𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Saturday, July 16, 2022
┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅
Generated Sun 17 Jul 02:39:43 BST 2022
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈
Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕
Gemini index for the day: gemini://gemini.techrights.org/2022/07/16/


╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕
  Previous bulletins in IPFS (past 21 days, in chronological order):

QmRnbEP8kvfDSZqPYikywBMxdJ2dsMPv4ujj2tKn8HPofU
QmRdcPDNXG7La9xrpj9Te3TGetenUACvpQoAsNtm1XNbZY
QmWvpCp84jsz33ggJ9VGNJLVVweLbvAgZC4QSMMpMtjws4
QmTanxCbrRzbMhGwCHPd6tznN3vqohgB6ksoqtyCiMnDFL
QmSGNyqayw9Kb8GtH2D4DicRMEG9NuJ9kQEJo4KgFc1NeH
QmcVu8iJ8yJqBwWTWX3TYY3ChamvbJm15Ne1VJxfTjdLY6
QmSDCize8znng3qFHzA4NgsDaeV7fzdXZrj1CKRp5JBbgK
QmW2xppCHSDJtWfjB5RvaKrsEtS7w97YEMS3ePee6oW9Mp
QmSGhRVAV44sV2y4ZAiDWo9kvmhjvgBBfpAKFP6AdRx6Pc
Qmf7RX5zTm8khR5YEXJ6a48wsPiHG9zDm63S7nvMHXK1PE
QmZQcpV8gJiG7uwAzM2U75TrNyBfZY4RZNaGfhLLDxdSqB
QmajcAdRfWtgWFRoBM7yDJL3X8EJ5w8Wxf6CNnraP2EQo6
QmateHRg7s96CyDx4BcnezZSfn66P9YWrKiMv5VvFfNyEU
QmehYSPymw58ozer2trPYvEomCKmEguPNgE3qdCbXcmNW9
QmP3Nw5usXTHPhcMx8yZ9TYsWzwSKRw9BNnbjhkoJ88gpe
QmNt7g1pzLJJDE5MHZ21wEEuyos1W3DFP2LTSjB2FLPJPi
QmXniW6uykwhxPzQFCih3ywbRTbNtozdD9MTkKJWNUUis7
Qmba4Ap4JVU96TSWT1jJZfQAasTyweA1EFu92C6ULqfYVF
QmQDNYLCxwvKJsAAbaMfkydsH6iMivVs54xVt3e1WhRa4V
QmZrgDSeEPr5Tk1kd6ixcTH5gK8gVF6UWZ8USDWkwExtL2
QmdVCZ22xUbZkpsSDmSDMrnFTMypCGWw1f2punvumLq2NJ


╒═══════════════════ 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

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

(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/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.16.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ 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:


   1. The_EPO_Bubble_—_Part_I_—_An_“Unprecedented_Surge”
   2. The_EPO_Bubble_—_Part_II_—_Signs_of_a_Deflating_Bubble?
   3. The_EPO_Bubble_—_Part_III_—_Dividing_Up_the_Spoils…
   4. YOU ARE HERE ☞ A Cashflow Problem Looming on the Horizon?
                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇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. █


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣦⣄⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠂⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⢹⣿⣷⣶⣿⣤⡄⠀⢀⣴⣷⠖⠃⠀⢀⣠⣾⣿⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣀⣀⣀⣠⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⡿⠿⠿⠿⠻⠛⣠⣼⣿⣷⡾⠛⠁⠀⣀⣴⣿⣿⣿⣿⣧⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠋⠉⠉⢹⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⢰⣶⣶⣦⣼⣿⠉⠉⢈⣉⣨⣽⣿⣿⣿⣿⣿⣿⣿⢰⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠮⣦⣤⣿⣿⣿⣏⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⠛⡋⠘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣤⣤⣤⣤⡶⠶⠶⠶⠚⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠠⠘⠋⠉⠙⡁⠋⣿⣿⣀⠃⠀⢘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠉⠀⠠⠎⡘⢛⠿⡟⠀⠀⠀⠠⠚⠋⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠀⠀⠀⠀⠀⣀⣰⠛⠁⠀⠀⠀⠀⢒⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣶⣿⣿⣿⣶⣦⣀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀
⢀⡄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠈⠹⠻⢿⣿⣿⣿⠛⣿⣿⣷⠈⢻⣿⣿⣿⣿⣿⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⢸⠁⢰⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠸⣹⣷⡀⣿⣿⣿⣧⡀⠙⢿⣿⣿⡇⠀⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⢈⠀⢴⢀⡇⠀⣀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣠⣤⣤⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣿⣿⣿⣷⣝⢷⡀⠀⡿⠉⠁⡀⣼⣿⣷⡖⠒⠒⠒⠂⠀⠀⠉⠉⠉⠁⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀
⣤⣄⠀⠉⠃⢀⣿⠀⡆⠀⠘⣻⣿⣿⣿⣿⣿⣟⠀⠀⠈⠀⠉⠛⠻⢖⡯⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠋⠻⣿⣿⣧⠈⠁⠀⠀⠀⢉⣻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢙⣿⣿⣦⣄⠀⠑⠹⠇⡇⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠚⠼⠓⢆⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠹⡻⠀⠀⠀⣿⡤⠚⠁⢹⣿⣿⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⠆⠀⣐⡶⣶⡦⠀⡀⠁⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢱⠀⠀⣸⣿⣿⡏⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡆⠀⣿⡇⢠⡅⠀⢻⣦⣄⢸⣿⣿⣿⣿⣿⣿⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣤⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠇⠀⣿⠁⢸⡇⠐⡸⠉⣿⣿⣿⡟⢛⠿⠿⠇⠀⠀⢸⣿⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣿⣶⣾⣿⣿⣿⣿⣿⡇⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣴⠴⠶⠶⣶⣶⣶⣶⣖⣃
⣨⣒⡼⣿⠀⢸⠀⠀⡇⢠⡏⣿⣷⡆⠈⠉⠀⡁⠀⠀⢸⣿⡄⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⡀⣀⠀⠀⣀⣤⣴⠀⠀⠰⠿⠀⠀⠸⣿⣿⣛⣛⣛⣛⣿⣿⣿⣭⣭⣭⣽⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣮⣝⡀⠀⡇⢸⡇⠀⠀⠀⣀⣀⣠⣧⠤⠤⠾⢿⣷⠀⠀⠀⢘⣛⡇⠀⠀⣨⣭⠝⣈⠠⠄⢐⢶⣶⠀⠀⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠟
⠻⠿⣿⣿⣿⡟⠅⣵⣾⣽⣇⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠘⣿⠇⠀⠰⠏⠀⠀⠀⠙⠀⠂⠀⠘⠂⢰⣿⣿⡇⠘⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠿⠋⠙⠇⠠⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢟⣟⢿⣿⣿⣟⣿⡿⣟⣿⣟⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣭⣯⣯⣤⣿⣿⣴⣵⣽⣥⣿⣿⣥⣼⣯⣼⣾⣿⣥⣿⣧⣽⣵⣿⣿⣶⣵⣵⣼⣿⣮⣿⣴⣵⣼⣿⣯⣼⣵⣼⣼⣿⣧⣼⣯⣿⣿⣿⣿⣭⣮⣯⣽⣿⣿⣯⣿⣵⣿⣿⣯⣽⣼⣿⣿⣼⣿⣿⣿⣯⣿⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣯⡛⡝⣿⣿⣿⡻⣻⡻⠻⣻⣻⡏⣿⣻⡛⡻⣻⣛⢻⣟⣟⠟⢻⣟⠛⣽⢩⣿⡝⢟⡿⣟⡟⠛⣿⣻⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣿⡿⢿⣿⣿⠿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣼⣯⣿⣟⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣽⣿⣯⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⣿⣿⣿⣿⡿⣿⢛⣿⣿⣿⣧⣿⣷⣿⣿⣾⣾⣿⣿⣭⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣽⣿⣿⣿⣯⣿⣿⣿⣿⣽⣿⣿⣿⣯⣿⣿⣿⣿⣽⣿⣿⣿⣯⣿⣿⣿⣿⣽⣿⣿⣿⣯⣿⣿⣿⣿⣽⣿⣿⣿⣯⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣭⣭⣭⣽⣿⣿⣿⣿⣽⣿⣿⣿⣿⣯⣽⣯⣿⣿⣽⣿⣽⣿⣯⣿⣭⣿⣿⣯⣿⣽⣿⣯⣽⣭⣿⣿⣯⣯⣿⣿⣯⣿⣭⣿⣿⣿⣯⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡾⣾⡿⡾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 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


⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠋⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠉⠓⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣤⣤⣤⣤⣤⣄⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡿⣟⣿⠶⠫⠶⢾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⠛⣾⡟⠁⠀⠀⠀⠀⠀⠘⣂⣘⣇⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡟⠀⣼⠟⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⡘⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⢻⠉⠉⠙⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⢀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⣻⣿⣿⣿⣷⠀⠀⠀⠀⢠⣴⣤⣀⡠⣴⣿⣧⣄⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡟⠀⠀⠀⠀⠀⠀⠐⢛⣛⠛⠛⢛⡿⠿⠿⣿⡇⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠉⢿⣿⡟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⢠⣆⣀⣀⣀⣀⣰⣷⡀⠀⢙⣷⢻⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠛⠃⠀⠶⠾⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠄⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⠿⡿⣿⣿⣿⣿⡏⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⢩⣿⣷⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠄⠀⢸⣧⡀⠀⠀⠀⠀⠈⣸⣦⣄⣠⣿⣽⣿⠃⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠆⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣒⣖⣉⢿⣇⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠟⠀⢰⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⣨⣩⣽⡿⠏⠀⢹⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣼⣿⣷⣾⣿⣿⡙⢻⣿⣿⣿⣿⣿⣿⡇
⠸⠂⠀⠻⣿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⠇⠀⠀⠀⠙⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⡿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡆⠀⠀⠀⠐⠻⠿⣿⣿⣦⣄⣀⣀⣀⣄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠛⣻⣿⠘⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣧⠀⠀⠀⠀⠀⢈⢳⣤⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢰⣦⣤⣤⣾⣿⣿⣿⣶⣶⣿⣧⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⡀⠠⣤⣀⠀⠀⣀⣾⣿⣧⣀⣀⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠻⣿⣿⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣷⣶⣾⣿⣿⣿⣿⣷⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⡇⠀⣤⠀⠀⠀⠰⠟⠶⠾⠿⢇⣿⣿⡟⣹⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⠿⣿⣿⡿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣇⠀⠀⠀⠀⠠⢤⣤⣬⣿⣿⣾⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣀⣼⣿⣿⡟⣿⠋⠀⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠀⠘⢺⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠲⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢈⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⢿⣿⣧⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡆⠀⠀⠀⠀⠀⠀⠉⠉⠻⠻⠋⢸⣿⠟⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⣿⣿⣿⣿⡿⠛⠷⠀⠀⣰⣿⣿⣿⣿⣉⣴⠟⠋⠻⣿⡟⢿⣿⣿⣿⣿⣿⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠀⠀⠀⠀⠀⠀⡏⢻⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠄⠀⠄⠀⠀⠨⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣼⠟⠁⠀⠀⠀⢀⠐⠾⣿⣿⣿⣿⣿⡿⢧⠀⠀⠀⠻⣿⣾⣿⣿⣿⣿⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⣠⣷⣾⣿⣿⣿⣿⣿⣿⣿⣀⡐⠁⠄⠀⠀⠄⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⠀⠀⠀⠈⠙⠛⠋⠩⠿⢿⠂⠋⠉⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡠⠄⢀⣠⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠶⠶⣶⠂⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣦⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠈⠙⠏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢠⣤⣤⣤⣤⣤⣄⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡿⢟⣿⠖⠧⠶⡾⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⢫⣾⠟⠁⠀⠀⠀⢀⠀⢛⣀⣺⣜⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡏⠀⣼⠏⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣦⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⣏⠉⠉⠙⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢢⣴⣀⣀⣤⣼⣿⣦⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡏⠀⠀⠀⠀⠀⠀⠘⢛⡟⠛⠛⢻⡿⠿⢿⣿⡆⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠙⢿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⢲⣆⣀⣀⣀⣀⣼⣧⡀⢀⣙⡇⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⠙⠀⠀⠾⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⡿⢿⢿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣸⣦⡀⠀⠀⠀⠀⠁⣾⣦⣄⣴⣯⣻⡿⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠛⠻⠏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣲⣆⣙⣿⡇⠀⣴⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠏⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣬⣭⣽⡿⠇⠈⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢡⣿⣿⣶⣿⣿⣍⠻⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠀⠀⠻⣿⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⠁⠀⠀⠈⢹⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠇⠀⢸⢿⣿⣿⣿⣿⣿⣆⣹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠿⠀⠀⠀⠀⠈⠻⠿⢿⣷⣤⣤⣀⢀⣤⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠋⢛⣿⡌⢻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠰⢾⣤⣀⠀⠀⠀⠀⣸⡵⣴⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣶⣦⣤⣴⣿⣿⣿⣷⣶⣾⣷⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣴⣾⣷⠀⠀⠀⢀⣤⣾⣿⣿⣄⣀⢀⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠈⠻⠿⣟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣷⣶⣾⣿⣿⡧⢸⣿⣄⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⠏⣸⣿⣿⣿⣿⣷⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⠀⢠⡄⠀⠀⠀⠛⠓⠺⠿⠷⢹⣿⡿⣻⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣇⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷⠀⠛⢿⣿⠿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠁⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠶⢶⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠃⠈⠛⠻⣿⣿⣿⣿⣿⣿⡇⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⣿⣿⣿⠟⠉⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⣤⣴⡾⠛⠉⣹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠛⠉⣿⡿⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⡿⠋⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠀⠀⠀⠀⠀⠸⠉⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠠⠤⠄⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢾⣿⣿⣾⢿⣿⣿⣿⣿⣿⣟⣟⣿⣿⠀⠀⢰⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣆⡀⠐⠀⠀⠀⠢⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠭⠿⠶⠊⠁⠁⠙⠻⠄⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⡰⣤⠄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠶⠶⣶⠀⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⡻⠿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠙⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠉⠻⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣠⣤⣤⣤⣤⣤⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡿⣟⡿⠟⠭⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⢻⣾⠛⠁⠀⠀⢀⣀⠈⢓⣀⣷⡘⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠏⠀⣾⠋⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣎⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⡏⠉⠉⢹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡟⠀⠀⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⡄⠀⠀⠀⠀⣤⣦⣀⣠⢤⣿⣷⣤⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡏⠀⠀⠀⠀⠀⠀⠚⢻⠿⠛⠛⢿⡟⠻⣿⣿⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠻⣿⣟⠛⠙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⣲⣅⣀⣀⣀⣠⣾⣧⡀⣈⣹⡞⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠀⠐⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⠿⠿⣿⣿⣿⣿⠁⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠈⢉⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣸⣧⡀⠀⠀⠀⠈⢉⣿⠦⢤⣴⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠘⠛⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢤⣶⣆⣙⣿⡄⠀⣼⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠋⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⣠⣤⣬⣽⠿⠁⠈⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⣾⣿⣿⣿⣿⣯⡙⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠀⠀⠻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡿⠀⠀⠀⠈⢻⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⠗⠀⠐⠿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠙⠯⠀⢰⣿⠄⠘⠟⢩⣿⣧⣦⣴⣂⣦⣤⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⡋⠹⢿⣇⠹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣰⣿⡄⠰⣶⡄⠀⠀⢸⣟⣴⣿⣦⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢴⣶⣶⣶⣿⣿⣿⣿⣶⣶⣿⣶⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣀⠢⢿⣿⣾⣿⠟⢁⣴⣿⣿⣦⣤⣼⣷⣿⣟⣏⣠⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠈⠛⠿⢿⡛⠛⢟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣷⣶⣿⣿⣿⠀⢼⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⢿⠛⣻⣿⣿⣿⣿⣿⣿⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⠀⣦⠀⠀⠀⠘⠛⠛⠻⠿⢆⣿⣿⢋⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠇⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠠⢿⣏⣿⣿⣿⣿⣿⣧⠈⠙⠿⢿⠿⠃⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢸⡿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠲⠶⣶⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⡿⣿⣿⣿⡷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⣿⡟⠁⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠘⠉⠁⢸⣿⠉⠃⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠠⠗⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣴⣿⣿⣿⣿⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠃⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠠⠤⠤⣀⠐⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠘⠿⣿⣿⣟⣻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠐⠂⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠻⠿⠫⠉⠁⠉⠉⠙⠻⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠅⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡰⣶⠖⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠶⠲⣶⠈⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠙⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠈⠋⠇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡿⣿⡿⠟⠭⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⢻⣿⠛⠁⠀⠀⢀⣀⢈⢃⣀⣳⡙⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠏⠀⣾⠋⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣷⡌⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣹⠉⠉⠉⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡟⠀⠀⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⢀⣤⣄⣄⣤⣴⣿⣧⣄⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⢘⠻⠿⠛⠛⣿⡟⠻⣿⣿⢸⣿⣿⣿⣿⣆⠀⠀⠀⠀⠈⠻⣿⡟⠋⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠂⠀⠀⠀⠀⠀⣿⣢⣤⣀⣠⣤⣿⣦⣀⣀⣹⠸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠉⠁⠀⣒⣾⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⡿⠻⠿⢿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⠉⣹⣿⡷⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣸⣦⠀⠀⠀⠀⠀⢀⡿⠶⠤⣾⣿⣿⠏⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢬⣽⣥⣝⣿⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠃⠀⣾⣿⣿⠇⠀⡤⠀⠀⠀⠀⢤⣤⣬⣿⠿⠁⠈⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⣽⣿⣿⣿⣿⣍⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⠀⠐⠻⠿⠀⠀⠀⢹⣧⣤⠀⠀⠀⠈⣿⡟⠀⠀⢸⣿⣿⡏⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠂⠀⠸⠿⣿⣿⣿⣿⣿⣆⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠀⠀⠀⠀⠙⠇⠀⠀⢸⣿⣿⣷⠀⣻⣷⣶⣶⣤⣦⣄⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣟⠁⠽⢿⠀⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠁⠀⠀⠐⣣⡄⠀⠀⢠⣾⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠠⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⣀⡀⠠⠀⣰⣿⠀⠀⣠⣾⣿⣷⣤⣤⡈⡋⠼⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠉⠻⠛⣍⡉⢛⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣾⣿⣿⠇⠀⠀⣿⣇⣠⣾⣿⣿⣿⣿⣿⣿⣧⠁⠀⠀⠀⢹⣿⣿⣿⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡏⣻⣿⢸⣿⣿⣿⣿⣿⣿⣿⣀⢸⡆⠀⠀⠀⠉⠉⠙⠛⠓⣼⣿⡏⣽⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠟⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣸⣿⣿⣿⡇⠈⠛⠿⠟⠋⠀⠸⢹⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⡿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣘⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⣿⣿⡿⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠨⠿⠿⡿⣿⡟⣿⣿⣿⡇⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣿⣿⡆⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠈⠀⠀⠀⠀⢸⠃⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠏⠇⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢰⣿⣿⣿⣿⣿⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠈⠀⣸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠠⠄⠤⠀⢙⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⣟⠀⠀⠈⠻⠿⣿⣿⣽⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠁⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠒⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠛⠛⠓⠀⠀⠀⠀⠈⠙⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡶⣶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠖⠲⣶⠀⠶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣾⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠙⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠉⠹⠏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢠⣤⣤⣤⣤⣤⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣟⡿⠟⠭⢿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⢻⣿⠛⠀⠀⠀⢀⣀⣈⣃⣘⣧⡹⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠏⢀⣿⠃⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⡜⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡏⠉⠉⠙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡟⠀⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣇⠀⠀⠀⠀⢰⣴⣤⣀⣤⣾⣿⣤⣄⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⠐⠙⠻⠯⠉⠛⣿⠛⠛⣿⣧⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠙⣿⣿⠛⠉⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⣿⣦⣀⣠⣤⣠⣿⣦⣀⣀⣿⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠉⠀⣐⣺⡿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿⠻⠿⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣈⣽⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣸⣦⠀⠀⠀⠀⢰⣽⡿⠶⠴⠾⣿⣿⠇⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⢀⣿⣿⡇⠀⠀⢀⣼⡿⠀⠬⣭⣥⣽⣿⠀⠠⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠃⠀⣾⣿⣿⠇⠀⠀⡏⠀⣷⠀⢤⣦⣴⣽⠿⠀⠉⢿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⣾⣿⣿⣿⣿⣷⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⠀⠈⠻⠟⠀⠀⠀⠀⠐⢸⡏⠀⠀⠀⣿⡟⠀⠀⡑⠘⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⠗⠀⠈⠟⠿⣿⣿⣿⣿⣷⡸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠙⠃⠀⣰⣿⠀⢹⣿⣿⣿⣷⣶⣢⣶⣶⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣍⠈⠿⣇⢹⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣾⠃⠀⠀⠐⣧⡀⠀⠀⠛⠋⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢲⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⣠⣠⣤⠈⠀⠁⠀⢀⣠⣾⣿⣷⣤⣤⠀⠂⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠙⠛⢻⣉⣉⣛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡿⠀⠀⢠⣠⣤⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⢰⣿⣿⣿⣿⣯⢻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡃⣿⡿⢸⣿⣿⣿⣿⣿⣿⣇⣐⣧⠀⠀⠀⠈⠉⠉⠙⠛⢲⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡏⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⣿⣿⣿⣿⣿⡆⠈⠛⠿⠋⠁⠀⠽⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠟⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢈⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣻⣿⣿⣿⣇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣾⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⣟⢻⣿⣿⣿⠀⠀⠀⠀⣾⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡯⠁⠈⠀⠀⠀⠀⡟⠺⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⢁⣀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠠⠤⠤⠈⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠟⠁⠉⠛⢿⣯⣽⡿⠿⠿⠟⠋⠉⠉⠉⠻⡇⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣂⡀⠀⠀⠀⠀⠂⢤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⡿⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡷⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⠷⠲⣶⠀⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣰⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠁⠻⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣠⣤⣤⣤⣤⣄⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⡿⠻⠭⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⢻⡿⠋⠀⠀⠀⢀⡀⡙⣀⣘⣆⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠏⢀⡿⠃⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⡝⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡉⠉⠉⢹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡏⠀⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡆⠀⠀⠀⠀⣤⣦⣄⣠⣴⣿⣷⣤⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠁⠀⠀⠀⠀⠘⠻⠍⠉⠛⣿⠛⠻⣿⡇⣸⣿⣿⣿⣷⡀⠀⠀⠀⠈⠹⣿⡟⠋⠙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⣶⣀⣄⣀⣤⣴⣿⣄⣀⣌⣷⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠉⠁⢀⣒⣛⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⠟⠿⢿⣿⣿⣿⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣉⣿⡿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣼⣦⠀⠀⠀⠀⣤⣼⠘⠷⠴⢿⣿⣿⣿⣇⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠉⠛⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⢀⣿⣿⡆⢠⣦⢀⣿⢁⠤⣬⣭⣤⣹⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠃⠀⣾⣿⢿⠁⢸⣿⡶⠀⠘⢠⠶⠤⣤⣿⠟⢹⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢰⣿⣿⣿⣿⣿⣌⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⠀⠈⠛⠛⠀⠀⠸⠻⢷⣄⣠⡏⠀⠀⣿⡇⠀⢘⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠃⠀⠙⠻⢿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠙⠂⠀⢼⣿⣿⠉⠉⣛⣷⣶⣦⣤⣴⣦⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣏⡀⠹⣷⡈⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠠⣤⠀⣀⠼⠃⠀⠀⣠⠀⠀⠀⠀⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⣀⣠⣾⣮⠄⠈⠀⢀⣤⣾⣿⣷⣦⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⢻⣿⢿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠙⠛⣏⣉⣩⣽⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣷⣿⣿⣿⣿⣿⠀⣀⣤⣾⣿⣿⣿⣿⣿⣦⠀⢿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡏⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣀⣸⡆⠀⠀⠀⠀⠈⢉⣙⠃⣾⣿⢃⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢿⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠉⠛⠟⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠸⠛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⠻⠛⠿⠙⣿⣿⠿⠇⠀⠀⠀⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⢸⠃⢹⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⠟⠋⠉⠻⠿⠿⠿⠀⢹⣿⣿⣿⣿⣿⣿⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⡠⠤⠤⣋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠋⠀⠈⠻⢫⠼⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠲⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣞⡻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠿⣶⠀⠶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣾⣿⣿⣿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠉⠇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⣀⣹⣯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⡿⠻⠭⢽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⢻⡿⠋⠀⠀⠀⢀⡀⢙⣀⣉⣌⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠏⢀⡿⠃⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣶⠙⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠉⠉⠉⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡏⠀⠀⠁⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠀⠀⠀⠀⠠⢦⣤⣤⣤⣾⣿⣦⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠁⠀⠀⠀⠀⠙⠿⠍⠉⠛⣿⠛⠻⣿⡇⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⢻⣿⡛⠉⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠰⣶⣠⣄⣀⣠⣴⣿⣄⣤⣬⣷⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠀⢀⣚⣛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣟⠉⠿⢿⣿⣿⡇⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⡗⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣸⣦⠀⢀⠀⠀⠸⣿⣟⢠⢦⢿⣿⣿⡇⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣿⣿⡄⢸⡆⣀⣠⠛⠁⠀⡀⠤⣿⣿⣿⣷⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠃⠀⣼⣿⠿⠁⢸⡿⢿⣿⣶⠇⣼⠀⠈⣿⣿⣿⠹⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣾⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⠀⠀⠙⠋⠀⠀⠘⠉⠀⠈⠻⣿⡏⠀⣾⣿⣿⣿⠀⠉⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠿⠗⠀⠈⠛⠿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣮⣾⡍⠀⠀⠈⢹⣿⣿⠀⠀⠈⠉⣟⣿⣾⣶⣴⣶⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣠⣼⣯⡀⢘⣻⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠉⠀⢀⡄⠀⠈⢿⣿⡆⣾⣷⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⣀⣠⣾⣿⣿⣿⠁⠀⣤⣾⣿⡄⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⡏⣿⡟⢿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠈⠙⢹⣄⣈⣭⣏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣷⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⡎⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠅⣿⡟⢸⣿⣿⣿⣿⣿⣿⣇⣀⣷⠀⠀⠀⠀⢀⣀⣉⣉⣸⣿⣏⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠻⣿⣿⣿⣿⣿⣿⣿⠁⢀⣸⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠛⠉⠀⠀⠨⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣸⣿⣿⣿⣿⣿⡏⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠛⠹⣿⡿⠿⠀⠀⠀⠀⣾⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⣴⣿⣿⣿⣿⣿⣿⣯⣽⠿⠿⠿⠿⠿⢿⡧⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠿⠘⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠏⠀⢉⡍⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⡤⠄⣬⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠏⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⣀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠇⠶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣴⣿⣿⣿⡟⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠙⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠈⠹⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢠⣤⣤⣤⣤⣤⣀⣈⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⡿⠻⠭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⣿⡿⠋⠀⠀⠀⢀⡀⢛⣀⣹⣌⢿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠇⢠⡿⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦⠹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⠉⠉⠙⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡏⠀⠈⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠂⣿⣿⣿⣇⠀⠀⠀⠀⠰⣾⣤⣤⣤⣾⣿⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠙⠯⠍⠉⢻⡿⠛⢻⣿⡆⣿⣿⣿⣿⣄⠀⠀⠀⠀⠈⢿⣿⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠰⣷⣤⣤⣄⣤⠘⣷⣶⣤⣬⡗⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣛⣛⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⠃⡈⢸⣿⣿⡇⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣸⣆⠀⠀⠀⠀⠈⣿⠿⡸⠉⣿⣿⣿⣇⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣿⣿⡆⢸⡄⣴⣶⣇⡨⠃⠀⣿⣿⣿⠏⢰⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣟⣛⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠋⠀⣼⣿⠻⠀⢸⠇⠋⠙⢿⣯⣼⠀⣿⣿⣿⠀⠙⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢰⣿⣿⣿⣿⣿⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⠀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣎⣹⠟⠸⢿⣿⣿⠀⠀⠙⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠿⠂⠀⠙⠙⢿⣿⣿⢿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠿⠀⠀⠘⣿⣿⠀⠀⠀⠈⢸⣿⣿⣿⣦⣶⣶⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⡀⢀⣀⣴⣿⣆⠀⣑⣿⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡋⠀⢀⠀⠀⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣀⣠⣠⣾⣿⣿⣿⡿⠁⢰⣿⣆⠰⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢹⣿⡿⣿⣿⣿⣿⣿⣿⣤⠀⢀⠀⠀⠈⠉⠦⣤⣴⣿⡝⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣷⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⢸⣿⠇⣿⣿⣿⣿⣿⣿⣿⣤⣼⡆⠀⠀⠀⠀⢀⣠⣬⣁⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠘⠻⣿⣿⣿⣿⣿⣿⡏⠀⠀⢹⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠰⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣿⣿⣿⣿⣿⣿⠁⠀⠀⣾⣿⣿⡇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠛⠁⢻⡿⠛⠇⠀⠀⠀⠀⡿⢽⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣨⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠛⠛⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠘⡁⠸⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⠇⠀⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⠄⠠⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠏⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⢀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⢷⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣾⣿⣿⡿⠛⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠁⠻⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣠⣤⣤⣤⣤⣤⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⡿⠛⠭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⢿⡿⠋⠀⠀⠀⢀⡀⢓⣈⣹⣌⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠏⢠⡿⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦⠹⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡌⠉⠉⢹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡏⠀⠈⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⠀⠀⠀⠀⢷⣷⣤⣴⣴⣿⣷⣦⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠉⠯⠍⠉⢹⡟⢛⡻⣿⡆⣿⣿⣿⣿⣄⠀⠀⠀⠀⠘⣿⡏⠉⠈⢉⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠸⢶⣤⣄⣤⣴⡀⠷⢨⣧⣬⡗⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣨⣿⣛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⢡⣤⣨⣿⣿⡇⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣄⣿⡿⢪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣸⣆⠀⠀⠀⠀⠀⠽⠟⡼⠀⣛⣿⣿⣧⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠉⠉⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣿⣿⡆⢀⠀⢾⣿⣿⣴⠁⠄⣿⣿⣿⠏⢰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⢻⣿⣟⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠏⠀⢰⣿⠻⠀⠸⠅⠀⢈⠙⢿⣾⣆⣿⣿⣿⠀⠹⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⣼⣿⣿⣿⣿⣷⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠀⠀⠉⠉⠀⠀⠀⠀⠀⠐⠨⣨⡛⠈⣿⣿⡟⠀⠀⢩⣿⣷⣆⣀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠟⠀⠀⠋⠻⢿⣿⡿⢿⣷⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣻⡟⠃⠀⠀⣿⡇⠀⠀⢀⠀⢺⣿⣿⣿⣶⣶⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣀⠀⣠⣼⣿⣄⢀⣺⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣯⠆⠀⠀⣰⣿⡇⠀⢀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣀⣀⡀⢠⣿⣿⣿⣿⡏⣸⣷⠀⢻⣿⣷⣴⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⡟⢹⣿⢻⣿⣿⣿⣿⣿⣷⡄⠀⡀⠀⠀⠉⠡⠄⢤⣵⣯⠹⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣷⣷⣿⢶⣿⣿⣿⣿⣿⠈⢹⣿⡆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⢿⣿⣿⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠇⢸⣿⢸⣿⣿⣿⣿⣿⣿⣷⣤⣿⡄⠀⠀⠀⠀⣠⣤⣌⣨⣿⣏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠙⠿⣷⣿⣿⣿⣿⣿⠃⠀⠀⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠁⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⠀⠀⢠⣿⣿⣿⣿⣿⡟⠀⠀⢴⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠃⣿⡟⠛⠃⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣇⣵⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠉⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⠀⢸⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⠃⠰⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⠃⠀⠴⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⢀⡄⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⢿⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣰⣿⣿⡿⠟⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠈⠙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠁⠇⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣠⣤⣤⣤⣤⣤⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⡿⠫⠭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⢿⡿⠋⠀⠀⠀⢀⡀⢛⣀⣫⣌⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠋⢠⡿⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠈⠉⠉⢽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡏⠀⠈⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡆⠀⠀⠀⠀⢶⣦⣤⣤⣾⣿⣷⣤⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠉⠯⠍⠉⢹⡟⢛⡻⣿⡀⣿⣿⣿⣷⣀⠀⠀⠀⠀⠙⣿⡋⠁⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⣆⣠⣄⣤⣴⡀⠲⢬⣶⣬⡗⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣹⣟⡋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⠥⠤⣼⣿⣿⡇⠸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣤⣠⣿⡗⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣸⣆⠀⠀⠀⠀⠀⠘⠎⡰⠀⢸⣿⣿⣧⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣿⣿⡆⠘⠀⠸⢿⣿⣤⡇⡀⢸⣿⣿⠃⣰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠟⢻⣿⣋⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠟⠀⢰⣿⠛⠀⠀⠆⠀⠀⠈⠻⣿⣇⣿⣿⣿⠀⠹⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠙⣹⡏⠀⠀⢹⣿⣶⣀⣀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠹⠟⠀⠈⠉⠻⣿⡿⠿⣿⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣺⡟⠃⠀⠀⣿⠁⠀⠀⠀⠀⣰⣟⣟⣿⣶⣶⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⣀⣀⣀⣤⣿⣧⣀⣀⣪⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠁⠀⠀⣼⣿⡀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⢿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⠀⣀⣠⣤⡤⢠⣾⣿⣿⣿⡏⣠⣧⠀⣻⣿⣧⣴⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⣿⣟⢿⣿⣿⣿⣿⣿⣷⡄⠀⡀⠀⠀⠉⠰⠠⢤⣾⣏⢻⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⢰⣶⣾⢰⣶⣾⣿⣯⣿⡿⣷⣮⢿⢰⣶⣾⣷⣿⢾⣾⣾⣿⣷⣿⣏⠹⢿⢿⣿⡿⠋⠻⢿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠃⣿⡏⢸⣿⣿⣿⣿⣿⣿⣧⣤⣷⠀⠀⠀⠀⠀⣤⣤⣄⣼⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡟⢸⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⠁⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⢸⣿⣇⢸⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⡿⠛⠹⠀⠀⠀⠀⣸⠨⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣼⣿⣿⢸⣿⣿⡟⣻⣿⣇⣿⣿⠀⣿⣿⡛⣿⣷⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣮⣿⣿⣾⣿⣿⣷⡇⠉⠍⠉⠁⠈⠉⠉⢷⣽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⢀⠠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡟⠀⠰⠂⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⡄⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣴⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠇⠰⠰⠶⠖⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠺⡿⢿⠏⠋⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠘⠇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⣀⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⡿⠫⠽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠿⣿⡿⠋⠀⠀⢀⣀⣀⣉⣤⣷⣜⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠏⢠⡟⠁⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣦⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠉⠉⠉⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡏⠀⠈⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡀⠀⠀⠀⠰⢶⣤⣤⣤⣾⣿⣦⣤⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠉⠋⠉⠉⢹⡟⢉⠻⣿⡀⣿⣿⣿⣧⣀⠀⠀⠀⠀⢛⣿⠉⠁⠉⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠐⣷⣤⣤⣤⣴⡀⠒⣼⣦⣼⡏⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣭⣿⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⢥⡤⣼⣿⣿⠇⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⣄⣼⣿⢏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣸⣆⠀⠀⠀⠀⠀⡸⠞⣲⠀⢸⣿⣿⡧⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣿⣿⡆⠘⠀⠸⢿⣿⣴⠃⡄⢸⣿⣿⠁⣸⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠛⣿⣿⣉⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠟⠀⢰⣿⠛⠀⠀⠄⠀⠀⠀⠻⣷⣆⣿⣿⡏⠀⠹⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣸⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⢀⡿⠀⠙⣹⡇⠀⠀⢹⣿⣶⣄⣀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠉⠉⠛⠃⠀⠉⠙⢿⣿⠿⠿⣿⡎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡿⡿⠃⠀⠀⣿⠀⠀⠀⠀⠀⢸⣯⣻⣿⣷⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⣠⣼⣿⣦⣀⣈⣷⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠅⠀⠀⣼⣿⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠻⢿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠀⣀⣤⣤⡤⢠⣾⣿⣿⣿⡟⣠⣇⠈⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⢸⣿⡟⣿⣿⣿⣿⣿⣿⣶⠀⢀⠀⠀⠀⠁⠢⠤⢴⣾⡌⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⢰⣶⣾⢰⣶⣾⣿⢿⣿⡿⣷⣮⢿⢰⣶⣿⣷⣿⢾⣿⣿⣿⣷⣿⡇⠻⠿⣿⣿⠟⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡅⠸⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣦⣼⣇⠀⠀⠀⠀⠤⣤⣤⣤⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡏⢸⣿⣿⣿⣿⣿⡏⣿⣿⢸⢸⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⢿⣿⣿⣧⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠒⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣇⢸⣿⣿⣿⣿⣿⡇⣿⣿⢸⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠸⡏⠁⠉⠀⠀⠀⠀⡿⢺⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⢸⣿⣿⡟⣻⣿⣇⣿⣿⠀⣿⣿⡛⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠃⠈⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣽⣿⣾⣿⣿⣷⡗⠉⠉⠉⠁⠈⠉⠉⢷⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣠⡄⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣾⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠇⠠⠴⠶⠖⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢤⡿⠿⠿⠛⠁⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠉⠋⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠈⠹⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣤⣤⣤⣤⣤⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⠟⠭⠽⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠟⣿⠟⠁⠀⠀⢀⣀⣈⣩⣤⣶⡜⢿⣿⣿⣿⣯⠀⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⢰⠟⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠁⠉⠩⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣷⠀⠀⠀⠀⠐⢾⣦⣤⣴⣿⣿⣦⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⢸⣿⠃⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⢹⡏⡉⠻⣿⢸⣿⣿⣿⣦⡀⠀⠀⠀⠀⢛⣿⠉⠈⢉⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⢸⣿⠀⠀⠀⠀⠀⠘⣷⣦⣤⣤⣴⡀⠲⣿⣤⣼⡏⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢬⣭⣏⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣧⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⢡⢤⣿⣿⣿⠀⢹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢠⣤⣾⡿⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣼⣆⠀⠀⠀⠀⠀⡳⠙⡔⠀⣿⣿⣿⡆⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⣿⣿⠀⠐⠀⠾⣿⣧⣜⢀⠀⣿⣿⡟⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⠻⣿⣏⣹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠋⠀⢰⡿⠛⠀⠈⠄⠀⠀⠙⠿⣿⢤⣿⣿⡇⠀⢻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⣼⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃
⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡏⠈⠏⣿⠃⠀⠀⠹⣷⣆⢀⣀⠀⠀⢀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠛⠁⠀⠉⠙⢿⡿⠿⢿⣷⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢨⡟⠁⠀⢸⣿⠀⠀⠀⠀⢀⢺⣽⣿⣷⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣀⣀⣀⣤⣿⣷⣄⣨⣽⣆⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣾⠀⠀⢠⣾⣿⠀⠀⣸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠻⣿⡿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠀⣀⣠⣤⣄⢀⣾⣿⣿⣿⡏⣰⡆⢙⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡏⢹⣿⢹⣿⣿⣿⣿⣿⣿⡆⠀⣀⠀⠀⠀⠐⠄⠤⢶⣧⠹⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⢰⣶⣾⢰⣶⣾⣿⢿⣿⡿⣷⣮⣧⢳⣶⣿⣷⣿⢾⣿⣿⣿⣷⣿⡇⠛⠿⣿⠿⠋⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠃⢸⡿⢸⣿⣿⣿⣿⣿⣿⣷⣴⣿⡄⠀⠀⠀⠠⠤⢶⣤⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡏⢸⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣇⢸⣿⣿⣿⣿⣿⡇⣿⣿⠸⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠈⠁⠀⠀⠀⢸⡇⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⢸⣿⣿⡟⣻⣿⣇⣿⣿⠀⣿⣿⡛⣿⣷⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⠀⠀⠀⠀⠘⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣽⣿⣾⣿⣿⣷⡇⠉⠉⠉⠁⠈⠉⠉⣷⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡟⠀⠐⠃⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣤⣠⡴⣫⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣴⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠇⠠⠰⠶⠖⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣸⢿⢿⠛⠋⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠁⠋⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣠⣤⣤⣤⣤⣤⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⠟⠭⠽⡿⠿⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠟⣿⠛⠁⠀⠀⢀⣀⣈⣩⣼⣦⡙⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⠿⣿⣿⢿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⠁⢸⠃⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠉⢽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣇⠀⠀⠀⠀⠲⣶⣦⣤⣶⣿⣷⣦⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⢸⣿⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠉⣿⢏⡙⢿⣇⢸⣿⣿⣿⣄⡀⠀⠀⠀⠈⠻⡏⠁⠈⣹⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⢸⡿⠀⠀⠀⠀⠀⢲⣶⣤⣤⣤⣖⠑⢶⣷⣤⣽⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⢭⣭⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣇⠀⠀⡀⠀⠀⠀⠈⠙⣻⣿⣿⣤⣼⣿⣿⣿⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣴⣿⠏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣷⠀⠀⣿⡄⠀⠀⠀⠀⠀⠂⠡⠇⢘⣿⣿⣿⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⢸⣿⠀⠀⣿⣿⠀⠀⠀⠶⣷⣄⡌⢠⢸⣿⣿⡏⢀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⠛⣻⣿⣭⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⢸⠃⠀⣾⡟⠃⠀⠠⠀⠀⠈⠛⢿⣷⣸⣿⣿⠁⠀⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⢠⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠙⠩⣿⠀⠀⠀⠽⠷⡠⣀⡀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠙⠃⠀⠈⠉⠛⣿⠛⠛⢿⣎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡴⠓⠀⠀⣾⡇⠀⠀⢀⣀⢀⣾⣸⣷⣷⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣄⣀⣠⣼⣿⣦⣠⣬⣽⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣶⠀⠀⣴⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⠻⡿⠏⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⠀⠀⣠⣤⠄⣰⣿⣿⣿⣿⠃⣼⠀⣹⣿⣿⣶⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⠁⣿⡇⢿⣿⣿⣿⣿⣿⣷⠀⢠⡀⠀⠀⠀⠐⠐⠶⠿⡌⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⢰⣶⣾⢰⣶⣾⣿⢯⣿⡿⣷⣮⡇⢷⣾⣿⣷⢿⢾⣿⣿⣿⣷⣿⠉⠹⢿⠿⠋⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣇⠈⠀⡿⠃⣾⣿⣿⣿⣿⣿⣿⣷⣾⣧⠀⠀⠀⠀⠰⠶⣶⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡟⢸⣿⣿⣿⣿⣿⡇⣿⣿⢀⢸⣿⢹⣿⣸⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⢸⣿⣧⢸⣿⣿⣿⣿⣿⡇⣿⣿⠸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠈⠀⠀⠀⠀⠟⠙⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⢸⣿⣿⡟⣻⣿⣇⣿⣿⠀⣿⣿⡛⣿⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⣿⣷⠇⠉⠉⠉⠁⠈⠉⠉⣷⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⠏⠀⠘⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⡼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣾⣿⣟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠄⠰⠰⠶⠆⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠘⡛⠩⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠈⠇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣤⣤⣤⣤⣤⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⠟⠭⠽⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠟⣿⠛⠁⠀⠀⢀⣀⣈⣉⣔⣦⡻⣿⣿⣿⣿⠆⠀⠀⠀⠀⠾⠿⠿⡿⢿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⠁⢸⠏⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣷⡜⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠃⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡆⠀⠀⠀⠐⠲⣶⣦⣶⣾⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁
⢸⣿⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠉⣿⢋⠙⢿⡇⢸⣿⣿⣷⣄⠀⠀⠀⠀⠈⢿⠍⠀⢈⣽⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⢸⡿⠀⠀⠀⠀⠀⢒⣦⣤⣤⣤⣆⠑⣾⣷⣤⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠤⢭⣭⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣇⠀⠀⡀⠀⠀⠀⠈⠙⣿⣿⣟⣤⣽⣿⣿⡟⠀⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢤⣼⣿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣷⠀⠀⣿⡄⠀⠀⠀⠀⠀⠊⢩⠆⢸⣿⣿⣿⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⢸⣿⠀⠠⣿⣿⠀⠀⠀⢾⣷⣤⡏⠀⢸⣿⣿⡇⢠⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⠋⣿⣿⣭⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀
⢸⠃⠀⣾⡟⠃⠀⠰⠀⠀⠉⠛⢷⣷⣸⣿⣿⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡋⠀⣸⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⡀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠛⢹⡟⠀⠀⠀⠽⠦⣄⣄⠀⠀⠀⡀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠁⠛⠁⠀⠉⠉⢻⣿⠛⠻⣿⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⣴⠏⠀⠀⣿⡇⠀⠀⢀⣀⣨⣯⣼⣿⣶⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣤⣤⣤⣴⣾⣿⣦⣤⣬⣧⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡧⠀⠀⣴⣿⡇⠀⢀⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⠿⠿⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠀⢤⣰⣶⠀⣰⣿⣿⣿⣿⢁⣶⢀⣽⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⢸⣿⡏⣿⣿⣿⣿⣿⣿⣷⠀⢠⠀⠀⠀⠐⠂⠒⠺⠿⢈⣿⣿⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢰⣶⣮⢰⣶⣾⣿⢿⣿⡿⣷⣮⠸⣷⣾⣿⣷⢻⢾⣿⣿⣿⣷⣿⠈⠻⢿⡟⠉⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⡆⠈⠸⡿⠃⣿⣿⣿⣿⣿⣿⣿⣶⣾⣇⠀⠀⠀⠀⠲⠶⣶⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡏⢸⣿⣿⣿⣿⣿⡇⣿⣿⠀⢸⣿⢹⣿⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⡿⢿⣿⣿⣧⠀⠀⠀⠀⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⢸⣿⣧⢸⣿⣿⣿⣿⣿⡇⣿⣿⠘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠁⠀⠀⠀⠀⠇⢙⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣼⣿⣿⢸⣿⣿⡟⣹⣿⣇⣿⣿⠀⣿⣿⡛⣿⣷⣿⣿⣿⣿⣿⠇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⣿⣷⠃⠉⠉⠉⠁⠈⠉⠉⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⠇⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣶⣤⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣰⣿⣿⠙⠛⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠙⠉⠉⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠈⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠈⠘⠊⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣤⣤⣤⣤⣤⣄⣠⣿⣼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⠟⠭⠽⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠟⣿⠋⠀⠀⠀⣀⣀⣘⣁⣀⣤⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠿⠿⠿⠿⢿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡟⠁⢸⠃⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⡝⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠨⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡀⠀⠀⠀⠘⠶⣶⣶⣶⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀
⢸⡿⠀⠀⠀⠀⠀⠀⠈⠹⠉⠉⠙⣿⢋⠻⢿⡇⣸⣿⣿⣷⣄⠀⠀⠀⠀⠉⠿⠀⠀⣉⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆
⢸⡗⠀⠀⠀⠀⠀⠳⣦⣤⣤⣴⡆⠛⣿⣦⣤⣿⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⠤⢭⣭⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⠀⡀⠀⠀⠀⠈⠛⣿⣿⣯⡤⣽⣿⣿⡏⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⢀⣿⡄⠀⠀⠀⠀⠘⠎⢹⠀⢸⣿⣿⡷⠀⢹⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃
⢸⡟⠀⢸⣿⡗⠀⠀⠰⠿⣷⣤⡁⡀⢸⣿⣿⠁⢠⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⠟⢩⣿⣯⣽⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄
⢸⠁⠀⠿⠏⠁⠀⠰⠀⠀⠈⠻⣿⡇⣾⣿⣿⠀⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⣿⣿⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠋⢹⡏⠀⠀⠀⠿⠣⣤⡄⡀⠀⢀⡀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠈⠋⠀⠀⠀⠈⣻⡟⠛⠻⣷⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⡌⠃⠀⢀⣿⠀⠀⠀⣀⣀⣸⣧⣽⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣤⣤⣤⣶⣿⣷⣦⣴⣾⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡆⠀⢀⣾⣿⡀⠀⢀⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠛⠻⠛⠙⠻⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⠀⢀⣰⣶⣠⣼⣿⣿⣿⣿⢠⣧⢀⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡏⢸⣿⢸⣿⣿⣿⣿⣿⣿⡇⠀⣄⠀⠀⠀⠀⠂⠚⠻⠷⣸⣿⡏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢰⣶⣾⢰⣶⣾⣿⢿⣿⡿⣷⣮⢸⣷⣿⣿⣶⢿⢾⣿⣿⣿⣷⣿⠈⠹⠿⠋⠈⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠸⠟⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⡄⠀⠀⠀⠀⠒⢻⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡟⢸⣿⣿⣿⣿⣿⡇⣿⣿⠀⢸⣿⢹⣿⡸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠻⠏⢿⣿⣿⡇⠀⠀⠀⢸⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣧⢸⣿⣿⣿⣿⣿⡇⣿⣿⠀⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠸⠁⢸⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⡟⣹⣿⣇⣿⣿⠀⣿⣿⡛⣿⣷⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠀⠀⠀⠀⠀⠈⠀⣸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⣿⡧⠁⢉⠉⠉⠁⠈⠉⠩⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⠃⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢀⣾⣿⣯⡭⠉⠋⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⢿⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠙⠁⠁⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠈⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠹⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢠⣤⣤⣤⣤⣤⣀⣸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⠟⠭⢽⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⢛⣿⠋⠀⠀⠀⣀⣀⢘⣁⣰⣎⠻⣿⣿⣿⡷⠀⠀⠀⠀⠰⠾⠿⠿⠿⢿⡿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡟⠀⠼⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⣿⣿⠀⠀⠀⠀⠘⢶⣶⣶⣞⢿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⠀
⢸⡿⠀⠀⠀⠀⠀⠀⠈⠹⠉⠉⠙⣿⢉⠻⣿⡇⣿⣿⣿⣧⡄⠀⠀⠀⠀⠹⠧⠀⢀⣨⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡆
⢸⡇⠀⠀⠀⠀⠐⢳⣶⣤⣤⣴⡆⠲⣿⣤⣤⡟⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠴⣿⣥⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⠀⡀⠀⠀⠀⠉⢛⣿⣿⣧⡬⣽⣿⣿⡇⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⢴⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⢠⣷⡄⠀⠀⠀⠀⠘⠈⡽⠀⢸⣿⣿⡷⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃
⢸⡇⠀⢸⣿⡇⠀⠀⠰⠿⣷⣠⠀⡄⣿⣿⣿⠀⢸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣽⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣤⡄
⠘⠀⠀⠿⠏⠁⠀⠐⠀⠀⠈⠻⣿⡆⣿⣿⡏⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢠⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣁⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠐⠉⣽⠇⠀⠀⠀⠟⠦⣤⣄⣀⠀⣀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠘⠁⠀⠀⠀⠉⣿⠛⠛⠿⡇⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠌⠁⠀⢸⣿⠀⠀⠀⣀⣀⣼⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢠⣦⣤⣴⣾⣿⣷⣤⣶⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⠄⠀⢠⣿⣿⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⡿⣿⡿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠙⠿⠋⠛⠛⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⠀⣤⣴⣶⢴⣾⣿⣿⣿⡿⢰⡇⢨⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⡇⣿⣷⢸⣿⣿⣿⣿⣿⣿⡆⠠⡆⠀⠀⠀⠈⠀⠛⠛⠇⣻⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢰⣶⣾⢰⣶⣾⣿⢯⣿⡿⣷⣮⢸⣷⣿⣿⣶⣿⢾⣿⣿⣿⣷⣷⠈⠻⠟⠋⠁⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠿⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢀⣛⣻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡟⢸⣿⣿⣿⣿⣿⡇⣿⣿⠸⢸⣿⢹⣿⣹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠻⣿⣿⢿⠀⠀⠀⠀⢸⣋⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣷⢸⣿⣿⣿⣿⣿⡇⣿⣿⠀⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠘⠈⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⡟⢹⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⣿⡇⠀⣉⠉⠉⠁⠈⠉⠩⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣿⣿⣿⠋⠀⠩⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⢷⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠈⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠈⠈⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠛⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣠⣶⣤⣤⣴⣦⣀⣼⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⠋⠭⢽⢿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⢻⡿⠋⠀⠀⠀⣀⣀⣘⣁⣰⣎⠻⣿⣿⣿⡇⠀⠀⠀⠀⠰⠿⠿⠿⠿⢿⢿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡏⠀⠼⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⡀⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣷⠀⠀⠀⠀⠙⢷⣶⣶⣟⢿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣈⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀
⢸⡟⠀⠀⠀⠀⠀⠀⠈⠩⠉⠉⠙⣿⣉⠻⣿⡇⣿⣿⣿⣧⡀⠀⠀⠀⠈⠹⠇⠀⣀⣸⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⡆
⢸⡇⠀⠀⠀⠀⠀⢱⣶⣤⣤⣴⡆⢲⣿⣤⣤⡇⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠶⣾⡅⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⠀⡄⠀⠀⠀⠉⢋⣿⣿⣧⠬⣿⣿⣿⡇⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠲⢴⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⢰⣷⡄⠀⠀⠀⠀⠘⠊⣝⠀⣹⣿⣿⡇⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁
⢸⡇⠀⢸⣿⡇⠀⠀⠰⠿⣷⣠⡁⡄⣿⣿⣿⠀⢼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡟⠉⣿⣿⣿⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣴⡆
⠘⠀⠀⠿⠋⠁⠀⠐⠀⠀⠈⠛⢷⣆⣷⣿⡇⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡁⠀⣸⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠉⣿⠃⠀⠀⠀⠻⠲⢤⡄⡀⠀⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠈⠁⠀⠀⠀⢹⣿⠉⠙⠿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠁⠀⢸⣟⠀⠀⠀⣤⣄⣺⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢰⣶⣶⣶⣾⣿⣷⣶⣶⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⠀⢠⣿⣷⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⢿⣿⡿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠈⠙⠛⠉⠙⠛⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠐⣤⣴⡐⣠⣿⣿⣿⣿⡟⢰⡆⢨⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠀⣿⡇⣿⣿⣿⣿⣿⣿⣿⠀⢰⡀⠀⠀⠀⠉⠉⠙⠛⠂⣿⡿⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢰⣶⣾⢰⣶⣾⣿⣯⣿⡿⣷⣮⢹⣷⣿⣿⣶⣿⢾⣿⣿⣿⣷⡇⠉⠻⠟⠋⠈⠈⠹⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢈⣛⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⡇⣿⣿⠘⢸⣿⢹⣿⣹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⣿⡿⣿⠀⠀⠀⠀⣿⢻⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣷⢸⣿⣿⣿⣿⣿⡇⣿⣿⠀⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡃⠈⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⡟⢹⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡂⠀⠀⠀⠀⠀⣁⣠⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⣿⡅⠀⣩⠉⠉⠁⠈⠉⢩⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣰⣿⣿⣷⠆⠂⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠷⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠈⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠁⠃⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣴⣶⣶⣦⣶⣤⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⠫⠽⠶⠿⢿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⢻⡟⠉⠀⠀⠀⣀⣀⣉⣥⣰⣎⠻⣿⣿⣿⡇⠀⠀⠀⠀⠸⠿⠿⠿⠿⣿⠿⢿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡏⠀⡞⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣧⠀⠀⠀⠀⠛⣿⣶⣾⡿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠁⠀⠀
⢸⡟⠀⠀⠀⠀⠀⠀⠈⠙⠊⠉⢙⡿⣉⠹⢿⡀⣿⣿⣿⣦⡀⠀⠀⠀⠈⠻⠆⠀⣀⣼⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⡆
⢸⡇⠀⠀⠀⠀⠀⠻⣶⣶⣦⣶⡅⠒⣿⣤⣶⡇⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⠲⣶⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⠀⡀⠀⠀⠀⠈⢩⣿⢿⣣⠤⣽⣿⣿⡃⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠲⠾⠿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⢸⣿⡀⠀⠀⠀⠀⠘⠈⡽⠀⣿⣿⣿⠇⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠁
⢸⡇⠀⣸⣿⡇⠀⠀⠘⠻⣿⣤⠀⠀⣿⣿⡿⠀⢼⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠟⢀⣿⣿⣾⣿⣏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣴⡆
⠈⠀⠀⠿⠁⠀⠀⠘⠀⠀⠈⠛⢿⢤⣿⣿⡇⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⡀⠀⣾⢿⣿⣿⣿⣿⣆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢘⠉⣿⠁⠀⠀⠐⠛⢧⣤⣄⣀⣀⣄⢀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠉⠀⠀⠀⠀⣹⣏⠉⠙⢿⠌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠰⠈⠀⠀⣠⡇⠀⠀⠠⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣶⣶⣶⣾⣿⣿⣷⣶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠀⠀⢰⣿⣧⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢻⣿⡿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠛⠋⠈⠙⣛⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⠐⣦⣶⣿⣦⣿⣿⣿⣿⡇⢲⡆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠹⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⠀⣲⡀⠀⠀⠀⠁⠉⠙⠛⢨⣿⡏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢰⣶⣾⢰⣶⣾⣿⣯⣿⡿⣷⣦⢻⣷⣿⣿⣶⣿⢾⣿⣿⣿⣷⡇⠀⠛⠛⠁⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡏⢸⣿⣿⣿⣿⣿⡇⣿⣿⠸⢹⣿⢹⣿⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠛⢻⣿⠿⠟⠀⠀⠀⠀⡿⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠁⠸⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⡟⢹⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⣿⠅⠀⡭⠉⠉⠁⠈⠉⢩⣷⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⢀⡀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣴⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠸⢿⡿⠏⠉⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⠷⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠈⢙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠃⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣶⣶⣶⣶⣶⣦⣤⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⠿⠋⠵⠶⠾⢿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠟⢻⡟⠉⠀⠀⢀⣀⣀⣉⣥⣴⣎⠻⣿⣿⣿⠇⠀⠀⠀⠀⠻⠛⠻⠟⠻⡿⠿⠿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠟⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣧⠀⠀⠀⠀⠛⢿⣿⣿⠿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠀⠀⠀
⢸⡏⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢹⡯⡉⠹⢿⡀⣿⣿⣿⣦⠀⠀⠀⠀⠈⠻⠂⠀⣀⣾⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⡆
⢸⡇⠀⠀⠀⠀⠈⠿⣷⣶⣶⣶⡅⢻⣿⣤⣾⡇⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠒⢲⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⠀⡄⠀⠀⠀⠈⠹⠿⢿⣳⠦⣿⣿⣿⠁⢘⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠲⠾⠟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⢸⣿⡄⠀⠀⠀⢀⠘⠈⡝⠀⣿⣿⣿⠃⢨⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠁
⢸⠇⠀⣸⣿⡇⠀⠀⠘⠻⣷⣤⢀⠀⣿⣿⡏⠀⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⠋⣰⣿⣿⣾⣿⡍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣶⡆
⠈⠀⠘⠿⠁⠀⠀⠉⠀⠀⠈⠛⢿⢠⣿⣿⠃⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⣯⠀⠀⡿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣠⣤⣌⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠨⠀⡿⠀⠀⠀⠈⠙⢱⣆⣠⣄⣤⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠁⠀⠀⠀⠀⣹⣏⠉⠙⢻⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣐⠘⠀⠀⣠⡇⠀⠀⢠⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠀⠀⣴⣿⣧⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⢹⣿⢻⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠈⠛⢋⠉⢙⣹⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⠘⢤⣶⣞⣶⣿⣿⣿⣿⠇⢸⡆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠹⢸⣿⠈⣿⣿⣿⣿⣿⣿⣷⣀⣺⡀⠀⠀⠀⠀⢉⣉⡙⢺⣿⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢰⣶⣾⣿⣿⣿⡿⣷⣦⢻⣷⣿⣿⣶⣿⢶⣿⣿⣿⣷⡇⠁⠋⠉⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣏⢸⣿⣿⣿⣿⣿⡇⣿⣿⠸⢸⣿⢹⣿⣸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠟⢻⣿⠿⡇⠀⠀⠀⠰⡏⢿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠁⢘⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⡟⢹⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⣿⠁⠀⠭⠉⠉⠁⠈⠉⢩⣷⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⣀⡀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣾⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢺⡿⡿⠓⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⠷⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠈⢉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠃⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣴⣶⣶⣶⣶⣤⣤⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⠟⠩⠶⠖⠾⢿⢿⡿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠟⢹⡟⠁⠀⠀⢀⣀⣄⣩⣥⣴⣎⠻⣿⣿⣿⠇⠀⠀⠀⠀⠺⠛⠻⠟⠻⡿⠿⠿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠟⠁⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣇⠀⠀⠀⠀⠛⢿⣿⢿⠿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⠀⠀⠀
⢸⡏⠀⠀⠀⠀⠀⠀⠀⠓⠂⠀⢹⡏⡉⠹⢿⣠⣿⣿⣿⣦⠀⠀⠀⠀⠈⠻⠂⠀⣀⣾⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⡇
⢸⡃⠀⠀⠀⠀⠀⠳⣷⣶⣶⣾⡁⢻⣿⣶⣾⡇⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠒⢲⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡆⠀⢀⡄⠀⠀⠀⠈⠱⠿⢿⣱⠢⣿⣿⣿⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠲⠿⠟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⢸⣿⡀⠀⠀⠀⢀⠀⠉⠈⠀⣿⣿⣿⠃⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠁
⢸⠇⠀⣼⣿⡇⠀⠀⠘⠻⣷⣬⢠⠀⣿⣿⡇⠀⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡿⠋⢠⣿⣿⣿⣿⡍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⢠⣶⡆
⠈⠀⠘⠛⠀⠀⠀⠁⠀⠀⠈⠛⢿⢰⣿⣿⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⣧⠀⠀⠿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⣄⣌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠈⠀⡟⠀⠀⠀⠈⠙⣢⡤⣤⣠⣤⣄⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠀⠀⠀⣽⣅⠈⠙⢻⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠊⠈⠀⠀⣤⡇⠀⠀⢠⣷⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣶⣶⣶⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠀⠀⣶⣿⣧⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡿⢹⣿⢿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠈⠙⢁⡉⢉⣹⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⠘⣠⣶⢞⣴⣿⣿⣿⣿⠃⢺⡄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠇⢸⣿⠈⣿⣿⣿⣿⣿⣿⣧⣀⣶⠀⠀⠀⠀⠀⢉⣉⡙⣼⣿⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢰⣶⣾⣿⣿⣷⡿⣷⣦⢻⣷⣿⣿⣶⣿⢶⣿⣿⣿⣷⡇⠀⠋⠉⠁⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡆⠀⠘⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣏⢸⣿⣿⣿⣿⣿⡇⣿⣿⢸⢹⣿⢹⣿⣸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⢻⠟⠛⠇⠀⠀⠀⢸⠇⢹⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢈⠀⢸⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⡟⢸⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⣿⠁⠀⠍⠉⠉⠁⠈⠉⢩⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⣀⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢠⣾⣿⣿⠟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠿⠿⠋⠉⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⠷⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠈⢩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠂⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣶⣶⣶⣶⣶⣦⣤⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⠟⠑⠒⠲⠾⡿⢿⡿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠛⣹⡟⠁⠀⠀⢀⣤⣤⣩⣤⣴⣎⠻⣿⣿⣿⠇⠀⠀⠀⠀⠛⠛⠛⠟⠿⡿⠿⠿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠃⠐⠟⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣧⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡇
⢸⣿⠀⠂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣇⠀⠀⠀⠀⠙⣿⣿⠿⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⣏⡍⠹⢿⣰⣿⣿⣿⣦⠀⠀⠀⠀⠀⠛⠀⠀⢤⣿⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⡆
⢸⠁⠀⠀⠀⠀⠀⠷⣷⣶⣶⣮⡈⢻⣿⣶⣾⠃⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠒⢻⣶⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡆⠀⢠⡄⠀⠀⠀⠈⠹⠿⣿⣴⠲⣿⣿⣿⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠓⠿⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⢸⣿⠀⠀⠀⢀⣀⡈⢁⠈⠀⣿⣿⡿⠁⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠁
⢸⠃⢀⣼⣿⠀⠀⠀⠚⠻⢷⣾⣠⠀⣿⣿⡇⠀⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠿⠃⣼⣿⣿⣿⣿⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⣴⣿⡆
⠀⠀⠘⠛⠀⠀⠀⠁⠀⠀⠈⠙⠿⢸⣿⣿⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢟⣧⠀⠰⢿⢿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣤⣤⣌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠐⣀⡏⠀⠀⠀⠈⠉⢦⢤⣤⣤⣤⣄⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠀⠀⠀⣿⣁⠈⠙⢷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣆⡂⠈⠀⠀⣴⡇⠀⠀⢰⣶⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⣿⣶⣶⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡟⢀⠀⣾⣿⣧⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡿⢹⣿⢻⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠈⠙⢁⣉⣉⣹⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⠘⣤⣾⡝⣾⣿⣿⣿⣿⠃⢸⡄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠇⢸⣿⢸⣿⣿⣿⣿⣿⣿⣧⣀⣷⠀⠀⠀⠀⠀⣈⣉⡑⣿⣿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢰⣶⣾⣿⣿⣷⡿⣷⣦⢻⣷⣿⣿⣶⣿⢾⣿⣿⣿⣷⡃⠀⠛⠋⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣏⢸⣿⣿⣿⣿⣿⡇⣿⣿⢸⢹⣿⢹⣿⣸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⢻⠟⠛⠃⠀⠀⠀⢸⡇⢹⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⣿⢿⣿⡇⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢨⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⡟⢸⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⣯⠁⠀⠏⠉⠉⠁⠈⠉⢭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⢀⣀⣀⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣰⣿⣿⣟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡘⠿⠟⠓⠉⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⠷⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠈⢩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣶⣶⣶⣶⣶⣦⣤⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⠟⠑⠒⠲⠿⡿⠿⡿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠛⣹⡟⠁⠀⠀⢀⣤⣄⣭⣤⣼⣌⠻⣿⣿⣿⠃⠀⠀⠀⠀⠚⠛⠛⠛⠻⡿⠿⠿⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠃⠐⠋⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡇
⢸⣿⠀⠂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⢠⣿⣿⣇⠀⠀⠀⠀⠙⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⡀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⡏⡌⠛⢿⣸⣿⣿⣿⣦⠀⠀⠀⠀⠀⠛⠀⠀⢴⣿⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡆
⢸⠁⠀⠀⠀⠀⠀⠷⣶⣶⣶⣯⡈⢻⣷⣶⣾⠁⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⠒⢺⣶⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⢠⡄⠀⠀⠀⠈⠹⡿⣿⡖⠲⣿⣿⣿⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠓⠿⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⢸⣿⠀⠀⠀⢀⣀⠘⢀⠃⠀⣿⣿⡿⠁⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠉⠁
⢸⠃⢀⣼⣿⠁⠀⡀⠛⠻⢷⣤⣀⢀⣿⣿⡇⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⠁⣼⣿⣿⣿⣿⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣴⣿⡆
⠀⠀⠘⠛⠀⠀⠀⠁⠀⠀⠈⠙⠿⢼⢿⣿⠀⠀⠘⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢛⣧⠀⢠⢿⢿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⣤⣌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢐⡏⠀⠀⠀⠈⠉⢔⠤⣄⣤⣤⣄⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠀⠀⠀⣿⣄⠈⠙⢧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⡀⠀⠀⢀⣼⡇⠀⠀⢰⣶⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠐⣿⣾⡶⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡗⠀⠀⣿⣿⣧⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡏⣿⣿⢻⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠈⠉⢁⣀⣉⣽⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⠀⢤⡶⠍⣾⣿⣿⣿⣿⠁⢸⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠇⢹⣿⢸⣿⣿⣿⣿⣿⣿⣧⣀⣷⠀⠀⠀⠀⠀⢈⣉⡁⣿⣿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢰⣶⣾⣿⣿⣷⡿⣷⣦⢻⣷⣿⣷⣶⣿⢶⣾⣿⣿⣷⠃⠀⠙⠉⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣇⢸⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⢹⣿⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⢻⠟⠛⠃⠀⠀⠀⢸⠀⢹⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠉⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⣿⢿⣿⡇⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠨⠀⢸⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⡟⢸⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⣯⠁⠀⠏⠉⠉⠁⠈⠉⢩⣷⣿⣿⣿⣿⣿⣿⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⢀⣀⣠⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢀⣼⣿⣿⡿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠚⢿⠟⠛⠁⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢛⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠈⠀⠈⢩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣶⣶⣶⣶⣶⣤⣴⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡿⠛⠑⠒⠲⠿⡿⢿⡿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠛⣹⠋⠀⠀⠀⢠⣤⣤⣥⣤⣾⣌⢻⣿⣿⣿⠀⠀⠀⠀⠀⠛⠛⠛⠛⠻⡿⠿⠿⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠁⠀⠋⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⣰⣧⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡇
⢸⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⡆⠀⠀⠀⠈⠛⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀
⢸⠃⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⢸⣥⡌⠻⢿⢸⣿⣿⣿⣦⠀⠀⠀⠀⠙⠛⠀⠀⣴⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡇
⢸⠁⠀⠀⠀⠀⠀⢷⣶⣶⣶⣯⠈⢻⣷⣶⣾⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⠒⢲⣶⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠀⠀⢰⡀⠀⠀⠀⠉⠺⡿⣿⡖⢺⣿⣿⣿⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠓⠿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠀⠀⣾⣷⠀⠀⠀⢀⣀⠊⢱⠃⢨⣿⣿⡿⠀⣸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠉⠁
⠸⠀⢀⣿⣿⠀⠀⡀⠋⠻⢷⣆⡀⢸⣿⣿⠃⠐⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠿⢁⣼⣿⣿⣿⣿⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣴⣿⡆
⠀⠀⠘⠛⠀⠀⠀⠁⠀⠀⠈⠙⡟⣼⣿⣿⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⣥⠄⠸⢿⣿⣿⣿⣿⣷⡬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣴⠂⠁⢰⠇⠀⠀⠀⠈⠻⣶⢤⣤⣤⣴⣄⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠀⠀⢀⣿⡁⠉⠛⠇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣸⣤⡂⠀⠀⢀⣼⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠰⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⡀⠀⣴⣿⣿⣿⡇⠀⠀⣿⣿⣇⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡏⣿⣿⢿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠈⠛⢁⣀⣉⣽⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣤⣿⣏⣾⣿⣿⣿⣿⠁⢺⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠇⣿⡿⢸⣿⣿⣿⣿⣿⣿⣧⣀⣷⠀⠀⠀⠀⠁⠈⠉⣳⣿⣿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢰⣶⣾⣿⣿⣷⡿⣷⣦⢿⣷⣿⣷⣶⣿⢾⣿⣿⣿⣷⠃⠀⠙⠉⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣧⢸⣿⣿⣿⣿⣿⡇⣿⣿⢸⢹⣿⢹⣿⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⢻⠟⠛⠃⠀⠀⠀⢼⠈⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⣿⢻⣿⡇⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠉⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⡏⢸⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠠⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⡯⠁⠀⠏⠉⠉⠁⠈⠉⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⣀⣠⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⢀⣾⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⢿⠟⠛⠁⠀⠀⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠟⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠈⠽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠘⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢰⣶⣶⣶⣶⣶⣤⣼⣷⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡿⠛⠓⠒⠶⢿⡿⢿⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⠋⣼⠋⠀⠀⠀⣠⣤⣌⣥⣬⣷⡝⢿⣿⣿⡿⠀⠀⠀⠀⠀⠛⠛⠛⠛⢿⠿⠿⠿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡿⠁⠨⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡎⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡇
⢸⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡄⠀⠀⠀⠘⠻⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⢀⠀⠀
⢸⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣿⣡⠉⠻⣇⢸⣿⣿⣷⡄⠀⠀⠀⠀⠘⠓⠀⢀⣴⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣾⣿⡆
⢸⠀⠀⠀⠀⠀⠈⢿⣷⣶⣶⣧⠈⣾⣷⣶⣿⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠒⠒⣲⣦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠀⠀⢰⠀⠀⠀⠀⠉⢿⢿⣯⡖⢺⣿⣿⡇⠀⣻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠘⠺⠿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠀⠀⣿⣧⠀⠀⠀⢀⣀⠉⡘⠁⢸⣿⣿⠟⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠃
⠘⠀⢠⣿⠿⠀⠀⠀⠛⠿⣧⣇⡄⢸⣿⣿⠀⠸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⢅⣾⣿⣿⣿⣷⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢶⣶⡆
⠀⠀⠘⠋⠀⠀⠈⠀⠀⠀⠉⠻⠧⣿⣿⡇⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⣤⠀⢼⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⣤⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⢸⠃⠀⠀⠀⠉⠙⡤⣠⣤⣤⣤⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⢠⣯⡈⠉⠛⠇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣠⣄⠀⠁⠀⢠⣾⠀⠀⠀⣰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠲⣿⣷⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⡀⢀⣼⣿⣿⣿⠆⡀⠰⣿⣿⣄⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⡏⣿⡟⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠈⠋⣀⣈⣩⣽⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣥⣿⣇⣾⣿⣿⣿⡿⠀⢷⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠃⣿⡇⢸⣿⣿⣿⣿⣿⣿⣇⣀⣆⠀⠀⠀⠀⠁⠉⠙⣣⣿⣟⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢰⣾⣾⣿⢯⣶⡿⣷⣮⢿⣷⣿⣷⣶⢿⢾⣿⣿⣿⣷⠀⠈⠉⠉⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢈⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⢸⢻⣿⢹⣿⣸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠙⠉⣿⠟⠛⠀⠀⠀⠀⣿⠈⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⣿⢻⣿⡇⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠇⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⡇⢸⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⡏⠁⠰⠉⠉⠉⠁⠈⠉⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⣠⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣾⣿⡿⠿⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠿⡿⡟⠃⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠏⠶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠂⠀⢀⡀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢻⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠈⠀⠉⡽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠙⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢰⣶⣶⣶⣶⣦⣤⣼⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠿⠋⠓⠒⠾⢿⠿⣿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⢋⡾⠉⠀⠀⠀⣤⣤⣬⣥⣬⣧⡙⣿⣿⣿⡿⠀⠀⠀⠀⠐⠛⠛⠛⠛⢿⠿⠿⠿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡟⠀⠘⠁⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣇⠀⠀⠀⠀⢀⠀⠀⠀⠀⣸⡆⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡇
⢸⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡅⣼⣿⣿⡄⠀⠀⠀⠈⠻⣿⡿⠽⠿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠀⢀⠀⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢀⣿⣠⠉⢿⡇⣿⣿⣿⣷⡆⠀⠀⠀⠀⠐⠓⠀⢠⣴⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⡆
⠈⠀⠀⠀⠀⠀⠐⣾⣶⣶⣾⡅⠙⢿⣶⣶⡟⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠒⠒⣶⡦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⠀⠀⣠⠀⠀⠀⠀⠉⢿⢿⣷⠒⣿⣿⣿⡇⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠘⠷⠿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⠀⠀⣿⣇⠀⠀⠀⣀⡈⠉⡞⠀⣹⣿⣿⠇⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠃
⠈⠀⣠⣿⡿⠀⠀⠈⠛⠿⣦⡄⡂⣹⣿⣿⠀⢸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⢠⣿⣿⣿⣿⣧⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠠⣶⣶⡆
⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠉⠻⢷⣿⣿⡇⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢋⣤⠀⣾⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣤⣤⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠠⠀⣾⠁⠀⠀⠀⠉⢁⣤⣠⣠⣤⣤⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡈⠉⠻⡆⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⣠⣿⠀⠀⠀⣶⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⣀⡀⠀⢀⣼⣿⣿⣿⠂⡀⢸⣿⣿⣄⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⠛⣿⡟⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠈⢛⣌⣈⣩⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣯⣭⢷⣿⣿⣿⣿⡏⠀⡧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠁⣿⡇⢻⣿⣿⣿⣿⣿⣿⣆⣐⡆⠀⠀⠀⠀⠀⠉⠙⣿⣿⡏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢰⣾⣾⣿⢯⣶⡿⣷⣮⢿⣷⣿⣷⣶⢿⢶⣿⣿⣿⣷⠀⠉⠋⠁⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠁⠁⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠐⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⢸⢻⣿⢹⣿⣸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⣿⠛⠛⠀⠀⠀⠀⡿⠈⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢨⢸⣿⣿⢸⣿⣿⣿⢹⣿⡇⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠃⠀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣿⡅⢸⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠄⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⡏⠁⠐⠉⠉⠉⠁⠈⠉⣽⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣀⣀⣄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⡏⠃⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠏⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣴⣿⣿⡇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠙⢿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠈⠀⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢴⣶⣶⣶⣶⣦⣤⣼⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⠟⠓⠒⠛⠿⣻⡻⢿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠟⢡⡟⠁⠀⠀⢀⣤⣤⣬⣤⣬⣧⡙⣿⣿⣿⡟⠀⠀⠀⠀⠘⠛⠛⠛⠻⢿⠿⠿⠿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡏⠀⠘⠁⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡄⠀⢀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡇
⢸⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡀⠀⠀⠀⠈⠻⣿⡯⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⢀⠀⠁
⠘⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⢸⢏⣄⠹⢿⡄⣿⣿⣿⣷⡄⠀⠀⠀⠀⠘⠃⠀⢠⣼⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⡆
⠈⠀⠀⠀⠀⠀⠰⣾⣶⣶⣾⡄⢙⣿⣶⣾⡇⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠒⠒⣶⡦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣤⠀⠀⠀⠀⠙⠿⢿⣷⠓⣿⣿⣿⡇⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠾⠟⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⠀⢰⣿⡆⠀⠀⢀⣀⡘⠁⠟⠀⣿⣿⣿⠃⢀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠃
⠈⠀⣼⡿⡇⠀⠀⠈⠙⢷⣴⣠⠀⣿⣿⡗⠀⢺⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡿⠟⣰⣿⣿⣿⣿⣆⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠠⣶⣶⡆
⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠉⢻⢱⠿⣿⠇⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣩⡦⠀⣿⣿⣿⣿⣿⣿⣆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠆⠠⠀⡞⠀⠀⠀⠀⠉⢡⣤⣤⣤⣤⣦⣀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠈⠀⠀⠀⠀⣼⣇⠈⠉⠻⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠉⠀⠀⣴⡇⠀⠀⠀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⣀⣀⠀⣠⣾⣿⣿⡷⢀⠀⢺⣿⣷⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⠛⣿⡟⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠉⢹⣀⣈⣭⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣷⣿⣴⣿⣿⣿⣿⠇⠘⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠀⣿⡇⣿⣿⣿⣿⣿⣿⣿⣄⣰⡄⠀⠀⠀⠀⠈⠉⠙⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢰⣾⣾⣿⢯⣶⡿⣷⣮⢿⣷⣿⣶⣶⣿⢾⣿⣿⣿⣷⠀⠉⠉⠁⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠋⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⣿⣿⢿⣿⡇⣿⣿⢸⢻⣿⢹⣿⣹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⣿⠛⠛⠀⠀⠀⠀⣏⠸⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠈⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢈⢸⣿⣿⢸⣿⣿⡟⢸⣿⡇⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢁⣠⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠸⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⢸⣿⣿⢸⣿⣿⡅⢸⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⠍⠁⠐⠉⠉⠉⠀⠈⠉⣽⣿⣿⣿⣿⣿⣿⣷⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣠⡄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⡏⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠏⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⢿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠠⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠃⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣴⣶⣶⣶⣶⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡿⠛⠑⠚⠟⠛⣿⠻⠿⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠟⢱⡏⠀⠀⠀⢠⣤⣤⣤⣦⣼⣦⡹⣿⣿⣿⡇⠀⠀⠀⠀⠘⠛⠛⠛⠛⢿⠿⠿⠿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠃⠀⠊⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⢀⣾⣄⠀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡇
⢸⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠀⠀⠀⠀⠉⠻⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠸⡇⡄⠙⢿⡐⣿⣿⣿⣷⡄⠀⠀⠀⠀⠘⠃⠀⢠⢼⡯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠢⣿⣶⣶⣯⠄⢙⣿⣶⣿⠇⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠚⣷⡆⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⡄⠀⠀⠀⠀⠘⡟⣿⣾⠒⣿⣿⣿⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠺⠛⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⡄⠀⠀⢀⣀⠈⢡⠃⠀⣿⣿⡿⠁⢠⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⢿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠙⠃
⠀⠀⣼⡿⠇⠀⠀⠈⠙⢧⣤⣰⠀⣿⣿⡇⠀⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⠿⠃⣼⣿⣿⣿⣿⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠠⢾⣶⡆
⠀⠀⠛⠁⠀⠀⠀⠀⠀⠈⠙⠿⢼⠿⣿⠀⠀⠈⢻⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠛⣡⠄⢰⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣦⣤⣬⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠄⠀⡏⠀⠀⠀⠈⠉⡥⠆⣠⣠⣤⣤⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⣿⣅⠉⠙⢻⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⢀⣴⡇⠀⠀⢐⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠰⢿⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⣀⡀⠀⣰⣿⣿⣿⡟⢀⠀⣿⣿⣧⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⢹⣿⡟⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠙⣁⣀⣉⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢺⣯⡳⣼⣿⣿⣿⣿⠁⠘⡄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠸⣿⡇⣿⣿⣿⣿⣿⣿⣷⣀⣲⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣦⢰⣿⣾⣿⢯⣶⡿⣷⣮⣿⣷⣿⣶⣶⣿⢶⣿⣿⣿⣶⠀⠈⠉⠁⠀⠀⠈⡿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠁⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠒⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⣿⣿⢸⣿⡇⣿⣿⢹⢿⣿⢻⣿⣹⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠸⡿⠙⠁⠀⠀⠀⢰⡇⠸⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⢸⣿⣿⡏⢸⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⢸⣿⣿⢸⣿⣿⡄⢸⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⠉⠁⠂⠉⠉⠉⠀⠈⢩⣽⣿⣿⣿⣿⣿⣿⣧⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣠⣤⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣼⣿⣿⣿⡯⠀⠁⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠃⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠩⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣶⣶⣶⣶⣶⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡿⠋⠑⠚⠟⢟⣟⠿⡿⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠋⣱⠋⠀⠀⠀⢠⣤⣤⣵⣤⣵⣌⠻⣿⣿⣿⡇⠀⠀⠀⠀⠘⠛⠛⠛⠛⢿⠿⠿⠿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠁⠀⠋⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⡆⠀⠀⠀⠀⣀⠀⠀⠀⢀⣿⡀⠀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡇
⢘⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣷⠀⠀⠀⠀⠉⠻⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⢀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠸⠣⡄⠛⢿⠸⣿⣿⣿⣷⡄⠀⠀⠀⠀⠘⠃⠀⢠⣾⠏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⡆
⠀⠀⠀⠀⠀⠈⠰⣿⣶⣾⣯⠈⢻⣷⣾⣿⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⢚⣷⡦⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⡄⠀⠀⠀⠈⠸⣟⣿⡞⢺⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠺⠟⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⡀⠀⠀⣀⣀⠈⠡⠃⢸⣿⣿⡟⠀⢸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠙⠃
⠀⢀⣼⣿⠃⠀⠀⠉⠻⣧⣤⣔⢨⣿⣿⠇⠐⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⠿⢃⣾⣿⣿⣿⣷⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠠⢾⣿⡆
⠀⠈⠛⠀⠀⠀⠁⠀⠀⠈⠙⡿⢼⠿⣿⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢛⣡⠀⢸⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣦⣤⣬⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠄⢀⡏⠀⠀⠀⠈⢉⡴⡄⣀⣤⣤⣦⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠀⠀⢨⣯⡈⠙⠻⠇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⢀⣾⡇⠀⠀⢐⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠸⢿⣿⣾⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⣀⡀⠀⣴⣿⣿⣿⡟⢀⠀⣿⣿⣧⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⢹⣿⡟⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠈⠋⣁⣉⣉⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢺⣧⠞⣼⣿⣿⣿⣿⠁⠸⡄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡇⠘⢸⣿⠇⣿⣿⣿⣿⣿⣿⣧⣀⣆⠀⠀⠀⠈⠉⠉⠙⢳⣿⣟⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣦⢰⣿⣾⣿⢯⣶⡿⣷⣮⣿⣷⣿⣶⣶⣿⢾⣿⣿⣿⣶⠀⠈⠙⠁⠀⠀⠈⡿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⣿⣿⢸⣿⡇⣿⣿⢹⢿⣿⢹⣿⣻⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠸⡿⠛⠋⠀⠀⠀⢸⠧⢸⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⢸⣿⣿⠇⢸⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⣤⣼⣿⣿⣿⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⢸⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢠⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⣿⠉⠁⠂⠉⠉⠉⠁⠈⢩⣽⣿⣿⣿⣿⣿⣿⣧⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⣤⣤⣤⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣾⣿⣿⣿⡏⠀⠙⣿⣿⠟⠉⠙⠛⠁⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠁⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣼⣿⣿⣿⣿⡇⠀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠻⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠩⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠃⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣶⣶⣶⣶⣶⣦⣤⣿⣾⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡿⠋⠐⠚⠟⢟⣟⠿⡿⢿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡿⠋⣼⠋⠀⠀⠀⢠⣤⣤⣥⣤⣽⣌⠻⣿⣿⣿⡇⠀⠀⠀⠀⠚⠛⠛⠛⠛⢿⠿⠿⠿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠁⠀⠋⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⡆⠀⠀⠀⠀⢀⠀⠀⠀⢠⣿⡀⠀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⠀⠀⠀⠀⠉⠿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠠⠀⠀⠉⠀⢀⠾⢡⡀⠛⣷⢸⣿⣿⣿⣷⡄⠀⠀⠀⠀⠘⠂⠀⢠⣾⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠺⣿⣶⣾⣧⠈⢿⣷⣾⣿⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⢚⣷⡦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢠⡄⠀⠀⠀⠀⠹⣿⣿⡞⢺⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠛⠛⠛⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣾⣿⠀⠀⠀⣀⣀⠉⠸⠃⢸⣿⣿⡟⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠈⠙⠃
⠀⢀⣾⣿⠀⠀⠀⠉⠻⣧⣅⡄⢸⣿⣿⠇⠐⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣰⣾⣿⣿⣿⣏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠠⢾⣿⡆
⠀⠘⠛⠀⠀⠀⠁⠀⠀⠈⠙⡟⣾⢿⣿⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠋⣤⠀⣾⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣨⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠁⢸⠇⠀⠀⠀⠈⠉⡴⡆⢀⣠⣤⣤⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⠀⠁⣨⣏⠉⠛⠿⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣠⣴⣤⡀⠀⠀⢠⣾⠀⠀⠀⢰⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢶⣶⣶⣶⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⣀⡀⠀⣴⣿⣿⣿⠇⡀⠐⣿⣿⣧⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⢹⣿⡟⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠘⢛⡈⠉⣙⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣴⣾⣿⣿⣿⣿⠀⠻⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠸⢸⣿⠇⣿⣿⣿⣿⣿⣿⣇⣐⡄⠀⠀⠀⠉⠉⠙⠛⣿⣿⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢰⣿⣾⣿⢧⣶⡿⣷⣮⣿⣷⣷⣶⣶⣿⢾⣿⣿⣿⣶⠀⠉⠋⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠰⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⣿⣿⢸⣿⡇⣿⣿⢹⢿⣿⢹⣿⣻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠘⡿⠉⠋⠀⠀⠀⢰⠇⢼⣿⣿⣿⣿⣿⠿⢻⡆⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⢸⣿⣿⠇⢸⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⡇⠀⣠⣷⡀⢲⡇⡄⠘⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣸⣿⣿⢸⣿⣯⡄⢺⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡆⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠋⠀⠻⡿⠃⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⡯⠉⠁⠂⠉⠉⠉⠀⠈⢩⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣽⣿⣿⣿⡏⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿⣿⣿⡇⢸⣿⠟⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠀⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣼⢿⣅⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⠹⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⢨⢻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠃⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣶⣶⣶⣶⣶⣦⣤⣿⣾⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⣿⠟⠋⠒⠛⠛⢛⡟⢿⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡿⠉⣼⠁⠀⠀⠀⣤⣤⣤⣶⣶⣷⡈⢿⣿⣿⣿⡇⠀⠀⠀⠀⠘⠛⠛⠛⠛⣿⠿⠿⠿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⠁⠀⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣧⠀⠀⠀⠀⠙⠻⣿⡿⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣁⠀⢀⠈⠁
⠀⠀⠀⠀⠀⢀⠀⠈⠁⠀⠀⢿⢤⠈⠻⣇⢸⣿⣿⣿⣷⡄⠀⠀⠀⠀⠘⠂⠀⠤⣾⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⡆
⠀⠀⠀⠀⠀⠘⢿⣿⣶⣾⡥⠘⢻⣷⣾⣿⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⢚⣷⠆⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢠⡀⠀⠀⠀⠀⢻⢻⣷⡟⢺⣿⣿⣧⠀⢹⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠛⠻⠛⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⠀⠀⠀⣀⣠⠁⡜⠀⢸⣿⣿⠏⠀⣸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠈⠙⠃
⠀⢠⣿⢿⠀⠀⠀⠉⠻⣦⣥⡆⢸⣿⣿⠂⠘⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠿⠟⣼⣿⣿⣿⣿⡍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠠⢾⣿⡆
⠀⠘⠋⠀⠀⠀⠀⠀⠀⠈⢻⠇⡿⢿⡇⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⢁⡄⢀⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣤⣄⣼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠠⠁⢸⠁⠀⠀⠀⠉⢉⡵⡀⢂⣠⣤⣦⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⠀⠀⠀⠀⣽⡉⠉⠛⠷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣠⣤⣠⡀⠀⠀⢠⣿⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠠⣶⣶⣶⣾⣿⣿⣶⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⠀⢀⣼⣿⣿⣿⠃⡀⠰⣿⣿⣆⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢻⣿⡿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠙⢉⠉⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣡⣿⣿⣿⣿⡿⠀⠳⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⡆⠘⢸⣿⠃⣿⣿⣿⣿⣿⣿⣤⣰⣠⡄⠀⠈⠉⠉⣻⢷⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢰⣿⣾⣿⢣⣶⡿⣷⣮⣿⣷⣷⣶⣷⣿⢾⣿⣿⣿⣶⠀⠉⠛⠀⠀⠀⠈⡿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⠉⣿⣤⣶⢾⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⣿⡟⢸⣿⡇⣿⣿⢹⢿⣿⢹⣿⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠹⡿⠛⠋⠀⠀⠀⠀⠇⢜⣿⣿⣿⣿⡿⠿⠾⢿⣿⣇⠙⠉⠁⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢸⣿⣿⢸⣿⣿⠃⢸⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣴⣶⣾⣿⣿⣿⣯⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣼⣿⣿⢸⣿⣧⡄⢺⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡆⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⡏⠉⠁⠀⠉⠉⠉⠀⠈⢭⣿⣿⣿⣿⣿⣿⣿⡅⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣀⣀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⣿⣿⣿⣷⠈⣿⣿⣿⣿⣶⣤⣠⣺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣷⠀⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠈⠹⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢨⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠃⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣷⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠠⣶⣶⣶⣶⣶⣦⣤⣿⣾⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠟⠉⠒⠛⠛⢻⡟⢿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡟⢉⡾⠁⠀⠀⠀⣤⣤⣤⣶⣶⣧⡈⢿⣿⣿⣿⠇⠀⠀⠀⠀⠘⠛⠛⠛⠻⡿⠿⠿⠿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠀⠘⠃⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⡄⠀⠀⠀⠀⡀⠀⠀⢀⢠⣿⡀⠀⢌⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠸⣿⠿⣿⢿⣿⣿⣿⣿⡇⢻⣿⣿⣧⠀⠀⠀⠀⠙⠿⣿⠿⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⣀⠈⠃
⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⡀⢟⢤⠈⠻⣇⢾⣿⣿⣿⣶⡀⠀⠀⠀⠀⠚⠂⠀⠤⣿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⡆
⠀⠀⠀⠀⠀⠙⢾⣿⣾⣿⡥⠙⣿⣷⣿⡟⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣷⠦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢠⡀⠀⠀⠀⠁⢻⢻⣷⠓⣻⣿⣿⡇⠀⢹⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠛⠿⠛⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣧⠀⠀⢀⣀⡼⠁⡟⠀⣾⣿⣿⠏⠀⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠈⠙⠃
⠀⢠⣿⠿⠀⠀⠈⠉⠻⣶⣤⡂⣿⣿⡿⠀⠸⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⠿⢃⣾⣿⣿⣿⣯⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠠⢾⣿⡆
⠀⠙⠋⠀⠀⠀⠀⠀⠀⠈⢻⠷⡿⢿⡇⠀⠀⠙⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⣠⠄⢘⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣨⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠈⠀⣺⠀⠀⠀⠀⠉⣉⣦⢆⣤⣠⣴⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠉⠀⠀⠈⢈⣿⡉⠙⠛⠇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣤⣦⣄⠈⠀⠀⣰⣿⠀⠀⠀⣸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢰⣶⣶⣶⣾⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⠀⣠⣾⣿⣿⣿⠂⡀⢸⣿⣿⣆⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢻⣿⠻⣿⣿⣿⣿⣷⡄⠀⠀⠀⢼⡝⣃⢉⣉⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⢷⣿⣿⣿⣿⡏⠀⠳⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⢸⣿⠁⣿⣿⣿⣿⣿⣷⣤⣷⠀⢈⣡⣾⡿⣿⣿⡿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣷⣾⣿⢡⣶⡿⣷⣮⣿⣷⣷⣶⣷⣿⢾⣿⣿⣷⣶⠀⠉⠉⠀⠀⠀⠙⡿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠁⠀⡿⣿⣿⣿⣿⣿⣿⡟⠾⠋⣻⣿⣿⠟⡹⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⣿⡏⢸⣿⡏⣿⣿⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠸⡏⠉⠃⠀⠀⠀⠘⠃⢸⣿⣿⣿⣿⠿⠁⠀⠀⠀⠉⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢸⣿⣿⢸⣿⡿⠁⢸⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢸⣿⣧⡔⢸⣿⣇⣿⣿⠀⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⠍⠉⠁⠀⠉⠉⠉⠁⠈⣭⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⣧⢘⣿⣿⣿⣿⣿⣏⣸⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⣷⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠻⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⢸⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡷⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢠⣶⣶⣶⣶⣶⣤⣴⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢿⡿⠛⠑⠊⠛⠛⣻⡻⠿⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠟⢡⡿⠁⠀⠀⢀⣤⣤⣤⣶⣾⣧⡘⢿⣿⣿⣿⠇⠀⠀⠀⠀⠛⠛⠛⠛⠛⡿⠿⠿⠿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⠀⠘⠁⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⡀⠀⠀⠀⠀⣀⠀⠀⣀⣰⣷⡀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠼⡿⠿⡿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣧⠀⠀⠀⠀⠙⠿⡿⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⠀⣀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡸⡇⣄⠘⢻⡆⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠛⠀⠠⠤⣿⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡆
⠀⠀⠀⠀⠀⠰⢿⣷⣾⣿⡄⠙⣿⣾⣿⡇⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢻⣷⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣤⠀⠀⠀⠀⠐⢿⣿⣵⠓⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢠⣿⡇⠀⠀⢀⣀⡌⢀⠍⠀⣿⣿⣿⠃⢀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠈⠙⠃
⠀⣰⡿⠏⠀⠀⠈⠙⢿⣦⣠⠀⣿⣿⡿⠀⠺⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⠟⢠⣿⣿⣿⣿⣏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠰⢿⣿⡆
⠀⠙⠃⠀⠀⠀⠀⠀⠀⠉⢻⢲⠿⢿⠇⠀⠀⠙⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⣠⠀⣸⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣦⣤⣬⡄
⠀⠀⠀⠀⠀⠀⠀⡀⢀⢠⠇⠘⠀⡾⠀⠀⠀⢈⠉⣩⣠⣆⣤⣤⣤⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠁⠀⠀⠀⢨⣯⡉⠙⠻⠇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⣼⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢴⣶⣶⣶⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⠀⣠⣾⣿⣿⡿⢀⠀⢸⣿⣿⣄⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢻⣿⢻⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠙⠁⣉⣩⣿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⡟⣿⣿⣿⣿⣿⠇⠈⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⢿⣿⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⢸⣿⠀⣿⣿⣿⣿⣿⣧⣤⣧⢠⣴⢶⣿⣏⣡⡶⢿⣯⣼⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⣾⣿⢠⣶⡿⣷⣮⣿⣷⣶⣶⣷⣿⣾⣿⣿⣷⣶⠀⠉⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⢀⡿⣿⣿⣿⣿⣿⣿⡟⠈⠉⠈⠛⢿⣯⡶⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⢸⣿⣿⠇⢸⣿⡏⣿⣿⢻⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠸⡟⠉⠁⠀⠀⠀⠸⠁⣼⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠈⠉⠘⢩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢈⢸⣿⣿⢸⣿⡟⠀⢸⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣇⣴⣶⣆⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣽⣿⣿⢸⣿⣧⡔⢸⣿⣇⣿⣿⠈⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣾⠉⠉⠁⠀⠉⠉⠉⠁⠈⣽⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢹⣿⣿⣿⣇⠹⣿⣿⣿⣿⣿⣿⠁⣀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣼⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⡟⠀⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⣶⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠻⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⢨⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢰⣶⣶⣶⣶⣶⣦⣴⣿⣾⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢿⡿⠋⠑⠚⠛⠛⣻⠻⠿⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠏⢱⡟⠀⠀⠀⢠⣤⣤⣤⣶⣾⣦⡙⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⠛⠛⠛⠻⡟⠿⠿⠿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠚⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⠀⠀⠀⠀⠀⣀⠀⠀⡀⣰⣧⡀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠾⡿⢿⡿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣇⠀⠀⠀⠀⠙⢿⡿⠽⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⡀⠈⠃
⠀⠀⠀⠀⠀⣀⠀⠉⠀⢀⠸⡣⡄⠘⢻⡄⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠛⠀⠠⠤⢿⠎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⡆
⠀⠀⠀⠀⠀⠑⢿⣿⣿⣿⡄⠹⣿⣾⣿⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢻⣷⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣆⠀⠀⠀⠀⠐⢟⣿⣾⠓⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣿⡇⠀⠀⢀⣠⡌⢨⠁⠠⣿⣿⣿⠃⢀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠙⠃
⠀⣼⡿⡇⠀⠀⠈⠙⢿⣷⣴⢀⣿⣿⡟⠀⢹⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⡿⠟⢡⣿⣿⣿⣿⣧⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠴⢿⣷⡆
⠀⠙⠃⠀⠀⠀⠀⠀⠀⠙⡻⢾⠿⢿⠂⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⣀⠀⢘⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⡏⠀⠀⠀⢀⠉⣠⣠⣠⣤⣤⣴⣦⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠁⠀⠀⠁⢠⣯⡈⠉⠛⠇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⢀⣾⡇⠀⠀⠀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠶⢶⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⠀⣠⣿⣿⣿⡟⢀⠀⢾⣿⣷⣄⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⢻⣿⢻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠨⢃⣈⣩⣿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠠⣽⡿⣿⣿⣿⣿⣿⠇⠈⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠁⢸⢿⢀⣿⣿⣿⣿⣿⣧⣤⣧⢠⣶⠞⣿⣯⣵⠿⣻⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢰⣾⣾⡿⢠⣶⡿⣷⣯⣿⣷⣶⣾⣷⣿⢾⣿⣿⣷⣶⠀⠈⠉⠀⠀⠀⠙⡿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⢸⡿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⣿⠃⢸⣿⡟⣿⣿⢿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠏⠉⠁⠀⠀⠀⢸⣇⣸⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⢸⣿⣿⢸⣿⡟⠀⢸⣿⡇⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⢀⣴⣾⣷⣀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣹⣿⣿⢸⣿⣧⡔⢸⣿⣇⣿⣿⠈⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣮⠉⠉⠁⠀⠉⠉⠉⠁⠨⣽⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢹⣿⣿⣿⣷⡘⢻⣿⣿⣿⣿⣿⣇⣀⡀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠿⣶⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠹⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠁⠀⢩⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢠⣶⣶⣶⣶⣶⣦⣴⣿⣾⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⠋⠑⠛⠛⠛⣻⡻⠟⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠋⣱⠏⠀⠀⠀⢠⣤⣤⣴⣶⣾⣦⡙⣿⣿⣿⣿⠄⠀⠀⠀⠀⠛⠛⠛⠛⠻⡟⠻⠿⠿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠋⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⠀⠀⠀⠀⠀⣀⡀⠀⣀⣰⣧⡀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⡾⣿⣿⡿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣆⠀⠀⠀⠀⠙⢿⣿⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⣀⠀⠁
⠀⠀⠀⠀⢀⡀⠀⠉⠀⠀⠸⡣⡄⠘⢻⡄⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠛⠀⠠⠤⢿⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠒⢷⣷⣿⣿⡄⢹⣿⣾⣿⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢻⣷⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣄⠀⠀⠀⠀⠘⣟⣿⡟⢻⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡇⠀⠀⢀⣀⠏⢸⠁⢸⣿⣿⡿⠁⢠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⠙⠃
⠀⣼⡿⡇⠀⡀⠈⠹⢷⣧⣼⢰⣿⣿⠏⠀⢻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡞⠟⢣⣿⣿⣿⣿⣷⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠴⢿⣿⡆
⠀⠙⠃⠀⠀⠀⠀⠀⠀⠉⡿⢾⠿⣿⠀⠀⠀⠙⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⢠⡄⠠⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣰⡁
⠀⠀⠀⠀⠀⠀⠀⠠⠠⣼⠃⠚⢀⡏⠀⠀⠀⠀⢉⣪⣻⣦⣤⣤⣴⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠉⠀⠀⠀⡀⣾⣄⠈⣙⣃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣼⣤⡄⠀⠀⢀⣿⡇⠀⠀⠀⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠶⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⠀⣠⣿⣿⣿⡟⢀⠀⢾⣿⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⢹⣿⢻⣿⣿⣿⣿⣧⡀⠀⡀⠀⠀⠀⢃⣠⣬⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠠⣿⡿⣽⣿⣿⣿⣿⠃⠘⠆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠁⢸⣿⢀⣿⣿⣿⣿⣿⣷⣤⣿⠀⣶⡟⢿⣿⣵⡾⢟⣿⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⣾⡟⢠⣶⡿⣷⣯⣿⣷⣶⣾⣶⣿⣾⣿⣿⣷⣶⠀⠉⠉⠁⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⢰⡿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠉⠈⠙⣿⣾⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⢸⣿⣿⠁⢸⣿⡟⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⠟⠉⠁⠀⠀⠀⢸⣃⣼⣿⣿⣿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠛⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣸⣿⣿⢸⣿⡏⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣄⣴⣿⣿⣧⡄⠀⠀⠀⠀⠘⠻⠿⣿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢸⣿⣧⡔⢸⣿⣇⣿⣿⡈⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢠⣤⡄⣤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡃⠀⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣮⠉⠉⠁⠀⠉⠉⠉⠁⢩⣽⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⣇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⠀⡠⠇⠻⢞⣜⣚⣿⣿⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠶⠷⢶⣿⣿⢷⢾⣿⣛⣿⣟⣛⢫⢿⣳⡿⣯⢭⣯⡍⣽⡯⡏⡏⣯⢹⢱⣩⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡷⢸⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⢇⠿⠻⣹⣿⣿⣿⡇
⢸⣿⠿⣶⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⢃⣛⣫⣟⣷⣬⣿⣥⣥⣥⣮⣭⣮⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠹⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠉⠈⢽⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡿⠷⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢠⣶⣶⣶⣶⣶⣦⣴⣿⣾⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠿⠋⠐⠙⠋⠛⣟⠻⡟⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⠋⣸⠇⠀⠀⠀⢠⣤⣤⣴⣶⣾⣆⡹⣿⣿⣿⣿⠅⠀⠀⠀⠀⠛⠛⠛⠛⠻⡟⠻⠿⠿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠋⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⠀⠀⠀⠀⠀⣠⡀⠀⠀⣰⣧⡀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⢿⣿⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣆⠀⠀⠀⠀⠙⣿⡿⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⣀⠈⠃
⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀⢼⣡⡀⠙⢿⡄⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠛⠀⠠⠤⢿⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠈⠒⣿⣶⣿⣿⠈⢹⣿⣾⣿⠇⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠘⢻⣷⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⣆⠀⠀⠀⠀⠚⣟⣿⡿⢹⣿⣿⣿⡀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡇⠀⠀⢠⣤⡎⣸⠁⢸⣿⣿⡿⠀⣰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⢿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠙⠃
⠀⣼⡿⡇⠀⡀⠈⠹⢷⣷⣼⢸⣿⣿⠇⠀⢻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡾⠛⠃⣾⣿⣿⣿⣿⣄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠴⢿⣿⡆
⠀⠙⠁⠀⠀⠀⠀⠀⠀⠉⡿⣾⠿⣿⠀⠀⠀⢙⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⢀⡔⠠⣿⠿⣿⣿⣿⣿⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⢐⡇⠀⠀⠀⠀⠨⣼⣎⣦⣴⣶⣴⣆⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈⠀⠀⠀⡀⣾⣦⡀⣈⣁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣴⣤⡄⠀⠀⢀⣮⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠾⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⡀⠀⣴⣿⣿⣿⡇⢀⠀⣿⣿⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢹⣿⢻⣿⣿⣿⣿⣧⡀⠀⡀⠀⠀⠀⢘⣠⣤⡾⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⣿⡇⣼⣿⣿⣿⣿⠁⠘⠆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⡿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠁⢸⣿⢀⣿⣿⣿⣿⣿⣧⣬⣿⡄⣴⡿⢻⣿⣷⡾⢟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⣾⡏⢠⣶⡿⣷⣯⣿⣷⣶⣾⣶⣿⢾⣿⣿⣷⣶⠀⠉⠉⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠉⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⣿⠁⢸⣿⡗⣿⣿⣿⣿⣿⢹⣿⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⠟⠋⠁⠀⠀⠀⢸⣇⣼⣿⣿⣿⠿⠟⠋⢀⠀⠀⠀⠀⠀⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⢹⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣀⣴⣿⣿⣧⣀⠀⠀⠀⠀⠘⠹⠿⣿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢸⣿⣧⡔⢸⣿⣇⣿⣿⡈⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢠⣤⡄⣤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⠀⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⣮⠉⠉⠁⠀⠉⠉⠉⠁⢩⣽⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣰⣠⣇⠻⢜⣜⣚⣿⣿⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠰⠷⢶⣿⣿⢷⢾⣿⣛⣿⣟⣛⢣⢽⣻⡿⣯⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡷⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⢇⠿⠻⣹⣿⣿⣿⡇
⢸⣿⠿⣶⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⢃⣛⣪⣟⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠙⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠈⢬⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣶⣶⣶⣶⣶⣦⣴⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠟⠋⠐⠙⠛⢛⡟⠿⠟⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⠋⣼⠇⠀⠀⠀⣠⣤⣤⣴⣶⣿⣆⠹⣿⣿⣿⣿⠁⠀⠀⠀⠀⠛⠛⠛⠛⠛⡟⠛⠿⠿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠋⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⠀⠀⠀⠀⢀⣠⠀⠀⡀⣰⣧⡀⠀⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣇⠀⠀⠀⠀⠉⠿⡿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⠀⣀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⢞⢡⡀⠙⢿⠘⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠛⠀⠠⠤⢿⠎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠲⢿⣶⣿⣯⠈⢹⣷⣿⣿⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⣻⣷⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⣄⠀⠀⠀⠀⠚⣿⣿⡏⢻⣿⣿⣿⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡆⠀⠀⣠⣤⠋⠼⠁⢸⣿⣿⡟⠀⣰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⢿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠙⠃
⢀⣾⡿⠇⠀⡀⠉⠻⣿⣧⡆⢸⣿⣿⠇⠀⢻⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⠛⠇⣾⣿⣿⣿⣿⣆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠴⢿⣿⡆
⠀⠙⠁⠀⠀⠀⠀⠀⠀⠙⠟⡿⠿⣿⠀⠀⠀⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⢠⡖⠠⡿⠿⣿⣿⣿⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠁⢠⡇⠀⠀⠀⠈⠉⢄⣴⣦⣴⣦⣶⣦⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠀⠀⠀⢀⣾⣦⡀⣈⣉⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣶⣤⡄⠀⠀⢀⣿⡇⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠾⠿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣄⡀⠀⣴⣿⣿⣿⡏⢀⠀⣿⣿⣷⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⢹⣿⢹⣿⣿⣿⣿⣧⠀⠀⡀⠀⠀⠀⢈⣠⣤⡾⣿⣿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⣽⡗⣼⣿⣿⣿⣿⠀⠸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡄⠁⢸⣿⢀⣿⣿⣿⣿⣿⣧⣬⣿⡄⣴⡿⢻⣿⣷⣾⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⣾⡏⢠⣶⡿⣷⣯⣿⣷⣶⣾⣶⣿⢾⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⣿⠀⢸⣿⡗⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠟⠉⠁⠀⠀⠀⢸⣗⣸⣿⣿⣿⡿⠟⠋⢀⡀⠀⠀⠀⠀⠙⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⢹⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣀⣴⣿⣿⣿⣄⡀⠀⠀⠀⠘⠩⠿⢿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢸⣿⣧⡆⢸⣿⣇⣿⣿⡈⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢠⣤⡄⣤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⠁⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⡮⠉⠉⠁⠀⠉⠉⠉⠁⢫⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⣇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣸⣠⣇⡻⢜⣜⣚⣿⣿⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠰⠷⢶⣿⣿⢿⢾⣿⣛⣿⣟⣛⢣⢽⣻⡾⣯⣭⣯⡍⣽⡯⡏⡏⣯⢹⢱⣩⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡷⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣹⣿⣿⣿⡇
⢸⣿⠿⣶⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⣛⣪⣟⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠹⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⢨⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢰⣾⣷⣶⣶⣶⣦⣶⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠟⠉⠐⠉⠙⢛⣟⠿⠟⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⠉⣼⠃⠀⠀⠀⣠⣤⣤⣴⣶⣿⣆⠹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠛⠛⠛⠛⠛⡟⠛⠿⠿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠃⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡀⠀⠀⠀⢀⣀⡀⠀⡀⣰⣧⡀⠀⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⠀⠂⠀⠀⠀⠀⢿⣿⣿⢿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣇⠀⠀⠀⠀⠙⢿⡿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⣀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢞⢠⠀⠙⢿⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠛⠀⠠⠤⠿⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠲⢿⣾⣾⣧⢈⢻⣷⣿⣿⠀⢻⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠙⣻⣷⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⣄⠀⠀⠀⠀⠛⣻⣿⡏⢻⣿⣿⣿⠀⠨⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡆⠀⠀⣠⣤⡋⠈⠁⢺⣿⣿⡟⠀⣰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⢿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠙⠃
⠀⣾⡿⠇⠀⡀⠉⠻⣿⣧⡆⢸⣿⣿⠇⠀⢻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⡾⠛⠃⣾⣿⣿⣿⣿⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠴⠿⣿⡇
⠀⠙⠁⠀⠀⠀⠀⠀⠀⢙⠟⡿⠿⡿⠀⠀⠀⢹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠛⢀⡖⠀⢿⡿⣿⡿⢿⣿⣆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⣤⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠁⣰⠇⠀⠀⠀⢀⠈⢩⣶⣶⣴⣶⣴⣦⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠈⠀⠀⠀⡀⣾⣦⡀⣈⣉⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢠⣥⣤⡀⠀⠀⢠⣿⡇⠀⠀⢈⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠻⠿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⢀⣴⣿⣿⣿⠇⢀⠀⣿⣿⣷⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢻⣿⢹⣿⣿⣿⣿⣷⠀⠀⡀⠀⠀⠀⢈⣤⣤⣾⣿⣿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣽⡟⣾⣿⣿⣿⣿⠀⠸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⢿⣿⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠁⢸⣿⠀⣿⣿⣿⣿⣿⣧⣬⣿⡄⢶⣟⢻⣿⣷⣾⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⣾⡇⢠⣶⡿⣷⣯⣿⣷⣶⣶⣶⣿⢾⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⢀⣿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⢸⣿⣿⠀⢸⣿⡗⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠟⠉⠁⠀⠀⠀⢸⣟⣘⣿⣿⣿⡿⠟⠋⢀⡀⠀⠀⠀⠀⠘⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⢹⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡄⣴⣿⣿⣿⣤⡀⠀⠀⠀⠘⠹⠿⣿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢿⣿⣿⢸⣿⣧⡆⢸⣿⣇⣿⣿⡊⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢠⣤⡄⣤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⠇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⡮⠉⠉⠁⠀⠉⠉⠉⠁⢫⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣸⣠⣇⡻⢞⣜⣚⣿⣿⣧⣷⣽⣯⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠰⠷⢶⣿⣿⢿⢖⣟⣛⣿⣟⣛⢻⢬⣻⡿⣯⣭⣯⡍⣽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡷⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⣿⠿⣶⠀⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⣛⣪⣟⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠙⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠉⢨⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣷⣶⣶⣶⣦⣶⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠟⠉⠈⠉⠙⢛⣟⠿⠟⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠉⣼⠃⠀⠀⠀⣠⣤⣤⣴⣶⣿⣄⠹⣿⣿⣿⣿⠇⠀⠀⠀⠀⠛⠛⠛⠛⠛⡟⠛⠿⠿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠈⠃⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡀⠀⠀⠀⢀⣠⡀⠀⡀⣰⣧⣀⢀⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⠀⠀⠀⠀⠀⠰⣿⢿⣿⢿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣇⠀⠀⠀⠀⠈⠿⡿⠿⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⣀⡀⠃
⠀⠀⠀⠀⢀⠀⠈⠁⠀⡀⢟⢠⠀⠙⣿⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠛⠀⠠⠴⠿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠰⢿⣿⣾⣧⠨⢹⣷⣿⣿⠀⢻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠙⣻⣷⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢠⣄⠀⠀⠀⠀⠻⣻⣿⡏⢻⣿⣿⣿⠀⢨⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡆⠀⠀⣠⣤⠁⡝⠀⢺⣿⣿⡏⠀⣼⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⢿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠉⠃
⢠⣾⡿⠇⠀⡀⠉⠻⣿⣧⡆⢸⣿⣿⠇⠀⢻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⠛⠣⣾⣿⣿⣿⣿⣆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠴⠿⣿⡇
⠀⠙⠁⠀⠀⠀⠀⠀⠀⢙⠟⡿⠿⡿⠀⠀⠀⢹⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠋⢀⡦⠀⢿⠿⣿⡿⢿⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣦⣤⣬⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠁⣸⠃⠀⠀⠀⢀⠉⢫⣷⡶⣴⣶⣶⣦⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⢀⣾⣦⣀⣈⣉⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣠⣿⣥⡄⠀⠀⢠⣾⡀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠻⠿⢿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⢀⣴⣿⣿⣿⠇⣀⠀⣿⣿⣷⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢹⣿⠹⣿⣿⣿⣿⣷⡄⠀⡀⠀⠀⠀⢈⣤⣴⣾⣿⣿⡿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣽⡟⣾⣿⣿⣿⣿⠀⠸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⢿⣿⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⡿⠀⣿⣿⣿⣿⣿⣧⣤⣿⡆⢾⣿⣻⣿⣷⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⣾⡇⢠⣶⡿⣷⣯⣿⣷⣶⣶⣶⣿⢾⣿⣿⣷⣶⠀⠀⠁⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⢸⣿⡿⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠸⠟⠉⠁⠀⠀⠀⢸⣏⣘⣿⣿⣿⡿⠟⠋⢀⡀⠀⠀⠀⠀⠘⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣺⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣻⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠀⣴⣿⣿⣿⣤⡀⠀⠀⠀⠐⠩⠿⣿⠿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣺⣿⣿⢸⣿⣧⡆⢸⣿⣇⣿⣿⣈⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢠⣤⡄⣤⣍⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⡎⠉⠉⠁⠀⠉⠉⠉⠁⢫⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⣇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⣿⣸⣡⣇⡻⣜⣜⣚⣿⣻⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠰⠷⢶⣿⣿⢿⢖⣟⣛⣿⣟⣻⢻⢽⣻⡿⣯⢭⣯⡍⣽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡷⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⣿⠷⣶⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⣛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠁⠀⠙⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠠⢻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠿⠿⠷⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠠⣾⣿⣾⣶⣿⣶⣶⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠟⠉⠈⠉⠙⢛⡟⠿⠟⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⢉⣼⠃⠀⠀⠀⣤⣤⣤⣶⣶⣷⣄⠻⣿⣿⣿⣿⠇⠀⠀⠀⠀⠛⠛⠛⠛⠛⡟⠛⠻⠿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠘⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡀⠀⠀⠀⢀⣠⣀⠀⣀⣸⣷⣀⢀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⠀⠀⠀⠀⠀⠰⢿⢿⣿⢿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣇⠀⠀⠀⠀⠉⠻⣿⠻⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⢀⡈⠃
⠀⠀⠀⠀⢀⡀⠈⠁⠀⡀⣟⢤⠀⠛⣧⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠛⠀⠠⠴⠿⠎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠰⢿⣾⣿⣧⠨⢻⣷⣿⣿⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⣻⣿⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢠⣄⠀⠀⠀⠀⢻⣻⣿⡏⣻⣿⣿⣿⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠛⠛⠋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡆⠀⠀⣠⣬⠉⡟⠀⣾⣿⣿⡏⠀⣼⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⢿⣿⣙⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠃
⢠⣾⡿⠇⠀⠀⠉⠻⣿⣧⡇⢸⣿⣿⠃⠀⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⠛⠃⣾⣿⣿⣿⣿⣆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠰⠿⣿⡇
⠀⠙⠁⠀⠀⠀⠀⠀⠈⢙⠗⡿⢿⡟⠀⠀⠀⣹⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠛⢀⡶⠀⠿⠿⢿⡿⢿⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⠀⠀⣸⠁⠀⠀⠀⢀⠈⢻⣷⣶⣤⣦⣶⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⣀⣼⣧⣀⣈⣉⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣠⣴⣥⡀⠀⠀⢰⣾⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠻⠿⢿⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⡀⢀⣼⣿⣿⣿⠃⡀⠐⣿⣿⣷⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⢻⣿⡙⣿⣿⣿⣿⣿⡄⠀⣀⠀⠀⠀⢈⣤⣴⣾⣿⣿⡿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⢧⣾⣿⣿⣿⣿⠀⠸⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠙⢿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢸⣿⠃⣿⣿⣿⣿⣿⣷⣤⣽⡆⠴⣿⣻⣿⣷⣿⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⣾⡇⢠⣶⡿⣷⣯⣿⣷⣶⣾⣶⣿⢾⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⢸⣿⡿⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠘⡏⠉⠃⠀⠀⠀⢰⣏⣈⣿⣿⣿⡿⠟⠋⢁⣀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⢻⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡇⢠⣾⣿⣿⣥⡀⠀⠀⠀⠀⠋⠿⢿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢸⣿⣧⡇⢸⣿⣇⣿⣿⡊⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢠⣤⡄⣤⣍⢭⢩⢹⡟⡍⢲⢂⡎⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⡎⠉⠉⠁⠀⠉⠉⠉⠁⢫⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣸⣣⣇⡻⣜⣜⣚⣿⣻⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠉⠀⠀⠐⠷⢶⣿⣿⢿⢗⣟⣛⣿⣟⣻⢻⢭⣻⡿⢿⣭⣯⡍⣽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡷⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⣿⠷⣶⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⣛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠘⣿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠨⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠰⣾⣿⣾⣶⣿⣶⣶⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠟⠁⠉⠉⠙⢻⠛⠻⠛⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⢁⡾⠁⠀⠀⠀⣤⣤⣤⣶⣶⣧⣌⠻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠛⠛⠛⠛⠛⡛⠛⠛⠿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠘⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⡀⠀⠀⠀⢀⣀⡀⢀⡀⣰⣷⣀⢀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⠀⠀⠀⠀⠀⠰⣿⠿⢿⢿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣇⠀⠀⠀⠀⠙⠻⡿⠳⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⡠⣛⢤⠀⠛⣧⠘⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠛⠀⠠⠤⠿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠰⢾⣶⣿⡇⠈⢿⣷⣿⣿⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⣻⣿⠔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣄⠀⠀⠀⠀⠻⣻⣿⠋⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠛⠛⠋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣾⣿⡆⠀⠀⣤⣬⠁⡏⠀⣾⣿⣿⡇⠀⣼⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⢿⣿⣙⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⠃
⢠⣿⡿⠃⠀⠀⠉⠻⣿⣧⡇⣼⣿⡿⠃⠀⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⠙⠏⣾⣿⣿⣿⣿⣆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠰⠿⣿⠇
⠈⠙⠀⠀⠀⠀⠀⠀⠀⢙⠗⡿⢿⡗⠀⠀⠀⣹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠛⢀⣶⠀⠽⠿⢿⡿⢿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣦⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣸⠁⠀⠀⠀⢀⠈⢿⣷⣖⣴⣶⣶⣦⣄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣀⣈⣙⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣠⣥⣄⡀⠀⠀⢰⣾⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠺⠟⢿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣄⡀⢀⣼⣿⣿⣿⠇⣀⠘⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⢺⣿⠙⣿⣿⣿⣿⣿⣄⠀⢀⠀⠀⠀⢈⣤⣴⣾⣿⣿⡿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣽⢀⣾⣿⣿⣿⡟⠀⠸⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠿⢿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢸⡿⠃⣿⣿⣿⣿⣿⣿⣤⣼⡆⠴⣿⣹⣿⣷⣿⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⣾⠇⢠⣶⡿⣷⣿⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⢸⣿⡟⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡏⠀⠁⠀⠀⠀⢰⣏⣈⣿⣿⣿⡿⠟⠋⠁⡀⠀⠀⠀⠀⠈⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⢼⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⢿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⢠⣾⣿⣿⣤⡀⠀⠀⠀⠀⠛⠿⢿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣻⣿⣿⢸⣿⣧⡇⢸⣿⣇⣿⣿⣈⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⣤⡄⣤⣌⢭⢩⢹⡟⡍⢲⢂⡄⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⡎⠉⠉⠁⠀⠉⠉⠉⠁⢩⣽⣿⣿⣿⣿⣿⣿⣯⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⣿⣸⣧⣇⡻⣜⣜⣚⣿⣻⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢗⣟⣛⣿⣟⣻⢻⢽⣫⡿⢿⣭⣯⡍⣽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡷⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⣿⠷⣶⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠘⢿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠨⢿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢠⣾⣿⣾⣶⣿⣶⣶⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠋⠀⠉⠉⠛⢻⠛⠻⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢡⡟⠀⠀⠀⢀⣤⣤⣤⣶⣶⣷⣌⠻⣿⣿⣿⣿⠇⠀⠀⠀⠀⠛⠛⠛⠛⠛⡛⠛⠻⠿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠘⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⠀⣀⣸⣷⣀⢀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⠀⠀⠀⠀⠀⠸⣿⡿⡿⢿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣇⠀⠀⠀⠀⠘⠿⡿⠿⠚⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⡰⣣⣆⠈⠻⣧⠸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠛⠀⠠⠴⠿⠎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠲⢷⣶⣿⡆⡉⣿⣷⣿⡿⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⣻⣿⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣰⣄⠀⠀⠀⠘⢻⣿⣿⠋⣿⣿⣿⡗⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠛⠛⠋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⡄⠀⢀⣠⣌⢁⡏⠀⣿⣿⣿⡇⢀⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⢿⣟⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⠃
⢠⣿⠿⠁⠀⠈⠙⢻⣿⣤⡃⣿⣿⡿⠁⠈⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⠹⠟⣾⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠴⠿⣿⠇
⠈⠉⠀⠀⠀⠀⠀⠀⠈⣹⢳⡿⢿⡇⠀⠀⠀⣽⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠋⢀⣶⠀⠽⠿⢿⡿⢿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣦⣤⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠈⠀⣺⠀⠀⠀⠀⣀⠉⢲⣿⡖⣴⣦⣶⣦⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣼⣦⣀⣈⣹⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣰⣭⣄⠀⠀⠀⣼⣿⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠺⠿⢿⠯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣄⡀⢀⣼⣿⣿⣿⠃⡀⠸⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⢹⣿⠙⣿⣿⣿⣿⣿⣄⠀⢀⠀⠀⠀⢈⣤⣶⣾⣿⣿⡿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⢰⣿⣿⣿⣿⡟⠀⠑⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢸⣿⠃⣿⣿⣿⣿⣿⣿⣤⣼⡆⠴⣿⣻⣿⣷⣿⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⣾⠃⢠⣶⡿⣷⣯⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⢸⣿⡏⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⡟⠉⠃⠀⠀⠀⢸⣇⣼⣿⣿⣿⡿⠟⠋⢀⣀⠀⠀⠀⠀⠈⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⢠⣾⣿⣿⣦⡀⠀⠀⠀⠀⠋⠿⢿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢸⣿⣧⡇⢸⣿⣇⣿⣿⣙⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢠⣤⡄⣤⣌⢭⢩⢹⡟⡍⢲⢂⡎⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢼⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⡌⠉⠉⠁⠀⠉⠉⠉⠁⢫⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣼⣧⣇⡻⣜⣜⣚⣿⣿⣧⣷⣽⣯⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢇⣟⣛⣿⣟⣻⢻⢽⣻⡿⢿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡷⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡷⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⡿⠳⣶⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠙⢿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠨⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢰⣿⣿⣿⣾⣷⣶⣾⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠋⠀⠉⠉⠛⣿⠛⠿⠻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢰⡏⠀⠀⠀⢠⣤⣤⣴⣶⣾⣦⡈⢻⣿⣿⣿⣿⠃⠀⠀⠀⠐⠛⠛⠛⠙⠛⡛⠛⠛⠿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠛⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⡀⢀⢀⣸⣧⣀⢀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⠀⠀⠀⠀⠀⠿⣿⣿⡿⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠙⠿⡿⠗⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⣀⡀⠃
⠀⠀⠀⠀⠀⠀⠉⠀⢀⠸⡣⡆⠈⢻⡆⢻⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠋⠀⠠⠼⠿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠐⠳⢷⣾⣿⡄⡙⣿⣾⣿⡇⠈⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⠉⢻⣿⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣠⡀⠀⠀⠀⠘⣛⣿⣿⢙⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⠀⠀⢠⣤⣌⢰⠁⠰⣿⣿⣿⠁⢠⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⢿⣟⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠁
⢰⣿⢿⠀⠀⠈⠙⢿⣿⣴⠀⣿⣿⡟⠀⠘⢿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⠹⠟⣾⣿⣿⣿⣿⣏⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠴⠿⣿⡇
⠈⠉⠀⠀⠀⠀⠀⠀⠉⠻⢸⠿⣿⠇⠀⠀⠀⣿⣷⣧⢀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠋⢀⡶⠀⠽⠿⢿⡿⢿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣦⣤⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠘⢀⣿⠀⠀⠀⠀⡀⠈⢵⣾⣶⣴⣶⣶⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣼⣦⣀⣈⣙⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣴⣯⣄⠈⠀⠀⣼⣿⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠺⠿⢿⠏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⣄⠀⣠⣾⣿⣿⣿⠀⡀⢸⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⠹⣿⣿⣿⣿⣷⡄⠀⢀⠀⠀⠀⢈⣤⣶⣾⣿⣿⡿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠿⢰⣿⣿⣿⣿⡇⠀⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠿⣿⣿⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⢸⢿⠀⣿⣿⣿⣿⣿⣿⣤⣽⡆⠴⣿⣻⣿⣷⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢰⣶⣾⢸⣿⣾⠁⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢸⡏⠉⠁⠀⠀⠀⢸⣏⣺⣿⣿⣿⡿⠟⠋⢁⣀⠀⠀⠀⠀⠘⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡆⢠⣾⣿⣿⣥⡀⠀⠀⠀⠀⠻⠿⣿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣻⣿⣿⢸⣿⣷⡄⢸⣿⣇⣿⣿⣙⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢠⣤⡄⣤⣍⢭⢩⢹⡟⡍⢲⢂⡎⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⠌⠉⠉⠁⠀⠉⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣸⣧⣇⣻⣜⣜⣚⣿⣿⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢇⣟⣛⣿⣟⣻⢻⢽⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡷⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⡿⠳⣶⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢹⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠘⢿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠨⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢰⣿⣿⣿⣾⣿⣶⣶⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠿⠋⠈⠉⠉⠛⡿⠛⠟⠻⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢰⠏⠀⠀⠀⢠⣤⣤⣴⣶⣾⣦⡈⢻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠛⠛⠛⠙⠛⡛⠛⠛⢿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠛⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⠀⣀⣸⣧⣀⢀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢿⡇
⠀⠀⠀⠀⠀⠾⣿⠿⠿⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⣿⠿⠗⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⠀⣀⡈⠃
⠀⠀⠀⠀⠀⠀⠉⠀⢀⢸⣣⡆⠈⢻⡆⢻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠋⠀⠠⠼⠿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠐⠻⢿⣿⣿⡄⡽⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠉⣻⣿⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣤⡀⠀⠀⠀⠘⢻⣿⣿⢹⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠛⠛⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⠀⠀⢠⣤⣍⢰⠃⠰⣿⣿⣿⠁⢠⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣿⣿⢿⣿⣹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁
⢰⣿⠿⠀⠀⠈⠙⢿⣿⣼⢀⣿⣿⡟⠀⠘⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⠙⠛⣾⣿⣿⣿⣿⣧⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠰⠿⢿⡇
⠘⠋⠀⠀⠀⠀⠀⠀⠉⠻⢺⠿⣿⠇⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠋⢀⡶⠀⠿⠿⢿⡿⢿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣦⣤⡅
⠀⠀⠀⠀⠀⠀⡀⠀⣼⠇⠘⢀⡿⠀⠀⠀⠀⣀⡉⢽⣾⣶⣶⣶⣶⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⡀⣀⣼⣧⣄⣀⣭⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣴⣤⣄⠈⠀⠀⣾⣿⠀⠀⠀⣹⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠺⠟⢿⠯⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⣄⠀⣠⣾⣿⣿⡿⠀⡀⢸⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⠙⣿⣿⣿⣿⣷⡄⠀⢀⠀⠀⣀⣈⣤⣶⣾⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠽⢰⣿⣿⣿⣿⡇⠀⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠿⣿⣿⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⢸⢿⠀⣿⣿⣿⣿⣿⣿⣤⣿⡆⠾⣿⣹⣿⣿⣿⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢰⣶⣾⢸⣿⣾⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡏⠉⠁⠀⠀⠀⢸⣷⣼⣿⣿⣿⡿⠟⠋⣁⣀⠀⠀⠀⠀⠘⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡆⢀⣾⣿⣿⣧⡄⠀⠀⠀⠐⠫⠿⢿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢽⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢠⣤⡄⣤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⣧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢼⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⠌⠉⠉⠁⠀⠉⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣸⣧⣇⣻⣜⣜⣚⣿⣿⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢇⣟⣛⣿⣟⣻⢻⢽⣫⡿⢿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⠸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⡿⠳⣶⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢻⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠘⢿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠊⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠿⡿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢰⣿⣿⣿⣿⣿⣶⣾⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡿⣿⠟⠉⠈⠉⠉⠋⢿⠙⠛⠻⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⣰⠏⠀⠀⠀⢠⣶⣤⣶⣶⣾⣦⡈⢻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠙⠉⠉⠙⠛⡋⠛⠛⢻⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠋⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣀⡀⡀⣸⣧⣀⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢿⡇
⠀⠀⠀⠀⠀⠾⠿⠿⠿⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⠿⠿⠓⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⠀⣀⣀⠁
⠀⠀⠀⠀⠀⠀⠉⠀⢀⢸⣳⡆⠈⢻⡆⢻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠉⠀⠀⠾⠿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇
⠀⠀⠀⠀⠐⠻⢿⣿⣿⢄⡼⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⢈⠉⣹⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣤⡀⠀⠀⠀⠘⢿⣿⣿⢩⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠛⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⠀⠀⢠⣤⣌⢠⠃⠠⣿⣿⣿⠁⢠⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⢿⣿⣭⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⠁
⢰⣿⠿⠀⠀⠈⠙⢻⣿⣼⢀⣿⣿⡟⠀⠘⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡞⠙⠋⣾⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠰⠿⢿⡇
⠘⠋⠀⠀⠀⠀⠀⠀⠉⠻⢸⠟⣿⠇⠀⠀⠀⣿⣿⣧⢀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠋⠀⡶⠀⠿⠿⢿⡿⠿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⠀⢠⡿⠀⠀⠀⢀⣄⡈⣼⣿⣶⣴⣶⣶⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣀⣀⣼⣧⣄⣠⣬⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⢀⣾⣏⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠺⠟⢿⠯⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⣄⠀⣠⣿⣿⣿⡿⠀⡀⢸⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⠸⣿⣿⣿⣿⣷⡤⠀⣀⠀⠀⣀⣈⣴⣶⣾⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠿⢶⣿⣿⣿⣿⡇⠀⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠿⢿⡿⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⠿⠀⣿⣿⣿⣿⣿⣷⣤⣿⡆⠾⣿⣙⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⢰⣶⣾⢸⣿⣾⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⢾⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⡏⠉⠁⠀⠀⠀⢸⣿⣾⣿⣿⣿⡿⠟⠋⣀⣀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡆⢠⣾⣿⣿⣧⡄⠀⠀⠀⠀⠫⠿⣿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢸⣿⣯⡅⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⢠⣤⡄⣤⣍⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⠌⠉⠉⠁⠀⠉⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣸⣧⣇⡻⣜⣜⣚⣿⣻⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢇⣟⣛⣿⣟⣻⢻⢭⣫⡿⢿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⠸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⡿⠲⣶⠈⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠼⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⡟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣶⣾⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠟⠁⠈⠉⠉⠫⠯⠛⡛⠻⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣸⠃⠀⠀⠀⣠⣶⣴⣶⣶⣾⣦⡈⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠛⠉⠉⠉⠙⡋⠛⠛⣻⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠃⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣀⣀⣀⣼⣷⣄⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⡇
⠀⠀⠀⠀⠀⠿⠿⠿⠿⢿⡿⢿⣿⣿⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠉⢻⣿⠛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⣀⡀⠁
⠀⠀⠀⠀⢀⠀⠁⠀⢀⢞⣲⡄⠈⣻⡆⢹⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠉⠀⠀⣺⡿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠻⢿⣿⣷⢄⢼⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢈⡉⣹⣿⢆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣤⡀⠀⠀⠀⠘⣟⣿⡏⢹⣿⣿⣿⡃⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⠀⣿⣿⠀⠀⢠⣤⣍⠸⠁⢸⣿⣿⣿⠀⢰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⢿⣯⣽⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢈⠁
⢸⣿⠿⠀⠀⠈⠙⢿⣷⣬⢸⣿⣿⠟⠀⠘⢿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠟⠙⠛⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠐⠻⠿⠇
⠘⠃⠀⠀⠀⠀⠀⠀⠉⡿⢺⠟⣿⠁⠀⠀⠀⣿⣿⣧⠄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⠋⠠⡷⠀⠻⠿⢿⠿⠿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣴⡄
⠀⠀⠀⠀⠀⠀⡄⠀⢸⠃⠘⢀⡏⠀⠀⠀⣀⣄⣠⣮⣷⣿⣶⣷⣶⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⣀⣾⣷⣄⣤⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣼⣤⣆⠀⠀⢀⣷⣇⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠛⠛⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣄⠀⣠⣿⣿⣿⡟⠀⡀⢻⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⠘⣿⣿⣿⣿⣷⡄⠀⣀⠀⠀⣀⣨⣴⡶⣿⣿⣿⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⠙⢶⣿⣿⣿⣿⠃⠀⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠿⣿⡿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠿⠀⣿⣿⣿⣿⣿⣷⣤⣿⡆⠾⣿⣹⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡾⠀⢠⣶⡿⣷⣿⣿⣷⣶⣶⣶⣿⢾⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠈⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠈⠁⠀⠀⠀⢸⣻⣼⣿⣿⣿⡿⠛⢋⣁⣀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡄⢠⣾⣿⣿⣧⡄⠀⠀⠀⠀⠩⠿⣿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣤⡄⣤⣍⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⣧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⠈⠉⠉⠁⠀⠉⠉⠉⠁⣯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⣿⣺⣧⣇⡻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢇⣟⣛⣿⣟⣻⢻⢭⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⡿⠲⣶⠀⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠿⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠈⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢿⡟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣶⣾⣿⣷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠟⠁⠈⠉⠉⠫⡯⠛⡋⠻⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣸⠃⠀⠀⠀⣠⣶⣴⣶⣶⣿⣤⡘⢿⣿⣿⣿⣿⠃⠀⠀⠀⠈⠉⠉⠉⠉⠙⡋⠛⠛⢻⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠃⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡗⠈⣿⣿⣿⣿⡀⠀⠀⠀⢀⣠⣀⣀⣀⣼⣷⣄⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠿⠿⠿⠿⣿⡿⢿⣿⣷⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⢿⣟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⣀⣀⡃
⠀⠀⠀⠀⠀⠀⠁⠀⢀⢚⣲⡄⠈⣻⡄⢻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠉⠀⠀⣺⡿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠻⢿⣿⣷⢀⢼⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢈⣉⣹⣿⢆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣤⡀⠀⠀⠀⠘⣟⢿⡏⢹⣿⣿⣿⠃⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⠐⣿⣿⠀⠀⢠⣤⡀⡸⠁⢸⣿⣿⣿⠀⣰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⢿⣯⣭⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⢈⠁
⢸⣿⠟⠀⠀⠈⠙⢿⣧⣬⢸⣿⣿⠛⠀⠘⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠟⠙⠛⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠐⠿⢿⡇
⠘⠃⠀⠀⠀⠀⠀⠀⠈⡛⢻⠛⣿⠀⠀⠀⠠⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⠋⠠⡶⠀⠻⠿⢿⠿⠿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠃⠀⢠⡏⠀⠀⠀⣀⣀⣀⣼⣿⣾⣶⣶⣶⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⣄⣾⣷⣄⣤⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣴⣦⣄⠀⠀⢀⣿⣇⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠻⠛⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⣤⠀⣠⣿⣿⣿⡟⢠⡀⢻⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⢸⣿⠹⣿⣿⣿⣿⣷⡄⠀⣀⠀⠀⣀⣨⣴⡶⣿⣿⣿⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⠉⢶⣿⣿⣿⣿⠃⠀⠃⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠿⣿⡿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠿⠀⣿⣿⣿⣿⣿⣷⣤⣿⡆⠾⣿⣹⣿⣿⣟⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡾⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⢾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⢠⡟⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⡏⠀⠁⠀⠀⠀⢸⣿⣼⣿⣿⣿⡿⠛⠋⣁⣀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢺⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠀⢠⣾⣿⣿⣷⡄⠀⠀⠀⠀⠩⠿⢿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢿⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⢠⣤⡄⣤⣌⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣾⣧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⠈⠉⠉⠁⠀⠉⠉⠉⠁⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⣿⣸⣧⣇⡻⣜⣜⣚⣿⣻⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢇⣟⣛⣿⣟⣻⢻⢭⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⡟⠲⣶⠀⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠻⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠞⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠈⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠿⠟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢿⣿⠟⠁⠉⠉⠉⠫⠯⠛⡋⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣼⠁⠀⠀⠀⣰⣶⣴⣶⣶⣿⣤⡘⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠉⠉⠉⠉⢙⡉⠛⠛⣻⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠃⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⠀⠀⠀⠀⢀⣠⣀⣀⣀⣼⣧⣄⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠿⠿⠿⠿⣿⡿⢿⣿⣷⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠉⠿⣿⠛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⣀⣀⡁
⠀⠀⠀⠀⠀⠀⠁⠀⣀⢚⣲⡀⠉⣻⡆⢻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠉⠀⠀⣺⡿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠻⢿⣿⣷⢠⢽⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣉⣽⣿⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣤⡀⠀⠀⠀⠛⣿⢿⡏⢹⣿⣿⣿⠁⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠛⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⢸⣿⣿⠀⠀⣠⣤⡄⡼⠀⢸⣿⣿⣿⠀⣰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⢿⣯⣽⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠁
⢸⡿⠏⠀⠀⠉⠙⢷⣧⣦⢸⣿⣿⠋⠀⠘⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠟⠙⠙⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠐⠻⠿⡇
⠘⠃⠀⠀⠀⠀⠀⠀⠉⡟⢿⠛⣿⠀⠀⠀⠀⣿⣿⣧⠄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠙⠋⢠⡿⠀⠻⠟⢿⠟⠿⢿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢸⡇⠀⠀⠀⣀⣀⣀⣾⣾⣿⣷⣶⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣀⣀⣄⣿⣷⣤⣤⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣾⣤⣄⠀⠀⢀⣿⣇⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠛⠛⢿⠯⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⣄⠀⣰⣿⣿⣿⡟⢠⡀⢻⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⠸⣿⣿⣿⣿⣷⡄⠀⣀⠀⠀⣄⣨⣶⡶⣿⣿⣿⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠰⡅⣾⣿⣿⣿⣿⠃⠀⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠻⠿⣿⠟⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠸⠿⠀⣿⣿⣿⣿⣿⣷⣤⣿⡆⠾⣿⢹⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⢰⣶⣾⢸⣿⡞⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠈⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⢠⡟⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠈⠁⠀⠀⠀⢸⣿⣼⣿⣿⣿⠿⠛⢉⣀⣀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢾⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣷⡄⠀⠀⠀⠀⠩⠿⣿⠿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢠⣤⡄⣤⣌⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⠈⠉⠉⠁⠀⠉⠉⠉⠁⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⣿⣺⣧⣇⡻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢗⣟⣛⣿⣟⣻⢻⢭⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⢻⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠜⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠈⢻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡿⠟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣾⣿⣷⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢿⣿⠟⠁⠉⠉⠉⠫⠯⠛⡋⠻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣼⠁⠀⠀⠀⣰⣶⣤⣶⣶⣿⣤⡘⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠉⠉⠉⠉⢙⡉⠛⠛⣻⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠃⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⠀⠀⠀⠀⢀⣠⣀⣀⣀⣼⣧⣄⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠿⠿⠿⠿⣿⡿⢿⣿⣧⢀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠉⠿⣟⠛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⣀⣀⡁
⠀⠀⠀⠀⠀⠀⠁⠀⣀⢾⣲⡀⠉⣿⡂⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠀⠐⣚⡟⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠻⢿⣿⣷⢀⢹⣿⣿⣿⠁⠘⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⣉⣽⣿⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣤⡀⠀⠀⠀⠚⣿⢿⡏⢹⣿⣿⣿⠁⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠛⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⠘⣿⣷⠀⠀⣠⣤⡁⡼⠀⢸⣿⣿⣿⠀⣸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⢻⣿⣽⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⢀⡈⠁
⢸⡿⠏⠀⠀⠉⠙⢿⣧⣆⢸⣿⣿⠃⠀⠘⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠟⠙⠋⣿⣿⣿⣿⣿⣧⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠐⠻⢿⡇
⠘⠃⠀⠀⠀⠀⠀⠀⢉⡟⡿⠛⣿⠀⠀⠀⠠⣿⣿⡧⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠛⠁⢠⡷⠀⠻⠟⢿⠟⠿⢿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢸⡇⠀⠀⠀⣐⣀⣠⢼⣿⣿⣶⣶⣾⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣀⣀⣀⣤⣿⣷⣤⣤⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢠⣾⣦⣄⠀⠀⢠⣿⣇⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠻⠛⢿⠫⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢄⠀⣰⣿⣿⣿⡏⢠⠀⢻⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⠸⣿⣿⣿⣿⣷⡄⠀⣀⠀⠀⣀⣠⣶⡾⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠖⣾⣿⣿⣿⣿⠁⠀⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠛⠿⠿⠛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⠿⠀⣿⣿⣿⣿⣿⣷⣤⣿⡆⠾⣯⣽⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⢰⣶⣾⢸⣿⡞⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⢾⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣿⡇⠀⠀⠀⢠⡿⢻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠁⠀⠀⠀⢸⣿⣼⣿⣿⣿⠿⠛⢉⣀⣀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡁⢰⣿⣿⣿⣷⡄⠀⠀⠀⠀⠹⠿⡿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣤⡄⣤⣌⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⠈⠉⠉⠁⠀⠉⠉⠉⠑⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⣿⣺⣣⣇⡻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢗⣟⣛⣿⣟⣻⢻⢭⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠈⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠻⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠊⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠈⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣾⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢿⡿⠋⠁⠉⠙⠙⠹⠋⠛⡙⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡾⠁⠀⠀⠀⣴⣦⣴⣶⣶⣷⣤⡙⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠉⠉⢙⡉⠛⠛⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠃⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠠⣤⣀⣀⢀⣼⣧⣄⣐⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠿⠿⠿⠿⣿⡿⣿⣿⣇⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⠿⡟⠛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⡀⢻⣲⠀⢉⣿⠂⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠀⠐⣚⡟⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠻⢿⣿⣷⢀⢿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣉⣽⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⣤⡀⠀⠀⠀⠻⣿⣿⠏⢹⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠛⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡇
⠸⣿⣧⠀⠀⣤⣴⡀⡛⠀⢾⣿⣿⣷⠀⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣯⣽⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⠈⠁
⢸⡿⠇⠀⠀⠉⠛⣿⣧⡇⣸⣿⣿⠃⠀⠘⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠏⡝⠙⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠒⠿⠿⠇
⠘⠁⠀⠀⠀⠀⠀⠀⢈⠇⡿⢻⡿⠀⠀⠀⠰⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠛⠁⠰⠟⠀⠻⠿⢿⠟⠿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠁⢸⡇⠀⠀⢀⣀⣀⡀⢼⣿⣷⣦⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣀⣀⣤⣿⣷⣤⣤⣬⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣶⣦⣄⠀⠀⣰⣿⡇⠀⠀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠛⠛⢿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡀⠀⣴⣿⣿⣿⡏⢠⠀⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢹⣿⠸⣿⣿⣿⣿⣷⡄⠀⣀⠀⢀⣀⣡⣶⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⠸⣿⣿⣿⣿⣿⠀⠈⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⠻⠿⠿⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡆⠁⢸⠿⠀⣿⣿⣿⣿⣿⣧⣤⣿⡆⠿⠯⡽⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⢰⣶⣾⢸⣿⡎⠀⢠⣶⣿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠉⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⢠⡿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠁⠀⠀⠀⣸⣷⣾⣿⣿⣿⠟⠛⢉⣀⣀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣼⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣠⢰⣿⣿⣿⣶⡄⠀⠀⠀⠀⠱⠿⢿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣤⡄⣤⣜⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⣿⣺⣧⣇⡻⣜⣜⣚⣿⣿⣧⣷⣽⣯⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢗⣟⣛⣿⣟⣛⢻⢭⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠈⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢻⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠻⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠊⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠈⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣾⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢿⡿⠋⠁⠉⠙⠙⠹⠋⢛⡛⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡾⠁⠀⠀⠀⣴⣦⣴⣶⣶⣷⣤⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠉⠉⢙⡉⠛⠛⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠃⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠠⣤⣀⣀⢀⣾⣧⣄⣐⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⡇
⠀⠀⠀⠀⠰⠿⠿⠿⠿⣿⠿⣿⣿⡇⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⠿⡟⠛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣠⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣛⣲⠀⢙⣷⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠁⠀⢐⣚⡟⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠿⣿⣿⡧⣀⢿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣉⣽⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⣤⡀⠀⠀⠀⠻⡻⣿⠏⢿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠛⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⠸⣿⡇⠀⠀⣤⣴⠀⡛⠀⢿⣿⣿⣷⠀⣼⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⡿⣿⣯⣽⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⡈⠁
⢸⡿⠇⠀⠀⠉⠛⢿⣧⡇⣸⣿⣿⠃⠀⠘⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡙⠙⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠘⠻⢿⠇
⠘⠁⠀⠀⠀⠀⠀⠀⢈⠇⡿⢛⡿⠀⠀⠀⠸⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠙⠁⠰⠗⠐⠛⠿⣿⠟⠿⢿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢸⡇⠀⠀⢀⣀⣀⣀⢼⣿⣶⣶⣶⣶⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣀⣀⣤⣿⣷⣤⣤⣬⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣾⣦⡄⠀⠀⣰⣿⡇⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠛⠛⢿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣴⣿⣿⣿⠇⢠⠀⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡿⢸⣿⠸⣿⣿⣿⣿⣷⡄⠀⡀⠀⢀⣀⣡⣶⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⠪⣾⣿⣿⣿⣿⠀⠈⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠙⠻⢿⡿⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⠿⠀⣿⣿⣿⣿⣿⣷⣤⣿⡄⠿⡯⢽⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⢰⣶⣾⢸⣷⡎⠀⢠⣶⣿⣿⣿⣿⣷⣶⣶⣶⣿⢾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⡿⣿⣿⣿⡇⠀⠀⠀⢰⣿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠁⠀⠀⠀⣸⣷⣾⣿⣿⣿⠿⠛⢉⣀⣀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣼⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠁⢰⣿⣿⣿⣶⡄⠀⠀⠀⠀⠹⠿⣿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣤⡄⣤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣺⣣⣇⣻⣜⣜⣚⣿⣿⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢖⣟⣛⣿⣟⣛⢻⢽⣻⡿⣿⣭⣯⡍⡭⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠻⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠚⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠈⢻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢿⡿⠋⠀⠉⠉⠙⠹⠉⢛⡛⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡾⠀⠀⠀⠀⣴⣶⣴⣶⣶⣷⣦⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠉⠉⢙⡉⠙⠛⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠃⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠠⣤⣄⣀⢤⣾⣧⣄⣰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⡇
⠀⠀⠀⠀⠸⠿⠿⠿⠿⣿⠿⣿⣿⡇⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠹⢿⡟⠛⠙⢛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⣀⣀⡁
⠀⠀⠀⠀⠀⠈⠀⠀⡀⣟⣶⠀⢙⣷⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⢀⣐⣚⡛⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠙⠿⣿⣿⡧⣀⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣈⣽⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⡀⠀⠀⠀⠻⣿⣿⠋⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⢸⣿⡇⠀⠀⣤⣤⠀⡛⠀⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣯⣽⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⣀⣈⠁
⢸⡿⠇⠀⠀⠉⠛⣿⣧⡇⣾⣿⣿⠃⠀⢹⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠹⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠘⠻⠿⡇
⠘⠁⠀⠀⠀⠀⠀⠀⢉⠃⡿⢻⡟⠀⠀⠀⠸⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠙⠁⢰⠗⠐⠛⠟⣿⠛⠿⢿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣾⡆
⠀⠀⠀⠀⠀⠀⡀⠀⡾⠀⠁⣸⡇⠀⠀⢀⣐⣀⣀⢽⣿⣿⣦⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣀⣀⣀⣤⣿⣷⣤⣤⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣾⣦⡄⠀⠀⣸⣿⡇⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠛⠛⢿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣴⣿⣿⣿⠇⢠⠈⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡟⢹⣿⠸⣿⣿⣿⣿⣷⡄⠀⡀⠀⢀⣀⣡⣶⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠭⣿⣿⣿⣿⣿⠀⠘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠙⠛⢿⡿⠟⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⠿⠐⣿⣿⣿⣿⣿⣧⣬⣿⡄⠿⡯⢽⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢰⣶⣾⢸⣿⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⡿⣿⣿⣿⡇⠀⠀⠀⢰⡿⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡟⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠁⠀⠀⠀⣸⣵⣼⣿⣿⣿⠟⠛⢉⣀⣄⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣠⢴⣿⣿⣿⣶⡄⠀⠀⠀⠀⠽⠿⣿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢾⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢠⣤⡄⣤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⣿⣺⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠉⠀⠀⠐⠷⢶⣿⣿⢿⢖⣟⣛⣿⣟⣻⢻⢭⣻⡿⣿⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⠸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠈⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⢻⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠚⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⡈⠈⢻⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣛⠛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡿⠋⠀⠉⠉⠉⠽⠝⢛⠙⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡿⠀⠀⠀⢀⣴⣶⣶⣶⣾⣷⣤⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠉⠉⢹⡉⠉⠙⢻⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠃⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⠀⠀⠀⠀⠠⣤⣄⣠⣠⣾⣧⣄⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠻⡇
⠀⠀⠀⠀⠸⠿⠿⠿⠿⣿⠿⢿⣿⡇⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⠟⡟⠉⠙⢛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⣠⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⡰⣓⣦⠈⢙⣷⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣐⣚⡛⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠘⠿⣿⣿⡆⣀⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣽⣿⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⡀⠀⠀⠀⢻⡻⣽⠉⣿⣿⣿⣟⠀⢀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⢸⣿⡇⠀⠀⣤⣴⠀⡏⠀⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣹⣿⡿⣿⣯⣽⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣈⠁
⢸⡿⠇⠀⠀⠉⠛⣿⣧⡇⣿⣿⣿⠁⠀⠙⢿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠟⢻⣿⣿⣿⣿⣿⣆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠘⠛⢿⠇
⠘⠁⠀⠀⠀⠀⠀⠀⢉⠃⡟⢻⡟⠀⠀⠀⠸⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠛⠁⢰⠟⠐⠛⠛⣿⠛⠿⣿⡎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⡀⠀⡾⠀⢁⣾⠁⠀⠀⢀⣠⣄⣤⢾⣿⣷⣶⣶⣶⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣀⣀⣠⣴⣿⣶⣤⣤⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣾⣦⡄⠀⠀⣸⣿⡄⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠛⠛⡟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡄⢀⣼⣿⣿⣿⠇⢠⠘⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡏⢸⣿⢸⣿⣿⣿⣿⣷⠄⢀⡀⠀⢀⣀⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠡⣿⣿⣿⣿⡿⠀⠘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠛⢿⠿⠋⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⠿⢸⣿⣿⣿⣿⣿⣧⣬⣿⡔⢿⠯⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢰⣶⣾⢸⣿⡆⠀⢠⣶⣿⣿⣿⣿⣷⣶⣶⣷⣿⣾⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⡿⣿⣿⣿⡇⠀⠀⠀⢸⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣸⣿⣿⢸⣿⡇⠀⢸⣿⡏⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠁⠀⠀⠀⣸⣥⣼⣿⣿⣿⠟⠛⢉⣀⡄⠀⠀⠀⠀⠈⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣽⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣀⣴⣿⣿⣿⣶⡄⠀⠀⠀⠀⠽⠿⣿⠿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢿⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢠⣤⡄⣤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡃⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢼⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⣿⣺⣣⣇⣻⣞⣜⣚⣿⣿⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠉⠀⠀⠰⠷⢶⣿⣿⢿⢖⣟⣻⣿⣟⣻⢻⢼⣻⡿⣿⣭⣯⡍⡭⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠇⠲⣶⠀⢶⠄⠰⠲⠶⠆⠀⠀⠀⠀⣻⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⣛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⢻⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠊⢯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⣀⣀⡀⢀⡀⠈⢻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣛⠛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡿⠋⠀⠉⠉⠙⠽⠝⢛⡙⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡿⠀⠀⠀⢀⣴⣶⣶⣶⣾⣷⣄⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠉⠉⢹⡉⠉⠙⢻⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠃⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⠀⠀⠀⠀⠠⣤⣄⣀⣠⣿⣧⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢻⡇
⠀⠀⠀⠀⠸⠿⠿⠿⠿⣿⠿⢿⣿⡇⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⠛⠋⠉⠙⢛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⣓⣶⠀⣙⣷⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣐⣛⡛⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠿⣿⣿⣆⡀⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣈⣽⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⡀⠀⠀⠀⢻⡻⣿⠉⣿⣿⣿⣟⠀⢘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⢸⣿⡇⠀⠀⣤⣤⢀⡏⠀⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣹⣿⡿⣿⣧⣼⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣈⠁
⢸⡿⠇⠀⠀⠀⠛⣿⣧⡇⣿⣿⣿⠁⠀⠙⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠏⢻⣿⣿⣿⣿⣿⣆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠘⠻⢿⠇
⠘⠁⠀⠀⠀⠀⠀⠀⢙⠃⡟⢻⡟⠀⠀⠀⠸⢿⣿⣷⠄⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠁⢰⠟⠀⠛⠛⣿⠛⠿⣿⡞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠁⢾⠁⠀⠀⢀⣠⣀⣀⢼⣻⣿⣶⣶⣶⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⣠⣴⣿⣶⣤⣤⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣷⣦⡀⠀⠀⣸⣿⡄⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⠛⡟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡀⢀⣴⣿⣿⣿⠇⢠⠈⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡏⢸⣿⢸⣿⣿⣿⣿⣷⠀⢀⡄⠀⢀⣀⣥⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⣿⣿⣿⣿⡿⠀⠘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠛⠻⠿⠏⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⠻⢸⣿⣿⣿⣿⣿⣧⣬⣿⡐⠿⡯⠿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢰⣶⣾⢸⣿⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⢾⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠘⠛⠻⢿⡿⣿⣿⣿⡇⠀⠀⠀⢸⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡟⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣸⣤⣼⣿⣿⣿⠟⠛⢉⣀⣄⠀⠀⠀⠀⠈⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣏⡀⣴⣿⣿⣿⣶⡀⠀⠀⠀⠀⠼⠿⣿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢿⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣟⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢠⣤⡄⣤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡃⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣺⣣⣇⣻⣞⣜⣚⣿⣿⣧⣷⣽⣯⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠉⠀⠀⠠⠷⢶⣿⣿⢿⢖⣟⣛⣿⣟⣻⢻⢽⣻⡿⣿⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠇⠲⣶⠀⠶⠄⠰⠲⠶⠆⠀⠀⠀⠀⢿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⣛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⢻⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⡤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠊⢯⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣀⣀⣀⣀⡀⠈⢻⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡛⠛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡿⠋⠀⠉⠉⠙⠽⠝⢛⡙⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡿⠀⠀⠀⢀⣴⣦⣶⣶⣾⣿⣤⠹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠉⠉⢹⡉⠉⠙⢻⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⠀⠀⠀⠀⠠⣤⣤⣀⡠⣾⣷⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠻⡇
⠀⠀⠀⠀⠸⠿⠿⠿⠿⣿⠿⢿⣿⡇⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⠛⣋⠉⠉⠛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⣠⣀⡁
⠀⠀⠀⠀⠀⠈⠀⠀⡐⢓⣦⠀⣙⣷⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣐⣚⣋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠿⣿⣿⣇⣈⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣽⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⡀⠀⠀⠀⢻⡹⣽⠁⣿⣿⣿⣟⠀⢘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⢸⣿⡇⠀⠀⣤⣴⠀⡏⠀⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣹⣿⡿⣿⣧⣼⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣈⠁
⢸⡟⠇⠀⠀⠀⠛⣿⣧⡇⣾⣿⡿⠁⠀⠙⢿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠏⢻⣿⣿⣿⣿⣿⣆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠘⠛⢿⠇
⠘⠁⠀⠀⠀⠀⠀⠀⢉⠃⡟⢛⡟⠀⠀⠀⠸⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠋⠁⢰⠗⠀⠛⠛⣿⠛⠿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠁⣸⠃⠀⠀⢀⣤⣄⣀⢾⣿⣷⣤⣶⣶⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣠⣤⣤⣿⣦⣤⣤⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣶⣤⡀⠀⠀⣸⣿⡀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠛⠛⡟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡀⢀⣴⣿⣿⣿⠇⢠⠈⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡟⢸⣿⠸⣿⣿⣿⣿⣧⠀⢀⡄⠀⢀⣄⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠑⣿⣿⣿⣿⡿⠀⠘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠛⠻⠿⠋⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⠛⢰⣿⣿⣿⣿⣿⣧⣬⣿⡔⠿⠯⠿⣿⣿⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠠⢰⣶⣾⢸⣷⡆⠀⢠⣶⣿⣿⣿⣿⣷⣶⣶⣶⣿⢾⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⡿⣿⣿⣿⡇⠀⠀⠀⢸⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡟⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣸⣤⣾⣿⣿⣿⠟⠋⢉⣀⣀⠀⠀⠀⠀⠈⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣯⣀⣰⣿⣿⣿⣶⡄⠀⠀⠀⠀⠼⠿⣿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣟⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢠⣤⡄⣤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⠃⡇⣷⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣺⣣⣇⣻⣞⣜⣚⣿⣿⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢔⣟⣛⣿⣟⣻⢻⢭⣻⡿⣿⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠇⠲⣶⠀⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢻⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⢻⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠊⢿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣀⣀⣀⣀⡀⠈⢻⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣛⠛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡿⠋⠀⠁⠉⠙⢽⠍⢛⡙⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⢀⣶⣦⣶⣶⣾⣿⣄⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠀⠈⢩⡉⠉⠉⢻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⣤⣤⣤⣠⣾⣷⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢻⡇
⠀⠀⠀⠀⠸⠿⠿⠿⠿⣿⠿⢿⣿⡇⢸⣿⣿⣿⣿⣇⡀⠀⠀⠀⠙⠋⡉⠉⠉⢛⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠀⣠⣀⡁
⠀⠀⠀⠀⠀⠈⠀⢀⡐⣓⣦⠀⣙⣷⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣛⣋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠘⠿⣿⣿⣆⣈⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣄⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⡀⠀⠀⠀⢻⡽⣿⠁⣿⣿⣿⣟⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⢸⣿⡇⠀⠀⣤⣤⢀⡏⠀⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣹⣿⡿⣿⣧⣾⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣈⡁
⢸⡟⠇⠀⠀⠀⠛⢿⣷⡇⣿⣿⣿⠁⠀⠙⢿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠟⢻⣿⣿⣿⣿⣿⣆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠘⠛⢿⡇
⠘⠁⠀⠀⠀⠀⠀⠀⢙⠓⠟⢻⡟⠀⠀⠀⠸⡿⢿⣷⡄⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠁⢰⠟⠜⠛⠛⣿⠛⠿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠁⢸⠃⠀⠀⢀⣤⣀⣄⣮⣷⣿⣶⣶⣶⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⣤⣴⣿⣶⣦⣤⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣷⣦⣀⠀⠀⣸⣿⡄⠀⢀⣠⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⠛⡟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡀⢀⣴⣿⣿⣿⠃⢠⠈⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡟⢸⣿⢸⣿⣿⣿⣿⣷⠀⢀⡀⠀⢀⣄⣥⣶⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⣿⣿⣿⣿⡿⠀⠘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠛⠻⠿⠋⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⠿⢸⣿⣿⣿⣿⣿⣧⣬⣿⡐⢿⣯⣿⣿⣿⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢰⣶⣾⢸⣿⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣷⣿⣾⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⡿⣿⣿⣿⡇⠀⠀⠀⢸⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡟⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⠀⠀⠀⠀⣸⣤⣾⣿⣿⣿⠟⠋⢁⣀⡀⠀⠀⠀⠀⠈⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣀⣰⣿⣿⣿⣶⡄⠀⠀⠀⠀⠼⠿⣿⠿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢻⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣟⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⢠⣤⡄⣤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣾⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡟⠈⠉⠉⠁⠀⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣺⣣⣇⣻⣞⣜⣚⣿⣿⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠠⠷⢶⣿⣿⢿⢔⣟⣛⣿⣟⣻⢻⢽⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⣗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠇⠲⣶⠀⠶⠄⠰⠲⠶⠆⠀⠀⠀⠀⢿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠻⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠠⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠂⢿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣀⣀⣀⣀⣀⠀⢹⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣟⣛⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡿⠋⠀⠁⠙⠘⠽⠍⢛⡙⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⢀⣶⣶⣶⣶⣿⣿⣤⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠁⠀⠈⢹⡍⠉⠉⢻⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⠀⠀⠀⠀⠠⣦⣤⣤⠀⣾⣷⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠻⡇
⠀⠀⠀⠀⠸⢿⠿⠿⠿⣿⠿⢿⣿⡇⢸⣿⣿⣿⣿⣇⡀⠀⠀⠀⠈⠉⠉⠉⠉⢛⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⣤⣀⡁
⠀⠀⠀⠀⠀⠀⠀⢀⠐⢓⣦⠀⢙⣷⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣉⣋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠿⣿⣿⣇⣜⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣄⣿⡿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⡀⠀⠀⠀⢹⡽⣽⠁⣿⣿⣿⣟⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⢸⣿⡇⠀⠀⣤⣤⢀⡏⠀⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⡿⣿⣧⣼⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣀⡁
⢸⡟⠇⠀⠀⠀⠛⢿⣷⡇⣼⣿⣿⠁⠀⠙⢻⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠏⢻⣿⣿⣿⣿⣿⣆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠘⠛⢿⡇
⠘⠁⠀⠀⠀⠀⠀⠀⢙⠃⡟⢻⡟⠀⠀⠀⠸⠿⢿⣷⡄⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠋⠀⢰⠏⠀⠛⠛⡿⠛⠿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡇
⠀⠀⠀⠀⠀⢀⠀⠀⡟⠀⠀⢼⠁⠀⠀⢀⣠⣠⣄⢦⣎⣟⣾⣶⣶⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⣤⣴⣿⣶⣤⣤⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣷⣆⡀⠀⠀⣸⣿⡄⠀⢀⣠⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠛⠻⡟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⠃⢠⠈⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⢸⣿⠘⣿⣿⣿⣿⣷⠀⢀⡀⠀⢀⣀⣥⣶⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⡿⠀⠘⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠛⠻⠿⠋⠋⠛⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠸⠛⢐⣿⣿⣿⣿⣿⣦⣼⣿⡐⢿⣯⣿⣿⣿⣯⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠠⢰⣶⣾⢸⣷⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⣿⢿⣿⣿⡇⠀⠀⠀⢸⡟⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡟⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣸⣤⣾⣿⣿⣿⠟⠋⢁⣀⣄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢺⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢀⣰⣿⣿⣿⣶⡄⠀⠀⠀⠀⠼⠿⣿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢼⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢠⣤⡄⣤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠱⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣺⣣⣇⣻⣜⣜⣚⣿⣿⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢀⣟⣛⣿⣟⣻⢻⢯⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠇⠲⣶⠀⠶⠄⠰⠲⠶⠆⠀⠀⠀⠈⢽⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠻⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠄⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠁⠻⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⡟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⢀⣀⣀⣀⣀⣀⠀⣻⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡛⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡿⠋⠀⠁⠙⠉⠽⠍⢛⡙⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⢀⣶⣦⣶⣶⣿⣿⣤⠙⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢩⡍⠉⠉⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠴⣦⣤⣤⣤⣿⣷⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠙⠻⡇
⠀⠀⠀⠀⠸⢿⠿⠿⠿⣿⠿⢿⣿⡇⢸⣿⣿⣿⣿⣧⡀⠀⠀⠀⠈⠉⠁⠉⠉⢙⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⣤⣀⡀
⠀⠀⠀⠠⠀⠀⠀⢀⠐⣗⣦⠀⣙⣷⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣨⣭⣭⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠿⣿⣿⣇⣘⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣤⣿⡿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⡀⠀⠀⠀⢹⡽⣽⠁⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⢸⣿⡇⠀⠀⣤⣴⢀⡏⠀⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⡿⣻⣯⣾⣿⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣀⠁
⢸⡟⠇⠀⠀⠈⠛⣿⣷⡇⣿⣿⣿⠁⠀⠙⢻⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠛⢻⣿⣿⣿⣿⣿⣆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠘⠛⠿⡇
⠈⠁⠀⠀⠀⠀⠀⠀⢙⠛⡟⢻⡏⠀⠀⠀⠸⡿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠋⠉⠀⢰⠟⠨⠛⠻⣿⠛⠿⣿⡞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣼⠁⠀⠀⢀⣠⣀⣄⣾⣅⣿⣷⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣀⣀⣠⣴⣿⣦⣤⣤⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣴⣦⡀⠀⠀⣸⣿⣄⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠛⠻⡟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡀⢀⣼⣿⣿⣿⠃⢠⠈⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠿⢸⣿⠘⣿⣿⣿⣿⣷⠀⢠⡄⠀⢀⣀⣥⣶⢿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠐⣾⣿⣿⣿⡿⠀⠘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠈⠛⠻⠿⠋⠊⠛⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⠛⠀⣿⣿⣿⣿⣿⣦⣾⣿⡰⠿⡯⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠠⢰⣶⣾⢸⣷⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⡿⢿⣿⣿⡇⠀⠀⠀⢠⡟⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣸⣿⣿⢸⣿⡇⠀⢸⣿⡟⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⣸⣤⣾⣿⣿⣿⠟⠋⢉⣀⣄⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⣰⣿⣿⣿⣷⡄⠀⠀⠀⠈⠼⠿⣿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢺⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣟⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢠⣤⡄⣤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣧⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡟⠈⠉⠉⠁⠀⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣺⣣⣇⣻⣞⣜⣚⣿⣿⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢄⣟⣛⣿⣟⣻⢻⢿⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠇⠲⣶⠀⠶⠄⠰⠶⠶⠆⠀⠀⠀⠈⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡋⠀⠀⠈⠻⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠄⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠁⠻⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⢀⣀⣀⣀⣀⣄⣀⣹⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡛⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡿⠋⠀⠁⠙⠉⠽⠍⢛⡙⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⢀⣶⣶⣶⣶⣿⣿⣤⠙⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡍⠉⠉⢽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡅⢸⣿⣿⣿⣿⡀⠀⠀⠀⠴⣦⣤⣤⣤⣿⣷⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠙⢻⡇
⠀⠀⠀⠀⠸⢿⠿⠿⠿⣿⠿⢿⣿⡆⢸⣿⣿⣿⣿⣧⡀⠀⠀⠀⠈⠉⠁⠉⠈⠙⣟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠐⢗⣦⠀⣙⣷⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣬⣭⣭⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠁⠿⣿⣿⣇⣘⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣤⣾⡿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⡀⠀⠀⠀⢹⠽⣹⠁⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⢸⣿⡇⠀⠀⣤⣴⠀⡏⠀⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⡿⣻⣯⣼⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣀⡁
⢸⡟⠃⠀⠀⠀⠛⣿⣷⡇⣾⣿⣿⠁⠀⠙⢻⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⢚⣶⣾⣯⣛⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠃⠛⢻⣿⣿⣿⣿⣿⣄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠘⠛⢿⡇
⠈⠁⠀⠀⠀⠀⠀⠀⢙⠛⡟⢻⡏⠀⠀⠀⠸⡿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢾⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠀⢰⠟⠘⠛⠛⡿⠛⠿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⢀⣼⠁⠀⠀⢀⣠⣀⢄⣐⠑⣵⢶⠷⢿⣷⣶⣾⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⢟⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣀⣀⣠⣴⣿⣦⣤⣤⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣰⣵⣦⡀⠀⠀⣸⣿⣄⠀⢀⣠⣿⣿⣹⣿⣸⣿⢈⣿⣿⡇⣶⢻⣯⢻⣿⣽⣿⣿⣿⣟⣛⡿⣸⠿⠻⣿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠛⠻⡟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡀⢀⣼⣿⣿⣿⠃⢠⠈⣿⣿⣿⣷⣾⣿⣿⣿⣿⢸⣏⣿⢸⣧⣿⢸⡟⣿⠋⣿⣸⡟⣿⢀⡛⢹⣏⡃⣿⡇⣾⡟⣸⣗⡊⣾⢻⡇⢤⣤⡄⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠐⣾⣿⣿⣿⡿⠀⠘⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⠉⠁⠉⠘⠣⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⣼⡿⣾⣿⢺⣇⣿⡐⢿⡯⣿⣿⣿⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣷⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⡿⢷⣶⣶⡇⠉⠈⠁⢛⡛⢘⣣⣿⣸⡼⢿⣿⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡟⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⣸⣵⣾⣿⣿⣿⠛⠋⢁⣀⣄⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢼⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⣰⣿⣿⣿⣷⡄⠀⠀⠀⠈⠾⠿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢠⣤⡄⡤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡟⠈⠉⠉⠁⠀⠉⠉⠉⠱⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢼⣇⠧⢟⢿⣺⣣⣇⣻⣞⣜⣚⣿⣿⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢀⣛⣛⣿⣟⣻⢻⢽⣻⡿⣿⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠇⠲⣶⠀⠶⠄⠰⠲⠶⠆⠀⠀⠀⠀⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡃⠀⠀⠈⠻⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠄⠀⠠⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠁⠻⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⢀⣀⣀⣀⣠⣄⣀⣹⣫⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡛⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢻⠿⠋⠀⠁⠉⠉⠽⠍⢛⡉⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡏⠀⠀⠀⢀⣶⣶⣶⣾⣿⣿⣤⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡍⠉⠉⢽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠠⣦⣤⣤⣠⣾⣷⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠙⢻⡇
⠀⠀⠀⠀⠸⢿⠿⠿⠿⣿⠿⢿⣿⡆⢸⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠉⠀⠉⠈⠉⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠐⢕⣦⠀⣙⣷⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⣬⣭⣥⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠁⠿⣿⣿⣇⣘⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣤⣿⡿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣤⠀⠀⠀⠀⢻⡹⣹⠁⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⢸⣿⡇⠀⠀⣤⣴⠀⡇⠀⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⡿⣿⣯⣼⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣀⡁
⢸⡟⠇⠀⠀⠀⠛⢿⣷⡆⣿⣿⡟⠁⠀⠙⢻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⢚⣶⡾⣯⣛⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠙⢳⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠘⠛⢿⡇
⠈⠀⠀⠀⠀⠀⠀⠀⢉⠛⠟⢻⡇⠀⠀⠀⠘⠿⢿⢷⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢾⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠀⢰⠟⠈⠛⠻⠿⠻⠿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⢀⣼⠁⠀⠀⢀⣠⣀⢄⣀⠉⣴⢶⠷⢾⣷⣶⣾⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⢟⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣀⣀⣀⣴⣷⣦⣠⣤⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣴⣄⠀⠀⠀⣸⣿⣄⠀⢀⣠⣿⣿⣹⣿⣸⣿⢈⣿⣿⡇⣶⢳⣯⢹⣿⣽⣻⣿⡿⣟⣛⡿⣸⠿⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⠻⡟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⠃⢤⠈⣿⣿⣿⣷⣿⣿⣿⣿⣿⢸⣇⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡻⢸⣏⡃⣿⡇⣾⡟⣸⣗⡊⣾⢻⡇⢤⣤⡄⠀⢀⣐⣡⣶⣾⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⡟⠀⠘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⠉⠁⠉⠸⠃⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⢿⢸⣇⣿⠐⠿⢯⣿⣿⣿⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠠⢰⣶⣾⢸⣷⡆⠀⢠⣶⣿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⡿⢶⣶⣶⡇⠉⠈⠁⢛⡛⢘⣣⣿⣸⡼⢿⣿⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡟⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⣸⣥⣼⣿⣿⣿⠛⠋⢁⣀⡀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⢰⣾⣿⣿⣦⡀⠀⠀⠀⠉⠾⠿⢿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢻⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣟⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⢠⣤⡄⡤⣍⢭⢩⢹⡟⡍⢲⠂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡟⠈⠉⠉⠁⠀⠉⠉⠉⠱⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇⡅⣿⣿⢸⣸⠄⡏⡆⢸⢴⣇⠧⢟⢿⣺⣧⣇⢻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢀⣛⣛⣿⣟⣻⢻⢽⣻⡿⣿⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⢸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠇⠲⣶⠀⠶⠄⠰⠲⠶⠆⠀⠀⠀⠀⢻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡃⠀⠀⠈⠻⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠁⠻⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣤⣠⣠⣤⣤⣀⣹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡛⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢻⠿⠋⠀⠁⠉⠉⠽⠍⢛⡉⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⢀⣶⣶⣶⣶⣿⣿⣤⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡍⠉⠉⢽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⡀⠀⠀⠀⠠⣶⣤⣤⣠⣿⣷⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠙⠻⡇
⠀⠀⠀⠀⠸⢿⠿⠿⠿⣿⠿⢿⣿⡆⢸⣿⣿⣿⣿⣧⡀⠀⠀⠀⠈⠉⠀⠉⠈⠉⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⣠⣀⡁
⠀⠀⠀⠀⠀⠀⠀⢀⠐⢕⣦⠀⣙⣷⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⣬⣭⣥⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠿⣿⣿⣇⣘⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣤⣿⡿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣤⠀⠀⠀⠀⢻⡽⢻⠁⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⢸⣿⡇⠀⠀⣤⣴⠀⡇⠀⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⡟⣻⣯⣽⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣀⡁
⢸⡟⠇⠀⠀⠀⠛⢿⣷⡇⣿⣿⡟⠁⠀⠙⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⢚⣶⡾⣯⣛⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠃⠙⢻⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠘⠛⢿⡇
⠈⠀⠀⠀⠀⠀⠀⠀⢉⠋⠟⢻⡏⠀⠀⠀⠘⠿⢿⢷⡄⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢾⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠀⢰⠇⠀⠿⠿⡿⠿⢿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣼⠁⠀⠀⢀⣠⣀⢀⣐⠑⣳⢲⠷⢾⣷⣶⣾⣿⣿⣯⣿⣧⣟⣻⣿⣻⠷⢟⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣀⣀⣠⣰⣷⣤⣠⣬⣥⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣰⣶⣤⡀⠀⠀⣸⣿⣄⠀⢀⣠⣿⣿⣹⣿⣸⣿⢈⣿⣿⡇⣶⢻⣏⢹⣿⣽⣿⣿⡿⣟⣛⡿⣸⠿⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⠻⡟⠽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⠃⢤⠈⣿⣿⣿⣷⣿⣿⣿⣿⣿⢸⣏⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡻⢸⣏⡃⣿⡇⣾⡟⣸⣗⡊⣾⢻⡇⢤⣤⡄⠀⢀⣐⣡⣶⣾⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⡟⠀⠘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⠉⠁⠉⠸⠃⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢸⡿⣾⣿⢾⣇⣿⠠⢿⣯⣿⣿⣿⣫⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡆⠀⢠⣶⣿⣿⣿⣿⣷⣶⣶⣷⣿⣾⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⡿⣶⣶⣶⡇⠉⠈⠁⢛⡛⢘⣣⣿⣸⣼⢿⣿⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡟⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡃⠀⠀⠀⠀⠀⣸⣷⣼⣿⣿⣿⠛⠋⠁⡀⡀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⢰⣾⣿⣿⣦⡀⠀⠀⠀⠉⠾⠿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢺⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣟⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢠⣤⡄⡤⣍⢭⢩⢹⡟⡍⢲⠂⡏⡆⣎⣶⡧⡇⡇⣿⢿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡟⠈⠉⠉⠁⠀⠉⠉⠉⠑⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢰⣇⠧⢟⢿⣸⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢀⣚⣛⣿⣟⣻⢻⢿⣻⡿⣿⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣩⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⣗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⢸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠇⠲⣶⠀⠶⠄⠰⠰⠶⠆⠀⠀⠀⠀⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣭⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡃⠀⠀⠈⠻⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠁⠻⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣟⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣤⣤⣤⣤⣤⣀⣹⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡛⢛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⣻⠿⠋⠀⠁⠉⠉⠽⠉⢙⡉⢻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡏⠀⠀⠀⢀⣶⣶⣶⣾⣿⣿⣦⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡍⠉⠉⠽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡀⠀⠀⠀⠠⣶⣤⣤⣤⣿⣷⣦⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠻⠇
⠀⠀⠀⠀⠸⢿⠿⠿⠿⣿⠿⢿⣿⡇⢸⣿⣿⣿⣿⣧⣀⠀⠀⠀⠈⠉⠀⠉⠈⢉⣯⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠐⢿⣦⡀⣉⣷⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠤⣤⣭⣥⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠟⣿⣿⣆⣘⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢠⣤⣾⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣤⠀⠀⠀⠀⢹⠽⣻⠁⣿⣿⣿⡏⠀⢨⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⢸⣿⡇⠀⠀⣤⣼⠠⠃⡀⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⡿⣿⣯⣽⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣀⡀
⢸⡟⠇⠀⠀⠀⠙⢿⣷⡇⣿⣿⡿⠁⠀⠙⢻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⢚⣶⡶⣯⣛⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠃⠛⢳⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠘⠛⠿⡇
⠈⠀⠀⠀⠀⠀⠀⠀⢹⠓⠟⢻⡇⠀⠀⠀⠘⠿⢿⣿⡆⠀⠀⠀⠀⢀⠀⢠⣴⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢾⣿⣿⣿⣿⣿⣿⡿⠉⠉⠋⠀⢰⠆⠈⠿⠻⡿⠿⢿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠎⠈⢀⣸⠁⠀⠀⢀⣀⣠⢀⣐⠈⣑⢶⠷⢾⣿⣶⣾⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⢟⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣀⣀⣀⣰⣷⣤⣠⣬⣥⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣴⣤⡄⠀⠀⣸⣿⣆⠀⢀⣠⣿⣿⣹⣿⣸⣿⢈⣿⣿⡇⣶⢳⣏⢻⣿⣽⣻⣿⡿⣟⣛⡿⣈⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⠻⡟⠽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⠃⢠⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⢸⣇⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣸⣗⡊⣾⢻⡇⢤⣤⡄⠀⢀⣀⣡⣶⣾⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠐⣾⣿⣿⣿⡿⠀⠘⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⠉⠁⠉⠸⠣⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢸⡿⣾⢿⢺⣇⣿⡀⢿⡏⣿⣿⣿⣫⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣷⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢶⣶⣶⡧⠉⠈⠁⢛⡛⢘⣣⣿⣸⡼⢿⣿⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡟⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣸⣧⣴⣿⣿⣿⠟⠉⠁⣀⠀⠀⠀⠀⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣯⠀⢠⣾⣿⣷⣦⡀⠀⠀⠀⠈⠾⠿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣟⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⡄⡤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⡎⣶⡧⡇⡇⣿⢿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠑⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡅⣿⣿⢸⣸⠄⡏⡆⢸⢄⣇⠧⢟⣿⣸⣧⣇⢻⣞⣜⣚⣿⣿⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢀⣚⣛⣿⣟⣻⢻⢽⣻⡿⣿⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠗⠲⣶⠀⠶⠄⠰⠲⠶⠆⠀⠀⠀⠀⢹⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡃⠀⠀⠈⠹⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠀⠠⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠻⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣤⣤⣤⣤⣦⣄⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡛⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⣻⠿⠉⠀⠁⠁⠈⠭⠍⠛⡉⢻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡏⠀⠀⠀⢀⣶⣶⣶⣾⣿⣿⣦⠙⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⠀⠈⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡄⠀⠀⠀⠰⣶⣶⣴⣶⣿⣿⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠻⡇
⠀⠀⠀⠀⠘⠿⠿⠿⠿⣿⠿⢿⣿⡇⢸⣿⣿⣿⣿⣧⣀⠀⠀⠀⠈⠉⠀⠉⠈⢉⣿⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢯⣶⡀⣉⣷⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠤⢤⣿⣥⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠑⠿⣿⣿⣇⣘⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣤⣾⡿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣤⡀⠀⠀⠀⠹⠽⣻⠁⣿⣿⣿⡯⠀⢀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⢸⣿⡇⠀⠀⣤⣴⣀⡏⡀⢿⣿⣿⡇⠀⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⡿⣿⣟⣽⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⣀⡀
⢸⡟⠇⠀⠀⠀⠙⢿⣷⡇⣾⣿⣿⠁⠀⠘⢻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⢛⣵⡶⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠋⠛⢳⣿⣿⣿⣿⣷⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠘⠛⢿⡇
⠈⠀⠀⠀⠀⠀⠀⠀⢈⠃⠟⢻⡟⠀⠀⠀⠘⠿⠿⣿⡆⠀⠀⠀⠀⣀⠀⢀⣴⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢺⣿⣿⣿⣿⣿⣿⣿⠉⠉⠋⠀⢰⠆⠈⠻⠻⡿⠿⢿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢀⣸⡇⠀⠀⢀⣤⣀⢄⣀⠃⣱⢷⠷⢿⣿⣶⣾⣿⣿⣯⣿⣧⣟⣻⣿⣻⠷⢟⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣀⣀⣀⣰⣷⣄⣠⣬⣥⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣰⣶⣤⣄⠀⠀⣸⣿⣇⠀⢀⣠⣿⣿⣹⣿⣸⣿⢈⣿⣿⡇⣶⢻⣯⢻⣿⣽⣻⣿⡿⣟⣻⡿⣈⠿⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⠻⡏⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⠃⢠⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡏⢤⣤⡄⠀⢀⣐⣡⣶⣾⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣾⣿⣿⣿⣿⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⠍⠁⠉⠸⠣⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⣿⢿⣇⣿⠰⢿⣏⣿⣿⣿⣻⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣷⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⡿⢶⣶⢶⡷⠉⠈⠁⢛⡛⢘⣣⣿⣸⣼⢿⣿⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡟⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣠⣷⣼⣿⣿⣿⠟⠋⠁⣀⡀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⢠⣾⣿⣷⣦⡄⠀⠀⠀⠉⠾⠿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢺⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⡄⡤⣍⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡇⡇⣿⢿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠑⣯⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢜⣇⠧⢟⣿⣺⣧⣇⢻⣞⣜⣚⣿⣿⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢄⣚⣛⣿⣟⣻⢻⢽⣻⡿⣿⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠗⠲⣶⠀⠶⠄⠰⠰⠶⠆⠀⠀⠀⠀⣻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠹⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠄⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠙⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣤⣤⣴⣶⣶⣤⣼⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡛⢉⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢻⠿⠉⠀⠀⠀⠈⠩⠍⠙⡉⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡏⠀⠀⠀⢀⣶⣶⣶⣾⣿⣿⣦⡙⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⡆⠀⠀⠹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡄⠀⠀⠀⠐⢶⣶⡶⣶⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠻⡇
⠀⠀⠀⠀⠐⠿⠿⠿⠿⣿⠿⢿⣿⡇⢸⣿⣿⣿⣿⣧⣀⠀⠀⠀⠈⠁⠂⠀⢀⣉⣿⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢯⣶⡀⣉⣿⠀⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠦⢶⣶⣶⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠑⠿⣻⣿⣇⣈⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣤⣾⡿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣦⡀⠀⠀⠀⠹⠽⢻⠁⢿⣿⣿⡯⠀⢀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⢸⣿⡇⠀⠀⣤⣶⠀⡏⡀⢿⣿⣿⡇⠀⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⡿⢿⣟⣹⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⣄⡀
⢸⡟⠇⠀⠀⠀⠉⠿⣷⡇⣼⣿⣿⠁⠀⠈⢻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⢛⣵⡶⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠋⠛⢣⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠘⠛⠻⡇
⠈⠁⠀⠀⠀⠀⠀⠀⢈⠃⡟⢻⡟⠀⠀⠀⠘⠻⠿⠿⣆⠀⠀⠀⢀⣀⠀⢀⣾⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢺⣿⣿⣿⣿⣿⣿⣿⠋⠉⠛⠁⢰⠆⠀⠹⠻⡿⠿⢿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⣸⡇⠀⠀⠠⣤⣄⣄⣀⠄⣀⢶⠿⢿⣿⣶⣷⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⢟⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⣀⢠⣷⣤⣀⣬⣥⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣰⣷⣶⡄⠀⠀⣸⣿⣇⠀⢀⣠⣾⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢻⣯⢻⣿⣽⣻⣿⡿⣟⣛⡿⣁⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⠻⡋⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⠇⢠⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣟⡊⣾⢻⡏⢤⣤⡄⠀⢀⣀⣠⣶⣾⣿⣿⡿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠐⣾⣿⣿⣿⣿⠀⠈⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡯⠁⠉⠘⠃⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢸⡿⣾⣿⢿⣇⣿⡠⣿⣏⣿⣿⣿⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢶⣶⣶⣷⠉⠈⠁⠛⡛⢘⣣⣿⣺⡼⢿⣿⠁⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣠⣯⣼⣿⣿⡿⠛⠉⠀⣀⡀⠀⠀⠀⠀⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢼⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣷⠀⢠⣾⣿⣿⣦⡄⠀⠀⠀⠉⠾⠿⢿⠿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⡄⡤⣌⢭⢩⢹⡟⡍⢲⠂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠁⣯⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢤⣇⠧⢟⣿⣺⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢆⣘⣛⣿⣟⣻⢻⢼⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⠶⠄⠰⠲⠶⠆⠀⠀⠀⠀⢻⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠙⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠄⠀⠀⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠙⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢠⣤⣤⣴⣶⣶⣤⣼⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡛⢉⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⣻⡿⠋⠀⠀⠀⠈⠨⠍⠩⡉⠻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⠿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⢀⣶⣶⣶⣾⣿⣿⣦⠘⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⠀⠀⠻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⢶⣶⡶⣶⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠻⡇
⠀⠀⠀⠀⠀⠿⠿⠿⠿⣿⠿⠿⣿⡇⢸⣿⣿⣿⣿⣷⣀⠀⠀⠀⠈⠁⠂⠀⢀⣉⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠄⢭⣻⡀⣉⣿⠀⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠠⠶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠑⠿⣻⣿⣇⣘⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⣤⣾⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣦⡀⠀⠀⠀⠹⠽⣻⠃⢿⣿⣿⣯⠀⢀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⢸⣿⡇⠀⠀⢤⣴⠀⡏⡀⢿⣿⣿⡇⠀⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⡿⢿⣟⣻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⣀⡀
⢸⡟⠇⠀⠀⠀⠉⠿⣷⡇⣾⣿⣿⠁⠀⠈⢻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⢛⣵⡶⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠋⠛⢡⣽⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠈⠙⠻⡇
⠈⠁⠀⠀⠀⠀⠀⠀⢈⠃⠟⢻⡟⠀⠀⠀⠘⠿⠿⠿⡂⠀⠀⠀⢀⣀⠀⢀⣾⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⣿⠉⠉⠛⠁⢠⠄⠀⠹⠿⣿⠿⢿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⣸⡇⠀⠀⠠⣤⣄⣄⣐⠠⣊⢿⠿⢾⣿⣾⣿⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣀⠀⢠⣷⣄⣀⣬⣅⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣶⣶⡄⠀⠀⣰⣿⣇⠀⢀⣠⣾⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢻⣯⢻⣿⣽⣻⣿⡿⣟⣻⡿⣁⠿⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⢻⡋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⠇⢠⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡏⢤⣤⡄⠀⠀⣐⣡⣴⣶⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠐⣾⣿⣿⣿⣿⠀⠈⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠸⠣⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⣸⡿⣾⣿⢿⣇⣿⡀⣿⣏⣿⣿⣿⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣷⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢶⣶⣶⣷⠉⠈⠁⠛⣛⢘⣣⣿⣸⣼⢿⣿⠀⠀⠀⠀⠘⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⣧⣼⣿⣿⡿⠛⠉⠀⡀⡀⠀⠀⠀⠀⠉⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⢠⣾⣿⣿⣦⡀⠀⠀⠀⠉⠾⠿⢿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⣤⡄⡤⣌⢭⢩⢹⡟⡍⢲⠂⡏⡆⣎⣶⡧⡇⡇⣿⢿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠁⣯⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢜⣇⠧⢟⣿⣺⣧⣇⣻⣞⣜⣚⣿⣿⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢆⣚⣛⣿⣟⣻⢻⢽⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⠶⠄⠰⠰⠶⠆⠀⠀⠀⠀⢹⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⠛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠛⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠙⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢠⣤⣴⣶⣶⣶⣤⣼⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡛⢉⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢻⠿⠋⠀⠀⠀⠈⠨⠍⠉⡉⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢾⢿⢿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡏⠀⠀⠀⢀⣶⣶⣶⣾⣿⣿⣦⡘⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡅⠀⠀⠻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡆⠀⠀⠀⠐⢶⣶⡶⣶⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⡇
⠀⠀⠀⠀⠐⠿⠿⠿⠟⣿⠿⠿⣿⡇⢸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠈⠁⠀⠀⢀⣉⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠭⣻⡀⢉⣿⠀⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠶⢶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠑⠛⣻⣿⣇⣸⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣴⣿⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣦⡀⠀⠀⠀⠉⠽⢻⠃⢿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⡇
⢸⣿⡇⠀⠀⣤⣴⢀⠇⡀⢿⣿⣿⡷⠀⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⡿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣤⡀
⢸⡟⠇⠀⠀⠀⠉⠿⣷⡇⣾⣿⣿⠁⠀⠈⢻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⢛⣵⡶⣯⢟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⠋⠻⢡⣽⣿⣿⣿⣧⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠈⠙⠻⠇
⠈⠁⠀⠀⠀⠀⠀⠀⢈⠃⡟⢻⡟⠀⠀⠀⠘⠻⠿⡿⡷⠀⠀⠀⠀⣀⠀⠀⣾⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢺⣿⣿⣿⣿⣿⣿⡿⠛⠉⠛⠁⢠⠆⠈⠻⠿⣿⠿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠁⣸⡇⠀⠀⠠⣤⣤⣄⣀⠔⣕⢶⠿⢾⣿⣶⣿⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣀⢀⢠⣶⣄⣀⣉⣅⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣶⣴⡅⠀⠀⣰⣿⣇⡀⢀⣠⣾⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢳⣯⢻⣿⣽⣻⣿⡿⣟⣻⡿⣅⠿⠿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠻⢻⡋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⠇⢰⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣇⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡏⢤⣤⡄⠀⢀⣐⣡⣴⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠐⣾⣿⣿⣿⣿⠀⠈⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠸⠣⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢸⡿⣾⣿⢻⣇⣿⡀⣾⣟⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢶⣶⢶⣷⠉⠈⠁⠛⣛⠘⣣⣿⣹⣼⢿⣿⠀⠀⠀⠀⠘⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⣧⣼⣿⣿⣿⠛⠉⠀⣀⣀⠀⠀⠀⠀⠉⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢼⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣏⠀⢠⣾⣿⣿⣦⡀⠀⠀⠀⠩⠾⠿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢺⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⣤⡄⣤⣌⢭⢩⢹⡟⡍⢲⠂⡏⡆⣎⣾⡧⡇⡇⣷⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠁⣯⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢜⣇⠧⢟⣿⣺⣧⣇⣻⣞⣜⣚⣿⣿⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢆⣚⣛⣿⣟⣻⢻⢽⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⢶⠄⠰⠲⠶⠆⠀⠀⠀⠀⢹⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣷⣿⣿⣿⣿⣇⠀⠀⠀⠹⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠙⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢠⣤⣴⣶⣶⣶⣦⣼⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡋⢉⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢻⠿⠋⠀⠀⠀⠈⠨⠍⠉⡉⠻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣾⣿⢿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⢀⣶⣶⣶⣾⣿⣿⣦⡘⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡅⠀⠀⠻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡄⠀⠀⠀⠐⢶⣶⡶⣶⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠇
⠀⠀⠀⠀⠀⠿⠿⠿⠻⣿⠿⠿⣿⡇⢸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⢀⣉⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡔⢭⣻⡀⢉⣿⠀⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠶⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠱⠟⣻⣿⣇⣰⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣦⣿⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣦⡀⠀⠀⠀⠉⠽⢻⠃⢿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⡇
⢸⣿⡇⠀⠀⣤⣴⢀⠇⡀⢿⣿⣿⡧⠀⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⢿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣄⡀
⢸⡟⠇⠀⠀⠀⠉⠿⣷⡇⣼⣿⣿⠁⠀⠈⢻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⢛⣵⡾⣯⢟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠋⠻⢅⣽⣿⣿⣿⣧⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠈⠙⠻⡇
⠈⠁⠀⠀⠀⠀⠀⠀⢈⠃⡛⢻⡟⠀⠀⠀⠘⠻⠿⣿⡷⠄⠀⠀⢀⣀⠀⠀⣾⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢺⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠁⢠⠄⠀⠻⠿⣿⠿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠁⣸⡇⠀⠀⠠⣴⣤⣄⣐⠖⣇⢶⠿⢾⣿⣶⣿⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄⣀⣉⣁⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣶⣶⡥⠀⠀⣰⣿⣇⡀⢀⣠⣾⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢳⣯⢻⣿⣽⣿⣿⡿⣟⣻⡿⣁⠿⠿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠻⢿⡛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⠇⢰⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡏⢤⣤⡄⠀⠀⠀⣁⣤⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⠀⠈⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠘⠣⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢸⡿⣾⣿⢻⣇⣷⡀⣾⣟⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢶⣶⢶⣷⠉⠈⠁⠛⣛⠘⣣⣿⣸⣼⢿⣿⠀⠈⠁⠁⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⣧⣼⣿⣿⣿⠛⠉⠀⠀⢀⠀⠀⠀⠀⠉⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢼⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⢠⣾⣿⣿⣦⡀⠀⠀⠀⡩⠾⠿⢿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⡄⡤⣜⢭⢩⢹⡟⡍⢲⠂⡎⡆⡎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠁⣯⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢤⣇⠧⢟⣿⣺⣧⣇⣻⣜⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢆⣘⣛⣿⣟⣻⢻⢽⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣹⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⢟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢹⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣷⣿⣿⣿⣿⣇⠀⠀⠀⠛⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠠⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣤⣶⣶⣶⣶⣦⣼⣥⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡛⢍⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⣻⠿⠋⠀⠀⠀⠈⠨⠍⠉⡉⠻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢾⣿⠿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡏⠀⠀⠀⢀⣴⣶⣶⣾⣿⣿⣦⠘⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⠀⠀⠻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣬⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡆⠀⠀⠀⠐⢶⣶⢶⣶⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⡇
⠀⠀⠀⠀⠐⠛⠿⠿⠻⣿⠿⠿⣿⡇⢸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⢀⣉⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠄⢭⣿⡀⣉⣿⠀⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠠⢶⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠑⠟⣻⣿⣇⣐⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣴⣿⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣦⡀⠀⠀⠀⠉⡙⢻⠃⣿⣿⣿⣯⠀⢀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠉⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡇
⢸⣿⡇⠀⠀⣤⣴⣀⠆⡀⢿⣿⣿⡧⠀⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⡿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣄⡀
⢸⡟⠇⠀⠀⠀⠉⠿⣷⡇⣭⣿⣿⠁⠀⠈⢻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⢛⣵⡾⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠏⠻⢅⣿⣿⣿⣿⣦⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠛⢻⡇
⠈⠁⠀⠀⠀⠀⠀⠀⢀⠃⡟⢻⡟⠀⠀⠀⠈⠻⠿⠿⡳⠀⠀⠀⠀⣀⠀⠠⣾⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠁⢰⠄⠈⠻⢿⣿⢿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠞⠀⠁⣼⡇⠀⠀⠠⣤⣤⣄⣐⠢⣀⢾⠿⢾⣿⣾⣿⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣀⣀⣉⣁⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣶⣶⡤⠀⠀⣴⣿⣇⡀⢀⣠⣾⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢳⣯⢹⣿⣽⣿⣿⡿⣟⣛⡿⣁⠿⠿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠟⢿⡛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⡇⢰⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣇⣿⢸⣧⣿⢸⡟⣿⠋⣿⣸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡏⢤⣤⡄⠀⠀⠀⣁⣤⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡀⣾⣿⣿⣿⣿⠀⠈⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠸⠣⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢸⡿⣾⣿⢿⣇⣷⡠⣾⣟⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣷⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢶⣶⠶⢷⠉⠈⠁⠛⡛⢘⣣⣿⣹⣼⢿⣿⠀⠈⠁⠁⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⣯⣼⣿⣿⣿⠛⠉⠀⡀⣀⠀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢾⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠀⢀⣾⣿⣿⣦⡀⠀⠀⠀⡨⠾⠿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢽⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⡄⡤⣜⢭⢩⢹⡟⡍⢲⠂⡎⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠁⣯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢼⣇⠧⢟⣿⣺⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢆⣚⣛⣿⣟⣻⢻⢼⣻⡿⣿⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⠶⠄⠰⠴⠶⠆⠀⠀⠀⠀⢻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣷⣿⣿⣿⣿⣇⠀⠀⠈⠙⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣴⣶⣶⣶⣶⣦⣾⣥⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡋⣉⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⣻⠿⠃⠀⠀⠀⠈⠨⠍⠉⡉⠻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠾⠿⠿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡏⠀⠀⠀⢀⣴⣶⣶⣾⣿⣿⣦⡘⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⡻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⢶⣶⢶⣶⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⡇
⠀⠀⠀⠀⠀⠛⠿⠿⠻⣿⠿⠿⣿⡇⢸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠂⠀⢀⣉⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⣠⣤⡀
⠀⠀⠀⢀⠀⠀⠀⢀⠄⢭⣻⡀⣉⣿⠀⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠠⢶⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠙⠟⣻⣿⣇⣰⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣶⣿⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣦⡀⠀⠀⠀⠉⠽⢻⠁⢿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⡇
⢸⣿⡇⠀⠀⡤⣴⡀⡆⡀⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⡿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣄⡀
⢸⡟⠇⠀⠀⠀⠉⠿⣷⡇⣯⣿⣿⠁⠀⠈⢻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⢛⣵⡶⣯⢟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠋⠛⢅⣾⣿⣿⣿⣦⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠈⠛⢻⡇
⠈⠁⠀⠀⠀⠀⠀⠀⢀⠃⡛⢻⡟⠀⠀⠀⠈⠿⠿⠿⡢⠀⠀⠀⢀⣀⠀⠀⣾⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⡏⠋⠉⠛⠁⢠⠄⠈⠻⢿⣿⢿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠁⣼⡇⠀⠀⠠⣤⣤⣄⣐⠶⣀⢶⠷⢾⣿⣾⣿⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⢟⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣉⣁⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣴⣶⣶⡤⠀⠀⣴⣿⣇⡀⢀⣠⣾⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢳⣯⢻⣿⣽⣿⣿⡿⣟⣛⡿⣅⠿⠿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠻⢿⡛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⢀⣾⣿⣿⣿⠇⢰⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣇⣿⢸⣧⣿⢸⡟⣿⠋⣿⣸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡇⢤⣤⡄⠀⠀⠀⣁⣤⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⠀⠈⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠸⠣⠛⠘⠏⠹⢇⢿⠼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⣿⢿⣇⣧⡠⣾⣟⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡆⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢶⣶⣶⣷⠉⠈⠁⠛⡛⢘⣣⣿⣹⣼⢿⣿⠀⠈⠁⠁⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣠⣯⣼⣿⣿⣿⠛⠉⠀⡀⡀⠀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢼⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠀⢀⣾⣿⣿⣦⡀⠀⠀⠀⡠⠾⠿⢿⠿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⡄⡤⣍⢭⢩⢹⡟⡍⢲⠂⡏⡆⣎⣶⡧⡇⡇⣷⢿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠁⣯⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡅⣿⣿⢸⣸⠄⡏⡆⢸⢸⣇⠧⢟⣿⣺⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢄⣚⣛⣿⣟⣻⢻⢽⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠗⠲⣶⠀⠶⠄⠰⠴⠶⠆⠀⠀⠀⠀⢹⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣷⣿⣿⣿⣿⣅⠀⠀⠀⠹⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣤⣶⣶⣶⣶⣶⣾⣴⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡛⣉⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⣻⠿⠋⠀⠀⠀⠈⠨⠍⠉⡉⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⠾⠿⠿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⢀⣴⣶⣶⣾⣿⣿⣦⡘⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡆⠀⢀⡺⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⢶⣶⠶⣒⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠇
⠀⠀⠀⠀⠀⠛⠿⠿⠛⣿⠿⠿⣿⡇⢸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⢀⣉⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠄⢭⣷⡀⣈⣿⠀⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠤⢶⣶⣶⣦⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠑⠛⣿⣿⣇⣰⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢴⣾⣿⣿⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣦⡄⠀⠀⠀⠉⡙⣻⠁⢿⣿⣿⡿⠀⢀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠉⠉⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⡇
⢸⣿⡇⠀⠀⡤⣦⢀⠇⡀⢿⣿⣿⡗⠀⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⡿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⣄⡀
⢸⡟⠃⠀⠀⠀⠉⠿⣷⣇⣼⣿⣿⠁⠀⠈⢻⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⢛⣵⡾⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠏⠻⢅⣾⣿⣿⣿⣦⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠈⠛⢻⡇
⠀⠁⠀⠀⠀⠀⠀⠀⢀⠃⡟⢻⡟⠀⠀⠀⠘⠻⠿⠿⣷⠀⠀⠀⢀⣀⠀⠀⣾⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢺⣿⣿⣿⣿⣿⣿⡏⠋⠉⠛⠁⢠⠀⠀⠻⠿⣿⠿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠾⠀⠁⣸⡇⠀⠀⠠⣤⣄⣄⣁⠶⣀⢾⠿⢾⣿⣶⣿⣿⣿⣯⣿⣧⣟⣻⣿⣻⠷⢟⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀⣀⣉⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣾⣶⡦⠀⠀⣰⣿⣇⡀⢀⣠⣾⣿⣹⣿⣸⣿⢈⣿⣿⡇⣶⢳⣯⢻⣿⣽⣻⣿⡿⣟⣛⡿⣇⠿⠻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠻⢿⡙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⠇⢰⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡇⢤⣬⡄⠀⠀⠀⣡⣤⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⠀⠈⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠸⠣⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⣿⢿⣇⣷⣀⣾⣟⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣷⡎⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⢾⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢶⣶⣶⡷⠉⠈⠁⠛⣛⢘⣣⣿⣹⡼⢿⣿⠁⠀⠉⠁⠹⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡏⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⣧⣼⣿⣿⣿⠛⠉⠀⡀⡀⠀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⢠⣾⣿⣿⣦⡀⠀⠀⠀⡠⠾⠿⣿⠿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢼⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⡄⡤⣍⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣾⡧⡇⡇⣷⢿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠁⣯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡅⣿⣿⢸⣸⠄⡏⡆⢸⢼⣇⠧⢟⣿⣺⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢆⣘⣛⣿⣟⣻⢻⢽⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⠶⠄⠰⠰⠶⠆⠀⠀⠀⠀⢹⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣷⣿⣿⣿⣿⣅⠀⠀⠀⠹⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠉⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣴⣶⣶⣶⣶⣶⣾⣴⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡛⢍⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⠿⠋⠀⠀⠀⠈⠨⠍⠉⡉⠛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⢾⠿⠿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⢀⣴⣶⣶⣾⣿⣿⣦⡘⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⣇⠀⢀⡚⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⡆⠀⠀⠀⠐⢷⣶⠶⣲⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠇
⠀⠀⠀⠀⠀⠿⠿⠿⠛⣿⠿⠿⣿⣧⠰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⢀⣉⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠭⣿⡀⣈⣿⠀⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠤⣶⣶⣶⣦⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠛⣻⣿⣗⣴⣻⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣦⡀⠀⠀⠀⠉⡝⣻⠇⢺⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠉⠉⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⡇
⢸⣿⡇⠀⠀⡤⣶⣀⡋⡀⢻⣿⣿⡿⠀⢾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⡿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣤⡀
⢸⡟⠃⠀⠀⠀⠉⠿⣷⣇⣸⣿⣿⠁⠀⠈⠻⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣿⢛⣵⡾⣯⢟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠇⠛⠅⣼⣿⣿⣿⣧⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠈⠋⠻⡇
⠀⠁⠀⠀⠀⠀⠀⠀⢀⠃⡟⢻⡿⠀⠀⠀⠈⠻⠿⠿⢗⡀⠀⠀⠀⣀⠀⠀⣼⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠁⢠⠄⠀⠻⠿⣿⠿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠁⣼⡇⠀⠀⠀⣤⣄⣄⣁⠢⣂⢾⠿⢾⣿⣶⣿⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣀⣀⣉⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣰⣾⣶⣦⠀⠀⣰⣿⣇⡀⢀⣠⣾⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢻⣯⢻⣿⣽⣿⣿⡿⣟⣛⡿⣇⠿⠿⣿⡿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠻⢿⡋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⡇⢰⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢹⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡇⢤⣬⡄⠀⠀⠀⣡⣤⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⠀⠀⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠸⠣⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢸⡿⣾⣿⢿⣇⣷⣀⣾⣟⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡎⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢶⣶⠶⠷⠉⠈⠁⠛⣛⢘⣣⣿⣺⣼⢿⣿⠀⠀⠁⠁⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣀⣷⣬⣿⣿⣿⠛⠉⠀⡀⠀⠀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⢠⣾⣿⣿⣦⡀⠀⠀⠀⡠⠾⠿⣿⠿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢼⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⡄⡤⣍⢭⢩⢹⡟⡍⢲⠂⡏⡆⣎⣶⡧⡇⡇⣷⢿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠁⣯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡅⣿⣿⢸⣸⠄⡏⡆⢸⢼⣇⠧⢟⢿⣺⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠷⢶⣿⣿⢿⢆⣘⣛⣿⣟⣻⢻⢽⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠙⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠠⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠉⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣴⣶⣶⣶⣶⣶⣾⣶⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⣛⢏⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡾⠋⠀⠀⠀⠈⠨⠍⠹⡉⠛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠾⠿⠿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣦⡈⢻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡚⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢘⣿⣿⣿⣿⡆⠀⠀⠀⠀⢶⣶⠶⣲⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠇
⠀⠀⠀⠀⠐⠟⠿⠿⠟⣿⠿⠿⣿⣧⠸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⠀⣉⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠽⣻⡀⢈⣿⠀⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢤⣶⣶⣶⣦⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠚⣻⣿⣗⣼⣻⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣬⣿⣿⣿⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣦⡀⠀⠀⠀⠉⠽⣻⠇⢺⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠉⠉⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⡇
⢸⣿⡇⠀⠀⡤⣦⣀⡊⡀⢻⣿⣿⡿⠀⢾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⡿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣀⡀
⢸⡟⠃⠀⠀⠀⠉⠿⣷⣇⣸⣿⣿⠁⠀⠈⢻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⢛⣵⡾⣯⢟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠇⠛⢅⣾⣿⣿⣿⣧⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠈⠛⠻⠇
⠈⠁⠀⠀⠀⠀⠀⠀⢀⠃⣟⢻⡿⠀⠀⠀⠘⠻⠿⠿⢦⠀⠀⠀⢀⣀⠀⠀⣴⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢹⣿⣿⣿⣿⣿⣿⡏⠋⠉⠛⠁⢠⠄⠀⠹⠿⣿⠿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠑⣼⡇⠀⠀⠀⣤⣤⣄⣀⠰⣀⢶⠿⢾⣿⣶⣿⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⣀⣉⣤⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣰⣾⣶⣧⠀⠀⣰⣿⣇⡀⠀⣠⣾⣿⣹⣿⣸⣿⢈⣿⣿⡇⣶⢻⣯⢻⣿⣽⣿⣿⡿⣟⣛⡿⣇⠿⠿⣿⡿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠻⢿⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⡇⢰⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡇⢤⣬⡄⠀⠀⠀⣡⣴⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣾⣿⣿⣿⣿⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠘⠣⠛⠘⠏⠹⢇⢿⠼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⣿⢻⣇⣷⡀⣾⣟⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡎⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢲⣶⠶⢷⠉⠈⠁⠛⣛⢘⣣⣿⣺⣼⢿⣿⠁⠀⠁⠁⠸⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⣧⣬⣿⣿⣿⠛⠉⠀⣀⠀⠀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⢠⣾⣿⣿⣦⡀⠀⠀⠀⡠⠾⠿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣋⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⡄⡤⣝⢭⢩⢹⡟⡍⢲⠂⡏⡆⡎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢼⣇⠧⢟⣿⣼⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠉⠀⠀⠀⠷⢶⣿⣿⢿⢆⣘⣛⣿⣟⣻⢻⢽⣻⡿⣿⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⠴⠄⠰⠲⠶⠆⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣷⣿⣿⣿⣿⣅⠀⠀⠀⠙⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣴⣶⣶⣶⣶⣶⣾⣴⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⣛⢏⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡿⠋⠀⠀⠀⠈⠨⠍⠩⡉⠟⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠷⠿⠿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣦⡈⢻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢀⣚⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢘⣿⣿⣿⣿⡆⠀⠀⠀⠀⢶⣶⠶⣒⣻⣿⡶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠇
⠀⠀⠀⠀⠀⠻⠿⠿⠛⣿⠿⠿⣿⣇⠰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⠀⣈⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡄⢽⣻⡀⢈⣿⠀⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣤⣶⣶⣶⣦⡆⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠑⠞⣻⣿⣗⣰⣻⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣦⡀⠀⠀⠀⠉⡙⣻⠇⢸⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠉⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⡇
⢸⣿⡇⠀⠀⢤⣦⡀⡊⡀⢻⣿⣿⡿⠀⢾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⡿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣀⡀
⢸⡟⠃⠀⠀⠀⠉⠿⣷⣇⣼⣿⣿⠁⠀⠈⢻⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⢛⣵⡾⣯⢟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠃⠛⢅⣼⣿⣿⣿⣧⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠈⠙⠛⡇
⠈⠁⠀⠀⠀⠀⠀⠀⢀⠃⠟⢻⡿⠀⠀⠀⠘⠻⠿⠿⠇⠀⠀⠀⠀⣀⠀⠀⣼⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢹⣿⣿⣿⣿⣿⣿⡯⠉⠉⠛⠁⢠⠄⠀⠻⠿⣿⠿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠁⣼⡇⠀⠀⠀⣄⣦⢄⣀⠢⣐⢴⠿⢾⣿⣶⣶⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⣀⣉⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣾⣶⣦⠀⠀⣰⣿⣇⡀⠀⣠⣾⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢳⣯⢻⣿⣽⣿⣿⡿⣟⣛⡿⣇⠿⠿⣿⡿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠹⢻⡉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣴⣿⣿⣿⡇⢰⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣇⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡇⢤⣬⡄⠀⠀⢀⣡⣴⣶⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡯⠁⠉⠘⠃⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢸⡿⣾⢿⢻⣇⣷⡠⣾⣛⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡎⠀⢠⣶⡿⣷⣿⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢲⡶⠶⠷⠉⠈⠁⠛⡛⢘⣣⣿⣸⣼⢿⣿⠁⠈⠁⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣠⣧⣬⣿⣿⣿⠋⠉⠀⡀⡀⠀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣗⠀⢠⣾⣿⣿⣦⡀⠀⠀⠀⡠⠾⠿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢺⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣊⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⡄⡤⣍⢭⢩⢹⡟⡍⢲⢂⡎⡆⣎⣶⡧⡇⡇⣷⢿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡅⣷⣿⢸⣸⠄⡏⡆⢸⢴⣇⠧⢟⢿⣺⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠷⢶⣿⣿⢿⢄⣚⣛⣿⣟⣻⢻⢽⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⠶⠄⠰⠲⠶⠆⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠻⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢠⣤⣶⣶⣶⣶⣶⣾⣴⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⣛⢋⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡿⠋⠀⠀⠀⠈⠨⠍⠩⡉⠙⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⠷⠿⠿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣦⡈⢻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢀⡚⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠐⣿⣿⣿⣿⡆⠀⠀⠀⠀⢶⣶⠶⣒⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠇
⠀⠀⠀⠀⠀⠻⠿⠿⠛⣿⠿⠿⣿⣧⠰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⠀⣈⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠽⣻⡀⢈⣿⡁⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣶⣶⣾⣢⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠐⠛⣻⣿⣗⣼⣻⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣽⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣦⡄⠀⠀⠀⠉⡹⢻⠃⢸⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠉⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⡇
⢸⣿⡇⠀⠀⢤⣦⡠⡃⡀⢻⣿⣿⡿⠀⢾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⢹⣿⡿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣤⡀
⢸⡟⠃⠀⠀⠀⠙⠿⣷⣇⣼⣿⣿⠁⠀⠈⢻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣿⢛⣵⡾⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⠃⠛⢁⣾⣿⣿⣿⣧⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠈⠉⠛⡇
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠇⠟⢻⡿⠀⠀⠀⠈⠻⠿⠿⣇⠀⠀⠀⠀⣀⠀⢀⣾⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⡿⠉⠉⠛⠁⢠⠀⠀⠹⠿⣿⠿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠐⣸⡇⠀⠀⠀⣬⣤⣄⣀⠢⣐⢳⠿⢾⣿⣶⣾⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⣀⣉⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣾⣷⣤⠀⠀⣰⣿⣇⡀⠀⣠⣾⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢳⣯⢻⣿⣽⣻⣿⡿⣟⣛⡿⣇⠿⠿⣿⡿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠻⢻⡉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣴⣿⣿⣿⡇⢰⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢹⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡏⢤⣤⡄⠀⠀⢀⣣⣴⣶⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡯⠁⠉⠘⠃⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⣿⢿⣇⣷⡀⣾⣛⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡎⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠿⠲⣶⠶⢷⠉⠈⠁⠛⣛⠘⣣⣿⣹⣼⢿⣿⠀⠘⠁⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣠⣯⣬⣿⣿⣿⠋⠉⠀⣀⠀⠀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡧⠀⢠⣾⣿⣿⣦⡀⠀⠀⠀⡠⠾⠿⣿⠿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣚⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢢⣤⡄⡤⣜⢭⢩⢹⡟⡍⢲⠂⡌⡆⣎⣶⡧⡇⡇⣷⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡇⡅⣿⣿⢸⣸⠄⡏⡆⢸⠼⣇⠧⢟⢿⣺⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠉⠀⠀⠀⠷⢶⣿⣿⢿⢄⣛⣛⣿⣟⣻⢻⢽⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⠴⠄⠰⠶⠶⠆⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠹⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠀⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠃⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣴⣶⣶⣶⣶⣶⣾⣴⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⣛⢉⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡿⠋⠀⠀⠀⠈⠨⠍⠉⡉⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠿⠿⠿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡞⠀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣦⡈⢻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⢀⡺⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⢀⣜⣿⣿⣿⣿⣿⣿⣿⡇⠰⣿⣿⣿⣿⡆⠀⠀⠀⠀⢶⣶⠖⣒⣿⣿⡶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠇
⠀⠀⠀⠀⠀⢻⡿⠿⠛⣿⠿⠿⣿⣧⠰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⢀⣉⡿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⣀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠽⣻⡀⢈⣿⡁⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣶⣶⣶⣦⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠙⠟⣻⣿⣗⣼⣻⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣽⣿⣿⣿⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣦⡄⠀⠀⠀⠉⠙⢻⠃⢸⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⠉⠉⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⠇
⢸⣿⡇⠀⠀⢤⣤⡀⡂⡀⢻⣿⣿⡿⠀⢾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⡿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣠⡀
⢸⡟⠃⠀⠀⠀⠉⠿⣷⣇⣨⣿⣿⠁⠀⠈⢻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⢛⣵⡶⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⠃⠛⢅⣼⣿⣿⣿⣧⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠈⠙⢛⡇
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠇⠟⢛⡿⠀⠀⠀⠀⠻⠿⠿⡦⠀⠀⠀⠀⢀⠀⢀⣾⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⡯⠉⠉⠛⠁⢠⠀⠀⠹⠿⣿⠿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠑⣸⡇⠀⠀⠀⣌⣢⣄⣀⠦⣔⢾⠾⢾⣿⣾⣾⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⣀⣉⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣶⣶⡤⠀⠀⣰⣿⣇⡀⠀⣠⣾⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢳⣯⢹⣿⣽⣻⣿⡿⣟⣛⡿⣇⠿⠿⣿⡿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠻⢻⡋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠠⢀⣴⣿⣿⣿⡇⢰⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣇⣿⢸⣧⣿⢸⡟⣿⠋⣿⣸⡟⣿⢀⡛⢹⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡇⢤⣤⡄⠀⠀⢀⣣⣴⣶⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠸⠃⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⢿⢿⣇⣧⠠⣾⣛⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡎⠀⢠⣶⡿⣷⣯⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟⢲⡶⠶⢷⠉⠈⠁⠛⣛⠘⣣⣿⣸⣼⢿⣿⠀⠘⠁⠁⠹⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣠⣧⣬⣿⣿⣿⠋⠉⢀⣠⡀⠀⠀⠀⠀⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢼⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⢠⣾⣿⣿⣦⡀⠀⠀⠀⡠⠿⠿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣚⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢢⣤⡄⡤⣝⢭⢩⢹⡟⡍⢲⠂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠈⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢼⣇⠧⢟⢿⣺⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠉⠀⠀⠀⠷⢶⣿⣿⢿⢀⣛⣛⣿⣟⣻⢻⢽⣻⡿⣿⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣼⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⢹⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣅⠀⠀⠈⠹⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠃⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣤⣶⣶⣶⣶⣶⣾⣶⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⣛⢍⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡿⠋⠀⠀⠀⠈⠨⠍⠩⡉⠛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⠿⠿⠿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣦⡈⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠐⡺⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠐⣿⣿⣿⣿⡆⠀⠀⠀⠀⢶⣶⠖⣒⣿⣿⡶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠃
⠀⠀⠀⠀⠀⢿⠿⠿⠟⣿⠿⠿⣿⣧⠰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⢀⣉⣷⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣠⣦⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠯⣻⡀⢉⣿⡁⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣶⣶⣶⣢⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠐⠞⣻⣿⣗⣼⣻⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣽⣿⣿⣿⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣦⡄⠀⠀⠀⠉⡹⢻⠇⢸⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⠇
⢸⣿⡇⠀⠀⢤⣤⡠⡃⡀⢻⣿⣿⡿⠀⢾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣄⡀
⢸⡟⠃⠀⠀⠀⠙⠿⣷⣇⣨⣿⣿⠁⠀⠈⢻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣿⢛⣵⡾⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⠃⠻⢅⣾⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠉⠛⠇
⠈⠁⠀⠀⠀⠀⠀⠀⢀⠇⠟⢻⡿⠀⠀⠀⠈⠻⠿⢿⣇⠀⠀⠀⠀⣀⠀⠀⣾⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⡯⠉⠉⠛⠁⢠⠀⠀⠻⠿⣿⢿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⣸⡇⠀⠀⠠⣌⣢⣄⣀⠤⣄⢾⠿⢷⣿⣶⣾⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⣀⣉⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣶⣶⣤⠀⠀⣰⣿⣇⡀⠀⣠⣾⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢳⣯⢻⣿⣽⣻⣿⡿⣟⣛⡿⣇⠿⠿⣿⡿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠿⢿⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣴⣿⣿⣿⡇⢰⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢸⣧⣿⢸⡟⣿⠋⣿⣸⡟⣿⢀⡛⢹⣏⡃⣿⡇⣿⡟⣼⣗⡊⣿⢻⡇⢤⣤⡄⠀⠀⢀⣡⣴⣶⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠘⠃⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⣿⢻⣇⣧⡠⣾⣛⣿⣿⣿⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡎⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢲⡶⠶⡷⠉⠈⠁⠛⡛⠘⣣⣿⣸⡼⢿⣿⠀⠘⠁⠁⠹⢿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣠⣯⣴⣿⣿⣟⠛⠉⠀⣀⡀⠀⠀⠀⠀⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣼⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣯⠀⢠⣾⣿⣿⣦⡄⠀⠀⠀⡠⠿⠿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣋⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢢⣤⡄⡤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⡇⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⠈⠉⠉⠁⠀⠉⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢼⣇⠧⢟⢿⣾⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠉⠀⠀⠀⠷⢶⣿⣿⢿⢄⣚⣛⣿⣟⣻⢻⢽⣻⡿⣯⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⢶⠄⠰⠰⠶⠆⠀⠀⠀⠀⢹⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣷⣿⣿⣿⣿⣁⠀⠀⠈⠻⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠀⡠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠃⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣤⣶⣶⣶⣶⣶⣿⣤⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⣛⢉⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡿⠋⠀⠀⠀⠈⠨⠍⠉⡉⠟⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢿⠿⠿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣦⡈⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠐⡺⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠐⣿⣿⣿⣿⡄⠀⠀⠀⠀⢶⣶⠖⣒⣿⣿⡶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠃
⠀⠀⠀⠀⠀⠿⡿⠿⠟⣿⠿⠿⣿⣧⠰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⢀⣉⡷⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠯⣻⡀⢉⣿⡁⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣶⣶⣶⣠⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠟⢻⣿⣗⣼⣻⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣽⣿⣿⣿⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣦⡄⠀⠀⠀⠉⡹⢻⠃⣸⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⠇
⢸⣿⡇⠀⠀⡤⣤⡀⡇⡀⢻⣿⣿⡿⠀⢾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⡿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⢀⣤⡀
⢸⡟⠃⠀⠀⠀⠉⠿⣷⣇⣨⣿⣿⠁⠀⠈⠻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣿⢛⣵⡾⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⠃⠛⠅⣼⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠉⢻⠇
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠃⠟⢻⡿⠀⠀⠀⠀⠻⢿⢿⣄⠀⠀⠀⠀⢀⠀⠀⣼⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⡿⠉⠉⠛⠁⢠⡄⠀⠻⠿⣿⢿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠑⣸⡇⠀⠀⠠⣄⣢⣄⣐⠠⣄⢻⠷⢶⣿⣾⣷⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⣀⣉⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣶⣶⣦⠀⠀⣰⣿⣇⡀⠀⣠⣾⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢳⣯⢻⣿⣽⣻⣿⡿⣟⣛⡿⣇⠿⠿⣿⡿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠿⢿⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠠⢀⣴⣿⣿⣿⡇⢰⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡇⢤⣤⡄⠀⠀⢀⣡⣴⣶⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠘⠃⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⣿⢿⣇⣧⡠⣾⣛⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡎⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠞⢲⡶⠶⠷⠉⠈⠁⠛⡛⠘⣣⣿⣹⡼⢿⣿⠀⠘⠁⠁⠹⢿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣠⣧⣤⣿⣿⣿⠛⠉⢀⣀⡀⠀⠀⠀⠀⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢾⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⢠⣾⣿⣿⣦⠀⠀⠀⠀⡠⠿⠿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢿⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢢⣤⡄⡤⣝⢭⢩⢹⡟⡍⢲⠂⡏⡆⣎⣶⡧⠃⡇⣷⢿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠑⢯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡇⡅⣿⣿⢸⣸⠄⡏⡆⢸⢼⣇⠧⢟⣿⣺⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠉⠀⠀⠀⠷⢶⣿⣿⢿⢀⣛⣛⣿⣟⣻⢻⢽⣻⡿⣯⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣨⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡟⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⢶⠄⠰⠲⠶⠆⠀⠀⠀⠀⢸⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣷⣿⣿⣿⣿⣁⠀⠀⠈⠹⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠄⠄⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠃⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣤⣶⣶⣶⣶⣶⣾⣤⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡛⢉⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⠿⠋⠀⠀⠀⠈⠹⠅⠩⡉⠛⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⢿⠿⠿⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣦⡈⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠐⡺⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣜⣿⣿⣿⣿⣿⣿⣿⡇⠰⣿⣿⣿⣿⡄⠀⠀⠀⠀⢶⣶⠖⣒⣿⣿⡶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠃
⠀⠀⠀⠀⠀⠻⡿⠿⠛⣿⠿⠿⣿⣧⠰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣉⡷⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠿⣻⡀⢈⣿⠁⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣀⣶⣶⣶⣠⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠿⣫⣿⣗⣸⣻⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⣽⣿⣿⣿⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣦⡄⠀⠀⠀⠉⠝⢿⠃⢼⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠇
⢸⣿⡇⠀⠀⠠⣤⡀⡋⡀⢻⣿⣿⡿⠀⢾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⡿⢿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣤⡀
⢸⡟⠃⠀⠀⠀⠈⠿⣷⣇⣨⣿⣿⠁⠀⠈⠻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣿⢛⣵⡶⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⠃⠛⢅⣼⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠉⠻⠇
⠈⠁⠀⠀⠀⠀⠀⠀⢀⠇⡟⢛⡿⠀⠀⠀⠀⠿⢿⢿⠠⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⡏⠉⠉⠛⠁⢠⡄⠀⠹⠿⣿⢿⣿⣦⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠐⣸⡇⠀⠀⠠⣄⣠⢄⣀⠀⣜⢿⠷⢶⣷⣶⣾⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣾⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠈⠀⠀⠀⢠⣦⡀⣀⣉⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣶⣶⣄⠀⠀⣰⣿⣇⡀⠀⣠⣾⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢳⣏⢻⣿⣽⣻⣿⡿⣟⣛⡿⣇⠿⠿⣿⡿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠿⢿⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠠⢀⣴⣿⣿⣿⡇⢰⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣇⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡇⢤⣤⡄⠀⠀⢀⣡⣴⣶⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡯⠁⠉⠘⠣⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⢿⢿⣇⣧⢠⣾⣛⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡎⠀⢠⣶⡿⣷⣿⣿⣷⣶⣶⣶⣿⣾⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢲⡶⠶⠷⠉⠈⠁⠛⡛⠘⣣⣿⣻⡼⢿⣿⠀⠸⠁⠀⠹⢿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣠⣧⣴⣿⣿⣟⠛⠉⢀⡀⡀⠀⠀⠀⠀⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢼⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣇⠀⣠⣾⣿⣿⣤⠀⠀⠀⠀⡠⠿⠿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣚⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢢⣤⡄⡤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⠃⡇⣷⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⡇⡅⣿⣿⢸⣸⠄⡏⡆⢸⢼⣇⠧⢟⢿⣺⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠉⠀⠀⠀⠷⢶⣿⣿⢿⢀⣛⣛⣿⣟⣻⢻⢽⣻⡿⣯⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⢶⠄⠰⠲⠶⠆⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣁⠀⠀⠈⠻⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠀⡠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠃⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣤⣶⣶⣶⣶⣶⣾⣤⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡛⢉⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⠿⠋⠀⠀⠀⠈⠹⠅⠩⡉⠙⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠠⢿⠿⠿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣧⡈⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠐⡺⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠐⣿⣿⣿⣿⡆⠀⠀⠀⠀⢶⣶⠖⣒⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠃
⠀⠀⠀⠀⠀⢻⡿⠿⠛⣿⠿⠿⣿⣧⠰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⢀⣉⡷⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠿⣻⡀⣈⣿⡁⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣶⣶⣶⣠⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠾⣻⣿⣗⣸⣻⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⢇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣦⡄⠀⠀⠀⠉⡹⣿⠃⢼⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⠇
⢸⣿⣇⠀⠀⢠⣤⡀⡂⡀⢻⣿⣿⡿⠀⢾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣤⡀
⢸⡟⠃⠀⠀⠀⠈⠿⣷⡇⣸⣿⣿⠁⠀⠈⠻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⢛⣵⡾⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⠃⠛⠅⣾⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠉⠻⠇
⠈⠁⠀⠀⠀⠀⠀⠀⢀⠇⡟⢻⡟⠀⠀⠀⠀⠻⠿⢿⡦⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⡏⠉⠉⠛⠁⢠⡆⠀⠹⠿⣿⢿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠁⣸⡇⠀⠀⠠⣄⣠⢄⣀⠠⣄⢼⠿⢶⣿⣶⣾⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣾⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠈⠀⠀⠀⢠⣦⡀⣀⣉⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣶⣶⣦⠀⠀⣰⣿⣇⡀⠀⣠⣼⣿⣹⣿⣸⣿⢈⣿⣿⡇⣶⢳⣏⢻⣿⣽⣻⣿⡿⣟⣛⡿⣇⠿⠿⣿⡿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠿⢿⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠠⠀⣴⣿⣿⣿⡏⢰⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣇⣿⢸⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡇⢤⣤⡄⠀⠀⢀⣡⣴⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⠁⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠸⠃⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⢿⢻⣇⣦⣠⣾⣛⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣷⡞⠀⢠⣶⡿⣿⣿⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢲⡶⠶⣷⠉⠈⠁⠛⡛⠘⣣⣿⣹⣼⢿⣿⠀⠘⠁⠀⠹⢿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣠⣧⣤⣿⣿⣟⠋⠉⠀⡐⡀⠀⠀⠀⠀⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⠀⣠⣾⣿⣿⣦⡀⠀⠀⠀⡠⠿⠿⣿⠿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣛⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢢⣤⡄⡤⣝⢭⢩⢹⡟⡍⢲⠂⡏⡆⣎⣶⡧⠃⡇⣷⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⡿⠈⠉⠉⠁⠀⠉⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢼⣇⠧⢟⢿⣼⣧⣇⣻⣞⣜⣚⣿⣿⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠉⠀⠀⠀⠷⢶⣿⣿⢿⢄⣛⣛⣿⣟⣻⢻⢿⣻⡿⣯⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⢴⠄⠰⠲⠶⠆⠀⠀⠀⠀⢸⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡁⠀⠀⠈⠻⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠃⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣤⣶⣶⣶⣶⣶⣾⣤⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡋⢉⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⠿⠋⠀⠀⠀⠈⠹⠅⠩⡉⠙⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠠⢿⢿⢿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣧⡈⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠐⣿⣿⣿⣿⡄⠀⠀⠀⠐⢶⣶⠶⣒⣿⣿⡶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠃
⠀⠀⠀⠀⠀⠿⡿⠿⠛⣿⠿⠿⣿⣧⠰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣉⡷⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠯⣻⡀⢈⣿⡁⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣶⣶⣶⣀⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠺⢻⣿⣗⣼⣻⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⣽⣿⣿⣿⢇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣦⡄⠀⠀⠀⠉⡹⢿⡇⢸⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡇
⢸⣿⣷⠀⠀⢠⣤⡄⡞⠀⢸⣿⣿⡿⠀⢾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣄⡀
⢸⡿⠃⠀⠀⠀⠘⠿⣷⣇⣸⣿⣿⠁⠀⠈⠻⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣿⢛⣵⡾⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⠃⠻⠅⣾⣿⣿⣿⣦⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠙⢛⠇
⠀⠁⠀⠀⠀⠀⠀⠀⢀⡇⣟⢻⡿⠀⠀⠀⠀⠻⠿⢿⡆⠀⠀⠀⠀⢀⠀⢀⣶⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⡏⠉⠉⠛⠁⢠⡆⠀⠻⠿⣿⢿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠓⣸⡇⠀⠀⠠⣌⣦⣄⣀⠀⣀⢿⠷⢶⣿⣾⣾⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⢟⣾⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠈⠁⠀⠀⢠⣦⡀⣀⣉⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣶⣶⣤⠀⠀⣰⣿⣧⣀⠀⣠⣼⣿⣹⣿⣸⣿⢈⣿⣿⡇⣶⢳⣯⢻⣿⣽⣻⣿⡿⣟⣛⡿⣇⠿⠿⣿⡿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠻⢿⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠠⠀⣴⣿⣿⣿⡏⢰⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢺⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡇⢤⣤⡄⠀⠀⢀⣡⣴⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⠁⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡯⠁⠉⠘⠃⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⢿⢿⣇⣆⢠⣾⣛⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡞⠀⢠⣶⡿⣷⣿⣿⣷⣶⣶⣶⣿⢾⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠾⢲⣶⠶⢷⠉⠈⠁⠛⣛⠘⣣⣿⣸⣼⢿⣿⠀⠙⠋⠉⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣠⣧⣴⣿⣿⣟⠋⠉⠀⡐⡀⠀⠀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡷⠀⣠⣾⣿⣿⣦⡀⠀⠀⠀⡠⠿⠿⣿⠿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢻⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣚⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⣤⡄⡤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⡎⣾⡧⠃⡇⣷⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⠈⠉⠉⠁⠀⠉⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢴⣇⠧⢟⢿⣺⣧⣇⣻⣞⣜⣚⣿⣿⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠉⠀⠀⠠⠷⢶⣿⣿⢿⢄⣚⣛⣿⣟⣻⢻⢽⣻⡿⣯⢭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⣧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⠶⠄⠰⠲⠶⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡁⠀⠀⠈⠻⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠃⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣤⣶⣶⣶⣶⣶⣾⣤⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡫⢉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⠿⠋⠀⠀⠀⠈⠰⠁⠩⡁⠙⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⢿⢿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⢀⣴⣶⣶⣿⣿⣿⣷⡌⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⠻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣮⣿⣿⣿⣿⣿⣿⣿⡇⢐⣿⣿⣿⣿⡄⠀⠀⠀⠀⢶⣶⠶⣒⣿⣿⡶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠃
⠀⠀⠀⠀⠀⠛⡟⠛⠛⣿⠿⠿⣿⣧⠰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⢈⣉⡷⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡄⢿⣻⡀⣈⣿⡁⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣶⣶⣶⣀⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠁⠾⢻⣿⣷⣼⣻⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⣿⣿⣿⣿⢇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣦⡄⠀⠀⠀⠈⡽⢿⡇⢸⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡇
⢸⣿⣷⠀⠀⢠⣤⡄⡞⠀⢺⣿⣿⡿⠀⢾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣄⡀
⢸⡿⠃⠀⠀⠀⠘⠿⣷⣇⣸⣿⣿⠁⠀⠈⠻⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⢛⣵⡾⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⠃⠻⠅⣾⣿⣿⣿⣦⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠙⢛⠇
⠀⠁⠀⠀⠀⠀⠀⠀⢈⡇⣿⢻⡟⠀⠀⠀⠀⠻⠿⣿⡢⠄⠀⠀⠀⣀⠀⠀⣶⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⡟⠉⠉⠛⠁⢠⡆⠀⠻⠿⣿⢿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠒⣼⡇⠀⠀⠀⣌⣤⣄⣀⠤⣬⢻⠷⢶⣿⣶⣷⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⢟⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⢠⣦⡀⣈⣉⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣶⣶⣤⠀⠀⣠⣿⣧⣀⠀⣠⣼⣿⣹⣿⣸⣿⢈⣿⣿⡇⣶⢳⣯⢻⣿⣽⣻⣿⡿⣟⣛⡿⣇⠿⠿⣿⡿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠿⢿⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣴⣿⣿⣿⡏⠠⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢺⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡇⢤⣤⡄⠀⠀⢀⣡⣴⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣸⣿⣿⣿⣿⠁⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡯⠁⠉⠘⠃⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⣿⢿⣇⣆⢠⣾⣻⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡞⠀⢠⣶⡿⣷⣿⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠾⢲⡶⠶⡷⠉⠈⠁⠛⣛⠘⣣⣿⣹⣼⢿⣿⠀⠹⠋⠉⠹⢿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣠⣧⣴⣿⣿⣟⠛⠉⢀⣐⡄⠀⠀⠀⠀⠉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⠀⣠⣾⣿⣿⣦⡀⠀⠀⠀⡠⠿⠿⣿⠿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢼⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣋⣿⣿⡟⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢢⣤⡄⡤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⠃⡇⣿⣿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⠈⠉⠉⠁⠀⠉⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣸⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠉⠀⠀⠰⠷⢶⣿⣿⢿⢀⣛⣛⣿⣟⣻⢻⢽⣻⡿⣯⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⣧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡁⠀⠀⠈⠻⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠀⣠⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠃⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣤⣶⣶⣶⣶⣶⣾⣦⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡫⣉⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢻⠟⠁⠀⠀⠀⠀⠐⠂⢩⣀⠙⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢾⢿⢿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⢀⣾⣷⣶⣿⣿⣿⣶⡌⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡅⠀⢐⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠠⣮⣿⣿⣿⣿⣿⣿⣿⡇⠐⣿⣿⣿⣿⡄⠀⠀⠀⠐⢶⣶⠖⣒⣿⣿⡶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⠃
⠀⠀⠀⠀⠀⠛⡛⠛⠛⣿⠛⠻⣿⣧⠰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⢀⣉⡷⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣀⣦⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡄⢿⣹⣀⣈⣿⠅⢹⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣶⣶⣶⣀⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠺⢻⣿⣷⣼⣻⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⢇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣶⡄⠀⠀⠀⠈⡭⢿⡇⢸⣿⣿⣯⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⠇
⢸⣿⣿⠀⠀⢀⣤⣄⡞⠀⢸⣿⣿⡿⠀⢾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣤⡀
⢸⡿⠋⠀⠀⠀⠈⠿⣷⣇⣸⣿⣿⠁⠀⠈⠹⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣿⢛⣵⡾⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⠁⠛⠁⣼⣿⣿⣿⣦⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠙⢻⠃
⠈⠁⠀⠀⠀⠀⠀⠀⢀⡏⣿⢻⡟⠀⠀⠀⠀⠻⠻⣿⣧⢀⠀⠀⠀⣀⠀⠀⣼⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⠟⠙⠉⠛⠁⠠⣆⠀⠻⠿⣿⢿⣿⣦⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠓⣼⡇⠀⠀⠀⣬⣤⣀⣀⠀⣄⢼⠶⢶⣿⣶⣾⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢁⠀⠀⢠⣦⡀⣈⣉⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢠⣾⣦⣤⠀⠀⣠⣿⣧⣀⠀⣠⣼⣿⣹⣿⣸⣿⠈⣿⣿⡇⣶⢳⣏⢻⣿⣽⣿⣿⡿⣟⣻⡿⣇⠿⠿⣿⡿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠿⢿⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠠⢄⣠⣿⣿⣿⡏⠠⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢺⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡇⢤⣤⡄⠀⠀⢐⣠⣴⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⠁⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠸⠃⠛⠘⠏⠹⢇⢿⠼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⣿⢻⣇⣦⢠⣾⣻⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡞⠀⢠⣶⡿⣷⣿⣿⣷⣶⣶⣶⣿⣾⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠶⣶⠶⡷⠉⠈⠁⠛⣛⠘⣣⣿⣸⡼⢿⣿⠀⠙⠉⠉⠹⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⣠⣧⣬⣿⣿⡟⠋⠉⢀⣐⡀⠀⠀⠀⠀⠉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡅⠀⣰⣾⣿⣿⣦⠀⠀⠀⠀⡠⠿⠿⣿⠿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢼⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣚⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⣤⡄⡤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⠃⡇⣿⢿⠸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⠈⠉⠉⠁⠀⠉⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣸⡇⡅⣿⣿⢸⣸⠆⡏⡆⢸⢼⣇⠧⢟⢿⣺⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠉⠀⠀⠰⠷⢶⣿⣿⢿⢀⣛⣛⣿⣟⣻⢻⢿⣿⡿⣯⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣨⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⣧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⠶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⠻⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠠⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠃⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣤⣶⣶⣶⣶⣶⣾⣴⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡫⣉⣭⣭⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢻⠟⠉⠀⠀⠀⠀⠰⠂⢩⣄⠛⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠠⢾⠿⢿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⢀⣾⣷⣶⣿⣿⣿⣶⡌⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⡅⠀⢀⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣮⣿⣿⣿⣿⣿⣿⣿⡇⠐⣿⣿⣿⣿⡄⠀⠀⠀⠀⢲⣶⠖⣒⣿⣿⡶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠙⠃
⠀⠀⠀⠀⠀⠛⡛⠛⠛⣿⠛⠻⣿⣧⠰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣉⡧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡄⢿⣹⣀⣠⣿⡁⢹⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣶⣶⣶⣀⡄⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠚⢻⣿⣷⣴⣻⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⢇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢠⣶⡄⠀⠀⠀⠈⠽⢿⠇⢼⣿⣿⣯⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⡇
⢸⣿⣷⠀⠀⢠⣤⣄⡊⡀⢺⣿⣿⡿⠀⢾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣹⣿⣿⣿⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣤⡀
⢸⡿⠋⠀⠀⠀⠈⠿⣷⣇⣸⣿⣿⠀⠀⠈⠙⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣿⢛⣵⡾⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡴⠃⠻⢁⣼⣿⣿⣿⣆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⡉⠛⠃
⠈⠁⠀⠀⠀⠀⠀⠀⢀⡇⣿⢻⡟⠀⠀⠀⠀⠻⠿⣿⣢⡀⢀⠀⠀⠀⠀⢀⣾⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢺⣿⣿⣿⣿⣿⣿⠟⠉⠉⠛⠁⠠⡦⠈⠿⠿⣿⢿⣿⣦⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠉⣼⡇⠀⠀⠀⣤⣦⣀⣀⠠⣔⢾⠿⢶⣿⣶⣾⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⢟⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⣠⣦⣀⣈⣩⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢠⣶⣦⣤⠀⠀⣰⣿⣧⣀⠀⣠⣼⣿⣹⣿⣸⣿⢈⣿⣿⡇⣶⢳⣯⢻⣿⣽⣿⣿⡿⣟⣛⡿⣇⠿⠿⣿⡿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠿⢿⠉⢻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠠⠀⣴⣿⣿⣿⡏⠠⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢺⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢹⣏⡃⣿⡇⣾⡟⣼⣗⡊⣿⢻⡇⢤⣤⡄⠀⠀⢘⣠⣴⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣸⣿⣿⣿⣿⠃⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡏⠁⠉⠸⠃⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⢿⢿⣇⣆⢠⣾⣻⣿⣿⣿⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡞⠀⢠⣶⡿⣷⣿⣿⣷⣶⣶⣶⣿⢾⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠲⣶⠶⡷⠉⠈⠁⠛⣛⠘⣣⣿⣹⡼⢿⡿⠀⠘⠋⠉⠹⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⣠⣧⣤⣿⣿⡟⠋⠁⢀⣐⡀⠀⠀⠀⠈⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⣰⣾⣿⣿⣦⠀⠀⠀⠀⡴⠿⠿⣿⠿⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⣊⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⣤⡄⡤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡖⡎⣾⡧⠀⡇⣿⢿⡸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⠈⠉⠉⠁⠀⠉⠉⠉⠁⢯⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⡇⡅⣿⣿⢸⣸⠄⡏⡆⢸⢼⣇⠧⢟⢿⣸⣦⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠉⠀⠀⠐⠷⢶⣿⣿⢿⢀⣛⣛⣿⣟⣻⢻⢿⣿⡿⣯⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⡧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⡸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⠶⠄⠰⠲⠶⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠘⢻⣿⣿⣿⣿⡇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠠⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠃⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣤⣶⣶⣶⣶⣶⣾⣤⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⢟⡻⣉⣩⣭⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢻⠞⠁⠀⠀⠀⠈⠰⠂⢩⣄⠙⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠠⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠀⠀⠀⢀⣾⣷⣶⣿⣿⣿⣶⡌⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡍⠀⠀⡻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣮⣿⣿⣿⣿⣿⣿⣿⡇⢐⣿⣿⣿⣿⡄⠀⠀⠀⠀⢶⣶⠖⣒⣿⣿⡶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠙⠃
⠀⠀⠀⠀⠀⠛⡛⠛⠛⣿⠛⠻⣿⣧⠰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣉⡧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⣀⣦⡀
⠀⠀⠀⠀⠀⢀⣀⢀⡄⢿⣹⣀⣠⣿⡁⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣶⣶⣶⣀⡀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠚⢻⣿⣷⣸⣻⣿⣿⣿⡂⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⢇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⣦⡄⠀⠀⠀⠈⡽⢿⠇⢼⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠇
⢸⣿⣷⠀⠀⢠⣴⣄⡊⠀⢸⣿⣿⡿⠀⢾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣹⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣤⡀
⢸⡿⠋⠀⠀⠀⠈⠿⣷⣇⣸⣿⣿⠁⠀⠈⠙⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣿⢛⣵⡾⣯⣟⡭⣽⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣯⡴⠁⠿⢅⣾⣿⣿⣿⣄⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠉⢛⠃
⠈⠁⠀⠀⠀⠀⠀⠀⢀⡏⡿⢻⡿⠀⠀⠀⠀⠻⠿⣿⣦⠀⢀⠀⠀⣀⠀⢀⣶⣿⣷⣿⣷⣸⣷⣟⢸⡏⣿⢻⣿⣿⣿⣿⣿⣿⠟⠉⠙⠛⠁⢠⡄⠈⠿⢿⣿⢿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠃⣸⡇⠀⠀⠀⣄⣀⣀⣀⠀⣄⢽⠿⢶⣿⣶⣾⣿⣿⣯⣿⣧⣛⣻⣿⣻⠷⠟⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠁⠀⠀⣠⣧⡀⣈⣁⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣼⣶⣦⠀⠀⢠⣿⣧⣀⠀⣠⣼⣿⣹⣿⣸⣿⢈⣿⣿⡇⣶⢳⣏⢻⣿⣽⣿⣿⡿⣟⣛⡿⣇⠿⠿⣿⡿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠻⢿⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣠⣿⣿⣿⡟⠀⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣿⢺⣧⣿⢸⡟⣿⠋⣿⢸⡟⣿⢀⡛⢸⣏⡃⣿⡇⣾⡟⣼⣟⡊⣿⢻⡇⢤⣤⡄⠀⠀⢐⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣸⣿⣿⣿⣿⠇⠀⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡯⡁⠉⠸⠃⠛⠘⠏⠹⢇⢿⡼⡇⣾⣗⢲⡏⣿⢹⡇⣿⢛⢼⡿⣾⢿⢿⣇⣆⢠⣾⣻⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣾⢸⣿⡾⠀⢠⣶⡿⣷⣿⣿⣷⣶⣶⣶⣿⢾⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠻⠶⡶⠶⠷⠉⠈⠁⠛⣛⠘⣣⣿⣹⣼⢿⡿⠀⠹⠋⠉⠽⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢸⣿⣿⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢀⣠⣧⣬⣿⣿⡿⠛⠉⢀⣀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⢸⣿⣇⠀⢸⣿⡇⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⣠⣾⣿⣿⣦⠀⠀⠀⠀⡰⠿⠿⣿⠿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣺⣿⣿⢸⣿⣯⡄⢸⣿⣇⣿⣿⡊⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⣤⡄⡤⣝⢭⢩⢹⡟⡍⢲⢂⡏⡆⣎⣶⡧⠀⡇⣿⣿⡸⣝⢼⣿⡾⡇⣇⣿⢸⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣾⣿⣿⠈⠉⠉⠁⠀⠉⠉⠉⠁⢫⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣸⡇⡅⣿⣿⢸⣸⠇⡏⡆⢸⢼⣇⠧⢟⢿⣸⣧⣇⣻⣞⣜⣚⣿⣻⣧⣷⣽⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠐⠷⢶⣿⣿⢿⢀⣛⣛⣿⣟⣻⢻⢿⣻⡿⣯⣭⣯⡍⡽⡯⡏⡏⣯⢹⢱⣸⡖⡎⣶⢰⣿⣿⣿⣿⡇
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⣾⡁⠈⣿⢹⣧⡇⣿⢿⣿⣧⣸⣸⡟⡗⡗⣿⢻⢸⣞⣽⡗⢹⢼⣸⡷⡇⡇⣇⡇⢿⢿⠸⠟⠧⠇⠿⠻⣸⣿⣿⣿⡇
⢸⠟⠲⣶⠀⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢨⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠹⠀⠀⠛⠈⠃⠃⢛⣊⣿⣷⣬⣿⣥⣥⣥⣮⣽⣾⣿⣷⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠘⢻⣿⣿⣿⣿⡇

                    ䷩ 𝚕𝚒𝚗𝚎 2409

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/16/epo-iac-kangaroo-tribunal/#comments
    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


⣿⢼⠧⡧⢼⠤⡧⢼⠬⡧⣿⢼⡧⣿⢼⡧⣿⢼⡭⡯⣽⢽⡧⣿⢽⡯⣿⢽⡯⣯⣽⣭⣯⣿⣽⣯⣿⢽⡯⣯⣽⣭⣯⣽⣽⣯⣿⣽⣯⣯⣽⣭⣯⣽⣽⣯⣿⣽⣯⣿⣽⣭⣯⣽⣽⣯⣿⣽⣯⣯⣽⣭⣯⣿⣽⣯⣿⣽
⣿⣺⣗⣟⣺⣓⣗⣻⣚⣗⣿⣺⣗⣿⢺⡗⣿⣺⣛⣗⣿⢺⡗⣿⢺⡗⣿⢺⡗⣷⣾⢶⡷⣿⢺⡗⣿⢺⡗⣷⢺⠶⡷⣾⢺⡗⣿⢺⡗⣷⢾⠶⡷⢾⢾⡷⣿⢺⡷⣿⢾⠶⡷⣾⢾⡷⣿⢾⡷⣿⢾⠶⡷⣿⢾⡷⣿⢾
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠋⠋⠙⠉⠋⠙⠉⠋⠙⠙⠋⠛⠙⠋⠛⠙⠋⠋⠙⠙⠋⠛⠙⠋⠛⠙⠋⠛⠙⠛⠋⠛⠙⠋⠛⠙⠋⠛⠙⠛⠛⠛⠙⠋⠛⠙⠋⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠛⠛
⢸⣿⣿⣿⣿⣿⡇⠤⠶⠴⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠯⠭⠭⠍⠀⠀
⢸⣿⣿⣿⣿⣿⡇⠭⠭⠿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣷⢸⡏⣶⠱⢸⡿⢺⣿⣷⣾⣷⣸⡇⠀⡼⣿⡄⣿⢹⣾⡏⣷⣾⢳⣲⣷⣾⡇⡾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠛⠛⠙⠒⠀⠀
⠸⠿⠿⠿⠿⠿⠇⠋⠃⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠀⠉⠈⠁⠈⠁⠈⠉⠉⠈⠈⠈⠁⠈⠁⠉⠉⠛⠉⠘⠋⠁⠈⠁⠈⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠇⠛⠙⠛⠋⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠰⢆⣀⡀⣀⣀⣀⣀⣀⣀⣀⢐⡆⣴⣀⣆⢀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤⠸⠿⠇⠿⠿⠼⠿⠿⠿⠿⠼⠇⠿⠜⠧⠻⠭⠻⠯⠃⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⡄⠀⠀⠀⠀⢀⣠⣴⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠻⠒⠠⣶⣤⠈⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠾⣯⣥⣤⣽⢡⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠈⠽⢓⣶⣿⢲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⢠⣿⣿⣏⠙⢘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠠⣶⣆⣚⠟⠋⠀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⠈⢷⣶⣆⠀⢂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⡷⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠇⢸⣿⣿⣿⣷⠶⠿⢿⣤⠀⠘⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠟⠉⠉⠀⠉⠉⠉⠁⠠⡀⠀⠉⠁⠀⠀⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⣿⣻⣟⣿⣿⣿⣿⣿⡿⠟⠋⠉⠁⢸⢇⠀⠈⢿⣿⣿⣑⠘⠘⠀⢙⠂⠤⠑⠒⢿⣿⣿⣿⣿⣿⣟⣿⣻⣟⣿⣻⣿⡟⠁⠀⠀⠀⣀⡤⠊⠀⠀⢠⣹⣦⣤⣦⠀⠀⠀⠀⠴⣿⣿⣿⠟⠁⢻⣟⣿⣻⣿⣿⣿⣿⣟⣿⣻
⣿⣿⣯⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠘⢿⣧⣄⢂⡢⢹⠟⠋⠀⠀⠀⠀⢢⡄⠀⠈⣿⣿⣿⣿⣿⣯⠿⠙⠋⠛⠛⠛⠁⠀⣀⣴⣾⢋⡀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⢻⣿⣽⣿⣿⣿⣿⣯⣿⣽
⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠞⠃⠀⠀⠀⠀⠀⠀⠀⢩⣌⢮⣿⣿⣿⣿⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⣿⣿⣿⣿⡇⣿⣽⣧⣧⣿⣾⣼⣾⣿⣿⣮⣬⣄⣅⣍⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⣿⢾⡷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⣿⡇⣿⣿⢙⡟⢿⣿⢿⣿⡏⣿⣿⡻⢻⣿⣻⢿⡟⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢿⡿⢷⣿⢾
⣿⣻⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣃⣿⣛⠿⠿⢿⢿⣿⡟⣿⠻⣻⣿⣿⣿⣿⡟⠻⠷⠻⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⢾⣷⡚⣿⣻
⣿⣽⣠⣤⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⢽⣿⣶⣾⣶⣿⣾⣷⣷⣿⣾⣷⣿⣿⣾⣿⣿⣶⣴⣶⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢽⣿⢧⣿⣽
⣿⣿⡟⣛⣏⡅⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢀⣀⡀⠀⠘⣿⣿⣿⣿⣿⣿⢺⣿⣴⣽⣽⣯⣯⣿⣟⣯⣽⣼⣿⣭⣿⣭⣿⣽⣿⣯⣿⣿⡇⢰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣦⡌⢻⣿
⠛⠛⢣⠩⢨⡂⠈⠉⠉⠁⠁⠀⠀⠀⠀⠀⠈⠉⠉⠀⢿⣿⣛⡛⠛⠁⠀⠀⠀⣿⣿⣿⣿⣿⡅⣿⣹⣻⣟⣟⣿⣙⣹⣻⣿⣍⣛⣟⣻⣿⣛⣿⣿⣿⣿⣿⡇⠐⢚⣷⣒⣶⣦⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⡿⢿⣿⢸⣿
⠀⠀⢸⣧⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣒⡆⣿⡿⢿⢻⠻⠿⠿⣿⣿⣟⣿⠿⣿⡟⠿⡿⠿⣿⡿⣿⡟⡇⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⡶⣼⣶⣶⡿⠟⢛
⠀⠀⠘⣿⣀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⢷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠉⠭⠟⠋⠁⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠸⠃⠈⢻⢻⣿⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣭⣭⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⢿⠟⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠀⠐⠾⠿⠿⠿⠿⠿⠟⠓⠚⠛⠛⢀⠀⠀⢀⣠⣠⣤⣩⣽⡿⢀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁⠒⠅⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 2463

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/16/irc-log-150722/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/16/irc-log-150722/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.16.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Friday,_July_15,_2022⠀✐


Posted in IRC_Logs at 2:22 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-150722.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-150722.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-150722.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-150722.gmi
Over HTTP:


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


                                         #techrights_log_as_HTML5                                                                                  #boycottnovell_log_as_HTML5


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


                                    #boycottnovell-social_log_as_HTML5                                                                               #techbytes_log_as_HTML5


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


                                          #techrights_log_as_text                                                                                   #boycottnovell_log_as_text


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


                                     #boycottnovell-social_log_as_text                                                                                #techbytes_log_as_text


                          Enter_the_IRC_channels_now


===============================================================================
§ IPFS Mirrors⠀➾


CID                                              Description     Object type


                                                 IRC log for
 QmUjt8hREipbcMSbUEjMsbFpJkoxazs5qPsYTrGSzVFDDm #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmP3Z8RWshh1881z9P8k7UeSQdbSNircCASKXxGgbRuS3u (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmWScchfvor1zJEDuSBAuu6a4H2b26hnpNuwcPaaYiZ5WK social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmfW9rC2AACyBRtVCQdo6wwyvV2nJWhPQeZeaw9hMKp1ph social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmR6YiuMWCLpHaPZLZf5WMSj2pG6oYY11VnbdxrS7cFqth #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmVYCBnXr1p3DDTjmvZbzkXwaxCC1j2BefwraPYHrK2Niz (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 Qmd4UW7ak72Y46pGbZWeJkPbqovcBzKie4VuaZw7xfKyfL #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmcgAtVxFphYKd2TAmBSw9D6jnW9QQYMnjs9PUJRKjWBAw (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmdVCZ22xUbZkpsSDmSDMrnFTMypCGWw1f2punvumLq2NJ



                    ䷩ 𝚕𝚒𝚗𝚎 2590

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/07/16/microsoft-cuts-off-freesw/#comments
    Gemini version at gemini://gemini.techrights.org/2022/07/16/microsoft-cuts-off-freesw/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.16.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ 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⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ 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! █
_________
* As this_article_from_yesterday_put_it: “The European Union is run on a day-
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.


** EPO staff trusts them even less than it trusts Campinos. Based on the latest
survey as well as prior surveys.


                    🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇EPO_AC_trust_level⦈_
      Slide from the_EPO_Staff_Survey which ended a couple of months ago


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣡⣱⣍⠱⠡⠿⠀⠿⠩⠱⠉⠋⠼⠈⠌⠉⠡⠁⠏⠎⠸⠧⠉⠏⠙⠸⠎⠎⢏⢌⡱⣉⢎⣬⣿⣉⣧⣧⣬⣉⢌⣧⣎⣉⣏⢎⣉⣫⣯⡉⠊⣏⡉⢎⡡⣉⢎⣈⡡⣩⣉⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⠉⡛⠛⢸⢛⠛⡋⢛⡛⠙⣻⠛⣛⡛⡛⢉⠛⠛⠛⡏⣭⢟⠛⡟⢛⡟⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣷⣷⠘⠓⠚⠒⠚⠓⠒⠛⠓⠛⠛⠒⠚⠓⠓⠓⠛⠒⠓⠚⠚⠚⠓⠚⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣱⣔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣈⣺⣃⣽⣿⣿⣿⣏⣹⣀⣀⣃⣿⣿⣿⣿⣏⣑⣐⣅⣁⣿⣿⠿⢛⣷⡀⢑⣂⣨⣿⣿⣿⣿⣉⣇⣁⣊⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠛⠛⠻⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠿⠄⠛⠡⠿⠆⠋⠽⠿⠿⠿⠿⠿⠿⠧⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿
⣿⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣥⠸⣿⣄⠻⣦⢉⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣄⣠⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠷⡌⢻⣷⡈⣿⣦⣿⣿⣿⣿⣿⣿⡿⠿⣍⢸⣿⡏⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣦⣶⣼⠿⠟⠛⠛⠻⠿⢿⣿⣿⣶⡖⢘⢉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢤⠾⢷⡀⢶⣦⣄⣽⣷⣿⣿⣿⣿⣿⠿⣿⡇⢖⣠⠾⣦⣼⡇⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋⣭⡙⢻⣄⠺⠟⣻⣶⣿⣿⣿⣿⣿⣿⣿⠛⣧⣘⣛⢳⣬⣥⣾⣿⣿⡇⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣯⡈⢷⡌⢻⡿⢀⣿⣦⣾⣿⣿⣿⡟⢹⡄⢛⣅⠹⣷⠈⣯⣥⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣀⣤⡄⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣦⠘⣋⣿⣌⢻⣦⣴⣿⣿⣿⣿⣟⠻⣤⠻⣄⢺⣆⠻⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣀⣄⣹⣿⣿⡇⠀⠀⠒⠛⠀⠀⢸⣿⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⡍⢙⠻⢆⠹⣧⡘⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣄⡙⣦⠙⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⣾⣿⣿⠟⢋⣡⡄⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⡀⠈⠉⠉⠬⣍⢻⣆⠻⣶⣦⣼⣿⣿⣿⣿⣿⣿⠿⣿⣿⣧⡘⠟⢣⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠋⠉⠁⢲⣿⣛⡃⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢙⣛⡀⢀⡀⠀⠀⠛⠓⣛⣛⣛⣛⣛⣛⠛⠛⣃⣚⡙⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣓⢙⣛⣛⣛⣛⣛⣛⣛⣻
⣿⡟⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⣿⢿⣦⣤⣴⢠⠀⠀⠈⠛⢿⠿⣿⠁⣾⣷⠘⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿
⣿⠁⠛⠻⢿⣿⠿⠇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠡⠾⠿⠿⠿⠒⠚⠢⠀⠀⠀⠐⠈⠷⠤⠴⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠼⠿⠿⠿⠿⠿⠿⠿⠿⠜⠿⠿⠿⠿⠿⠿⢿
⣿⠀⣶⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⠀⠀⢀⣈⣉⠀⠀⠀⠀⢸⣿⠂⠀⠀⠀⠙⢿⣿⣿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿
⣿⠄⠹⢿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡆⠀⠀⣁⣄⠀⠀⠀⠀⠈⢪⡉⠁⠀⠀⠀⠀⠉⣉⡐⠚⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿
⣿⣥⠀⠒⠈⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⠀⠀⡄⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡔⣶⣶⣶⣶⣾
⠛⠉⠀⠀⢠⣴⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⢍⡉⠉⡁⢃⣦⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿
⠀⠀⣀⣤⡀⠙⢭⡅⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢨⡅⠀⣬⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣭⡅⠀⠀⠀⠀⠀⠀⠉⠉⣭⣭⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣄⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣅⢨⣭⣭⣽
⢀⣼⣿⣿⣿⣄⠈⠃⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⠀⢀⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣿⡧⠦⢤⣤⣌⢉⠉⠛⡛⠏⡉⢻⣿⣿⡟⢛⠛⢛⠛⠛⠛⢟⠛⠛⠛⠻⣿⣿
⣾⣿⣉⣍⣻⣿⣁⣀⠀⠀⠀⣀⣀⣀⣈⣉⣀⣀⡈⠀⣈⣉⣀⣀⣀⣀⣀⣀⣈⡉⠁⣀⣀⡉⠀⠀⠀⠀⠀⢀⣀⣀⣀⣉⣉⣀⣀⣉⣉⣉⣁⣀⣀⣀⣀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣉⣀⣁⣀⣉⣁⣉⣹
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠉⠃⢀⣈⣹⡿⠀⣰⣿⣿⣿⣿⣿⣿⣃⣉⡍⠁⣼⡿⠋⠀⠀⠀⠀⠀⠀⣨⣍⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣘⣍⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣉⣩⣹⣯⣉⣉⣈⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠈⠉⠁⠰⠿⠿⣿⣿⣿⣿⣿⣿⠟⠁⠘⠉⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2973

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 07.16.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


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?


===============================================================================
* Gemini_(Primer) links can be opened using Gemini_software. It’s like the
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.


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


╘══════════════════════════════════════════════════════════════════════════════╛
                       ¶ Lines in total: 6630
    ➮ Generation completed at 02:41, i.e. 77 seconds to (re)generate ⟲