favourites.gmi” page on my capsule, but it’s been
pretty neglected. This file is being removed and
replaced.
o § Politics⠀➾
# ⚓ Unconditional_Basic_Income⠀⇛
I believe we need UBI.
It’s one of the few policy proposals I’ve seen in
many years that has the option to make life
drastically better and safer for millions of
citizens.
You might, like me, have some long term qualms
about this. I’ve long seen UBI as maybe more of a
short-term “patch” solution (it doesn’t fix all
externalites and environmental problems of market
economies), but a desperately needed one.
If it also does end up working out long term,
that’d be gravy.
o § Technical⠀➾
# ⚓ Old_CPUs⠀⇛
Old computers along with old CPUs, are becoming a
better offer by the day, not only because of
consumerism and planned obsolescence, but because
of security.
From cca. 2008, Intel CPUs have Intel ME built in,
with AMD having its counterpart, AMD PSP. Both are
management engines, translated from non-corporate
speech, that means both are backdoored. Intel PSP
can be controlled remotely, several vulnerabilities
have been found in it. Luckily, it can be cleaned
with ME cleaner, which purges the most dangerous
parts from it, although it is a tedious process.
AMD PSP cannot be controlled remotely, at least
according to what is known, and some motherboards
can disable it.
[...]
Now yet another backdoor is coming, Microsoft
Pluton. Obviously being touted as a “security
enclave” that’s built into the CPU, it’s a bright
idea by Microsoft to secure computers, when they
haven’t even resolved the malware issue on their
own operating system. They partnered with Intel and
AMD, Pluton being present in all new CPUs. The
firmware of Pluton can be updated from Microsoft’s
operating system, which, at the moment, seems like
the same process as updating CPU microcode,
although it might be reserved for them only.
Last week, an article on Phoronix reportedly showed
that one of the laptops with Pluton cannot boot
GNU/Linux, all because of it not being “secure.”
Seemingly can be disabled, probably the same
process as secure boot. Microsoft isn’t to be
trusted, knowing their anti-competitive practices,
can only imagine in what ways Pluton will be
abused.
# ⚓ SSD1306_OLED_128×64_I2C_current_consumption⠀⇛
Out of curiosity I hooked up a small 0.96″ OLED
display to an amperemeter to measure its current
draw. I was fiddling around with it, connected to
the I2C bus of a Raspberry Pi, and wanted to get it
up and running without using any of the existing
libraries. Thus I had to send all the commands ‘by
hand’ and stumbled over all the initialisation
options mentioned in the datasheet of the driver
chip. There are several voltages, frequencies and
divider ratios to play around with, and I wondered
how they would influence the power consumption of
the display. After all, it might come in handy to
know exactly what to do to trim the current draw to
an absolute minimum, should this be necessary.
# § Science⠀➾
# ⚓ Democracy Now ☛ A_Look_Back_in_Time:_How_NASA’s_Webb
Telescope_Gives_Humanity_a_Revolutionary_New_View_of
Cosmos⠀⇛
NASA released revolutionary new images of the
cosmos this week that were taken by the James
Webb Space Telescope, the largest and most
powerful space observatory to date. Launched
in 2021, the JWST was designed to study star
and planet formation with exponentially more
accuracy and detail than its predecessor, the
Hubble Space Telescope. “We can actually
essentially watch the formation of stars,”
says astrophysicist Katie Mack. “There’s a
chance that it might find signatures
consistent with life in the atmospheres of
other stars.” We feature NASA’s new images,
like the Southern Ring Nebula, and Mack
discusses what humans can learn from the new
science about the cosmos, and ourselves.
# ⚓ Hackaday ☛ Liquid_Piston_Engine_Finally_Works⠀⇛
The first video from [3DPrintedLife]
attempting to make a liquid piston engine
was… well… the operative word is attempting.
The latest video, though, which you can see
below gets it right, at least eventually.. He
has a good explanation of the changes that
made the design better. Turns out, one change
that made a difference was to turn a key part
of the engine inside out. You can see the
video below.
# § Internet/Gemini⠀➾
# ⚓ Introducing_AuraGem_Music⠀⇛
AuraGem Music is a free music hosting service
that will let you upload mp3′s via Titan to
your own *private* library so that you can
play them from the capsule using your
identity certificate. Because of limited
storage, there is a quota system, which you
can find more information about on the
capsule.
[...]
Currently only mp3s are supported. However,
support for ogg’s will be added later. Files
that are identical, excluding audio header
and footers, as well as tags, will be
deduplicated to save on space. This ensures
that users have full advantage of as much
space as is possible. The quota system will
take deduplication into account by splitting
the quota of identical songs between all
users who have uploaded that song. It is
assumed that uploaded music has been
purchased, unless other evidence can be
shown, within a DCMA request, to prove
otherwise.
[...]
Lastly, AuraGem Music will always remain free
to use. However, because this service is run
solely by one individual, it cannot be
guaranteed that the service will not shut
down in the future due to financial issues,
server issues, etc. I do not ever intend to
sell this service to any companies unless
they are FOSS-Oriented and non-profit.
# ⚓ smolZINE_–_Issue_30smolZINE_–_Issue_30⠀⇛
This work is licensed under a Creative
Commons Attribution-ShareAlike 4.0
International License.
# § Programming⠀➾
# ⚓ Git_Branch_Descriptions⠀⇛
Here’s a neat little feature of git that I
just learnt about. It turns out that git
branches can have associated descriptions,
although they are local only. All you have to
do to set one is to run the command `git
branch –edit-description` which will open
your editor, just like writing a commit
message.
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World Wide Web but a lot lighter.
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