Tux Machines Bulletin for Monday, January 13, 2025
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Generated Tue 14 Jan 02:49:52 GMT 2025
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 http://news.tuxmachines.org


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

⦿ Tux Machines  -  9to5Linux Weekly Roundup: January 12th, 2025

⦿ Tux Machines  -  Audiocasts/Shows: Linux Out Loud, GNU World Order, This Week in Linux, mintCast, and The Linux Link Tech Show

⦿ Tux Machines  -  DXVK 2.5.3 Brings Improvements for Far Cry 5, Max Payne 3, and Other Games

⦿ Tux Machines  -  Enlightenment 0.27 Desktop Environment Released

⦿ Tux Machines  -  Free and Open Source Software

⦿ Tux Machines  -  Games: Bazzite and Bad Apple

⦿ Tux Machines  -  Games: Steam Deck, Native GNU/Linux Clients, and More

⦿ Tux Machines  -  GNU/Linux and Free Software Leftovers

⦿ Tux Machines  -  Hidden Files in Linux Explained

⦿ Tux Machines  -  How to Install FreeBSD 13 and 14 on Desktops

⦿ Tux Machines  -  KDE: kcursorgen and SVG cursors

⦿ Tux Machines  -  Kdenlive 24.12.1 and KDE in "Tech Over Tea"

⦿ Tux Machines  -  Linux 6.13-rc7

⦿ Tux Machines  -  Linux Devices and Open Hardware

⦿ Tux Machines  -  LXQt Wayland support is now here

⦿ Tux Machines  -  MX Linux 23.5 Brings Debian 12.9 and Xfce 4.20

⦿ Tux Machines  -  MX Linux 23.5 Released with Xfce 4.20 and Linux 6.12 LTS, Based on Debian 12.9

⦿ Tux Machines  -  Open Hardware: Open-Source Design, Arduino, Raspberry Pi, and More

⦿ Tux Machines  -  openSUSE Tumbleweed Now Offers Wayland Support for the LXQt Desktop

⦿ Tux Machines  -  Plop Linux – distribution designed for advanced Linux users

⦿ Tux Machines  -  Programming Leftovers

⦿ Tux Machines  -  Review: DAT Linux 2.0

⦿ Tux Machines  -  Shortwave Now Supports Play Internet Radio in the Background

⦿ Tux Machines  -  This Week in KDE Apps: Usability improvements, new features, and updated apps

⦿ Tux Machines  -  Tiling Shell’s Newest Feature Speeds Up Window Snapping

⦿ Tux Machines  -  Today in Techrights

⦿ Tux Machines  -  today's howtos

⦿ Tux Machines  -  today's howtos

⦿ Tux Machines  -  today's leftovers

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
https://tuxmachines.org/n/2025/01/13/9to5Linux_Weekly_Roundup_January_12th_2025.shtml
https://tuxmachines.org/n/2025/01/13/Audiocasts_Shows_Linux_Out_Loud_GNU_World_Order_This_Week_in_Li.shtml
https://tuxmachines.org/n/2025/01/13/DXVK_2_5_3_Brings_Improvements_for_Far_Cry_5_Max_Payne_3_and_Ot.shtml
https://tuxmachines.org/n/2025/01/13/Enlightenment_0_27_Desktop_Environment_Released.shtml
https://tuxmachines.org/n/2025/01/13/Free_and_Open_Source_Software.shtml
https://tuxmachines.org/n/2025/01/13/Games_Bazzite_and_Bad_Apple.shtml
https://tuxmachines.org/n/2025/01/13/Games_Steam_Deck_Native_GNU_Linux_Clients_and_More.shtml
https://tuxmachines.org/n/2025/01/13/GNU_Linux_and_Free_Software_Leftovers.shtml
https://tuxmachines.org/n/2025/01/13/Hidden_Files_in_Linux_Explained.shtml
https://tuxmachines.org/n/2025/01/13/How_to_Install_FreeBSD_13_and_14_on_Desktops.shtml
https://tuxmachines.org/n/2025/01/13/KDE_kcursorgen_and_SVG_cursors.shtml
https://tuxmachines.org/n/2025/01/13/Kdenlive_24_12_1_and_KDE_in_Tech_Over_Tea.shtml
https://tuxmachines.org/n/2025/01/13/Linux_6_13_rc7.shtml
https://tuxmachines.org/n/2025/01/13/Linux_Devices_and_Open_Hardware.shtml
https://tuxmachines.org/n/2025/01/13/LXQt_Wayland_support_is_now_here.shtml
https://tuxmachines.org/n/2025/01/13/MX_Linux_23_5_Brings_Debian_12_9_and_Xfce_4_20.shtml
https://tuxmachines.org/n/2025/01/13/MX_Linux_23_5_Released_with_Xfce_4_20_and_Linux_6_12_LTS_Based_.shtml
https://tuxmachines.org/n/2025/01/13/Open_Hardware_Open_Source_Design_Arduino_Raspberry_Pi_and_More.shtml
https://tuxmachines.org/n/2025/01/13/openSUSE_Tumbleweed_Now_Offers_Wayland_Support_for_the_LXQt_Des.shtml
https://tuxmachines.org/n/2025/01/13/Plop_Linux_distribution_designed_for_advanced_Linux_users.shtml
https://tuxmachines.org/n/2025/01/13/Programming_Leftovers.shtml
https://tuxmachines.org/n/2025/01/13/Review_DAT_Linux_2_0.shtml
https://tuxmachines.org/n/2025/01/13/Shortwave_Now_Supports_Play_Internet_Radio_in_the_Background.shtml
https://tuxmachines.org/n/2025/01/13/This_Week_in_KDE_Apps_Usability_improvements_new_features_and_u.shtml
https://tuxmachines.org/n/2025/01/13/Tiling_Shell_s_Newest_Feature_Speeds_Up_Window_Snapping.shtml
https://tuxmachines.org/n/2025/01/13/Today_in_Techrights.shtml
https://tuxmachines.org/n/2025/01/13/today_s_howtos.1.shtml
https://tuxmachines.org/n/2025/01/13/today_s_howtos.shtml
https://tuxmachines.org/n/2025/01/13/today_s_leftovers.shtml


                    ䷩ 𝚕𝚒𝚗𝚎 100

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/9to5Linux_Weekly_Roundup_January_12th_2025.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/9to5Linux_Weekly_Roundup_January_12th_2025.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 9to5Linux Weekly Roundup: January 12th,
2025⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Marius Nestor on Jan 13, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇9to5Linux_Weekly_Roundup⦈_


This has been a great week with lots of cool news and releases, starting with
the Firefox 134 web browser and continuing with the 16GB Raspberry Pi 5 model.
Fans of the KDE Plasma desktop environment received many goodies too, including
a beta version of the upcoming KDE Plasma 6.3 series.


This week also brought news about the upcoming Budgie 11 and Rust-based COSMIC
desktop environments, a new version of the Debian 12 “Bookworm” operating
system series, some great software releases including Calibre 7.24, Scribus
1.6.3, and Sigil 2.4, as well as a new release of the Tails amnesic incognito
live system.


On top of that, I show you how to install Linux kernel 6.12 LTS on Ubuntu and
how to switch the primary GPU to NVIDIA on Wayland. Below, you can check out
this week’s hottest news and access all the distro and package downloads
released this past week in the 9to5Linux weekly roundup for January 12th, 2025.


Read_on




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣠⣴⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣤⠀⠐⡆⢀⣀⠀⢀⡀⢰⠂⠀⢸⢀⠀⢀⠀⠀⣸⠊⢉⡆⣠⢤⠀⠀⠀⠀⣀⣀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⣿⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡰⠻⣄⢠⠃⣟⣊⠀⣗⣊⢸⠻⠅⢸⠸⣠⡎⠀⠀⣿⠶⣋⠀⣇⡼⢸⡠⢻⠰⠏⠸⡄⠯⣽⡄⣇⠜⡇⢸⣩⠇⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⣽⣿⣧⣄⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣈⡛⠿⠿⠿⢛⣁⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠿⠿⠿⠟⠀⠙⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 164

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/Audiocasts_Shows_Linux_Out_Loud_GNU_World_Order_This_Week_in_Li.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/Audiocasts_Shows_Linux_Out_Loud_GNU_World_Order_This_Week_in_Li.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Audiocasts/Shows: Linux Out Loud, GNU World
Order, This Week in Linux, mintCast, and The Linux Link Tech
Show⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 13, 2025


    * ⚓ Tux Digital ☛ Linux_Out_Loud_105:_Retro_Keyboards_to_Smart_Home_Wins⠀⇛


           In GNU/Linux Out Loud episode 105, the hosts look ahead to 2025
           with big GNU/Linux hopes and smart tech ideas! Nate shows off
           his retro-inspired keyboard. Bill has an update on Home
           Assistant voice control, and the team debates universal
           packages like AppImages and Flatpaks.


    * ⚓ GNU World Order (Audio Show) ☛ GNU_World_Order_598⠀⇛


           **libnma** , **mozilla-firefox** , **mozilla-thunderbird** ,
           **network-


           manager-applet** , **pan** , **pavucontrol** , **pidgin** ,
           **rdesktop** ,


           **rxvt-unicode** , **sane** from the **xap** software set of
           Slackware Linux.


           shasum -
           a256=ccf9c212691fb3bda12e99140784a7dbb939fbb7a19fa5fe65076bd397286930


    * ⚓ Tux Digital ☛ This_Week_in_Linux_293:_COSMIC_Alpha_5,_KDE_Plasma_6.3
      beta,_SteamOS_beyond_Steam_Deck_&_more_GNU/Linux_news⠀⇛


           This week in Linux, we have a lot to talk about. We’re gonna
           talk about some alphas and some betas and also some big news
           from Valve.


    * ⚓ This_Week_in_Linux_293:_COSMIC_Alpha_5,_KDE_Plasma_6.3_beta,_SteamOS
      beyond_Steam_Deck_&_more_GNU/Linux_news⠀⇛


           So we have KDE Plasma 6.3 beta that is coming out with System76
           releasing the Alpha 5 of the COSMIC Desktop Environment and
           Valve announced that SteamOS is going to expand beyond the
           Steam Deck. All of this and so much more on this week in Linux,
           the weekly news show that keeps you up to date with what's
           going on in the GNU/Linux and open source world. Now let's jump
           right into Your Source for GNU/Linux GNews.


    * ⚓ mintCast Podcast ☛ mintCast_452_–_Prognostication_Pandemonium!⠀⇛


           First up in the news: Not a lot of GNU/Linux news….but a lot of
           Mint News with 22.1 BETA Released


           Then in our Wanderings: Joe prepares the innards, Bill enjoys
           some butter with his jelly, Eric does nothing, Moss takes a
           break and All roads lead to Ubuntu for Majid


           In our Innards section: A look back at last years predictions,
           and making some predictions for 2025


    * ⚓ The TLLTS Podcast ☛ The_Linux_Link_Tech_Show_Episode_1081⠀⇛


           Joel gets toe socks.





                    ䷩ 𝚕𝚒𝚗𝚎 255

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/DXVK_2_5_3_Brings_Improvements_for_Far_Cry_5_Max_Payne_3_and_Ot.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/DXVK_2_5_3_Brings_Improvements_for_Far_Cry_5_Max_Payne_3_and_Ot.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ DXVK 2.5.3 Brings Improvements for Far Cry
5, Max Payne 3, and Other Games⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Marius Nestor on Jan 13, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇DXVK_2.5.3⦈_


DXVK 2.5.3 is here to improve support for various video games, including Halo:
The Master Chief Collection, TopSpin 2k25, Far Cry 5, Max Payne 3, Bright
Memory, Arcana Heart 3 LOVE MAX!!!!!, and The Hurricane of the Varstray -
Collateral hazard.


On top of that, DXVK 2.5.3 improves the debugging experience when
DXVK_DEBUG=markers is set, fixes a potential issue with handling NaN
tessellation factors in D3D11 hull shaders, fixes an issue with D3D9 shader
validation causing valid shader code to be rejected, and fixes a regression
that caused severe rendering issues in many D3D8 and D3D9 games that use fixed-
function rendering.


Read_on




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⢠⣤⣤⣤⣤⢠⣤⣤⣤⣄⣤⣤⣤⣤⡄⠀⢀⣠⣤⣄⡀⠀⠀⢠⣤⣤⣤⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢱⡎⣿⢸⣿⡙⣹⣿⢸⣇⢿⢹⣿⣿⡏⢫⣿⡇⠀⠘⠋⣁⣽⡿⠀⠀⣾⣯⣭⣍⠀⠀⠚⠋⣩⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⠇⣿⢸⣿⢣⢻⣿⢸⣿⠘⣼⣿⣿⡇⡌⣿⡇⠀⢰⣿⠛⠋⠁⠀⠀⣤⡁⢈⣿⠆⠀⣠⣄⢉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠸⠿⠿⠿⠿⠸⠿⠿⠿⠟⠻⠿⠿⠿⠇⠀⠘⠛⠛⠛⠛⠛⠃⠙⠛⠛⠉⠘⠛⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 314

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/Enlightenment_0_27_Desktop_Environment_Released.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/Enlightenment_0_27_Desktop_Environment_Released.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Enlightenment 0.27 Desktop Environment
Released⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Rianne Schestowitz on Jan 13, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Enlightenment_0.27⦈_


Quoting: Enlightenment 0.27 Desktop Environment Released —


     After more than a year in making after its previous 0.26 release, the
     lightweight modular desktop environment and compositing window
     manager Enlightenment has just rolled out its latest version, 0.27.


     Debuting an impressive 28 years ago—yes, that’s right, when GNOME or
     KDE didn’t exist yet—this project is one of the oldest still
     maintained open-source, desktop-focused endeavors. Remarkably, it
     continues to be actively developed, largely thanks to its original
     creator, Carsten Haitzler.


Read_on




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⣧⡀⣸⡇⢀⡎⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⣀⡿⠖⣛⣫⣯⣭⣙⣛⠲⢿⣀⣴⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡤⢛⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡻⣤⡞⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣵⣿⣿⠟⢋⣁⣤⣤⣤⣤⣈⠙⢿⣿⣿⣎⠁⠀⠀⣿⠘⠳⢄⢀⡠⣾⣲⡆⠀⡀⣺⣆⡀⢀⡀⢠⢀⢀⣀⡀⠀⠀⠀⢀⡀⡀⣀⡀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⣿⣿⣇⠀⠀⣿⠐⠃⣿⠉⣿⢿⣻⡿⣇⣽⢿⡏⣿⢸⣯⣯⡽⢾⡏⣹⣾⡇⢹⠊⣿⣾⡯⡷⣿⠉⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⡄⠀⠛⠒⠚⠛⠀⠛⠚⠛⢻⡟⢷⡟⠃⢛⢚⢗⢝⣛⣺⣳⣾⡟⠃⠘⠃⣿⣾⣟⣿⣿⣾⡟⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⡇⢈⣿⣿⠇⠀⢀⡴⠠⣄⠀⠀⣠⣾⣦⣭⣿⣾⣾⣾⣶⣶⣷⣿⣿⣷⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣧⣼⣿⣿⠀⠀⣼⠇⠀⢸⣷⢀⢅⡱⣹⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣧⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⠃⠀⠀⣿⡆⠀⢸⡟⠈⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⢿⣿⣿⣦⣄⣀⣀⣀⣀⣤⣶⡀⠈⠙⣡⡄⠀⠀⠈⠣⠀⠞⠱⠶⠾⠶⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠉⣷⣭⡻⠿⣿⣿⣿⣿⣿⡿⠿⢃⢤⣦⠉⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⡿⠋⣶⠖⢷⡆⠲⡶⠙⢿⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠏⠀⢸⠇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 374

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/Free_and_Open_Source_Software.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/Free_and_Open_Source_Software.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Free and Open Source
Software⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Rianne Schestowitz on Jan 13, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇play_timer⦈_


    * ⚓ Play_Timer_-_native-feeling_timers_-_LinuxLinks⠀⇛


           Play Timer aims to be as keyboard friendly as possible. Use
           navigation keys (arrows, tab, shift+tab, space, enter) or start
           inputting numbers right away.


           This is free and open source software.



    * ⚓ CHADTree_-_file_explorer_for_Neovim_-_LinuxLinks⠀⇛


           CHADTree is a file manager / file explorer for Neovim. There
           are projects that seek to move Vim in a different direction.
           One of these projects is Neovim.


           This is free and open source software.



    * ⚓ BUTT_-_broadcast_using_this_tool_-_LinuxLinks⠀⇛


           BUTT (Broadcast Using This Tool) is an easy to use streaming
           tool.


           The main purpose of BUTT is to stream live audio from your
           computers microphone or line input to an Icecast, Shoutcast or
           WebRTC (WHIP) server.


           This is free and open source software.




⠀⠀⠀⠀⠀⠀⠀⠺⠉⠀⠀⠀⣼⣿⣿⣿⣿⣿⡏⠀⠘⣿⣿⣶⡟⠀⠀⠉⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⢌⣀⢀⡀⠀⠀⠀⠀⠌⠀⠀⠠⡮⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡟⣦⣶⣿⣿⣿⣷⣤⡀⠀⠀⢀⠀⠀⠀⢀⣤⠴⠖⣚⣛⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢡⣦⠀⠉⠙⠛⠿⢛⣁⠀⠀⠀⠀⠀⠀⣠⡴⣞⣫⡽⡽⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣴⣶⣿⣿⣧⠀⠀⠀⣠⢞⣵⢺⠻⣿⣷⣖⣷⣿⣿⣌⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠻⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣼⣯⣿⣿⣷⣷⣿⣽⡋⠉⣿⣿⣿⣿⣯⣻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⣸⣇⣾⣌⣐⣽⣿⣿⣿⣵⡃⣯⣿⣿⣿⣿⣿⣿⣿⣿⣧⣇⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢻⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠀⢀⡴⠟⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⡄⣿⣻⣏⣰⣻⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⡀⠀⠀⢲⣄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢳⣽⣧⢿⣿⡿⣟⢿⣿⣿⣿⣧⣽⣿⣿⣿⣿⣇⣼⣿⣿⢯⠃⠀⠀⠠⣶⠄⠀⠀⠀⠀⣠⣿⣿⣿⡖⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢷⠹⣿⡻⣥⣬⣾⣿⢿⣿⣿⣿⣿⣿⡯⡋⢿⡟⡽⠃⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠳⣌⠿⣮⣟⢿⣢⣮⣿⣿⢍⣎⣿⡷⣟⣭⠞⠁⠀⣴⣆⠀⠀⠀⠀⠆⠀⠀⠀⣼⣾⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠈⠙⠮⡙⠻⠶⣿⡿⢿⣯⡝⠗⠋⠉⠀⢀⣠⣾⣿⣿⣆⠀⠀⠀⠀⠀⢴⣿⣍⣡⡀⢀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⢹⡿⠛⠓⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 446

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/Games_Bazzite_and_Bad_Apple.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/Games_Bazzite_and_Bad_Apple.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Games: Bazzite and Bad
Apple⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 13, 2025


    * ⚓ Forbes ☛ With_SteamOS_Expanding_Beyond_Steam_Deck,_Is_It_Game_Over_For
      Bazzite?⠀⇛


           Bazzite is currently the GNU/Linux darling of the PC handheld
           space, but will it continue to exist in a post-SteamOS world?


    * ⚓ Ruben Schade ☛ Bad_Apple!!_But_it’s_a_fluid_simulation⠀⇛


           A colleague shared this_Sebastian_Lague_video yesterday. One
           day I’ll stop being taken aback by how far this meme has gone,
           and the lengths people will go to recreate it. Amazing :).


    * ⚓ Hackaday ☛ Bad_Apple_But_It’s_6,500_Regex_Searches_In_Vim⠀⇛


           In the world of showing off, there is alongside ‘Does it play
           Doom?’ that other classic of ‘Does it play Bad Apple?’. Whereas
           either would be quaint in the context of the Vim editor, this
           didn’t deter [Nolen Royalty] from making Vim play the Bad Apple
           video. As this is a purely black and white video, this means
           that it’s possible to convert each frame into a collection of
           pixels, with regular expression based search and custom
           highlighting allowing each frame to be rendered in the Vim
           window.





                    ䷩ 𝚕𝚒𝚗𝚎 493

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/Games_Steam_Deck_Native_GNU_Linux_Clients_and_More.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/Games_Steam_Deck_Native_GNU_Linux_Clients_and_More.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Games: Steam Deck, Native GNU/Linux
Clients, and More⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 13, 2025


    * ⚓ Forbes ☛ Nvidia_Just_Solved_A_Huge_Steam_Deck_Problem._What_Happens
      Next?⠀⇛


           Nvidia is committing to Steam Deck, but what kind of impact
           will this news have? I asked a few big names in the GNU/Linux
           community to share their thoughts.


    * ⚓ Hackaday ☛ Custom_Case_Turns_Steam_Deck_Into_Portable_Workstation⠀⇛


           DIY portable computing takes many forms, and doesn’t always
           require getting down and dirty with custom electronics.
           [Justinas Jakubovskis]’s Steam Deck Play and Work case
           demonstrates this with some really smart design features.


    * ⚓ Boiling Steam ☛ New_Steam_Games_with_Native_GNU/Linux_Clients_-_2025-
      01-08_Edition⠀⇛


           Between 2025-01-01 and 2025-01-08 there were 14 New Steam games
           released with Native GNU/Linux clients. For reference, during
           the same time, there were 74 games released for backdoored
           Windows on Steam, so the GNU/Linux versions represent about
           18.9 % of total released titles. It’s another slow week as this
           was just after New Year, so we should not expect any big title
           to be released at that time.


    * ⚓ Hackaday ☛ Gaming_Table_Has_Lights,_Action⠀⇛


           We couldn’t decide if [‘s] Dungeons and Dragons gaming table
           was a woodworking project with some electronics or an
           electronics project with some woodworking. Either way, it looks
           like a lot of fun.


    * ⚓ Thomas Rinsma ☛ Tetris_in_a_PDF⠀⇛


           Recently, just for fun, I managed to create a playable version
           of Tetris inside a PDF. I posted about this a couple days ago
           on Hacker_News and Twitter. You can play it by opening this
           file in a compatible desktop browser (Firefox and anything
           Chromium-based). The “source code” can be found here.





                    ䷩ 𝚕𝚒𝚗𝚎 560

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/GNU_Linux_and_Free_Software_Leftovers.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/GNU_Linux_and_Free_Software_Leftovers.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ GNU/Linux and Free Software
Leftovers⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 13, 2025


    * § Distributions and Operating Systems⠀➾


          o § Fedora Family / IBM⠀➾


                # ⚓ Jon_Chiappetta:_I_forgot_to_post,_happy_new_year!⠀⇛


                       I’ve been trying to get things in order before the
                       end of last year and into this new year of 2025 so
                       I can try to lessen any worries that might come up.
                       I was doing a complete re-write of the core
                       network-wide proxy-service and this time I have
                       also tried to write it in both Python and C so the
                       code bases so mostly match and line up with each
                       other.


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


          o ⚓ David Revoy ☛ Krita_brushes_2025-01_bundle_-_David_Revoy⠀⇛


                 I'm starting the year with an update of my previous brush
                 bundle: it was starting to feel a bit outdated compared
                 to what I'm actually using. Even though it looks mostly
                 the same, under the hood all brushes got a lot of
                 improvements.


          o § Content Management Systems (CMS) / Static Site Generators (SSG)⠀➾


                # ⚓ Michał Sapka ☛ CrysBuilder,_the_static_site_builder⠀⇛


                       There comes a day in every man’s (or a woman’s!1)
                       life when writing custom static site builder is
                       only thing going forward. Hugo served me well for
                       years, but the site is now too big for it. 6k
                       subpages means fans party hard and dozens of
                       seconds of build time. But I also great huge
                       distaste for it due constant changes. I dread every
                       update, as the list of warnings may grow at any
                       random point. I also hate Go’s templating system as
                       it’s extremely annoying to do some cool things that
                       are not provided by Hugo’s out of the box.


          o § Programming/Development⠀➾


                # ⚓ SICP ☛ In_which_things_are_not_known⠀⇛


                       In the last episode—Is software engineering a
                       thing?—I (apparently controversially) suggested
                       that software is the reification of thought, and
                       that software engineering is thus the art of
                       reifying thought, and that thus there can’t be any
                       single one-size-fits-all software engineering [...]


                # ⚓ Rlang ☛ {SLmetrics}:_scalable_and_memory_efficient_AI/ML
                  performance_evaluation_in_R⠀⇛


                       On December 3rd, 2024, a post about the release of
                       {SLmetrics} was published. Today, January 11th,
                       2025, version 0.3-1 has been released and comes
                       with many new features. Among these are weighted
                       classification and regression metrics, OpenMP
                       support and a wide array of new evaluation metrics.


                # ⚓ Daniel Lemire ☛ JavaScript_hashing_speed_comparison:_MD5
                  versus_SHA-256⠀⇛


                       Hashing algorithms convert input data into a fixed-
                       size string of characters, known as a hash value or
                       digest. These algorithms are one-way functions,
                       meaning the original data cannot be feasibly
                       retrieved from the hash, which makes them useful
                       for data integrity, password storage, and digital
                       signatures.





                    ䷩ 𝚕𝚒𝚗𝚎 667

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/Hidden_Files_in_Linux_Explained.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/Hidden_Files_in_Linux_Explained.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Hidden Files in Linux
Explained⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Rianne Schestowitz on Jan 13, 2025


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


Quoting: Hidden Files in Linux Explained —


     If you’re new to the world of Linux, you’ve probably encountered the
     term “hidden files” quite often. But why are they actually? Are they
     secrets, mistakes, or just forgotten relics of the system? Well, it’s
     none of the above. In fact, as you will see below, they are something
     quite simple.


     In this article, we’ll unravel the mystery of hidden files in Linux.
     We’ll cover what they are, how to find them, and why you shouldn’t
     just delete them all willy-nilly (seriously, don’t do that) because
     they perform important functions – otherwise, they wouldn’t be
     hidden, would they?


Read_on




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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⡇⠀⠀⡇⠀⠀⣿⡟⠀⠀⣦⠀⠀⣿⡿⠻⣿⣧⠀⠀⣤⣤⣤⡅⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⡇⠀⠀⡇⠀⠀⠀⢀⣀⣼⣿⣧⣶⣰⣳⣄⣿⣿⣷⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⢰⣦⣶⡄⢠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠘⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣠⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⡆⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠸⠿⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 729

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/How_to_Install_FreeBSD_13_and_14_on_Desktops.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/How_to_Install_FreeBSD_13_and_14_on_Desktops.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ How to Install FreeBSD 13 and 14 on
Desktops⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 13, 2025


    * ⚓ Vermaden ☛ FreeBSD_Desktop_–_Part_2.2_–_Install_FreeBSD_13⠀⇛


           You just select Auto (ZFS) and then select GPT (BIOS+UEFI) for
           Partition Scheme and YES for Encrypt Disks option which will
           enable GELI full disk encryption.


    * ⚓ Vermaden ☛ FreeBSD_Desktop_–_Part_2.3_–_Install_FreeBSD_14⠀⇛


           You just select Auto (ZFS) and then select GPT (BIOS+UEFI) for
           Partition Scheme and YES for Encrypt Disks option which will
           enable GELI full disk encryption.





                    ䷩ 𝚕𝚒𝚗𝚎 762

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/KDE_kcursorgen_and_SVG_cursors.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/KDE_kcursorgen_and_SVG_cursors.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ KDE: kcursorgen and SVG
cursors⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Rianne Schestowitz on Jan 13, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HUGE_cursor⦈_


Quoting: kcursorgen and SVG cursors - KDE Blogs —


     In the latest Plasma 6.3 Beta, you will find a new executable named
     kcursorgen in /usr/bin. It can convert an SVG cursor theme to the
     XCursor format, in any sizes you like. Although this tool is intended
     for internal use in future Plasma versions, there are a few tricks
     you can play now with it and an SVG cursor theme.


     (Unfortunately, the only theme with the support that I know, besides
     Breeze, is Catppuccin. I have this little script that might help you
     convert more cursor themes.)


Read_on




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⢻⠟⠻⡿⠿⠿⠿⠿⠿⠿⣿⣿⣿⡟⡇⢸⣿⣿⣿⣿⣿⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
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⡏⢭⡍⡟⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡷⠶⣶⣶⣿⣿⣿⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
⡷⠶⢶⣷⣶⡶⢶⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡏⣿⣿⡆⠀⠀⠀⡏⠙⣿⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣟⢙⠉⠉⠉⣿⣿⠉⠉⠉⢋⣹⡉⣻⢩⡹⠉⢹⣿⣿⣿⡇⣿
⣧⣀⣀⣗⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣧⣤⣤⣤⣿⣿⣿⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
⣿⠏⢹⣟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡟⣿⣿⡇⠀⠀⠀⡟⠛⣿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⢛⠛⠛⠛⣿⣿⠛⠻⠛⢛⢻⠛⡛⣿⠛⢻⠛⢻⣿⣿⣧⣿
⣿⠤⠼⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣧⣤⣤⣤⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠐⠃⣇⣀⣀⣈⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡅⠀⠉⠉⡟⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠻⠛⠛⠛⣿⣿⠛⠟⢻⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢉⡛⡿⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣇⣀⣀⣀⣷⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣾⣶⣶⣶⣿⣿⣷⣷⣾⣷⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣭⣥⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⣿⣿⡏⠉⠉⠙⣿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⠿⠟⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⠿⠿⠿⣿⣿⠿⠿⠿⠿⢿⢿⠿⡿⣿⡿⢿⠿⢿⣿⣿⣿
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⣧⣬⣥⣷⣤⣤⣶⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣧⣾⣿⡇⠀⠀⠀⣧⣤⣀⣤⣤⣾⣿⣷⣌⢿⣶⣶⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣷⣴⣤⣄⣀⣿⣿⣤⣬⣤⣴⣬⣶⣧⣯⣤⣴⣤⣼⣿⣿⣿⣿
⡏⢠⡄⡟⠉⠛⠛⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣭⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠖⠲⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡇⠀⠀⠀⣏⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣯⣨⣀⣀⣀⣿⣿⣀⣐⣠⣧⣊⣄⣿⣀⣸⣢⣨⣿⣿⣿⣿⣿
⣿⣀⣠⣧⣀⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⠶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⠿⠷⠶⠶⠶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠻⢿⣿⠿⢿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⢿⣿⡟⠛⠟⢿⠿⢿⡿⡿⠿⠿⣿⡿⢿⣿
⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠿⠿⠿⠿⠿⠶⠶⠾⠴⠶⠶⠶⠶⠴⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠤⠤⠼⠿⠿⠶⠾⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⠶⠶⠾⠿⠧⠤⠤⠼⠴⠾⠤⠷⠴⠤⠿⠷⠾⠿

                    ䷩ 𝚕𝚒𝚗𝚎 824

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/Kdenlive_24_12_1_and_KDE_in_Tech_Over_Tea.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/Kdenlive_24_12_1_and_KDE_in_Tech_Over_Tea.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Kdenlive 24.12.1 and KDE in "Tech Over
Tea"⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 13, 2025


    * ⚓ Ubuntu Handbook ☛ Kdenlive_24.12.1_is_out_with_more_than_a_dozen_of
      bug-fixes⠀⇛


           Kdenlive, the popular KDE video editor, released the first
           maintenance update for the 24.12 series few days ago. It’s not
           officially announced in its website at the moment of writing,
           but the source tarball is out for those who want to compile by
           themselves. And, the Flatpak package has been updated for most
           GNU/Linux users.


    * ⚓ Nate Graham ☛ Interview_on_Tech_Over_Tea_about_fundraising,_money,_and
      design⠀⇛


           I recently sat down with Brodie Robertson again to appear on
           his Tech Over Tea show, this time on the subject of KDE’s
           recent fundraising, the role of money in open-source in
           general, and also design (I can never resist talking about
           this). If these topics interest you, check it out!





                    ䷩ 𝚕𝚒𝚗𝚎 864

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/Linux_6_13_rc7.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/Linux_6_13_rc7.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Linux 6.13-
rc7⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 13, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇By_Lf_Asia_-_Imported_from_500px_(archived_version)_by_the
Archive_Team._(detail_page),_CC_BY_3.0,_https://commons.wikimedia.org/w/
index.php?curid=108824226⦈_


    * ⚓ LWN ☛ Linux_6.13-rc7⠀⇛


           Well, it looked a bit quiet at the start of the week, but then
           things
           picked up, and we're definitely back to speed after the two
           quiet
           holiday weeks.


           This rc7 is slightly bigger than normal, but considering the
           timing,
           it's pretty much where I would have expected, and nothing
           really
           stands out. The diffstat looks fine, and the appended shortlog
           doesn't
           look strange either.


           So unless something odd happens the upcoming week, I expect to
           release
           a final 6.13 next week as per the normal schedule.


                              Linus


           PS: one final note on the holidays, and a check to see if
           anybody
           actually ever reads these weekly rc announcements of mine:


           For _me_ a traditional holiday activity tends to be a LEGO
           build or
           two, since that's often part of the presents both for Xmas and
           birthday, which pretty much coincide for me.


           So too this year.


           But in addition to the LEGO builds, this year I also ended up
           doing a
           number of guitar pedal kit builds ("LEGO for grown-ups with a
           soldering iron"). Not because I play guitar, but because I
           enjoy the
           tinkering, and the guitar pedals actually do something and are
           the
           right kind of "not very complex, but not some 5-minute 555 LED
           blinking thing".


           I've done quite a few, but the kits I really enjoyed doing were
           from
           Aion FX. And since I want to have the excuse to continue to do
           them,
           and since I don't actually have any _use_ for the resulting
           pedals
           (I've already foisted off a few only unsuspecting
           victims^Hfriends), I
           decided that I'm going to see if some hapless kernel developer
           would
           want one.


           So here's the deal: as an admittedly pretty weak excuse to keep
           buying
           and building kits, and still consider it "work", if any kernel
           developer (as defined as "has a commit authorship from the year
           2024
           in my kernel git tree") feels they really need a guitar pedal
           in their
           life, hand-built by yours truly, please send me an email
           (*from* that
           email address that is in the git tree) with the subject "I WANT
           A
           GUITAR PEDAL".


           Pick any in-stock pedal kit from


               https://aionfx.com/project-type/kit/


           and make sure it's actually in stock (because not all of them
           are).
           And next week, I'll pick one person at random - assuming
           anybody wants
           one - and will buy that kit with my own money (hashtag "not
           sponsored
           by Aion FX, I just really like their kits"), build it with my
           own
           shaky little fingers, and send it to the victim by US postal
           services.


           We're not talking Amazon two-day delivery here, just to be
           clear.
           Also, if you are not in the US, who knows what happens between
           USPS
           and you. I'll drop it off at the local post office, but I can't
           guarantee anything more than that.


           And it's may be worth noting that while I've had good success
           so far,
           I'm a software person with a soldering iron. You have been
           warned. I
           will test the result to the best of my abilities, and the end
           result
           may actually work (note: you will have to provide your own
           guitar,
           playing abilities, and pedal power supply). But you should set
           your
           expectations along the lines of "quality kit built by a SW
           person who
           doesn't know one end of a guitar from the other".
    * ⚓ LWN ☛ Kernel_prepatch_6.13-rc7⠀⇛


           Linus has released 6.13-rc7 for testing. ""So unless something
           odd happens the upcoming week, I expect to release a final 6.13
           next week as per the normal schedule"". Read the full
           announcement for your details on how to get a free guitar pedal
           assembled by Linus himself.




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣶⣶⣶⣶⣦⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣤⣤⣤⣄⣀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢋⣭⣿⣿⡟⠋⠁⠤⠚⠋⠉⠉⠫⠼⣽⠋⠹⠿⠛⠛⠻⢛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢃⣼⣿⣿⣿⠋⠀⢀⣠⣶⡀⣾⠉⠀⠀⠐⠢⠀⠀⠀⠀⠀⢀⡠⠛⡔⠊⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣥⣶⣿⣿⡿⠛⣡⣶⣾⣏⣷⣦⣔⣦⣤⣠⣶⣾⣿⣾⣷⣾⣶⣶⣶⣤⣤⣈⡻⠿⣿⣿⣿⣿⣿⣻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣬⣻⣿⣿⣿⣿⣿⣟⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠀⠀⠀⢀⢀⡄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡄⠀⠀⠀⡀⠄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠀⢀⣼⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠟⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣧⣼⣿⣟⣾⣷⣿⢷⣿⣿⣿⢿⣿⠋⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⢱⣸⣿⡏⣿⣿⠋⠸⣿⣿⠏⠏⡎⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⡇⣿⣿⠹⣿⡏⣰⢻⡏⢋⠀⣰⠀⠰⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡷⢸⣿⣿⣿⣽⣇⣿⠄⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⠟⡷⠂⠀⠀⣠⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠏⢛⡿⢷⠀⠀⠀⠘⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⡇⠈⠀⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢛⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡆⣼⠈⠀⠀⠀⠀⠀⠀⠇⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⠞⠛⠋⠉⠉⠀⠀⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣶⣅⣀⣀⣄⣀⣶⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠋⠹⣿⣿⣿⡇⠀⠀⢠⣦⣶⣆⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⣉⣨⣽⣭⣝⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⢸⣿⣿⠣⡀⣸⣿⣷⣶⣽⡒⠀⣿⠻⣿⣿⣿⣷⣶⣮⣽⣛⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠀⠀⠀⢀⡛⠛⠀⢻⣿⣿⣿⣿⣿⡇⣄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣈⣙⣻⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠁⠀⠀⠈⢻⣿⣿⣿⣿⣿⣀⣢⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡋⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣸⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣦⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⢠⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⣴⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣬⣭⣭⣭⣭⣥⠶⠂⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠛⠛⢉⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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                    ䷩ 𝚕𝚒𝚗𝚎 1067

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/Linux_Devices_and_Open_Hardware.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/Linux_Devices_and_Open_Hardware.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Linux Devices and Open
Hardware⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 13, 2025


    * ⚓ Linux Gizmos ☛ Upcoming_JF35_MTU1_Low_Profile_3.5″_Motherboard_with
      Intel_14th_Gen_Core_Ultra_Processors_and_Dual_2.5GbE_LAN⠀⇛


           This motherboard features the Intel 14th Gen Core Ultra 7 155U
           and Core Ultra 5 125U processors, formerly known as Meteor
           Lake-U, with a TDP of 15W. These processors incorporate Intel
           Iris Xe Graphics, enabling efficient multimedia processing
           alongside general computing tasks.


    * ⚓ Linux Gizmos ☛ Cost-Efficient_PICO2-XL_and_PICO2-XXL_OSHW_Boards_Now
      Available_for_Pre-Order⠀⇛


           Olimex has announced that the highly anticipated PICO2-XL and
           PICO2-XXL open-source hardware boards are now available for
           pre-order, with shipments starting on January 17, 2025. These
           boards expand on the Raspberry Pi PICO2, offering increased
           GPIO availability and improved memory configurations for
           enhanced development flexibility.


    * ⚓ Tom's Hardware ☛ Maker_builds_Raspberry_Pi_jukebox_and_loads_it_full_of
      custom_music⠀⇛


           Siuengr has built a jukebox from scratch using a Raspberry Pi
           as the main board and loaded it full of his favorite music.


    * ⚓ Hackaday ☛ Comparing_Ways_To_Add_Threads_To_Your_3D_Prints⠀⇛


           Adding threads to your 3D prints is a life-changing feature,
           but obviously there are a lot of trade-offs and considerations
           when deciding on how to go about this exactly. Between self-
           tapping screws, printed threads, heat inserts and a dozen other
           options it can be tough to decide what to go with. In a recent
           video [Thomas Sanladerer] runs through a few of these options,
           including some less common ones, and what he personally thinks
           of them.





                    ䷩ 𝚕𝚒𝚗𝚎 1128

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/LXQt_Wayland_support_is_now_here.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/LXQt_Wayland_support_is_now_here.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ LXQt Wayland support is now
here⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Rianne Schestowitz on Jan 13, 2025


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


Quoting: LXQt Wayland support is now here - openSUSE News —


     With the release of LXQt 2.1, we are pleased to announce the
     availability of Wayland compatibility for LXQt within Tumbleweed.


     This support is to be considered experimental at this point, and for
     most users, is likely not ready for daily driving.


     LXQt, unlike many other desktop environments, does not provide its
     own Window Manager. Under X11, the openSUSE-LXQt team defaults to
     using Openbox as its Window Manager. This decision carries over from
     upstream to the new Wayland support; the initial release of lxqt-
     wayland-sessions supports the following Wayland Compositors...


Read_on




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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 1181

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/MX_Linux_23_5_Brings_Debian_12_9_and_Xfce_4_20.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/MX_Linux_23_5_Brings_Debian_12_9_and_Xfce_4_20.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ MX Linux 23.5 Brings Debian 12.9 and Xfce
4.20⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Rianne Schestowitz on Jan 13, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇MX_Linux_23.5⦈_


Quoting: MX Linux 23.5 Brings Debian 12.9 and Xfce 4.20 —


     MX Linux has officially released MX Linux 23.5 “Libretto,” marking
     the fifth refresh of the MX-23 series, introducing a wealth of bug
     fixes, kernel updates, and application enhancements since the
     original MX-23 launch.


     Building upon the foundation of Debian 12.9, the new release
     incorporates all the latest updates from both the Debian and MX
     repositories.


     Perhaps the most striking update is the arrival of Xfce 4.20 in the
     main repositories. This long-awaited release brings a host of visual
     and performance enhancements for Xfce-based editions, including the
     Pi respin, thereby delivering a smoother, more polished desktop
     environment.


Read_on




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                    ䷩ 𝚕𝚒𝚗𝚎 1247

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/MX_Linux_23_5_Released_with_Xfce_4_20_and_Linux_6_12_LTS_Based_.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/MX_Linux_23_5_Released_with_Xfce_4_20_and_Linux_6_12_LTS_Based_.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ MX Linux 23.5 Released with Xfce 4.20 and
Linux 6.12 LTS, Based on Debian 12.9⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Marius Nestor on Jan 13, 2025,
updated Jan 13, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇MX_Linux_23.5⦈_


Based on the Debian 12.9 repositories, the MX Linux 23.5 release introduces the
latest and greatest Xfce 4.20 desktop environment, which is also available from
MX Linux’s repositories for existing users using the Xfce and Raspberry Pi
editions. One of the biggest features of Xfce 4.20 is experimental Wayland
support.


In addition, MX Linux 23.5 introduces several new applications in MX Linux’s
“test” repository, adds various UI improvements and better support for packages
in third-party repositories to MX Packageinstaller, and brings extra warnings
on the live system if persistence has been asked for on a read-only boot media.


Read_on


Update (by Roy)


The serial LLM slopper having a go:


    * ⚓ Say_goodbye_to_Windows_11_and_switch_to_MX_Linux_23.5_for_a_faster_PC⠀⇛


           Tired of the constant updates, bloat, and resource demands of
           Windows 11? Aren't we all? MX Linux could be the perfect
           solution to your woes, and thanks to its lightweight nature -
           - especially compared to Windows -- it could make your PC run
           even faster!


           The latest version of this lightweight Linux distribution has
           just been released, offering a Windows alternative that’s fast,
           user-friendly, and entirely free. Built on the rock-solid
           Debian 12.9 “Bookworm” base, MX Linux 23.5 combines
           performance, flexibility, and simplicity -- qualities that
           Microsoft's operating systems always seems to struggle with.




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⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠭⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠲⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⠿⠟⣛⠫⠉⠒⣈⣉⣠⣤⣴⣶⣶⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⡿⠿⠛⠉⠁⢐⣉⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠿⠿⠿⠿⠟⠟⠟⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠹⠈⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 1330

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/Open_Hardware_Open_Source_Design_Arduino_Raspberry_Pi_and_More.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/Open_Hardware_Open_Source_Design_Arduino_Raspberry_Pi_and_More.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Open Hardware: Open-Source Design, Arduino,
Raspberry Pi, and More⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 13, 2025


    * ⚓ Linux Gizmos ☛ Voice_Preview_Edition:_Open-Source_Design_with_Local
      Processing_Capabilities⠀⇛


           The Home Assistant Voice Preview Edition is an open-source
           voice assistant designed for integration with Home Assistant
           systems. It emphasizes privacy, local processing, and
           compatibility with smart home hardware, offering reliable
           performance and flexible usability.


    * ⚓ El País ☛ The_Spanish_hamlet_that_has_been_winding_the_church_clock_for
      244_years:_‘We_do_it_between_10_families’⠀⇛


           This reflection is shared by Marañón, who says that the effort
           to save the mechanism has brought back old memories to the
           minds of the elderly residents. Memories like those of Bernito,
           89, who still remembers that when he was a child, he was told
           by a clockmaker who came to repair it that the clock “was a
           human being, that it had organs and that its heart and liver
           were failing.” They have also discovered that decades ago “it
           was the children of each family who wound up the watch and
           then, at the end of the year, they would go round the houses
           and receive a small bonus as a reward.”


    * ⚓ Tom's Hardware ☛ Maker_builds_a_Raspberry_Pi_5_powered_stereoscopic_3D
      video_camera⠀⇛


           Sridhar Rajagopal has put together a cool stereoscopic 3D
           camera using a Raspberry Pi 5 and two camera modules.


    * ⚓ Tom's Hardware ☛ Researchers_3D-print_fully-functioning_microscope_in
      less_than_3_hours_—_total_system_costs_around_$60,_including_lenses,
      camera,_and_Raspberry_Pi⠀⇛


           Researchers from the University of Strathclyde in Glasgow,
           Scotland built the world's most affordable 3D-printed
           microscope that has a total production cost of around $60.


    * ⚓ Arduino ☛ This_maker_designed_a_custom_flight_controller_for_his
      supercapacitor-powered_drone⠀⇛


           Basic drones are very affordable these days—you can literally
           find some for less than the cost of a fast food drive-thru
           meal. But that doesn’t mean drones are easy to control. That is
           actually quite difficult, but manufacturers are able to work
           off of established reference designs.





                    ䷩ 𝚕𝚒𝚗𝚎 1403

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/openSUSE_Tumbleweed_Now_Offers_Wayland_Support_for_the_LXQt_Des.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/openSUSE_Tumbleweed_Now_Offers_Wayland_Support_for_the_LXQt_Des.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ openSUSE Tumbleweed Now Offers Wayland
Support for the LXQt Desktop⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Marius Nestor on Jan 13, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇LXQt_Wayland⦈_


As you may be aware, LXQt 2.1 is the first release of the lightweight desktop
environment to introduce an experimental Wayland session through the
implementation of a new component called lxqt-wayland-session. The Wayland
session supports several compositors, including Labwc, KWin, Wayfire, Hyprland,
Sway, River, and Niri.


While not many distros ship LXQt with Wayland support (due to the experimental
flag), you can give it a try in openSUSE Tumbleweed. However, openSUSE doesn’t
offer a dedicated live ISO image with the LXQt desktop, so you’ll have to
install it from the repositories on top of your existing environment or perform
a fresh install.


Read_on




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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⡿⣿⣿⠿⣿⣿⠿⠿⣿⣿⠿⢸⣿⣛⣖⣛⣻⣯⣭⣿⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⣾⣿⡦⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣿⣺⣿⣿⣤⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣟⣻⣛⣛⣛⣟⣛⣻⣻⣿⣿⣿⣿⣿⣀⣀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⢯⢿⣿⣿⣿⢿⢧⡼⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⠿⡿⠿⢿⠿⣿⡿⢿⠿⢿⢿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣽⣿⣿⡿⠿⠏⠩⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡰⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣷⠦
⠀⠀⠀⠀⠀⠀⠀⢻⣯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠾⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⡤⣤⡴⣤⣤⣶⣞⣷⣶⡖⢠⢤⡤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⡔⢠⣤⢤⣤⣤⣤⣤⣼⡖⠢⠠⠤⠤⠄⠠⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣦⣤⣤⣤⣤⡤⣶⢶⢶⣶⣶⣶⣶

                    ䷩ 𝚕𝚒𝚗𝚎 1460

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/Plop_Linux_distribution_designed_for_advanced_Linux_users.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/Plop_Linux_distribution_designed_for_advanced_Linux_users.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Plop Linux – distribution designed for
advanced Linux users⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Rianne Schestowitz on Jan 13, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Plop_Linux⦈_


Quoting: Plop Linux - distribution designed for advanced Linux users -
LinuxLinks —


     Plop Linux is a distribution built from scratch. It’s designed for
     advanced Linux users.


     You can use Plop Linux as...


Read_on




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠅⠀⠨⠀⠀⠄⠄⠀⠠⠀⠀⠅⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠅⠀⠨⠨⠀⠅⠅⠈⠨⠀⠀⠅⠀⠨⠈⠀⠅⠅⠨⠨⠀⠀⠅⠀⠨⠨⠀⠅⠅⠠⠠⠀⠀⠀⠀⠠⠠⠀⠀⠅⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠅⠀⠨⠠⠀⠅⠅⠀⠨⠀⠀⠅⠀⠨⠀⠀⠅⠅⠨⠨⠀⠀⠅⠀⠨⠀⠀⠅⠄⠨⠠⠀⠀⠀⠀⠠⠨⠀⠀⠅⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠅⠅⠨⠨⠀⠅⠅⠭⠨⠨⠅⠅⠅⠨⠨⠀⠅⠅⠬⠨⠨⠅⠅⠅⠨⠨⠀⠅⠅⠨⠨⠨⠅⠅⠅⠨⠨⠀⠅⠅⠨⠨⠨⠅⠅⠅⠨⠨⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣾⣶⣶⣷⣷⣶⣾⣶⠄⠅⠄⠨⠨⠀⠅⠅⠨⠨⠀⠀⠅⠅⠨⠨⠀⠅⠅⠨⠨⠠⠄⠅⠅⠨⠨⠀⠅⠅⠨⠨⠠⠅⠅⠅⠨⠨⠀⠀⠅⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⡏⠍⢸⠨⠉⠅⠅⠭⠨⠨⠅⠅⠅⠨⠨⠀⠅⠅⠭⠨⠨⠍⠍⠭⠩⠩⠭⠍⡏⠭⢩⠩⠭⠍⠭⠭⢩⠅⠅⡅⠨⠨⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⡇⠅⢸⠨⠀⠅⠅⠭⠨⠨⠅⠅⠅⠨⠨⠀⠅⠅⠬⠨⠨⠅⠅⠭⠨⢨⠀⠅⡇⠬⢸⠨⠅⡅⠭⠨⢸⠄⠅⡇⠨⢨⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⡏⠭⢽⠩⠭⠍⠭⠭⠩⠭⠍⡏⠭⠨⠨⠭⡯⠭⠭⠭⠭⠭⠭⠭⢭⢽⠭⠭⡯⠭⢽⠭⠭⡯⡭⠭⢽⠭⠭⡯⠭⢽⠩⠥⠅⠭⠨⠨⠀⠄⠄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⡇⠅⢸⠨⠀⡅⠅⠭⠨⠨⠅⡅⠥⢸⠨⠀⡇⡅⢭⢨⠨⠅⡇⡭⢸⢸⠭⡅⡇⢭⢽⠨⠭⡇⡯⢭⢸⠭⠅⡯⠭⢸⠨⠅⡇⠭⠨⠨⠀⠄⠅⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⡯⠭⢽⠭⠭⡯⠭⠭⠭⠭⠭⡯⠭⢽⠭⠭⡯⡯⢽⢽⠭⠭⡯⡯⢽⢽⠭⡯⡯⢽⢽⠭⠭⡯⡯⢽⢽⠭⠭⡯⠭⢽⠭⠭⡯⠭⠭⠭⠭⠅⠅⠤⠨⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⡇⠅⢸⠨⠀⡅⠅⠭⠨⠨⠅⡇⠭⢸⠨⠨⡇⡭⢽⢸⠭⠅⡇⡯⢽⢽⠭⡯⡯⢽⢽⠭⠭⡯⡯⢽⢽⠭⡭⡯⠭⢽⠩⠭⡇⠭⢭⢨⠥⠅⡇⠠⢨⠀⠀
⠛⠟⠟⠻⠻⠟⠟⡟⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⡯⠭⢽⠭⠭⡯⠭⠭⠽⠭⠭⡯⠭⢽⠭⠭⡯⡯⢽⢽⠭⠭⡯⡯⢽⢽⠭⡯⡯⢽⢽⠭⠭⡯⡯⢽⢽⠭⡯⡯⠭⢽⠭⠭⡯⠭⢽⢽⠭⠭⡯⠭⢽⠨⠄
⠅⠅⠍⠨⠨⠁⠅⡇⠩⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⡇⠍⢸⠨⠈⡅⠅⠭⢨⠨⠅⡇⠭⢸⢨⠭⡇⡯⢽⢹⠭⠭⡯⡯⢽⢽⠭⡯⡯⢽⢽⠭⠭⡯⡯⢽⢽⠭⡭⡯⠭⢽⠭⠭⡯⠭⢽⢹⠭⠅⡯⠭⢸⠨⠀
⠅⠅⠭⠨⠨⠭⠅⠯⠭⢼⠭⠭⡯⠭⢽⠭⠭⠭⠭⠭⢽⠭⠭⡯⠭⢽⠭⠭⡯⠭⠭⢽⠭⠭⡯⠭⢽⢽⠭⡯⡯⢽⢽⠭⠭⡯⡯⢽⢽⠭⡯⡯⢽⢽⠭⠭⡯⡯⢽⢽⠭⡯⡯⠭⢽⠭⠭⡯⠭⢽⢽⠭⠭⡯⠭⢽⠨⠅
⠀⠅⠀⠨⠨⠀⠅⠅⠨⢸⠈⠅⡇⠭⢸⠨⠉⠅⠅⠭⢸⠨⠅⡇⠍⢸⠨⠩⡇⠍⠭⢸⠩⠅⡯⠭⢹⢹⠭⡯⡯⢽⢽⠭⠭⡯⡯⢽⢽⠭⡯⡯⢽⢽⠭⠭⡯⡯⢽⢽⠭⡯⡯⠭⢽⠭⠭⡯⠭⢽⢹⠭⠅⡇⠭⢸⠈⠀
⠄⠅⠤⠨⠨⠀⠅⠅⠭⠸⠬⠭⡧⠭⢽⠬⠭⠥⠭⠭⢼⠭⠥⡯⠭⢽⠭⠭⡯⠭⠭⢽⠭⠭⡯⠭⢽⢽⠭⡯⡯⢽⢽⠭⠭⡯⡯⢽⢽⠭⡯⡯⢽⢽⠭⠭⡯⡯⢽⢽⠭⡯⡯⠭⢽⠭⠭⡯⠭⢽⠽⠭⠭⠯⠭⠸⠨⠁
⠀⠅⠀⠨⠨⠀⠅⠅⠈⠨⠀⠀⠇⠅⠨⠨⠉⠅⠅⠭⢸⠨⠅⡇⠭⢸⠨⠭⡇⠭⠭⢸⠭⠍⡯⠭⢽⢽⠭⡯⡯⢽⢽⠭⠭⡯⡯⢽⢽⠭⡯⡯⢽⢽⠭⠭⡯⡯⢽⢽⠭⡯⡯⠭⢽⠭⠭⡏⠭⠭⠨⠉⠅⠅⠀⠨⠀⠀
⠀⠅⠀⠨⠨⠀⠅⠅⠨⠨⠠⠅⠅⠭⠩⠬⠭⠥⠭⠭⢼⠭⠭⡯⠭⢽⠭⠭⡯⡯⢽⢽⠭⠭⡯⠭⢽⢽⠭⡯⡯⢽⢽⠭⠭⡯⡯⢽⢽⠭⡯⡯⢽⢽⠭⠭⡯⡯⢽⢽⠭⡯⡯⠭⢽⠭⠭⡯⠭⠭⠭⠭⠅⠅⠀⠨⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠅⠀⠨⠀⠀⠅⠀⠨⠨⠀⠅⠅⠭⢸⠨⠅⡇⠭⢽⠨⠭⡇⡯⠭⢸⠭⠭⡯⡭⢽⢽⠭⡯⡯⢽⢽⠭⠭⡯⡯⢽⢽⠭⡯⡯⢽⢽⠭⠭⡯⡯⢽⢽⠭⠭⡯⠭⢹⠨⠍⡇⠭⠨⠨⠀⠁⠅⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠄⠅⠀⠨⠀⠄⠅⠅⠨⠨⠤⠥⠭⠭⢼⠭⠭⡯⠭⢽⠭⠭⡯⡯⢽⢽⠭⠭⡯⡯⢽⢽⠭⡯⡯⢽⢽⠭⠭⡯⡯⢽⢽⠭⡯⡯⢽⢽⠭⠭⡯⡯⢽⢽⠭⠭⡯⠭⢽⠭⠭⠧⠭⠨⠨⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠅⠀⠨⠈⠀⠅⠅⠩⠸⠨⠅⡇⠭⢽⠩⠭⡏⡯⢽⢽⠭⠭⡯⡯⢽⢽⠭⡯⡯⢽⢽⠭⠭⡯⡯⢽⢽⠭⡯⡯⢽⢽⠭⠭⡯⡯⢽⢹⠭⠍⡏⠭⢸⠨⠅⠅⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠅⠀⠨⠨⠀⠅⠥⠭⠼⠬⠭⡯⠭⢽⠭⠭⡯⡯⢽⢽⠭⠭⡯⡯⢽⢽⠭⡯⡯⢽⢽⠭⠭⡯⡯⢽⢽⠭⡯⡯⢽⢽⠭⠭⡯⡯⠽⢽⠭⠭⡯⠭⠼⠨⠅⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠨⠈⠀⠅⠅⠨⠨⠨⠅⡇⠭⢹⠩⠭⡏⡯⢽⣽⠽⠯⠯⠯⠽⠽⠭⢯⡯⠿⠽⠽⠯⠯⠿⠽⢽⡭⠯⠯⠽⠽⠽⠯⠯⢯⠽⠼⠥⠧⠧⠬⠸⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤

                    ䷩ 𝚕𝚒𝚗𝚎 1518

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/Programming_Leftovers.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/Programming_Leftovers.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Programming
Leftovers⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 13, 2025


    * ⚓ Elias Mårtenson ☛ Advent_of_Code_2024_day_1,_part_2⠀⇛


           This is a short update to my previous post where I will solve
           the second part. At the end, I will also include one-line
           solutions to the two problems, which really doesn't involve
           more than removal of unnecessary variable assignments.


           Revisiting part 1, here's the full solution that was written in
           that post (with a few less variable reassignments): [...]


    * ⚓ Dan ☛ Why_I_Chose_Common_Lisp⠀⇛


           After ~7 years, I was done with Clojure. I was writing a some
           CLI apps, and I hated how long they took to start up. The
           community at large seemed not to care about this problem,
           except for the babashka folks. However, I spent long, hard
           hours banging my head against native-image and it just wasn't
           working out. It was incredibly painful, and at the end of it, I
           still didn't have standalone, fast-starting native executables.
           I decided that that was a requirement for my main driving hobby
           language, and that Clojure didn't have it. It was then that I
           decided to move on from Clojure.


    * ⚓ Tyler Russell ☛ My_Thoughts_on_Kotlin:_Perspectives_after_4_years_–
      tylerrussell.dev⠀⇛


           Having used Kotlin for over 4 years of my career now, I felt
           like I needed a better explanation. So for the last 3 months,
           every time I’ve had an “aha moment” that related to Kotlin,
           I’ve written it down. Both good and bad.


           After doing this for a while, I’ve come to the conclusion of
           what I suspected all along: there isn’t really a singular,
           special, or unique thing that I like about Kotlin. My enjoyment
           stems from an aggregation of lots of small, and not even
           necessarily unique, things. But when they are all put together,
           it just feels enjoyable.


    * ⚓ Brian Callahan ☛ Let's_port_the_GNAT_Ada_compiler_to_macOS/aarch64⠀⇛


           Getting a compiler written in its own langauge bootstrapped for
           a new platform


    * ⚓ Dirk Eddelbuettel ☛ Dirk_Eddelbuettel:_Rcpp_1.0.14_on_CRAN:_Regular
      Semi-Annual_Update⠀⇛


           The Rcpp Core Team is once again thrilled, pleased, and chuffed
           (am I doing this right for LinkedIn?) to announce a new release
           (now at 1.0.14) of the Rcpp package. It arrived on CRAN earlier
           today, and has since been uploaded to Debian. backdoored
           Windows and macOS builds tomorrow too. The release was only
           uploaded yesterday, and as always get flagged because of the
           grandfathered .Call(symbol) as well as for the url to the Rcpp
           book (which has remained unchanged for years) ‘failing’. My
           email reply was promptly dealt with under European morning
           hours and by the time I got up the submission was in state
           ‘waiting’ over a single reverse-dependency failure which … is
           also spurious, appears on some systems and not others, and also
           not new. Imagine that: nearly 3000 reverse dependencies and
           only one (spurious) change to worse. Solid testing seems to
           help. My thanks as always to the CRAN for responding promptly.


    * § Python⠀➾


          o ⚓ Jeff Triplett ☛ django-templated-email-md_notes_aka_if_you_want
            to_format_emails_with_Markdown,_use_it_-_Jeff_Triplett's
            Micro.blog⠀⇛


                 Forward Email’s products and services are fully open-
                 source if you care about such things.


          o ⚓ Bastian_Venthur:_Investigating_the_popularity_of_Python_build
            backends_over_time_(II)⠀⇛


                 Last_year, I analyzed the popularity of build backends
                 used in pyproject.toml files over time. This post is the
                 update for 2024.





                    ䷩ 𝚕𝚒𝚗𝚎 1630

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/Review_DAT_Linux_2_0.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/Review_DAT_Linux_2_0.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Review: DAT Linux
2.0⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Rianne Schestowitz on Jan 13, 2025


Quoting: DistroWatch.com: Put the fun back into computing. Use Linux, BSD. —


     I'd like to wrap up my observations on DAT Linux by talking about
     aspects of the distribution I enjoy. For me, the main thing which
     stood about about this Ubuntu re-spin was that the project's website
     was clear about what the project is, what it does, and who it is for.
     Too many projects, in my opinion, try to cover up their lack of
     technical merits by using flowery language. A lot of Ubuntu- and
     Arch-based projects use marketing terms like "modern", "innovative",
     and "collaborative" which mean absolutely nothing in the context of
     what the operating system can do or why someone might want to use it.
     DAT is more to the point, clearly stating its base (Ubuntu), its
     custom tools (like the DAT Linux Control Panel), and that its focus
     is on providing easy access to data science applications.


     This clear and concise approach - explaining exactly what the
     distribution does and who it is for, without wasting time with empty
     marketing phrases is refreshing. I also like that DAT Linux doesn't
     over-promise. It does exactly what it says on the website, no more
     and no less. There is no "working toward" or "coming soon" hype. DAT
     Linux provides easy access to data science applications while using
     Ubuntu as a base and the specific applications (with a description of
     each) is clearly displayed on the website.


     As I mentioned above, the DAT utilities for fetching and updating
     data science applications work. I lack the depth in data science to
     determine how well the provided tools function, but I did confirm a
     random handful did install, run, and could perform tasks like opening
     databases or spreadsheets.


     I also like that DAT uses a lightweight desktop which stays out of
     the way. LXQt is quite pleasant to use, being super fast, pleasantly
     light (compared with Plasma or GNOME), and I enjoyed the default dark
     theme.


     Where I think DAT shows a weak spot is with the many software and
     repository management tools. There are at least nine on the system,
     three custom tools for installing DAT's supported applications, plus
     at least five launchers imported from Ubuntu, plus Discover. This
     doesn't even take into account the command line utilities such as APT
     and Flatpak. This is likely to confuse inexperienced users as it's
     virtually impossible to tell which tool should be used for what
     without some trial and error.


     This is probably my only complaint about DAT Linux: the torrent of
     software management tools and duplication between them. The rest of
     the experience - the documentation, the system installer, the LXQt
     desktop, and the included desktop applications all provided excellent
     experiences. It's really nice for me to find a project which says
     what it does, does what it says, and has a clear focus without any
     major issues.


Read_on





                    ䷩ 𝚕𝚒𝚗𝚎 1709

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/Shortwave_Now_Supports_Play_Internet_Radio_in_the_Background.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/Shortwave_Now_Supports_Play_Internet_Radio_in_the_Background.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Shortwave Now Supports Play Internet Radio
in the Background⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 13, 2025


Shortwave, the modern free open-source internet radio player, finally adds
background playback support! Shortwave is an internet audio player designed for
GNOME Desktop, though it also works in most other GNU/Linux desktops and even
GNU/Linux phones.


Read_on





                    ䷩ 𝚕𝚒𝚗𝚎 1735

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/This_Week_in_KDE_Apps_Usability_improvements_new_features_and_u.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/This_Week_in_KDE_Apps_Usability_improvements_new_features_and_u.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ This Week in KDE Apps: Usability
improvements, new features, and updated apps⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Rianne Schestowitz on Jan 13, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Dolphin⦈_


Quoting: This Week in KDE Apps: Usability improvements, new features, and
updated apps - KDE Blogs —


     Welcome to a new issue of "This Week in KDE Apps"! Every week we
     cover as much as possible of what's happening in the world of KDE
     apps.


     This week we look at the usability improvements landing in Alligator,
     Dolphin, and Itinerary; new features for KMyMoney, Tokodon and
     NeoChat; and updated versions of Amarok and Skrooge.


Read_on




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠟⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣤⣤⣠⣴⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣤⣦⣤⣠⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣿⣿⣿⢌⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⡀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡙⣿⣿⠀⠀⠉⠉⣿⠻⠛⠛⠃⡇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣼⣿⣿⣀⣀⣀⣠⣷⣶⣶⣦⡂⣷⣤⡤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⣿⣿⠉⠉⠛⢛⣿⢿⠿⡿⠇⣿⣿⠀⠀⢸⣿⢀⠉⠩⠉⠍⠉⠉⠉⠈⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢈⣿⢃⠁⡉⣋⡃⠨⠉⠩⠉⠉⠉⢹⣿⣿⣿⣿⣿⡇⢿⠿⠿⡿⠿⡿⡿⡿⠿⣿
⣿⣿⣿⣱⣿⣿⠀⠀⠀⢸⣧⣤⣀⡄⡀⣿⣿⣷⣶⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣤⣤⣢⣼⣤⣤⣄⣤⣤⣼
⣿⣿⣿⣿⣿⣿⠟⠻⠿⠿⣿⣿⣿⣿⠃⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢊⣿⣿⠀⠀⠀⠀⡇⠀⠈⠉⠁⣿⣿⡗⠀⢻⣿⠰⡈⢁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢎⠍⡅⣍⣆⢸⣿⣿⣿⣿⣿⠀⢀⢉⡇⢆⡉⢉⢍⠉⢩⣉
⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠝⣿⣿⠃⠀⠀⢸⡏⠉⠙⠟⠃⣻⣿⠁⢈⢻⣿⢩⠝⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠫⡍⡛⡋⠛⠋⣽⣿⣿⣿⣿⣿⠃⡛⢛⠛⢋⠋⠋⢛⠛⡉⢻
⣿⣿⣿⣾⣿⣿⣦⣤⣤⣼⣷⣶⣶⣶⡆⣾⣿⣷⣶⣾⣿⣶⣷⣦⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣷⣿⣷⣾⣿⣿⣿⣿⣿⡇⣷⣷⣶⣿⣾⣾⣶⣷⣿⣾
⣿⣿⣿⠻⣿⣿⠉⠉⠉⠙⡟⠛⢿⠟⠂⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠿⠿⠿⠟⠟⠟⠿⠿⠟⢿
⣿⣿⣿⣵⣿⣿⡀⣀⣀⢀⣧⣤⣬⣤⡄⣼⣿⡇⡄⣽⣿⠨⠉⠉⠈⠉⠙⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠁⢹⢛⠉⠙⠉⢹⣿⣿⣿⣿⣿⡆⣤⣬⣤⣼⣤⣤⣬⣤⣧⣽
⣿⣿⣿⢿⣿⣿⠛⠛⠛⢻⡿⠿⣿⡿⢷⣿⣿⣷⣶⣿⣿⣶⣿⣾⣿⣾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⡿⣿⡿⣿⣿⡿⣿
⣿⣿⣿⣢⣿⣿⠀⠀⠀⢸⣇⣀⣘⣀⣀⣀⣀⣀⠀⢠⣠⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣄⡀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣀⣀⣆⣐⣀⣰⣀⣀⣐⣁⣆⣺
⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢌⣿⣿⠀⠀⠀⠀⡏⠈⠹⠉⠁⠉⠙⠙⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⢈⠋⠙⠉⠙⠉⢋⢉⠋⠉⠙⠙⠉⠨⠉⠙⠉⠙⠋⢉⠋⠙⡉⠩⠉⢫⠉⠉⠋⠋⠉⢹
⣿⣿⣿⣾⣿⣿⣤⣤⣤⣴⣿⣾⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡙⣿⣿⠀⠀⠉⢩⡿⠻⠻⠟⠛⢿⠛⠟⠛⠛⠛⠻⠻⠻⠙⠿⠟⠛⠛⠋⠟⢿⠛⠻⠛⠟⢻⣿⣿⢟⠋⠛⢻⣿⣿⠟⠛⠿⠻⠛⠻⠟⡟⢟⠿⠻⠻⠻⠛⢙⠻⠿⠛⢻⠻⠻⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣿⣀⣀⣀⣸⣷⣶⣶⣾⣶⣶⣶⣶⣀⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣆⣴⣶⣷⣶⣶⣶⣾⣿⣿⣾⣾⣶⣶⣶⣷⣶⣾⣾⣶⣾⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 1796

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/Tiling_Shell_s_Newest_Feature_Speeds_Up_Window_Snapping.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/Tiling_Shell_s_Newest_Feature_Speeds_Up_Window_Snapping.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Tiling Shell’s Newest Feature Speeds Up
Window Snapping⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 13, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Tiling_Shell⦈_


Window snapping GNOME extension Tiling Shell —not that you need an introduction
to it by now— adds a nifty new feature in its latest update.


Tiling Shell v16 introduces Windows Suggestions, a feature the add-on’s author
described as being able to “provide intelligent recommendations for other
windows to tile, making window management smoother and more intuitive.”


Per the GIF below, placing a window in a tile using the tiling system results
in on-screen suggestions for other windows to tile in the the remaining gaps.
If too many windows are open (so suggestions don’t fit within the available
space) it’s scrollable.


Read_on




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣀⣀⣀⣀⣀⣚⣸⣿⣇⣂⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⠀⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠠⠀⠄⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠄⠀⠀⠀⠶⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⡶⠖⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠟⡋⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠛⠑⡎⠁⣀⠀⠷⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣧⣠⣤⣶⣎⣴⣶⣂⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠻
⠐⠻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣟⣿⣿⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀
⠐⠉⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⡿⣿⣼⣿⡻⠁⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣇⠀⠀
⠀⣦⠀⠀⠀⠀⠉⠻⠿⠿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣧⡶⠀⠀⠀⣿⣿⠋⢻⣿⠏⠁⠀⠀
⢠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⠀⠀⠿⠏⠀⠈⠃⠀⠀⠀⠀
⠀⡄⠀⠀⠀⠀⠖⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣾⣿⡿⢿⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠉⠿⠿⠿⠿⣷⣦⡄⠘⠀⠀⠂⠒⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⡿⠿⠿⠿⡿⠿⠿⠿⠟⠃⠹⢿⠿⠿⠻⠿⠿⢿⣿⡿⠿⣶⠿⡃⠀⠀⢀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠁⠈⠀⠉⠉⠀⠀⠁⠈⠈⠀⠉⠁⠉⠁⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⡀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠚⠸⠿⠇⠂⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠃⠀⢠⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠷⠶⠶⢶⣶⠶⠶⠶⠶⠶⠽⠿⠶⠿⠦⠤⠤⠼⠤⠥⠭⠭⠭⠭⠭⠭⠭⠭⠭⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠿⡇⠚⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠠⠀⠄⠠⢰⣶⠖⢶⣶⢢⡖⠺⢴⠒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣤⣤⣤⣤⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⡶⠖⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⡋⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠑⡎⠁⣀⠀⠷⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣧⣠⣤⣶⣎⣴⣶⣂⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⢻
⠐⠻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣟⣿⣿⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀
⠐⠉⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⡿⣿⣼⣿⡻⠁⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣗⠀⠀
⠀⣦⠀⠀⠀⠀⠉⠻⠿⢿⣿⣿⣿⡿⠀⠀⠀⢉⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣧⡶⠀⠀⠀⣿⣿⠋⢻⣿⡟⠁⠀⠀
⢠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⠀⠀⠿⠏⠀⠈⠃⠀⠀⠀⠀
⠀⡄⠀⠀⠀⠀⠖⠀⢠⣄⣀⣀⣀⣀⡀⠀⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣾⣿⡿⢿⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠉⠿⠿⠿⣿⣿⣿⡇⠀⠀⠀⠂⠒⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⡿⠿⠿⠿⡿⠿⠿⠿⠟⠃⠹⢿⠿⠿⠻⠿⠿⢿⣿⡿⠿⣶⠿⡃⠀⠀⢀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠁⠈⠀⠉⠉⠀⠀⠁⠈⠈⠀⠉⠁⠉⠁⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⡠⣤⠀⢀⡀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣦⣤⣶⣶⣶⣶⣶⣶⢤⣶⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⢿⣿⣟⠿⢯⠉⣝⣻⣶⡟⣿⣾⣟⣛⣛⣛⣛⠛⠛⠛⠳⠓⠒⠊⢙⣙⡛⠓⣻⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠒⠸⠿⠇⠂⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢣⠗⠖⡒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠛⠛⣒⠒⠛⠛⠛⠛⠛⠛⠒⠛⠛⠛⠒⠛⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠘⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠋⠛⠙⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠸⠁⠄⠡⠰⠵⠖⠟⠴⠘⠀⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣤⣤⣤⣤⣀⡨⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⡶⠖⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠟⡉⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠸
⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠛⠁⡎⠁⣀⠀⠷⠇⠀⠀⠀⣿⣿⣿⣿⣿⡁⣤⣤⣤
⠘⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⣇⣠⣤⣶⣆⣤⣶⣀⣀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣿⣿⣿
⠐⠻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣟⣿⣿⠋⠀⠀⠀⣿⣿⣿⣿⣿⡇⣿⣿⣿
⠐⠉⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠸⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⣿⣼⣿⡻⠁⠀⠀⠀⠀⣿⢿⣿⣿⣿⠁⢿⣿⣿
⠀⣤⠀⠀⠀⠀⠉⠻⠿⠿⣿⣿⣿⡿⠠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⡿⣧⠶⠀⠀⠀⣿⣿⠋⢻⣿⠀⠈⠛⠋
⢠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⠀⠀⠟⠋⠀⠈⠁⠀⠀⢶⡿
⠀⡄⠀⠀⠀⠀⠆⠀⢀⢀⣀⣀⣀⣀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣾⣿⡿⢿⣿⣿⡿⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠿⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⢿⡿⠿⠿⠿⡿⠿⠿⠿⠏⠁⠰⠿⠟⠿⠻⠿⠿⢿⣿⡿⠿⡶⠟⡁⠀⠀⢀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠁⠀⠀⠀⠁⠀⠀⠁⠈⠈⠀⠉⠁⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡲⣤⠀⢀⡀⣀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣶⣦⣤⣤⣶⣶⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣻⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣟⠟⠛⠛⠻⠓⠖⣊⣙⣙⡛⢓⣻⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣀⣀⣀⣀⣀⣒⣸⣿⣇⣂⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⡿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⢿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡃⢣⠓⠒⡒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠛⠋⠀⠀⠉⠉⠉⠉⠉⠙⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣭⣿⡟⣿⠘⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⣤⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⣿⣿⣿⣿⣿⣿⠟⡛⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⠟⠉⠛⠛⡼⠃⡀⠀⣠⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠆⣀⣤⣤⡔⢉⣠⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠐⣻⢸⣿⣿⣿⣿⣿⣿⣿⣿⠸⠿⠿⢱⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠽⢥⣴⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣟⣿
⠐⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⠍⠀⠀⠀⠀⣿⣿⣿⣿⣟⣋⡅⢚⣛
⠀⣤⠀⠀⠀⠉⠻⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣷⡤⣤⠀⠀⠀⡥⠴⠏⢿⣿⠀⠀⠛⠋
⢠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡗⠀⠀⠀⡔⠀⠀⠘⠃⠀⠀⠦⠿
⠀⡄⠀⠀⠀⠀⠖⠀⢠⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⢿⠁⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠋⢿⡟⠻⣿⣿⣿⣿⣿⣿⣿⡛⠛⡋⠀⠀⢀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢄⠀⠂⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⢀⠀⠛⠏⠨⠄⠉⠏⠹⠛⠏⠹⠯⠀⠭⠥⠌⠤⠆⠵⠄⠀⠀⠀⠀⠀⠀⠀⣉⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣶⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣶⣦⣤⣴⣶⣶⣶⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠒⠒⠂⠂⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠓⠖⣊⣙⣙⡛⢓⣻⣿⣇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣚⣸⣿⣇⣂⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠉⠙⠚⠛⠛⠛⠛⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁⠐⠀⡄⣀⠀⡀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⡀⠀⡀⠀⣤⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⡤⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⡀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡷⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⠟⠻⢿⣿⠛⣛⠙⣿⡗⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣣⠆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⣿⣿⣤⣴⣿⣼⣻⣤⠤⢄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⢽⣧⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠾⣹⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠟⡁⠀⠀⢨⣿⣿⣿⣿⣿⣹⣿⣻⣻
⢠⣦⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⠀⡀⠈⣿⣿⣟⣿⣿⢿⣛⡿⠎
⢀⣶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠠⣿⣿⠖⢿⡾⢻⡿⢿⣾
⢠⣄⠀⠉⠉⠻⣿⠿⣿⣿⣟⣉⣉⡀⠀⠀⠀⠀⢤⣤⠀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡧⠀⠀⢐⣏⡩⢐⡫⢿⣺⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠸⠻⣿⢻⣿⣿⣶⣿⡄⠀⠈⢡⠀⠀⣄⣤⣠⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⠟⢛⣏⡞⠠⣖⣲⣲⣶⡾⠃⣯⣿⣿⡂⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣿⠛⠒⠀⠀⠀⠄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠋⠛⠋⠛⠉⠁⠀⢐⣀⠀⠻⠯⠽⠍⠯⠯⠽⠻⠿⠽⠿⠽⠯⠥⡟⢯⠿⠷⢮⣻⣬⡀⡽⢯⣾⣉⣟⣩⣕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣛⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢠⢐⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡁⣉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠚⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠋⠀⢸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠥⠀⠂⠂⠀⠂⠖⠖⠒⠒⠆⠲⠒⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⠛⢻⣿⡿⣟⣛⣽⡛⢛⣻⣿⣟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣚⣸⣿⣇⣂⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⢿⠿⠿⠿⠿⠿⢿⣿⣿⣿⠿⠿⠯⠉⠙⠚⠛⠛⠛⠛⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⠛⠛⠛⠉⠉⠉⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⠉⠐⠀⡄⣀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⡀⠀⡀⠀⣤⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⡤⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⡀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡷⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⠟⠻⢿⣿⠛⣛⠙⣿⡗⠀⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣣⠆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⣿⣿⣤⣴⣿⣼⣻⣤⠤⢄⠀⠐⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⢽⣧⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠾⣹⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠟⡁⠀⠀⢨⣿⣿⣿⣿⣿⣹⣿⣻⣻
⢠⣦⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⠀⡀⠈⣿⣿⣿⣿⣿⢿⣛⣿⣾
⢀⣶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠠⣿⣿⠖⢿⣾⣿⣿⣿⣿
⢠⣄⠀⠉⠉⠻⣿⠿⣿⣿⣟⣉⣉⡀⡄⠀⠀⠀⢤⣤⠀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡧⠀⢰⠰⣏⡫⢾⣽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠸⠻⣿⢻⣿⣿⣷⣿⡄⠀⠈⢡⠀⠀⣄⣤⣠⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⠟⢛⣏⡞⠠⣞⣲⢿⣶⣾⡿⣿⣿⣿⣺⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢟⣿⠛⠒⠀⠀⠀⠄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠋⠛⠋⠛⠉⠁⠀⢐⣀⠀⠻⠯⠽⠍⠯⠯⠽⠻⠿⠽⠿⠽⠯⠥⡟⢯⠿⠷⢮⣻⣯⡉⡽⢯⣿⣛⣟⣻⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣛⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⢦⣐⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⠤⠤⠤⠤⠠⡅⣍⣩⠤⠀⠄⠠⠠⠀⠀⠄⠄⠠⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠘⠚⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⠋⠀⢸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠅⠙⠙⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠥⠀⠒⠂⠀⠂⠟⠖⠒⠒⠆⠲⠒⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡜⢛⠛⢻⣿⡿⣿⣿⣽⡛⢛⣻⣾⣟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣚⣸⣿⣇⣂⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⢿⠿⠿⠿⠿⠿⢿⣿⣿⣿⠿⠿⠯⠉⠙⠚⠛⠛⠛⠛⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⢿⡟⠛⠉⠉⠉⠀⡀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⠉⠐⠀⡄⣀⡀⡀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⡀⠀⡀⠀⣤⡌⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⡤⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⡀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡷⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⠟⠻⢿⣿⠛⣛⠙⣿⡗⠀⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣣⠆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⣿⣿⣤⣴⣿⣼⣻⣤⠤⢄⠀⠐⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⢽⣧⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠾⣹⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠟⡁⠀⠀⢨⣿⣿⣿⣿⣿⣹⣿⣿⣻
⢠⣦⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⠀⡀⠈⣿⣿⣿⣿⣿⢿⣛⣿⣾
⢀⣶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠠⣿⣿⠖⢿⣾⣿⣿⣿⣿
⢠⣄⠀⠉⠉⠻⣿⠿⣿⣿⣟⣉⣉⡀⡄⠀⠀⠀⢤⣤⠀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡧⠀⢰⠰⣏⡫⢾⣽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠸⠻⣿⢻⣿⣿⣷⣿⡄⠀⠈⢡⠀⠀⣄⣤⣠⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⠟⢛⣏⡞⠠⣞⣲⢿⣶⣾⡿⣿⣿⣿⣺⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢟⣿⠛⠒⠀⠀⠀⠄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠋⠛⠋⠛⠉⠁⠀⢐⣀⠀⠻⠯⠽⠍⠯⠯⠽⠻⠿⠽⠿⠽⠯⠥⡟⢯⠿⠷⢮⣻⣯⡉⡽⢯⣿⣛⣟⣻⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣛⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⢦⣐⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⠤⠤⠤⠤⠠⡅⣍⣩⠤⠀⠄⠠⠠⠀⠀⠄⠄⠠⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠘⠚⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⠋⠀⢸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠅⠙⠙⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠥⠀⠒⠂⠀⠂⠟⠖⠒⠒⠆⠲⠒⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡜⢛⠛⢻⣿⡿⣿⣿⣽⡛⢛⣻⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣚⣸⣿⣇⣂⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⢿⠿⠿⠿⠿⠿⢿⣿⣿⣿⠿⠿⠯⠉⠙⠚⠛⠛⠛⠛⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠛⢹⣶⣶⣾⣾⣶⢶⣶⣶⣶⢶⢶⣶⡶⣶⢶⢿⢶⡶⣶⡶⢾⣿⣿⣿⣿⣿⡿⣶⣶⡷⠶⠶⠴⠦⠶⠦⠴⡦⢾⣶⣷⣶⣾⣶⣿⣶⣶⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠶⠆⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠶⠶⠶⠶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⡀⠀⡶⠀⣴⡌⠸⢶⣿⢶⣾⡷⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣶⣶⣦⣤⣤⣤⣤⣤⡤⠄⠀⠀⠀⢰⣶⣶⣶⣶⣶⡆⣿⣿⣿
⡟⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⡀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⣿⣿⣿
⡷⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⠟⠻⢿⣿⠛⣛⠙⣿⡗⠀⠠⢸⣿⣿⣿⣿⣿⡗⣿⣿⣿
⣣⠆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⣿⣿⣤⣴⣿⣼⣻⣤⠤⢄⠀⠐⢸⣿⣿⣿⣿⣿⡗⣿⣿⣿
⣯⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⢽⣧⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⠨⣿⣿⣿⣿⣿⣷⣿⣿⣿
⠾⣹⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠟⡁⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⣦⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⠀⡀⠈⣿⣿⣿⣿⣿⢿⣟⣿⣾
⢀⣶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠠⣿⣿⠖⢿⣾⣿⣿⣿⣿
⢠⣄⠀⠉⠉⠻⣿⠿⣿⣿⣟⣉⣉⡀⡄⠀⠀⠀⢤⣤⠀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡧⠀⢰⠰⣏⡫⢾⣽⣿⣿⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠸⠻⣿⢻⣿⣿⣷⡇⡄⠀⠈⢡⠀⠀⣄⣤⣠⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⠟⢛⣏⡞⠠⣞⣲⢿⣶⣾⡿⣿⣿⢿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢟⡇⠛⠒⠀⠀⠀⠄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠋⠛⠋⠛⠉⠁⠀⢐⣀⠀⠻⠯⠽⠍⠯⠯⠽⠻⠿⠽⠿⠽⠯⠥⡟⢯⠿⠷⢮⣻⣯⡉⡽⢯⣿⣿⣜⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣛⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⢦⣿⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠤⠤⠤⠠⡅⣍⣩⠤⠀⠄⠠⠠⠀⠀⠄⠄⠠⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠘⠚⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⠋⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠅⠙⠙⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠥⠀⠒⠂⠀⠂⠟⠖⠒⠒⠆⠲⠒⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡜⢛⠛⢻⣿⡿⣿⣿⣽⡛⣿⣻⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣀⣀⣀⣀⣀⣚⣸⣿⣇⣂⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⢿⠿⠿⠿⠿⠿⢿⠿⢿⡿⠿⠿⠯⠉⠙⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠋⣹⣶⣶⣾⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣦⣴⣶⣾⣶⣷⣶⣾⣶⣿⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⠠⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠀⠀⠀⠀⠠⡦⠴⠦⠦⠀⠀⠀⠀⠀⠀⠀⡂⠁⠀⠀⠀⠀⠀⠀⠀⠰⠄⠠⠄⠀⠶⠀⠶⠀⠶⠀⢀⡆⣿⣿⣿
⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣶⣶⣶⣶⣶⣶⣆⠀⡀⢀⠀⠀⠀⢠⣶⣦⣦⣀⠀⠇⣿⣿⣿
⡷⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣼⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⠛⠻⢿⣿⠛⣃⠙⣿⡗⠀⠠⢸⣿⣿⣿⡗⠀⡆⣿⣿⣿
⢣⠆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⣠⣿⣷⣠⣴⣯⡼⢻⣤⠄⢀⠀⠐⠸⣿⣿⣿⠄⠘⡗⣿⣿⣿
⣣⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⢽⣥⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⠨⣿⣿⣿⣴⣶⣷⣿⣿⣿
⠾⣩⡺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠟⡁⠀⠀⠨⣿⣿⣿⢺⣿⣿⣿⣿⣿
⢠⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⠀⡀⠈⣿⣿⣿⢸⣿⣿⣟⣿⣿
⢀⣶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠠⣿⣿⠖⢻⣿⣿⣿⣿⣿
⢠⣄⠀⠉⠉⠛⣿⠿⣿⣿⣟⣁⣀⡀⣿⠀⠀⠀⢄⣤⠀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠁⠀⢰⠰⣇⡫⢮⣿⢿⣻⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠸⠻⡿⢻⣿⣿⣿⠀⡀⠀⠈⢡⠀⠀⠄⣤⣠⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡟⠏⢙⣊⡜⠠⢞⣲⢿⣦⣾⣻⠓⣯⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣯⠀⠛⠒⠀⠀⠀⠄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠋⠛⠋⠛⠉⠁⠀⠐⣀⠀⠻⠯⠽⠍⠯⠯⠽⠻⠿⠹⠿⠽⠯⠥⡟⢯⠿⠷⢬⣻⣯⡉⡽⣿⣰⣾⣝⣻⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠐⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣓⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⢺⣶⣿⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠤⠤⠤⠠⡅⣍⣩⠤⠀⠄⠀⠀⠀⠀⠄⠄⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠘⠚⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⢺⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⠅⠙⠙⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠥⠀⠒⠂⠀⠂⠟⠒⠒⠒⠂⠒⠒⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡜⢛⠛⢻⣿⠿⣿⣿⣽⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣀⣀⣀⣀⣀⣚⣸⣿⣇⣂⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⢿⠿⠿⠿⠿⠿⢿⠿⢿⡿⠿⠿⠯⠉⠙⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠋⣹⣶⣶⣾⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣦⣴⣶⣾⣶⣷⣶⣾⣶⣿⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⢀⡀⠀⢀⢀⡀⡄⢄⠄⠐⡠⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⡆⣿⣿⣿
⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠓⠰⡆⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠰⠴⡶⢴⠦⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠠⠄⠠⡶⠀⡶⠀⠶⠐⠀⠇⣿⣿⣿
⡷⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠶⣶⠒⠲⢶⣶⠒⣂⠀⣴⡆⠀⠠⢠⣶⣶⣶⡄⠀⡆⣿⣿⣿
⢣⠆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⣠⣿⣷⣠⣴⣯⡼⢻⣤⠄⢀⠀⠐⠸⣿⣿⣿⠇⠘⡗⣿⣿⣿
⣣⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⢽⣥⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⠨⣿⣿⣿⣴⣶⣷⣿⣿⣿
⠾⣩⡺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠟⡁⠀⠀⠨⣿⣿⣿⢻⣿⣿⣿⣿⣿
⢠⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⠀⡀⠈⣿⣿⣿⣼⣿⣿⣿⣿⣿
⢀⣶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠠⣿⣿⠖⢻⣿⣿⣿⣿⣿
⢠⣄⠀⠉⠉⠛⣿⠿⣿⣿⣟⣁⣀⡀⣿⠀⠀⠀⢄⣤⠀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠁⠀⢰⠰⣇⡫⢮⣿⢿⣻⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠸⠻⡿⢻⣿⣿⡧⠀⡀⠀⠈⢡⠀⠀⠄⣤⣠⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡟⠏⢙⣊⡜⠠⢞⣲⢿⣦⣾⣿⠓⣯⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣗⠀⠛⠒⠀⠀⠀⠄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠋⠛⠋⠛⠉⠁⠀⠐⣀⠀⠻⠯⠽⠍⠯⠯⠽⠻⠿⠹⠿⠽⠯⠥⡟⢯⠿⠷⢬⣻⣯⡉⡽⣿⣰⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣓⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⢿⣶⣿⣿⣭⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠠⡅⣍⣩⠤⠀⠄⠀⠀⠀⠀⠄⠄⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠘⠚⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⢻⣹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⠅⠙⠙⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣼⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠥⠀⠒⠂⠀⠂⠟⠒⠒⠒⠂⠒⠒⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡜⢛⠛⢻⣿⠿⣿⣿⣽⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣀⣀⣀⣀⣀⣚⣸⣿⣇⣂⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⢿⠿⠿⠿⠿⠿⢿⠿⢿⡿⠿⠿⠯⠉⠙⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠋⣹⣶⣶⣾⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣦⣴⣶⣾⣶⣷⣶⣾⣶⣿⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⢀⡀⠀⢀⢀⡀⡄⢄⠄⠐⡠⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⡆⣿⣿⣿
⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢓⠴⡦⠄⠥⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠌⠄⠤⠤⠤⠤⢽⣧⠤⠤⠄⠀⠐⠐⡶⢔⠆⠀⠀⠀⠀⠀⠀⠀⠣⠦⠄⠤⠤⠤⠤⠤⠤⠴⠤⠤⠤⠤⡶⠤⡶⠤⠶⠴⠄⠇⣿⣿⣿
⡷⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡼⠰⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠲⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⣶⣶⠶⣶⠒⠲⢶⣶⠒⣂⠔⣴⡶⠀⠰⢤⣶⣶⣦⡆⢠⡆⣿⣿⣿
⢣⠆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⣠⣿⣷⣠⣴⣯⡼⢻⣤⠄⢀⠀⠐⠸⣿⣿⣿⠇⢸⡗⣿⣿⣿
⣣⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⢈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⢽⣥⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⠨⣿⣿⣿⡤⣶⣷⣿⣿⣿
⠾⣩⡺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠟⡁⠀⠀⠨⣿⣿⣿⠋⣿⣿⣿⣿⣿
⢠⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⠀⡀⠈⣿⣿⣿⣄⣿⣿⣿⣿⣿
⢀⣶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠠⣿⣿⠖⢛⣿⣿⣿⣿⣿
⢠⣄⠀⠉⠉⠛⣿⠿⣿⣿⣟⣁⣀⡀⣿⠀⠀⠀⢄⣤⠀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠁⠀⢰⠰⣇⡫⢮⡟⢿⣻⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠸⠻⡿⢻⣿⣿⣿⠀⡀⠀⠈⢡⠀⠀⠄⣤⣠⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡟⠏⢙⣊⡜⠠⢞⣲⢿⣦⣾⣷⢷⣯⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠀⠛⠒⠀⠀⠀⠄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠋⠛⠋⠛⠉⠁⠀⠐⣀⠀⠻⠯⠽⠍⠯⠯⠽⠻⠿⠹⠿⠽⠯⠥⡟⢯⠿⠷⢬⣻⣯⡉⡽⣗⣸⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠐⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣓⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⢿⣶⣿⣿⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠤⠤⠤⠤⠠⡅⣍⣩⠤⠀⠄⠀⠀⠀⠀⠄⠄⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠘⠚⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⢫⣹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⠅⠙⠙⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣴⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠥⠀⠒⠂⠀⠂⠟⠒⠒⠒⠂⠒⠒⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡜⢛⠛⢻⣿⠿⣿⣿⣽⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣀⣀⣀⣀⣀⣚⣸⣿⣇⣂⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠃⣹⣶⣶⣾⣾⣶⣶⣶⣶⣶⣦⣶⣶⣶⣶⣶⣿⣶⣾⣿⣶⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠍⠩⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⢋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⡀⠀⠀⠀
⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢃⠴⠦⠄⠥⠄⠤⠄⠤⠤⠤⠤⠤⠤⠄⠌⠄⠤⠤⠤⠤⢽⣧⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⠁⠀⠀⠀⢨⠄⢺
⡷⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡼⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡞⡁⠀⠀⠀⠀⠀⠀⠀⢼
⢣⠆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠛⠩⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸
⣣⣭⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣤⣬⣤⣤⣤⣤⣤⣤⣤⡤⣤⣤⣤⣤⣼
⠶⣠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⡿⠉⠉⠁⠉⢉⡉⡉⠉⠉⠉⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠈⠀⢸
⢠⣤⠀⠀⠀⠀⠀⠀⢸⠉⠉⠙⠛⠋⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠄⣀⡴⣼⣞⣶⣦⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⢀⣶⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠰⠶⠤⠤⠤⠤⠤⠤⠤⠀⠤⠀⠀⠶⠆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⡿⣻⡿⠟⠛⠻⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⢟⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢘⣛⣃⣂⣀⣀⠐⠀⠀⠀⠀⢀⣀⣛⡂⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⡬⠁⠀⡉⢁⠀⠀⠀⠀⠀⠀⠈⣤⡄⠀⠀⢸⡇⠡⠀⠀⠠⠄⠠⠴⣿⣷⣶⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠛⠓⠛⠛⠛⠀⠀⠀⠀⠀⠐⠛⠛⠂⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢹⡏⠈⠉⠝⠛⠻⠿⢿⣿⣿⣿⣿⣿⠿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣤⣤⣬⣭⣵⣴⣦⣤⣤⣶⣤⣤⣤⣤⣤⣿⣥⣤⣤⣼⠁⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠈⠈⠛⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢠⠶⠶⠴⠶⠶⠤⠶⠶⠴⠦⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡄⢠⠶⠶⠶⡶⠶⠶⠶⠶⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣚⣸⣿⣇⣂⣂⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠚⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠐⠀⠐⠟⠇⠚⠂⠘⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⠸⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠂⠀⠀⠀⠀⠐⠒⠂⠐⠐⠒⠒⠒⠐⠒⠒⠂⠐⠀⠀⠀⠀⠂⠀⠂⠀⠐⠐⠀⠒⠒⠀⠀⠋⠩⠙⠙⠛⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲
⠀⠀⠀⠀⠈⠀⠀⠀⢠⠐⠐⢠⣨⣭⣁⣉⣉⠀⠀⠀⠀⠀⠀⠈⠉⢭⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠛⠓⠛⠛⠛⠀⠀⠀⠀⠀⠐⠗⠒⠂⠀⠀⢸⣶⠶⡶⣖⣶⣶⡶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣤⣤⣼⣿⣿⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣿⣥⣤⣤⣼⠏⠉⠀⠀⠀⠈⠀⠀⠲⠏⠁⠃⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡄⣰⠶⣶⠶⡶⠶⠶⠶⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡐⡇⢹⠢⠒⠐⠒⠒⠒⠒⠒⢺⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠜
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠒⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠘⠂⠀⠶⠂⠐⠷⠀⠺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠀⠀⠖⠀⠐⠀⠐⠀⠴⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⣿⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠒⠒⠒⠂⠀⠀⠀⠀⠐⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠐⠒⠂⠐⠂⠒⠒⠒⠒⠒⠒⠒⠒⠛⡭⠝⠛⠛⠛⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠈⠉⠠⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲
⠀⠀⠀⠀⠈⠁⠀⠀⢠⡖⠾⢶⣾⣭⣍⣉⣉⠀⠀⠀⠀⠀⠀⠈⠉⢭⡅⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⢿⠟⠿⠿⠿⠂⠀⠀⠀⠀⠐⠿⣷⠂⠀⠀⢸⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣽⣿⣿⣷⣷⣧⣤⣤⣤⣤⣤⣤⣤⣿⣧⣤⣤⣼⠏⠉⠈⠉⠈⠋⠋⠛⠳⠟⠋⠃⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡄⣰⠶⣶⠶⣶⠶⠶⠶⠶⢶⡄⠀⠀⠈⠃⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡜⡇⢻⠶⢶⢲⡶⣶⡶⡶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠒⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠘⠂⠀⠶⠂⠐⠷⠀⠺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠀⠀⠖⠀⠐⠀⠐⠀⠴⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⣿⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠒⠒⠒⠂⠀⠀⠀⠀⠐⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠐⠒⠂⠐⠂⠒⠒⠒⠒⠒⠒⠒⠒⠛⡭⠝⠛⠛⠛⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠈⠉⠠⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲
⠀⠀⠀⠀⠈⠁⠀⠀⢠⡖⠾⢶⣾⣭⣍⣉⣉⠀⠀⠀⠀⠀⠀⠈⠉⢭⡅⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⢿⠟⠿⠿⠿⠂⠀⠀⠀⠀⠐⠿⣷⠂⠀⠀⢸⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣽⣿⣿⣷⣷⣧⣤⣤⣤⣤⣤⣤⣤⣿⣧⣤⣤⣼⠏⠉⠈⠉⠈⠋⠋⠛⠳⠟⠋⠃⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡄⣰⠶⣶⠶⣶⠶⠶⠶⠶⢶⡄⠀⠀⠈⠃⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡜⡇⢻⠶⢶⢲⡶⣶⡶⡶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠒⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠘⠂⠀⠶⠂⠐⠷⠀⠺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠀⠀⠖⠀⠐⠀⠐⠀⠴⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⣿⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠒⠒⠒⠂⠀⠀⠀⠀⠐⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠐⠒⠂⠐⠂⠒⠒⠒⠒⠒⠒⠒⠒⠛⡭⠝⠛⠛⠛⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠈⠉⠠⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲
⠀⠀⠀⠀⠈⠁⠀⠀⢠⡖⠾⢶⣾⣭⣍⣉⣉⠀⠀⠀⠀⠀⠀⠈⠉⢭⡅⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⢿⠟⠿⠿⠿⠂⠀⠀⠀⠀⠐⠿⣷⠂⠀⠀⢸⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣽⣿⣿⣷⣷⣧⣤⣤⣤⣤⣤⣤⣤⣿⣧⣤⣤⣼⠏⠉⠈⠉⠈⠋⠋⠛⠳⠟⠋⠃⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡄⣰⠶⣶⠶⣶⠶⠶⠶⠶⢶⡄⠀⠀⠈⠃⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡜⡇⢻⠶⢶⢲⡶⣶⡶⡶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠒⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠘⠂⠀⠶⠂⠐⠷⠀⠺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠀⠀⠖⠀⠐⠀⠐⠀⠴⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⣿⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠒⠒⠒⠂⠀⠀⠀⠀⠐⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠐⠒⠂⠐⠂⠒⠒⠒⠒⠒⠒⠒⠒⠛⡭⠝⠛⠛⠛⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠈⠉⠠⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲
⠀⠀⠀⠀⠈⠁⠀⠀⢠⡖⠾⢶⣾⣭⣍⣉⣉⠀⠀⠀⠀⠀⠀⠈⠉⢭⡅⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⢿⠟⠿⠿⠿⠂⠀⠀⠀⠀⠐⠿⣷⠂⠀⠀⢸⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣽⣿⣿⣷⣷⣧⣤⣤⣤⣤⣤⣤⣤⣿⣧⣤⣤⣼⠏⠉⠈⠉⠈⠋⠋⠛⠳⠟⠋⠃⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡄⣰⠶⣶⠶⣶⠶⠶⠶⠶⢶⡄⠀⠀⠈⠃⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡜⡇⢻⠶⢶⢲⡶⣶⡶⡶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠒⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠘⠂⠀⠶⠂⠐⠷⠀⠺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠀⠀⠖⠀⠐⠀⠐⠀⠴⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⣿⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠒⠒⠒⠂⠀⠀⠀⠀⠐⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠐⠒⠂⠐⠂⠒⠒⠒⠒⠒⠒⠒⠒⠛⡭⠝⠛⠛⠛⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠈⠉⠠⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲
⠀⠀⠀⠀⠈⠁⠀⠀⢠⡖⠾⢶⣾⣭⣍⣉⣉⠀⠀⠀⠀⠀⠀⠈⠉⢭⡅⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⢿⠟⠿⠿⠿⠂⠀⠀⠀⠀⠐⠿⣷⠂⠀⠀⢸⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣽⣿⣿⣷⣷⣧⣤⣤⣤⣤⣤⣤⣤⣿⣧⣤⣤⣼⠏⠉⠈⠉⠈⠋⠋⠛⠳⠟⠋⠃⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡄⣰⠶⣶⠶⣶⠶⠶⠶⠶⢶⡄⠀⠀⠈⠃⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡜⡇⢻⠶⢶⢲⡶⣶⡶⡶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠒⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠘⠂⠀⠶⠂⠐⠷⠀⠺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠀⠀⠖⠀⠐⠀⠐⠀⠴⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⣿⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠒⠒⠒⠂⠀⠀⠀⠀⠐⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠐⠒⠂⠐⠂⠒⠒⠒⠒⠒⠒⠒⠒⠛⡭⠝⠛⠛⠛⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠈⠉⠠⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲
⠀⠀⠀⠀⠈⠁⠀⠀⢠⡖⠾⢶⣾⣭⣍⣉⣉⠀⠀⠀⠀⠀⠀⠈⠉⢭⡅⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⢿⠟⠿⠿⠿⠂⠀⠀⠀⠀⠐⠿⣷⠂⠀⠀⢸⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣽⣿⣿⣷⣷⣧⣤⣤⣤⣤⣤⣤⣤⣿⣧⣤⣤⣼⠏⠉⠈⠉⠈⠋⠋⠛⠳⠟⠋⠃⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡄⣰⠶⣶⠶⣶⠶⠶⠶⠶⢶⡄⠀⠀⠈⠃⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡜⡇⢻⠶⢶⢲⡶⣶⡶⡶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠒⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠘⠂⠀⠶⠂⠐⠷⠀⠺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠀⠀⠖⠀⠐⠀⠐⠀⠴⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⣿⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠒⠒⠒⠂⠀⠀⠀⠀⠐⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠐⠒⠂⠐⠂⠒⠒⠒⠒⠒⠒⠒⠒⠛⡭⠝⠛⠛⠛⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠈⠉⠠⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲
⠀⠀⠀⠀⠈⠁⠀⠀⢠⡖⠾⢶⣾⣭⣍⣉⣉⠀⠀⠀⠀⠀⠀⠈⠉⢭⡅⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⢿⠟⠿⠿⠿⠂⠀⠀⠀⠀⠐⠿⣷⠂⠀⠀⢸⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣽⣿⣿⣷⣷⣧⣤⣤⣤⣤⣤⣤⣤⣿⣧⣤⣤⣼⠏⠉⠈⠉⠈⠋⠋⠛⠳⠟⠋⠃⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡄⣰⠶⣶⠶⣶⠶⠶⠶⠶⢶⡄⠀⠀⠈⠃⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡜⡇⢻⠶⢶⢲⡶⣶⡶⡶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠒⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠘⠂⠀⠶⠂⠐⠷⠀⠺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠿⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠀⠀⠆⠀⠐⠀⠐⠀⠴⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⣛⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢒⠒⠂⠀⠀⠀⠀⠐⠒⠒⠐⠒⠒⠒⠒⠐⠒⠒⢒⡒⠒⠀⠀⠀⠂⠀⠂⠐⠒⠒⠒⠒⠒⠒⠒⠛⡭⡝⠛⠛⠛⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠀⠉⠠⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⠭⠭⠭⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠉⠩⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲
⠀⠀⠀⠀⠈⠁⠀⠀⢠⡖⠞⢲⣾⣭⣍⣉⣉⠀⣿⠀⠀⠀⠀⠀⠀⢤⣤⣤⣄⣴⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣄⣶⣦⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⠿⠟⠿⠻⠿⣿⠀⠀⠀⠀⠐⠓⣒⣉⣉⣉⣙⣛⣙⣃⣓⢛⢓⡚⡚⣙⡛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣼⣿⣿⣷⣶⣦⣿⢀⣀⣀⣀⣀⡀⣙⣭⣋⣋⣽⡝⠋⠉⠉⠐⠂⠂⠒⠒⠓⠂⠂⠐⣂⣻⣿⣿⣷⣾⣿⣿⣿⣿⣿⣻⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿⠀⠀⠀⠀⠀⡀⣸⢿⣿⣿⣿⣷⢿⡶⡶⣶⣄⣀⠒⠒⠒⠒⠒⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⡄⡅⢻⣿⣿⣺⣿⣶⠶⡿⡿⣿⡏⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠒⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠘⠂⠀⠶⠂⠐⠷⠀⠺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠿⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠀⠀⠆⠀⠐⠀⠐⠀⠴⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⣛⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢒⠒⠂⠀⠀⠀⠀⠐⠒⠒⠐⠒⠒⠒⠒⠐⠒⠒⢒⡒⠒⠀⠀⠀⠂⠀⠂⠐⠒⠒⠒⠒⠒⠒⠒⠛⡭⡝⠛⠛⠛⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠀⠉⠠⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⠭⠭⠭⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠉⠩⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲
⠀⠀⠀⠀⠈⠁⠀⠀⢠⡖⠞⢲⣾⣭⣍⣉⣉⠀⣿⠀⠀⠀⠀⠀⠀⢤⣤⣤⣄⣴⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣄⣶⣦⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⠿⠟⠿⠻⠿⣿⠀⠀⠀⠀⠐⠓⣒⣉⣉⣉⣙⣛⣙⣃⣓⢛⢓⡚⡚⣙⡛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣼⣿⣿⣷⣶⣦⣿⢀⣀⣀⣀⣀⡀⣙⣭⣋⣋⣽⡝⠋⠉⠉⠐⠂⠂⠒⠒⠓⠂⠂⠐⣂⣻⣿⣿⣷⣾⣿⣿⣿⣿⣿⣻⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿⠀⠀⠀⠀⠀⡀⣸⢿⣿⣿⣿⣷⢿⡶⡶⣶⣄⣀⠒⠒⠒⠒⠒⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⡄⡅⢻⣿⣿⣺⣿⣶⠶⡿⡿⣿⡏⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠒⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠘⠂⠀⠶⠂⠐⠷⠀⠺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠿⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠀⠀⠆⠀⠐⠀⠐⠀⠴⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠈⠉⠛⢻⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠒⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⠀⠀⠀⠀⠠⠆⠀⠀⠘⠋⠑⠂⠐⠒⢒⠒⠂⠀⠀⠀⠀⠐⠒⠒⠐⠒⠒⠒⠒⠐⢺⠒⢒⡒⠒⠀⠐⠒⠂⠀⠂⠒⠒⠒⠒⠒⠒⠒⠒⠛⡭⡝⠛⠛⠛⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠈⠉⠠⢀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⣨⣍⣥⣿⠉⠍⠁⠉⠁⠉⠀⠉⠉⠉⠩⠯⠍⠉⠉⠉⠉⢹⠉⢩⠭⠭⠭⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠉⠩⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲
⠀⠀⠀⠀⠈⠁⠀⠀⢠⡖⠾⣷⣾⣭⣍⣿⣟⠀⣿⠀⠀⠀⠀⠀⠀⢤⣤⣤⣄⣴⣤⣤⣤⣤⣤⣤⣼⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣄⣶⣦⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⠿⠟⣿⣿⣿⣿⠁⠁⠁⠀⠐⠳⣒⣉⣉⣉⣙⣛⣙⣃⣓⢛⢓⣺⡚⣙⣛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣦⣽⣿⣿⣷⣿⣯⣿⢀⣀⣀⣀⣀⡀⣙⣭⣋⣫⣽⡝⠋⠉⠉⠐⠂⠒⠒⠒⠓⠂⠂⠐⣂⣻⣿⣿⣷⣾⣿⣿⣿⣿⣿⣻⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿⠀⠀⠀⠀⠀⡀⣸⢿⣿⣿⣿⣷⢿⡶⡶⣶⣄⣀⠒⠒⠒⠒⠒⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⡄⡅⢻⣿⣿⣺⣿⣶⠶⡿⣿⣿⡏⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠒⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠘⠂⠀⠶⠂⠐⠷⠀⠺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠿⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠀⠀⠆⠀⠐⠀⠐⠀⠴⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠈⠉⠛⢻⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠒⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⠀⠀⠀⠀⠠⠆⠀⠀⠘⠋⠑⠂⠐⠒⢒⠒⠂⠀⠀⠀⠀⠐⠒⠒⠐⠒⠒⠒⠒⠐⢺⠒⢒⡒⠒⠀⠐⠒⠂⠀⠂⠒⠒⠒⠒⠒⠒⠒⠒⠛⡭⡝⠛⠛⠛⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠈⠉⠠⢀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⣨⣍⣥⣿⠉⠍⠁⠉⠁⠉⠀⠉⠉⠉⠩⠯⠍⠉⠉⠉⠉⢹⠉⢩⠭⠭⠭⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠉⠩⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲
⠀⠀⠀⠀⠈⠁⠀⠀⢠⡖⠾⣷⣾⣭⣍⣿⣟⠀⣿⠀⠀⠀⠀⠀⠀⢤⣤⣤⣄⣴⣤⣤⣤⣤⣤⣤⣼⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣄⣶⣦⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⠿⠟⣿⣿⣿⣿⠁⠁⠁⠀⠐⠳⣒⣉⣉⣉⣙⣛⣙⣃⣓⢛⢓⣺⡚⣙⣛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣦⣽⣿⣿⣷⣿⣯⣿⢀⣀⣀⣀⣀⡀⣙⣭⣋⣫⣽⡝⠋⠉⠉⠐⠂⠒⠒⠒⠓⠂⠂⠐⣂⣻⣿⣿⣷⣾⣿⣿⣿⣿⣿⣻⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿⠀⠀⠀⠀⠀⡀⣸⢿⣿⣿⣿⣷⢿⡶⡶⣶⣄⣀⠒⠒⠒⠒⠒⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⡄⡅⢻⣿⣿⣺⣿⣶⠶⡿⣿⣿⡏⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠒⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠘⠂⠀⠶⠂⠐⠷⠀⠺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠿⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠀⠀⠆⠀⠐⠀⠐⠀⠴⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠈⠉⠛⢻⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠒⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⠀⠀⠀⠀⠠⠆⠀⠀⠘⠋⠑⠂⠐⠒⢒⠒⠂⠀⠀⠀⠀⠐⠒⠒⠐⠒⠒⠒⠒⠐⢺⠒⢒⡒⠒⠀⠐⠒⠂⠀⠂⠒⠒⠒⠒⠒⠒⠒⠒⠛⡭⡝⠛⠛⠛⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠈⠉⠠⢀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⣨⣍⣥⣿⠉⠍⠁⠉⠁⠉⠀⠉⠉⠉⠩⠯⠍⠉⠉⠉⠉⢹⠉⢩⠭⠭⠭⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠉⠩⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲
⠀⠀⠀⠀⠈⠁⠀⠀⢠⡖⠾⣷⣾⣭⣍⣿⣟⠀⣿⠀⠀⠀⠀⠀⠀⢤⣤⣤⣄⣴⣤⣤⣤⣤⣤⣤⣼⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣄⣶⣦⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⠿⠟⣿⣿⣿⣿⠁⠁⠁⠀⠐⠳⣒⣉⣉⣉⣙⣛⣙⣃⣓⢛⢓⣺⡚⣙⣛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣦⣽⣿⣿⣷⣿⣯⣿⢀⣀⣀⣀⣀⡀⣙⣭⣋⣫⣽⡝⠋⠉⠉⠐⠂⠒⠒⠒⠓⠂⠂⠐⣂⣻⣿⣿⣷⣾⣿⣿⣿⣿⣿⣻⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿⠀⠀⠀⠀⠀⡀⣸⢿⣿⣿⣿⣷⢿⡶⡶⣶⣄⣀⠒⠒⠒⠒⠒⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⡄⡅⢻⣿⣿⣺⣿⣶⠶⡿⣿⣿⡏⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠒⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠘⠂⠀⠶⠂⠐⠷⠀⠺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠿⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠀⠀⠆⠀⠐⠀⠐⠀⠴⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠈⠉⠛⢻⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠒⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⠀⠀⠀⠀⠠⠆⠀⠀⠘⠋⠑⠂⠐⠒⢒⠒⠂⠀⠀⠀⠀⠐⠒⠒⠐⠒⠒⠒⠒⠐⢺⠒⢒⡒⠒⠀⠐⠒⠂⠀⠂⠒⠒⠒⠒⠒⠒⠒⠒⠛⡭⡝⠛⠛⠛⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠈⠉⠠⢀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⣨⣍⣥⣿⠉⠍⠁⠉⠁⠉⠀⠉⠉⠉⠩⠯⠍⠉⠉⠉⠉⢹⠉⢩⠭⠭⠭⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠉⠩⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲
⠀⠀⠀⠀⠈⠁⠀⠀⢠⡖⠾⣷⣾⣭⣍⣿⣟⠀⣿⠀⠀⠀⠀⠀⠀⢤⣤⣤⣄⣴⣤⣤⣤⣤⣤⣤⣼⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣄⣶⣦⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⠿⠟⣿⣿⣿⣿⠁⠁⠁⠀⠐⠳⣒⣉⣉⣉⣙⣛⣙⣃⣓⢛⢓⣺⡚⣙⣛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣦⣽⣿⣿⣷⣿⣯⣿⢀⣀⣀⣀⣀⡀⣙⣭⣋⣫⣽⡝⠋⠉⠉⠐⠂⠒⠒⠒⠓⠂⠂⠐⣂⣻⣿⣿⣷⣾⣿⣿⣿⣿⣿⣻⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿⠀⠀⠀⠀⠀⡀⣸⢿⣿⣿⣿⣷⢿⡶⡶⣶⣄⣀⠒⠒⠒⠒⠒⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⡄⡅⢻⣿⣿⣺⣿⣶⠶⡿⣿⣿⡏⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠒⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠘⠂⠀⠶⠂⠐⠷⠀⠺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠿⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠀⠀⠆⠀⠐⠀⠐⠀⠴⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠈⠉⠛⢻⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠒⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⠀⠀⠀⠀⠠⠆⠀⠀⠘⠋⠑⠂⠐⠒⢒⠒⠂⠀⠀⠀⠀⠐⠒⠒⠐⠒⠒⠒⠒⠐⢺⠒⢒⡒⠒⠀⠐⠒⠂⠀⠂⠒⠒⠒⠒⠒⠒⠒⠒⠛⡭⡝⠛⠛⠛⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠈⠉⠠⢀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⣨⣍⣥⣿⠉⠍⠁⠉⠁⠉⠀⠉⠉⠉⠩⠯⠍⠉⠉⠉⠉⢹⠉⢩⠭⠭⠭⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠉⠩⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲
⠀⠀⠀⠀⠈⠁⠀⠀⢠⡖⠾⣷⣾⣭⣍⣿⣟⠀⣿⠀⠀⠀⠀⠀⠀⢤⣤⣤⣄⣴⣤⣤⣤⣤⣤⣤⣼⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣄⣶⣦⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⠿⠟⣿⣿⣿⣿⠁⠁⠁⠀⠐⠳⣒⣉⣉⣉⣙⣛⣙⣃⣓⢛⢓⣺⡚⣙⣛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣦⣽⣿⣿⣷⣿⣯⣿⢀⣀⣀⣀⣀⡀⣙⣭⣋⣫⣽⡝⠋⠉⠉⠐⠂⠒⠒⠒⠓⠂⠂⠐⣂⣻⣿⣿⣷⣾⣿⣿⣿⣿⣿⣻⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿⠀⠀⠀⠀⠀⡀⣸⢿⣿⣿⣿⣷⢿⡶⡶⣶⣄⣀⠒⠒⠒⠒⠒⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⡄⡅⢻⣿⣿⣺⣿⣶⠶⡿⣿⣿⡏⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠒⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠘⠂⠀⠶⠂⠐⠷⠀⠺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠿⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠀⠀⠆⠀⠐⠀⠐⠀⠴⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠈⠉⠛⢻⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠒⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⠀⠀⠀⠀⠠⠆⠀⠀⠘⠋⠑⠂⠐⠒⢒⠒⠂⠀⠀⠀⠀⠐⠒⠒⠐⠒⠒⠒⠒⠐⢺⠒⢒⡒⠒⠀⠐⠒⠂⠀⠂⠒⠒⠒⠒⠒⠒⠒⠒⠛⡭⡝⠛⠛⠛⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠈⠉⠠⢀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⣨⣍⣥⣿⠉⠍⠁⠉⠁⠉⠀⠉⠉⠉⠩⠯⠍⠉⠉⠉⠉⢹⠉⢩⠭⠭⠭⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠉⠩⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲
⠀⠀⠀⠀⠈⠁⠀⠀⢠⡖⠾⣷⣾⣭⣍⣿⣟⠀⣿⠀⠀⠀⠀⠀⠀⢤⣤⣤⣄⣴⣤⣤⣤⣤⣤⣤⣼⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣄⣶⣦⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⠿⠟⣿⣿⣿⣿⠁⠁⠁⠀⠐⠳⣒⣉⣉⣉⣙⣛⣙⣃⣓⢛⢓⣺⡚⣙⣛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣦⣽⣿⣿⣷⣿⣯⣿⢀⣀⣀⣀⣀⡀⣙⣭⣋⣫⣽⡝⠋⠉⠉⠐⠂⠒⠒⠒⠓⠂⠂⠐⣂⣻⣿⣿⣷⣾⣿⣿⣿⣿⣿⣻⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿⠀⠀⠀⠀⠀⡀⣸⢿⣿⣿⣿⣷⢿⡶⡶⣶⣄⣀⠒⠒⠒⠒⠒⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⡄⡅⢻⣿⣿⣺⣿⣶⠶⡿⣿⣿⡏⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠒⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠘⠂⠀⠶⠂⠐⠷⠀⠺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠿⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠀⠀⠆⠀⠐⠀⠐⠀⠴⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠈⠉⠛⢻⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠒⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⠀⠀⠀⠀⠠⠆⠀⠀⠘⠋⠑⠂⠐⠒⢒⠒⠂⠀⠀⠀⠀⠐⠒⠒⠐⠒⠒⠒⠒⠐⢺⠒⢒⡒⠒⠀⠐⠒⠂⠀⠂⠒⠒⠒⠒⠒⠒⠒⠒⠛⡭⡝⠛⠛⠛⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠈⠉⠠⢀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⣨⣍⣥⣿⠉⠍⠁⠉⠁⠉⠀⠉⠉⠉⠩⠯⠍⠉⠉⠉⠉⢹⠉⢩⠭⠭⠭⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠉⠩⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲
⠀⠀⠀⠀⠈⠁⠀⠀⢠⡖⠾⣷⣾⣭⣍⣿⣟⠀⣿⠀⠀⠀⠀⠀⠀⢤⣤⣤⣄⣴⣤⣤⣤⣤⣤⣤⣼⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣄⣶⣦⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⠿⠟⣿⣿⣿⣿⠁⠁⠁⠀⠐⠳⣒⣉⣉⣉⣙⣛⣙⣃⣓⢛⢓⣺⡚⣙⣛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣦⣽⣿⣿⣷⣿⣯⣿⢀⣀⣀⣀⣀⡀⣙⣭⣋⣫⣽⡝⠋⠉⠉⠐⠂⠒⠒⠒⠓⠂⠂⠐⣂⣻⣿⣿⣷⣾⣿⣿⣿⣿⣿⣻⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿⠀⠀⠀⠀⠀⡀⣸⢿⣿⣿⣿⣷⢿⡶⡶⣶⣄⣀⠒⠒⠒⠒⠒⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⡄⡅⢻⣿⣿⣺⣿⣶⠶⡿⣿⣿⡏⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠒⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠘⠂⠀⠲⠂⠐⠷⠀⠺⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠿⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠆⠀⠐⠀⠐⠀⠴⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⣛⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡿⣿⣟⣙⣉⣋⢋⠙⠛⠛⠛⠛⠛⢛⠛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠈⠉⠛⢻⠛⠛⠻⣿⣿⣿⣿⣿⣧⡌⠉⠉⠀⠉⠉⢹⣿⣿⡯⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣤⣤⣤⣦⠔⠂⠀⠂⠀⠀⢀⣀⣶⡶⠀⠀⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⠀⠀⠀⠀⠠⠆⠀⢈⣉⣹⣙⠛⠛⠛⢒⠒⠂⠀⠀⠀⠈⠛⣋⡋⠐⠒⠒⠒⠒⠐⢺⠒⢒⡒⠒⠀⠀⠀⠂⠀⠂⠐⠒⠒⠒⠒⠒⠒⠒⠛⡭⡝⠛⠛⠛⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠀⠉⠠⢀⠀⠀⠀⠀⠰⠶⠶⠶⠾⠿⠿⠿⠿⠿⠷⠿⢿⣷⣷⣿⣦⣷⣶⣿⣿⣿⣿⣿⣿⠉⠉⢹⠉⢩⠭⠭⠭⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠉⠩⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠓⠒⠚⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⢛⠛⣻⣿⣿⠛⠻⠟⠻⠟⠓⠒⠚⠒⠒⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣄⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣂⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠐⠀⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣟⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠤⢀⣤⣋⣫⠙⠙⠋⠉⠉⠐⠀⠲⠒⠒⠓⠂⠂⠐⣂⣻⣿⣿⣷⣾⣿⣿⣿⣿⣿⣻⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣾⣷⣷⣾⢿⣿⣿⢀⣀⢀⡀⢀⣀⢀⣀⢀⡀⠒⠒⠒⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣿⣿⣿⣿⣿⡿⣿⣿⠿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣺⣺⡿⠾⡿⢾⢿⡆⠀⠀⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠒⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠘⠂⠀⠲⠂⠐⠷⠀⠺⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠿⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠆⠀⠐⠀⠐⠀⠴⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⣛⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡿⣿⣟⣙⣉⣋⢋⠙⠛⠛⠛⠛⠛⢛⠛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠈⠉⠛⢻⠛⠛⠻⣿⣿⣿⣿⣿⣧⡌⠉⠉⠀⠉⠉⢹⣿⣿⡯⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣤⣤⣤⣦⠔⠂⠀⠂⠀⠀⢀⣀⣶⡶⠀⠀⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⠀⠀⠀⠀⠠⠆⠀⢈⣉⣹⣙⠛⠛⠛⢒⠒⠂⠀⠀⠀⠈⠛⣋⡋⠐⠒⠒⠒⠒⠐⢺⠒⢒⡒⠒⠀⠀⠀⠂⠀⠂⠐⠒⠒⠒⠒⠒⠒⠒⠛⡭⡝⠛⠛⠛⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠀⠉⠠⢀⠀⠀⠀⠀⠰⠶⠶⠶⠾⠿⠿⠿⠿⠿⠷⠿⢿⣷⣷⣿⣦⣷⣶⣿⣿⣿⣿⣿⣿⠉⠉⢹⠉⢩⠭⠭⠭⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠉⠩⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠓⠒⠚⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⢛⠛⣻⣿⣿⠛⠻⠟⠻⠟⠓⠒⠚⠒⠒⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣄⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣂⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠐⠀⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣟⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠤⢀⣤⣋⣫⠙⠙⠋⠉⠉⠐⠀⠲⠒⠒⠓⠂⠂⠐⣂⣻⣿⣿⣷⣾⣿⣿⣿⣿⣿⣻⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣾⣷⣷⣾⢿⣿⣿⢀⣀⢀⡀⢀⣀⢀⣀⢀⡀⠒⠒⠒⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣿⣿⣿⣿⣿⡿⣿⣿⠿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣺⣺⡿⠾⡿⢾⢿⡆⠀⠀⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣺⣸⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠷⠀⠺⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠿⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⢿⡿⣿⣏⣙⣉⣋⠉⠉⠙⠛⠛⠛⠛⢛⠙⣛⡛⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠈⠉⠙⢻⠛⠚⠫⣿⣿⣭⣿⣿⣧⡌⠉⠉⠀⠉⠙⣿⣭⣿⣿⣯⣭⣭⣻⣽⣭⣿⣿⡽⣹⡛⠛⠟⣛⠟⠩⠟⠿⠯⢿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣤⣤⣿⣆⠔⠂⠀⠂⠀⠀⣭⣭⣿⣛⣍⣉⣉⢉⢉⡉⣙⣋⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣭⣭⡍⠈⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⠀⠀⠀⠀⠠⠄⠀⢈⣉⣩⣙⠛⣿⡃⠂⠒⠂⠀⠀⠀⠾⠿⢿⠿⠾⠶⠶⠶⡶⠶⠾⠶⢒⡒⠐⠀⠀⠀⠂⠀⠂⠐⠒⠲⠶⠶⠾⠿⠿⠟⠈⠐⠀⠒⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠀⠉⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠿⠿⠿⠿⣿⣷⣬⣶⣦⣤⣄⣠⣿⣿⣿⣿⣯⣿⣭⣭⣭⣭⣍⣈⣩⣩⣭⣭⣉⣉⣉⣉⣉⣉⣉⣉⣁⣈⣰⣿⣷⣊⣁⣉⣉⣉⣩⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠓⠒⢚⣒⣚⣛⣛⣛⣛⣛⣛⣛⣛⣭⣉⣙⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣙⣛⣻⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣂⣺⡇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠⠀⠀⣿⣛⣛⣻⣇⣀⣒⣒⣐⣀⣀⣒⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⣼⣦⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⠄⠀⠛⠀⢸⣿⣿⣿⣻⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⠇⠤⠢⢠⣤⣤⣾⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣮⣽⣶⣾⣿⣿⣿⣿⣿⣿⡇⣠⣠⡀⠀⢀⣀⣀⢀⣀⢀⠀⣠⣀⡀⠀⣀⣄⠀⣿⣿⣿⣿⠼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣺⣸⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠷⠀⠺⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠿⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⢿⡿⣿⣏⣙⣉⣋⠉⠉⠙⠛⠛⠛⠛⢛⠙⣛⡛⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠈⠉⠙⢻⠛⠚⠫⣿⣿⣭⣿⣿⣧⡌⠉⠉⠀⠉⠙⣿⣭⣿⣿⣯⣭⣭⣻⣽⣭⣿⣿⡽⣹⡛⠛⠟⣛⠟⠩⠟⠿⠯⢿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣤⣤⣿⣆⠔⠂⠀⠂⠀⠀⣭⣭⣿⣛⣍⣉⣉⢉⢉⡉⣙⣋⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣭⣭⡍⠈⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⠀⠀⠀⠀⠠⠄⠀⢈⣉⣩⣙⠛⣿⡃⠂⠒⠂⠀⠀⠀⠾⠿⢿⠿⠾⠶⠶⠶⡶⠶⠾⠶⢒⡒⠐⠀⠀⠀⠂⠀⠂⠐⠒⠲⠶⠶⠾⠿⠿⠟⠈⠐⠀⠒⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠀⠉⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠿⠿⠿⠿⣿⣷⣬⣶⣦⣤⣄⣠⣿⣿⣿⣿⣯⣿⣭⣭⣭⣭⣍⣈⣩⣩⣭⣭⣉⣉⣉⣉⣉⣉⣉⣉⣁⣈⣰⣿⣷⣊⣁⣉⣉⣉⣩⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠓⠒⢚⣒⣚⣛⣛⣛⣛⣛⣛⣛⣛⣭⣉⣙⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣙⣛⣻⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣂⣺⡇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠⠀⠀⣿⣛⣛⣻⣇⣀⣒⣒⣐⣀⣀⣒⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⣼⣦⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⠄⠀⠛⠀⢸⣿⣿⣿⣻⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⠇⠤⠢⢠⣤⣤⣾⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣮⣽⣶⣾⣿⣿⣿⣿⣿⣿⡇⣠⣠⡀⠀⢀⣀⣀⢀⣀⢀⠀⣠⣀⡀⠀⣀⣄⠀⣿⣿⣿⣿⠼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣺⣸⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠷⠀⠺⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠿⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⢿⡿⣿⣏⣙⣉⣋⠉⠉⠙⠛⠛⠛⠛⢛⠙⣛⡛⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠈⠉⠙⢻⠛⠚⠫⣿⣿⣭⣿⣿⣧⡌⠉⠉⠀⠉⠙⣿⣭⣿⣿⣯⣭⣭⣻⣽⣭⣿⣿⡽⣹⡛⠛⠟⣛⠟⠩⠟⠿⠯⢿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣤⣤⣿⣆⠔⠂⠀⠂⠀⠀⣭⣭⣿⣛⣍⣉⣉⢉⢉⡉⣙⣋⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣭⣭⡍⠈⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⠀⠀⠀⠀⠠⠄⠀⢈⣉⣩⣙⠛⣿⡃⠂⠒⠂⠀⠀⠀⠾⠿⢿⠿⠾⠶⠶⠶⡶⠶⠾⠶⢒⡒⠐⠀⠀⠀⠂⠀⠂⠐⠒⠲⠶⠶⠾⠿⠿⠟⠈⠐⠀⠒⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠀⠉⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠿⠿⠿⠿⣿⣷⣬⣶⣦⣤⣄⣠⣿⣿⣿⣿⣯⣿⣭⣭⣭⣭⣍⣈⣩⣩⣭⣭⣉⣉⣉⣉⣉⣉⣉⣉⣁⣈⣰⣿⣷⣊⣁⣉⣉⣉⣩⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠓⠒⢚⣒⣚⣛⣛⣛⣛⣛⣛⣛⣛⣭⣉⣙⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣙⣛⣻⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣂⣺⡇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠⠀⠀⣿⣛⣛⣻⣇⣀⣒⣒⣐⣀⣀⣒⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⣼⣦⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⠄⠀⠛⠀⢸⣿⣿⣿⣻⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⠇⠤⠢⢠⣤⣤⣾⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣮⣽⣶⣾⣿⣿⣿⣿⣿⣿⡇⣠⣠⡀⠀⢀⣀⣀⢀⣀⢀⠀⣠⣀⡀⠀⣀⣄⠀⣿⣿⣿⣿⠼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣺⣸⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠷⠀⠺⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠿⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⢿⡿⣿⣏⣙⣉⣋⠉⠉⠙⠛⠛⠛⠛⢛⠙⣛⡛⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠈⠉⠙⢻⠛⠚⠫⣿⣿⣭⣿⣿⣧⡌⠉⠉⠀⠉⠙⣿⣭⣿⣿⣯⣭⣭⣻⣽⣭⣿⣿⡽⣹⡛⠛⠟⣛⠟⠩⠟⠿⠯⢿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣤⣤⣿⣆⠔⠂⠀⠂⠀⠀⣭⣭⣿⣛⣍⣉⣉⢉⢉⡉⣙⣋⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣭⣭⡍⠈⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⠀⠀⠀⠀⠠⠄⠀⢈⣉⣩⣙⠛⣿⡃⠂⠒⠂⠀⠀⠀⠾⠿⢿⠿⠾⠶⠶⠶⡶⠶⠾⠶⢒⡒⠐⠀⠀⠀⠂⠀⠂⠐⠒⠲⠶⠶⠾⠿⠿⠟⠈⠐⠀⠒⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠀⠉⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠿⠿⠿⠿⣿⣷⣬⣶⣦⣤⣄⣠⣿⣿⣿⣿⣯⣿⣭⣭⣭⣭⣍⣈⣩⣩⣭⣭⣉⣉⣉⣉⣉⣉⣉⣉⣁⣈⣰⣿⣷⣊⣁⣉⣉⣉⣩⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠓⠒⢚⣒⣚⣛⣛⣛⣛⣛⣛⣛⣛⣭⣉⣙⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣙⣛⣻⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣂⣺⡇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠⠀⠀⣿⣛⣛⣻⣇⣀⣒⣒⣐⣀⣀⣒⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⣼⣦⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⠄⠀⠛⠀⢸⣿⣿⣿⣻⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⠇⠤⠢⢠⣤⣤⣾⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣮⣽⣶⣾⣿⣿⣿⣿⣿⣿⡇⣠⣠⡀⠀⢀⣀⣀⢀⣀⢀⠀⣠⣀⡀⠀⣀⣄⠀⣿⣿⣿⣿⠼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣚⣸⣿⣇⣂⣂⣀⣀
⡟⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠗⠀⠺⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠶⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣯⢿⡿⣿⣏⣙⣉⣋⠉⠉⠙⠛⠛⠛⠋⠙⠙⠛⠛⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠉⠙⢹⠋⠒⠫⣿⣿⢭⢿⣿⣧⠌⠉⠉⠀⠉⠙⣿⣽⣿⣿⣯⣭⣭⣿⣽⣭⣿⣿⡽⣹⡛⠛⠟⣛⠟⠩⠟⠿⠯⢿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣦⣤⣤⣿⣆⠔⠀⠀⠂⠀⠀⣶⣦⣶⡶⣆⣤⣀⣀⣀⣀⣀⣀⡀⠀⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣶⣶⡌⠈⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠛⠀⠀⠀⠀⠀⠠⠀⠀⢈⣉⣉⣙⠋⣽⠛⠛⠛⠛⠛⠛⠛⡛⢛⢛⠛⢛⣟⢿⣟⣿⣻⣛⢟⡟⠻⣿⠿⢟⣿⣟⣿⣻⣻⣛⡟⢛⢿⠿⠟⣻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠀⠈⠀⠀⠀⠀⢸⡏⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⡉⢉⠉⡉⣿⣈⣐⣿⡏⠉⠩⠉⠩⠉⠉⠭⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠓⠒⢚⡀⠀⠀⣰⣆⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣠⣀⣀⣀⠀⠶⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣂⣸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠄⠠⠀⠀⣿⣛⣛⣻⡇⠀⠒⠒⠐⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣈⣭⣿⣤⣒⣤⡄⠛⠀⢸⣿⣿⣿⡣⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣶⣿⣿⣿⣿⣿⣟⣿⣿⣧⣤⣤⣾⣿⣿⣿⣗⣼⣿⣥⣠⣼⣯⣤⣤⣿⣦⡄⠛⡛⠃⠀⢙⡃⠐⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣩⣯⣉⢈⣩⣏⡉⣉⣹⣍⠁⢠⢄⠀⢀⣠⣄⡀⣿⣿⣿⣿⠜
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣚⣸⣿⣇⣂⣂⣀⣀
⡟⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠗⠀⠺⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠶⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣯⢿⡿⣿⣏⣙⣉⣋⠉⠉⠙⠛⠛⠛⠋⠙⠙⠛⠛⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠉⠙⢹⠋⠒⠫⣿⣿⢭⢿⣿⣧⠌⠉⠉⠀⠉⠙⣿⣽⣿⣿⣯⣭⣭⣿⣽⣭⣿⣿⡽⣹⡛⠛⠟⣛⠟⠩⠟⠿⠯⢿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣦⣤⣤⣿⣆⠔⠀⠀⠂⠀⠀⣶⣦⣶⡶⣆⣤⣀⣀⣀⣀⣀⣀⡀⠀⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣶⣶⡌⠈⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠛⠀⠀⠀⠀⠀⠠⠀⠀⢈⣉⣉⣙⠋⣽⠛⠛⠛⠛⠛⠛⠛⡛⢛⢛⠛⢛⣟⢿⣟⣿⣻⣛⢟⡟⠻⣿⠿⢟⣿⣟⣿⣻⣻⣛⡟⢛⢿⠿⠟⣻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠀⠈⠀⠀⠀⠀⢸⡏⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⡉⢉⠉⡉⣿⣈⣐⣿⡏⠉⠩⠉⠩⠉⠉⠭⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠓⠒⢚⡀⠀⠀⣰⣆⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣠⣀⣀⣀⠀⠶⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣂⣸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠄⠠⠀⠀⣿⣛⣛⣻⡇⠀⠒⠒⠐⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣈⣭⣿⣤⣒⣤⡄⠛⠀⢸⣿⣿⣿⡣⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣶⣿⣿⣿⣿⣿⣟⣿⣿⣧⣤⣤⣾⣿⣿⣿⣗⣼⣿⣥⣠⣼⣯⣤⣤⣿⣦⡄⠛⡛⠃⠀⢙⡃⠐⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣩⣯⣉⢈⣩⣏⡉⣉⣹⣍⠁⢠⢄⠀⢀⣠⣄⡀⣿⣿⣿⣿⠜
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣚⣸⣿⣇⣂⣂⣀⣀
⡟⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠗⠀⠺⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠶⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣯⢿⡿⣿⣏⣙⣉⣋⠉⠉⠙⠛⠛⠛⠋⠙⠙⠛⠛⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠉⠙⢹⠋⠒⠫⣿⣿⢭⢿⣿⣧⠌⠉⠉⠀⠉⠙⣿⣽⣿⣿⣯⣭⣭⣿⣽⣭⣿⣿⡽⣹⡛⠛⠟⣛⠟⠩⠟⠿⠯⢿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣦⣤⣤⣿⣆⠔⠀⠀⠂⠀⠀⣶⣦⣶⡶⣆⣤⣀⣀⣀⣀⣀⣀⡀⠀⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣶⣶⡌⠈⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠛⠀⠀⠀⠀⠀⠠⠀⠀⢈⣉⣉⣙⠋⣽⠛⠛⠛⠛⠛⠛⠛⡛⢛⢛⠛⢛⣟⢿⣟⣿⣻⣛⢟⡟⠻⣿⠿⢟⣿⣟⣿⣻⣻⣛⡟⢛⢿⠿⠟⣻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠀⠈⠀⠀⠀⠀⢸⡏⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⡉⢉⠉⡉⣿⣈⣐⣿⡏⠉⠩⠉⠩⠉⠉⠭⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠓⠒⢚⡀⠀⠀⣰⣆⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣠⣀⣀⣀⠀⠶⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣂⣸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠄⠠⠀⠀⣿⣛⣛⣻⡇⠀⠒⠒⠐⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣈⣭⣿⣤⣒⣤⡄⠛⠀⢸⣿⣿⣿⡣⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣶⣿⣿⣿⣿⣿⣟⣿⣿⣧⣤⣤⣾⣿⣿⣿⣗⣼⣿⣥⣠⣼⣯⣤⣤⣿⣦⡄⠛⡛⠃⠀⢙⡃⠐⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣩⣯⣉⢈⣩⣏⡉⣉⣹⣍⠁⢠⢄⠀⢀⣠⣄⡀⣿⣿⣿⣿⠜
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣚⣸⣿⣇⣂⣂⣀⣀
⡟⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠗⠀⠺⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠶⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣯⢿⡿⣿⣏⣙⣉⣋⠉⠉⠙⠛⠛⠛⠋⠙⠙⠛⠛⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠉⠙⢹⠋⠒⠫⣿⣿⢭⢿⣿⣧⠌⠉⠉⠀⠉⠙⣿⣽⣿⣿⣯⣭⣭⣿⣽⣭⣿⣿⡽⣹⡛⠛⠟⣛⠟⠩⠟⠿⠯⢿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣦⣤⣤⣿⣆⠔⠀⠀⠂⠀⠀⣶⣦⣶⡶⣆⣤⣀⣀⣀⣀⣀⣀⡀⠀⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣶⣶⡌⠈⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠛⠀⠀⠀⠀⠀⠠⠀⠀⢈⣉⣉⣙⠋⣽⠛⠛⠛⠛⠛⠛⠛⡛⢛⢛⠛⢛⣟⢿⣟⣿⣻⣛⢟⡟⠻⣿⠿⢟⣿⣟⣿⣻⣻⣛⡟⢛⢿⠿⠟⣻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠀⠈⠀⠀⠀⠀⢸⡏⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⡉⢉⠉⡉⣿⣈⣐⣿⡏⠉⠩⠉⠩⠉⠉⠭⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠓⠒⢚⡀⠀⠀⣰⣆⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣠⣀⣀⣀⠀⠶⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣂⣸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠄⠠⠀⠀⣿⣛⣛⣻⡇⠀⠒⠒⠐⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣈⣭⣿⣤⣒⣤⡄⠛⠀⢸⣿⣿⣿⡣⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣶⣿⣿⣿⣿⣿⣟⣿⣿⣧⣤⣤⣾⣿⣿⣿⣗⣼⣿⣥⣠⣼⣯⣤⣤⣿⣦⡄⠛⡛⠃⠀⢙⡃⠐⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣩⣯⣉⢈⣩⣏⡉⣉⣹⣍⠁⢠⢄⠀⢀⣠⣄⡀⣿⣿⣿⣿⠜
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣚⣸⣿⣇⣂⣂⣀⣀
⡟⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠗⠀⠺⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠶⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣯⢿⡿⣿⣏⣙⣉⣋⠉⠉⠙⠛⠛⠛⠋⠙⠙⠛⠛⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠉⠙⢹⠋⠒⠫⣿⣿⢭⢿⣿⣧⠌⠉⠉⠀⠉⠙⣿⣽⣿⣿⣯⣭⣭⣿⣽⣭⣿⣿⡽⣹⡛⠛⠟⣛⠟⠩⠟⠿⠯⢿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣦⣤⣤⣿⣆⠔⠀⠀⠂⠀⠀⣶⣦⣶⡶⣆⣤⣀⣀⣀⣀⣀⣀⡀⠀⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣶⣶⡌⠈⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠛⠀⠀⠀⠀⠀⠠⠀⠀⢈⣉⣉⣙⠋⣽⠛⠛⠛⠛⠛⠛⠛⡛⢛⢛⠛⢛⣟⢿⣟⣿⣻⣛⢟⡟⠻⣿⠿⢟⣿⣟⣿⣻⣻⣛⡟⢛⢿⠿⠟⣻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠀⠈⠀⠀⠀⠀⢸⡏⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⡉⢉⠉⡉⣿⣈⣐⣿⡏⠉⠩⠉⠩⠉⠉⠭⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠓⠒⢚⡀⠀⠀⣰⣆⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣠⣀⣀⣀⠀⠶⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣂⣸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠄⠠⠀⠀⣿⣛⣛⣻⡇⠀⠒⠒⠐⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣈⣭⣿⣤⣒⣤⡄⠛⠀⢸⣿⣿⣿⡣⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣿⣿⣿⣿⣸
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣶⣿⣿⣿⣿⣿⣟⣿⣿⣧⣤⣤⣾⣿⣿⣿⣗⣼⣿⣥⣠⣼⣯⣤⣤⣿⣦⡄⠛⡛⠃⠀⢙⡃⠐⣿⣿⣿⣿⢸
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣩⣯⣉⢈⣩⣏⡉⣉⣹⣍⠁⢠⢄⠀⢀⣠⣄⡀⣿⣿⣿⣿⠜
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣚⣸⣿⣇⣂⣂⣀⣀
⡟⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠗⠀⠺⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠶⠀⠘⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣯⢿⡿⣻⣏⣙⣉⣋⠉⠉⠙⠛⠛⠛⠋⠙⠙⠛⠛⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠉⠙⢹⠋⠒⠫⣿⣿⢭⢿⣿⣧⠌⠉⠉⠀⠉⠙⣿⣽⣿⣿⣯⣭⣭⣿⣽⣭⣿⣿⡽⣹⡛⠛⠟⣛⠟⠩⠟⠿⠯⢿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣦⣤⣤⣿⣆⠔⠀⠀⠂⠀⠀⣶⣦⣶⡶⣆⣤⣀⣀⣀⣀⣀⣀⡀⠀⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣶⣶⡌⠈⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠛⠀⠀⠀⠀⠀⠠⠀⠀⢈⣉⣉⣙⠋⣽⠛⠛⠛⠛⠛⠛⠛⡛⢛⢛⠛⢛⣟⢿⣟⣿⣻⣛⢛⡟⠻⣿⠿⢟⣿⣟⣿⣻⣻⣛⡟⢛⢿⠿⠟⣻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠀⠈⠀⠀⠀⠀⢸⡏⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⡉⢉⠉⡉⣿⣈⣐⣿⡏⠉⠩⠉⠩⠉⠉⠭⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠓⠒⢚⡀⠀⠀⣰⣆⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣠⣀⣀⣀⠀⠶⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣂⣸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠄⠠⠀⠀⣿⣛⣛⣻⡇⠀⠒⠒⠐⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣈⣭⣿⣤⣒⣤⡄⠛⠀⢸⣿⣿⣿⡣⠀⠀⠀⠀⠀⠀⠠⠭⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⣿⣿⣿⣿⣽
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣟⣿⣿⣧⣤⣤⣾⣿⣿⣿⣗⣼⣿⣥⣠⣼⣯⣤⣤⣿⣦⡄⠛⡛⠃⠀⢘⡃⡐⣿⣿⣿⣿⣼
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣩⣯⣙⢈⣩⣏⡉⣍⣹⣍⠁⢠⢄⠠⢀⣤⣌⡘⣿⣿⣿⣿⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣚⣸⣿⣇⣂⣂⣀⣀
⡟⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠗⠀⠺⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠶⠀⠘⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣯⢿⡿⣻⣏⣙⣉⣋⠉⠉⠙⠛⠛⠛⠋⠙⠙⠛⠛⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠉⠙⢹⠋⠒⠫⣿⣿⢭⢿⣿⣧⠌⠉⠉⠀⠉⠙⣿⣽⣿⣿⣯⣭⣭⣿⣽⣭⣿⣿⡽⣹⡛⠛⠟⣛⠟⠩⠟⠿⠯⢿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣦⣤⣤⣿⣆⠔⠀⠀⠂⠀⠀⣶⣦⣶⡶⣆⣤⣀⣀⣀⣀⣀⣀⡀⠀⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣶⣶⡌⠈⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠛⠀⠀⠀⠀⠀⠠⠀⠀⢈⣉⣉⣙⠋⣽⠛⠛⠛⠛⠛⠛⠛⡛⢛⢛⠛⢛⣟⢿⣟⣿⣻⣛⢛⡟⠻⣿⠿⢟⣿⣟⣿⣻⣻⣛⡟⢛⢿⠿⠟⣻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠀⠈⠀⠀⠀⠀⢸⡏⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⡉⢉⠉⡉⣿⣈⣐⣿⡏⠉⠩⠉⠩⠉⠉⠭⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠓⠒⢚⡀⠀⠀⣰⣆⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣠⣀⣀⣀⠀⠶⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣂⣸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠄⠠⠀⠀⣿⣛⣛⣻⡇⠀⠒⠒⠐⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣈⣭⣿⣤⣒⣤⡄⠛⠀⢸⣿⣿⣿⡣⠀⠀⠀⠀⠀⠀⠠⠭⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⣿⣿⣿⣿⣽
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣟⣿⣿⣧⣤⣤⣾⣿⣿⣿⣗⣼⣿⣥⣠⣼⣯⣤⣤⣿⣦⡄⠛⡛⠃⠀⢘⡃⡐⣿⣿⣿⣿⣼
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣩⣯⣙⢈⣩⣏⡉⣍⣹⣍⠁⢠⢄⠠⢀⣤⣌⡘⣿⣿⣿⣿⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣚⣸⣿⣇⣂⣂⣀⣀
⡟⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠗⠀⠺⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠶⠀⠘⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣯⢿⡿⣻⣏⣙⣉⣋⠉⠉⠙⠛⠛⠛⠋⠙⠙⠛⠛⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠉⠙⢹⠋⠒⠫⣿⣿⢭⢿⣿⣧⠌⠉⠉⠀⠉⠙⣿⣽⣿⣿⣯⣭⣭⣿⣽⣭⣿⣿⡽⣹⡛⠛⠟⣛⠟⠩⠟⠿⠯⢿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣦⣤⣤⣿⣆⠔⠀⠀⠂⠀⠀⣶⣦⣶⡶⣆⣤⣀⣀⣀⣀⣀⣀⡀⠀⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣶⣶⡌⠈⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠛⠀⠀⠀⠀⠀⠠⠀⠀⢈⣉⣉⣙⠋⣽⠛⠛⠛⠛⠛⠛⠛⡛⢛⢛⠛⢛⣟⢿⣟⣿⣻⣛⢛⡟⠻⣿⠿⢟⣿⣟⣿⣻⣻⣛⡟⢛⢿⠿⠟⣻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠀⠈⠀⠀⠀⠀⢸⡏⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⡉⢉⠉⡉⣿⣈⣐⣿⡏⠉⠩⠉⠩⠉⠉⠭⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠓⠒⢚⡀⠀⠀⣰⣆⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣠⣀⣀⣀⠀⠶⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣂⣸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠄⠠⠀⠀⣿⣛⣛⣻⡇⠀⠒⠒⠐⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣈⣭⣿⣤⣒⣤⡄⠛⠀⢸⣿⣿⣿⡣⠀⠀⠀⠀⠀⠀⠠⠭⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⣿⣿⣿⣿⣽
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣟⣿⣿⣧⣤⣤⣾⣿⣿⣿⣗⣼⣿⣥⣠⣼⣯⣤⣤⣿⣦⡄⠛⡛⠃⠀⢘⡃⡐⣿⣿⣿⣿⣼
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣩⣯⣙⢈⣩⣏⡉⣍⣹⣍⠁⢠⢄⠠⢀⣤⣌⡘⣿⣿⣿⣿⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣚⣸⣿⣇⣂⣂⣀⣀
⡟⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠗⠀⠺⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠶⠀⠘⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣯⢿⡿⣻⣏⣙⣉⣋⠉⠉⠙⠛⠛⠛⠋⠙⠙⠛⠛⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠉⠙⢹⠋⠒⠫⣿⣿⢭⢿⣿⣧⠌⠉⠉⠀⠉⠙⣿⣽⣿⣿⣯⣭⣭⣿⣽⣭⣿⣿⡽⣹⡛⠛⠟⣛⠟⠩⠟⠿⠯⢿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣦⣤⣤⣿⣆⠔⠀⠀⠂⠀⠀⣶⣦⣶⡶⣆⣤⣀⣀⣀⣀⣀⣀⡀⠀⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣶⣶⡌⠈⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠛⠀⠀⠀⠀⠀⠠⠀⠀⢈⣉⣉⣙⠋⣽⠛⠛⠛⠛⠛⠛⠛⡛⢛⢛⠛⢛⣟⢿⣟⣿⣻⣛⢛⡟⠻⣿⠿⢟⣿⣟⣿⣻⣻⣛⡟⢛⢿⠿⠟⣻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠀⠈⠀⠀⠀⠀⢸⡏⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⡉⢉⠉⡉⣿⣈⣐⣿⡏⠉⠩⠉⠩⠉⠉⠭⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠓⠒⢚⡀⠀⠀⣰⣆⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣠⣀⣀⣀⠀⠶⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣂⣸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠄⠠⠀⠀⣿⣛⣛⣻⡇⠀⠒⠒⠐⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣈⣭⣿⣤⣒⣤⡄⠛⠀⢸⣿⣿⣿⡣⠀⠀⠀⠀⠀⠀⠠⠭⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⣿⣿⣿⣿⣽
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣟⣿⣿⣧⣤⣤⣾⣿⣿⣿⣗⣼⣿⣥⣠⣼⣯⣤⣤⣿⣦⡄⠛⡛⠃⠀⢘⡃⡐⣿⣿⣿⣿⣼
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣩⣯⣙⢈⣩⣏⡉⣍⣹⣍⠁⢠⢄⠠⢀⣤⣌⡘⣿⣿⣿⣿⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣚⣸⣿⣇⣂⣂⣀⣀
⡟⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠗⠀⠺⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠶⠀⠘⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣯⢿⡿⣻⣏⣙⣉⣋⠉⠉⠙⠛⠛⠛⠋⠙⠙⠛⠛⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠉⠙⢹⠋⠒⠫⣿⣿⢭⢿⣿⣧⠌⠉⠉⠀⠉⠙⣿⣽⣿⣿⣯⣭⣭⣿⣽⣭⣿⣿⡽⣹⡛⠛⠟⣛⠟⠩⠟⠿⠯⢿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣦⣤⣤⣿⣆⠔⠀⠀⠂⠀⠀⣶⣦⣶⡶⣆⣤⣀⣀⣀⣀⣀⣀⡀⠀⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣶⣶⡌⠈⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠛⠀⠀⠀⠀⠀⠠⠀⠀⢈⣉⣉⣙⠋⣽⠛⠛⠛⠛⠛⠛⠛⡛⢛⢛⠛⢛⣟⢿⣟⣿⣻⣛⢛⡟⠻⣿⠿⢟⣿⣟⣿⣻⣻⣛⡟⢛⢿⠿⠟⣻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⢸⠀⠈⠀⠀⠀⠀⢸⡏⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⡉⢉⠉⡉⣿⣈⣐⣿⡏⠉⠩⠉⠩⠉⠉⠭⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠓⠒⢚⡀⠀⠀⣰⣆⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣠⣀⣀⣀⠀⠶⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣂⣸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠄⠠⠀⠀⣿⣛⣛⣻⡇⠀⠒⠒⠐⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣈⣭⣿⣤⣒⣤⡄⠛⠀⢸⣿⣿⣿⡣⠀⠀⠀⠀⠀⠀⠠⠭⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⣿⣿⣿⣿⣽
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣟⣿⣿⣧⣤⣤⣾⣿⣿⣿⣗⣼⣿⣥⣠⣼⣯⣤⣤⣿⣦⡄⠛⡛⠃⠀⢘⡃⡐⣿⣿⣿⣿⣼
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣩⣯⣙⢈⣩⣏⡉⣍⣹⣍⠁⢠⢄⠠⢀⣤⣌⡘⣿⣿⣿⣿⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣺⣸⣿⣇⣢⣂⣀⣀
⡟⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠷⠀⠺⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠶⠀⠘⠛⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣿⣿⣯⢿⡿⣿⣏⣙⣉⣋⠉⠉⠙⠛⠛⠛⠋⠛⠙⠛⠛⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠉⠙⢻⠛⠚⠫⣿⣿⢭⢿⣿⣧⣬⣭⣭⣤⣭⣽⣿⣵⣿⣿⣯⣭⣭⣿⣽⣭⣿⣿⣽⣽⣿⣿⣿⣿⣿⣭⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣿⠀⠀⢠⡤⠤⠤⠤⠤⠴⠶⠦⡤⠤⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⠀⠸⠃⠂⠀⢀⣂⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠐⠀⠀⠀⠒⠐⠂⢒⣀⠂⣿⢿⠿⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⠿
⢸⠀⠉⠀⠀⠀⠀⢸⡄⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠖⠂⠀⠀⠀⣿⣈⣐⣿⡏⠉⠩⠉⠩⠉⠉⠽⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠓⠒⢚⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⢷⡋⡉⠁⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣂⣺⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣛⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⣿⣛⣛⣻⠀⠠⠤⠄⠀⠤⠤⠀⠀⠤⠠⠠⠤⠤⠀⠀⠤⠤⠀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⠛⠀⢸⣿⣿⣿⣺⣿⣿⣟⢿⣿⣿⣟⣿⣿⣿⠠⢄⠠⠄⠤⢏⠤⠤⣿⣿⣿⣿⣽
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣾⣿⣿⣿⣗⣼⣿⣥⣤⣽⣭⣤⣤⣿⣦⡀⠻⡟⢣⣶⣿⣷⡖⣿⣿⣿⣿⣼
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣭⣟⣿⣿⣿⣿⣇⣑⣦⣉⣐⣒⣐⣀⣤⣷⣦⣀⣐⣂⣘⣛⣿⣟⣛⣿⣿⣿⣿⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣺⣸⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠷⠀⠺⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠶⠀⠘⠛⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡟⣻⡿⣿⡿⠿⡿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠄⣵⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣭⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣩⣽⣴⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠁⠒⠐⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⠿
⢸⠀⠉⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣴⣷⣴⣷⣬⣭⣴⣧⣶⣶⣶⣶⣶⡶⠖⠒⠀⠀⠀⣿⣈⣰⣿⡏⠉⠩⠉⠩⠉⠉⠽⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣶⡷⣶⣿⣿⡛⠛⠛⢷⡋⡉⠁⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡿⣿⣿⣿⣿⡭⠭⢉⣥⢉⣽⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⣿⣛⣛⣻⠀⠠⠤⠄⠀⠤⠤⠀⠀⠤⠠⠠⠤⠤⠀⠀⠤⠤⠀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠉⠉⣉⣉⡉⢉⣉⣉⣉⣉⣉⣙⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣟⣉⣉⣉⣉⣙⠛⣉⣉⣉⣉⣙⣿⣿⣿⣿⣿⣾⣿⡇⠛⠀⢸⣿⣿⣿⣺⣿⣿⣟⢿⣿⣿⣟⣿⣿⣿⠠⢄⠠⠄⠤⢏⠤⠤⣿⣿⣿⣿⣽
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣧⣤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣾⣿⣿⣿⣗⣽⣿⣥⣤⣽⣭⣤⣤⣿⣦⡀⠻⡟⢣⣶⣿⣷⡖⣿⣿⣿⣿⣼
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣭⣟⣿⣿⣿⣿⣇⣑⣦⣉⣐⣒⣐⣀⣤⣷⣦⣀⣐⣂⣘⣛⣿⣟⣛⣿⣿⣿⣿⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣺⣸⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠷⠀⠺⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠶⠀⠘⠛⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡟⣻⡿⣿⡿⠿⡿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠄⣵⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣭⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣩⣽⣴⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠁⠒⠐⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⠿
⢸⠀⠉⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣴⣷⣴⣷⣬⣭⣴⣧⣶⣶⣶⣶⣶⡶⠖⠒⠀⠀⠀⣿⣈⣰⣿⡏⠉⠩⠉⠩⠉⠉⠽⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣶⡷⣶⣿⣿⡛⠛⠛⢷⡋⡉⠁⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡿⣿⣿⣿⣿⡭⠭⢉⣥⢉⣽⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⣿⣛⣛⣻⠀⠠⠤⠄⠀⠤⠤⠀⠀⠤⠠⠠⠤⠤⠀⠀⠤⠤⠀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠉⠉⣉⣉⡉⢉⣉⣉⣉⣉⣉⣙⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣟⣉⣉⣉⣉⣙⠛⣉⣉⣉⣉⣙⣿⣿⣿⣿⣿⣾⣿⡇⠛⠀⢸⣿⣿⣿⣺⣿⣿⣟⢿⣿⣿⣟⣿⣿⣿⠠⢄⠠⠄⠤⢏⠤⠤⣿⣿⣿⣿⣽
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣧⣤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣾⣿⣿⣿⣗⣽⣿⣥⣤⣽⣭⣤⣤⣿⣦⡀⠻⡟⢣⣶⣿⣷⡖⣿⣿⣿⣿⣼
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣭⣟⣿⣿⣿⣿⣇⣑⣦⣉⣐⣒⣐⣀⣤⣷⣦⣀⣐⣂⣘⣛⣿⣟⣛⣿⣿⣿⣿⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣺⣸⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠷⠀⠺⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠶⠀⠘⠛⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡟⣻⡿⣿⡿⠿⡿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠄⣵⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣭⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣩⣽⣴⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠁⠒⠐⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⠿
⢸⠀⠉⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣴⣷⣴⣷⣬⣭⣴⣧⣶⣶⣶⣶⣶⡶⠖⠒⠀⠀⠀⣿⣈⣰⣿⡏⠉⠩⠉⠩⠉⠉⠽⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣶⡷⣶⣿⣿⡛⠛⠛⢷⡋⡉⠁⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡿⣿⣿⣿⣿⡭⠭⢉⣥⢉⣽⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⣿⣛⣛⣻⠀⠠⠤⠄⠀⠤⠤⠀⠀⠤⠠⠠⠤⠤⠀⠀⠤⠤⠀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠉⠉⣉⣉⡉⢉⣉⣉⣉⣉⣉⣙⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣟⣉⣉⣉⣉⣙⠛⣉⣉⣉⣉⣙⣿⣿⣿⣿⣿⣾⣿⡇⠛⠀⢸⣿⣿⣿⣺⣿⣿⣟⢿⣿⣿⣟⣿⣿⣿⠠⢄⠠⠄⠤⢏⠤⠤⣿⣿⣿⣿⣽
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣧⣤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣾⣿⣿⣿⣗⣽⣿⣥⣤⣽⣭⣤⣤⣿⣦⡀⠻⡟⢣⣶⣿⣷⡖⣿⣿⣿⣿⣼
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣭⣟⣿⣿⣿⣿⣇⣑⣦⣉⣐⣒⣐⣀⣤⣷⣦⣀⣐⣂⣘⣛⣿⣟⣛⣿⣿⣿⣿⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣺⣸⣿⣇⣢⣂⣀⣀
⡟⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠷⠀⠺⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠶⠀⣸⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡟⣻⡿⣿⡿⠿⡿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠄⣵⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣭⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣩⣽⣴⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠁⠒⠐⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⠿
⢸⠀⠉⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣴⣷⣴⣷⣬⣭⣤⣥⣶⣶⣶⣶⣶⡶⠖⠂⠀⠀⠀⣿⣈⣰⣿⡏⠉⠩⠉⠩⠉⠉⠽⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣶⡷⣶⣿⣿⡛⠛⠛⢷⡋⡉⠁⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡿⣿⣿⣿⣿⡍⠍⢉⣥⢉⣽⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⣿⣛⣛⣻⠀⠠⠤⠄⠀⠤⠤⠀⠀⠤⠠⠠⠤⠤⠀⠀⠤⠤⠀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠉⠉⣉⣉⡉⢉⣉⣉⣉⣉⣉⣙⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣟⣉⣉⣉⣉⣙⠛⣉⣉⣉⣉⣙⣿⣿⣿⣿⣿⣾⣿⡇⠛⠀⢸⣿⣿⣿⣺⣿⣿⣟⢿⣿⣿⣟⣿⣿⣿⠠⢄⠠⠄⠤⢏⠤⠤⣿⣿⣿⣿⣽
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣧⣤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣾⣿⣿⣿⣗⣼⣿⣥⣤⣽⣭⣤⣤⣿⣦⡀⠻⡟⢣⣶⣿⣷⡖⣿⣿⣿⣿⣼
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣭⣟⣿⣿⣿⣿⣇⣑⣦⣉⣐⣒⣐⣀⣤⣷⣦⣀⣐⣆⣸⣟⣿⣟⣛⣿⣿⣿⣿⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣺⣸⣿⣇⣢⣂⣀⣀
⡟⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠷⠀⠺⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠶⠀⣸⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡟⣻⡿⣿⡿⠿⡿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠄⣵⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣭⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣩⣽⣴⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠁⠒⠐⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⠿
⢸⠀⠉⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣴⣷⣴⣷⣬⣭⣤⣥⣶⣶⣶⣶⣶⡶⠖⠂⠀⠀⠀⣿⣈⣰⣿⡏⠉⠩⠉⠩⠉⠉⠽⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣶⡷⣶⣿⣿⡛⠛⠛⢷⡋⡉⠁⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡿⣿⣿⣿⣿⡍⠍⢉⣥⢉⣽⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⣿⣛⣛⣻⠀⠠⠤⠄⠀⠤⠤⠀⠀⠤⠠⠠⠤⠤⠀⠀⠤⠤⠀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠉⠉⣉⣉⡉⢉⣉⣉⣉⣉⣉⣙⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣟⣉⣉⣉⣉⣙⠛⣉⣉⣉⣉⣙⣿⣿⣿⣿⣿⣾⣿⡇⠛⠀⢸⣿⣿⣿⣺⣿⣿⣟⢿⣿⣿⣟⣿⣿⣿⠠⢄⠠⠄⠤⢏⠤⠤⣿⣿⣿⣿⣽
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣧⣤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣾⣿⣿⣿⣗⣼⣿⣥⣤⣽⣭⣤⣤⣿⣦⡀⠻⡟⢣⣶⣿⣷⡖⣿⣿⣿⣿⣼
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣭⣟⣿⣿⣿⣿⣇⣑⣦⣉⣐⣒⣐⣀⣤⣷⣦⣀⣐⣆⣸⣟⣿⣟⣛⣿⣿⣿⣿⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣺⣸⣿⣇⣢⣂⣀⣀
⡟⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠷⠀⠺⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠶⠀⣸⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡟⣻⡿⣿⡿⠿⡿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠄⣵⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣭⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣩⣽⣴⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠁⠒⠐⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⠿
⢸⠀⠉⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣴⣷⣴⣷⣬⣭⣤⣥⣶⣶⣶⣶⣶⡶⠖⠂⠀⠀⠀⣿⣈⣰⣿⡏⠉⠩⠉⠩⠉⠉⠽⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣶⡷⣶⣿⣿⡛⠛⠛⢷⡋⡉⠁⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡿⣿⣿⣿⣿⡍⠍⢉⣥⢉⣽⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⣿⣛⣛⣻⠀⠠⠤⠄⠀⠤⠤⠀⠀⠤⠠⠠⠤⠤⠀⠀⠤⠤⠀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠉⠉⣉⣉⡉⢉⣉⣉⣉⣉⣉⣙⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣟⣉⣉⣉⣉⣙⠛⣉⣉⣉⣉⣙⣿⣿⣿⣿⣿⣾⣿⡇⠛⠀⢸⣿⣿⣿⣺⣿⣿⣟⢿⣿⣿⣟⣿⣿⣿⠠⢄⠠⠄⠤⢏⠤⠤⣿⣿⣿⣿⣽
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣧⣤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣾⣿⣿⣿⣗⣼⣿⣥⣤⣽⣭⣤⣤⣿⣦⡀⠻⡟⢣⣶⣿⣷⡖⣿⣿⣿⣿⣼
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣭⣟⣿⣿⣿⣿⣇⣑⣦⣉⣐⣒⣐⣀⣤⣷⣦⣀⣐⣆⣸⣟⣿⣟⣛⣿⣿⣿⣿⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣺⣸⣿⣇⣢⣂⣀⣀
⡟⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠷⠀⠺⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠶⠀⣸⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡟⣻⡿⣿⡿⠿⡿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠄⣵⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣭⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣩⣽⣴⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠁⠒⠐⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⠿
⢸⠀⠉⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣴⣷⣴⣷⣬⣭⣤⣥⣶⣶⣶⣶⣶⡶⠖⠂⠀⠀⠀⣿⣈⣰⣿⡏⠉⠩⠉⠩⠉⠉⠽⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣶⡷⣶⣿⣿⡛⠛⠛⢷⡋⡉⠁⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡿⣿⣿⣿⣿⡍⠍⢉⣥⢉⣽⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⣿⣛⣛⣻⠀⠠⠤⠄⠀⠤⠤⠀⠀⠤⠠⠠⠤⠤⠀⠀⠤⠤⠀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠉⠉⣉⣉⡉⢉⣉⣉⣉⣉⣉⣙⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣟⣉⣉⣉⣉⣙⠛⣉⣉⣉⣉⣙⣿⣿⣿⣿⣿⣾⣿⡇⠛⠀⢸⣿⣿⣿⣺⣿⣿⣟⢿⣿⣿⣟⣿⣿⣿⠠⢄⠠⠄⠤⢏⠤⠤⣿⣿⣿⣿⣽
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣧⣤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣾⣿⣿⣿⣗⣼⣿⣥⣤⣽⣭⣤⣤⣿⣦⡀⠻⡟⢣⣶⣿⣷⡖⣿⣿⣿⣿⣼
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣭⣟⣿⣿⣿⣿⣇⣑⣦⣉⣐⣒⣐⣀⣤⣷⣦⣀⣐⣆⣸⣟⣿⣟⣛⣿⣿⣿⣿⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣺⣸⣿⣇⣢⣂⣀⣀
⡟⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠷⠀⠺⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠶⠀⣸⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡟⣻⡿⣿⡿⠿⡿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠄⣵⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣭⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣩⣽⣴⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠁⠒⠐⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⠿
⢸⠀⠉⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣴⣷⣴⣷⣬⣭⣤⣥⣶⣶⣶⣶⣶⡶⠖⠂⠀⠀⠀⣿⣈⣰⣿⡏⠉⠩⠉⠩⠉⠉⠽⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣶⡷⣶⣿⣿⡛⠛⠛⢷⡋⡉⠁⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡿⣿⣿⣿⣿⡍⠍⢉⣥⢉⣽⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⣿⣛⣛⣻⠀⠠⠤⠄⠀⠤⠤⠀⠀⠤⠠⠠⠤⠤⠀⠀⠤⠤⠀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠉⠉⣉⣉⡉⢉⣉⣉⣉⣉⣉⣙⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣟⣉⣉⣉⣉⣙⠛⣉⣉⣉⣉⣙⣿⣿⣿⣿⣿⣾⣿⡇⠛⠀⢸⣿⣿⣿⣺⣿⣿⣟⢿⣿⣿⣟⣿⣿⣿⠠⢄⠠⠄⠤⢏⠤⠤⣿⣿⣿⣿⣽
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣧⣤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣾⣿⣿⣿⣗⣼⣿⣥⣤⣽⣭⣤⣤⣿⣦⡀⠻⡟⢣⣶⣿⣷⡖⣿⣿⣿⣿⣼
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣭⣟⣿⣿⣿⣿⣇⣑⣦⣉⣐⣒⣐⣀⣤⣷⣦⣀⣐⣆⣸⣟⣿⣟⣛⣿⣿⣿⣿⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣺⣸⣿⣇⣢⣂⣀⣀
⡟⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠷⠀⠺⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠶⠀⣸⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡟⣻⡿⣿⡿⠿⡿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠄⣵⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣭⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣩⣽⣴⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠁⠒⠐⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⠿
⢸⠀⠉⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣴⣷⣴⣷⣬⣭⣤⣭⣶⣶⣶⣶⣶⡶⠖⠂⠀⠀⠀⣿⣈⣰⣿⡏⠉⠩⠉⠩⠉⠉⠽⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣶⡷⣶⣿⣿⡛⠛⠛⢷⡋⡉⠁⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡿⣿⣿⣿⣿⣍⠍⣉⣥⢉⣽⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⣿⣛⣛⣻⠀⠠⠤⠄⠀⠤⠤⠀⠀⠤⠠⠠⠤⠤⠀⠀⠤⠤⠀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠉⠉⣉⣉⡉⢉⣉⣉⣉⣉⣉⣙⣉⣉⣉⣉⣉⣉⣉⣋⣙⣉⣉⣹⣟⣉⣉⣉⣉⣙⠛⣉⣉⣉⣉⣙⣿⣿⣿⣿⣿⣾⣿⡇⠛⠀⢸⣿⣿⣿⣺⣿⣿⣟⢿⣿⣿⣟⣿⣿⣿⠠⢄⠠⠄⠤⢏⠤⠤⣿⣿⣿⣿⣽
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣧⣤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣾⣿⣿⣿⣗⣼⣿⣥⣤⣽⣭⣤⣤⣿⣦⡀⠻⡟⢣⣶⣿⣷⡖⣿⣿⣿⣿⣼
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣭⣟⣿⣿⣿⣿⣇⣑⣦⣉⣐⣒⣐⣀⣤⣷⣦⣀⣐⣆⣸⣟⣿⣟⣛⣿⣿⣿⣿⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣺⣸⣿⣇⣢⣂⣀⣀
⡟⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠷⠀⠺⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠶⠀⣸⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡟⣻⡿⣿⡿⠿⡿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠄⣵⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣭⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣩⣽⣴⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠁⠒⠐⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⠿
⢸⠀⠉⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣴⣷⣴⣷⣬⣭⣤⣭⣶⣶⣶⣶⣶⡶⠖⠂⠀⠀⠀⣿⣈⣰⣿⡏⠉⠩⠉⠩⠉⠉⠽⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣶⡷⣶⣿⣿⡛⠛⠛⢷⡋⡉⠁⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡿⣿⣿⣿⣿⣍⠍⣉⣥⢉⣽⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⣿⣛⣛⣻⠀⠠⠤⠄⠀⠤⠤⠀⠀⠤⠠⠠⠤⠤⠀⠀⠤⠤⠀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠉⠉⣉⣉⡉⢉⣉⣉⣉⣉⣉⣙⣉⣉⣉⣉⣉⣉⣉⣋⣙⣉⣉⣹⣟⣉⣉⣉⣉⣙⠛⣉⣉⣉⣉⣙⣿⣿⣿⣿⣿⣾⣿⡇⠛⠀⢸⣿⣿⣿⣺⣿⣿⣟⢿⣿⣿⣟⣿⣿⣿⠠⢄⠠⠄⠤⢏⠤⠤⣿⣿⣿⣿⣽
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣧⣤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣾⣿⣿⣿⣗⣼⣿⣥⣤⣽⣭⣤⣤⣿⣦⡀⠻⡟⢣⣶⣿⣷⡖⣿⣿⣿⣿⣼
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣭⣟⣿⣿⣿⣿⣇⣑⣦⣉⣐⣒⣐⣀⣤⣷⣦⣀⣐⣆⣸⣟⣿⣟⣛⣿⣿⣿⣿⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣺⣸⣿⣇⣢⣂⣀⣀
⡟⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠷⠀⠺⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠶⠀⣸⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡟⣻⡿⣿⡿⠿⡿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠄⣵⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣭⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣩⣽⣴⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠁⠒⠐⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⠿
⢸⠀⠉⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣴⣷⣴⣷⣬⣭⣤⣭⣶⣶⣶⣶⣶⡶⠖⠂⠀⠀⠀⣿⣈⣰⣿⡏⠉⠩⠉⠩⠉⠉⠽⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣶⡷⣶⣿⣿⡛⠛⠛⢷⡋⡉⠁⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡿⣿⣿⣿⣿⣍⠍⣉⣥⢉⣽⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⣿⣛⣛⣻⠀⠠⠤⠄⠀⠤⠤⠀⠀⠤⠠⠠⠤⠤⠀⠀⠤⠤⠀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠉⠉⣉⣉⡉⢉⣉⣉⣉⣉⣉⣙⣉⣉⣉⣉⣉⣉⣉⣋⣙⣉⣉⣹⣟⣉⣉⣉⣉⣙⠛⣉⣉⣉⣉⣙⣿⣿⣿⣿⣿⣾⣿⡇⠛⠀⢸⣿⣿⣿⣺⣿⣿⣟⢿⣿⣿⣟⣿⣿⣿⠠⢄⠠⠄⠤⢏⠤⠤⣿⣿⣿⣿⣽
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣧⣤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣾⣿⣿⣿⣗⣼⣿⣥⣤⣽⣭⣤⣤⣿⣦⡀⠻⡟⢣⣶⣿⣷⡖⣿⣿⣿⣿⣼
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣭⣟⣿⣿⣿⣿⣇⣑⣦⣉⣐⣒⣐⣀⣤⣷⣦⣀⣐⣆⣸⣟⣿⣟⣛⣿⣿⣿⣿⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣺⣸⣿⣇⣢⣂⣀⣀
⡟⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠷⠀⠺⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠶⠀⣸⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡟⣻⡿⣿⡿⠿⡿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠄⣵⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣭⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣩⣽⣴⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠁⠒⠐⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⠿
⢸⠀⠉⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣴⣷⣴⣷⣬⣭⣤⣭⣶⣶⣶⣶⣶⡶⠖⠂⠀⠀⠀⣿⣈⣰⣿⡏⠉⠩⠉⠩⠉⠉⠽⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣶⡷⣶⣿⣿⡛⠛⠛⢷⡋⡉⠁⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡿⣿⣿⣿⣿⣍⠍⣉⣥⢉⣽⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⣿⣛⣛⣻⠀⠠⠤⠄⠀⠤⠤⠀⠀⠤⠠⠠⠤⠤⠀⠀⠤⠤⠀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠉⠉⣉⣉⡉⢉⣉⣉⣉⣉⣉⣙⣉⣉⣉⣉⣉⣉⣉⣋⣙⣉⣉⣹⣟⣉⣉⣉⣉⣙⠛⣉⣉⣉⣉⣙⣿⣿⣿⣿⣿⣾⣿⡇⠛⠀⢸⣿⣿⣿⣺⣿⣿⣟⢿⣿⣿⣟⣿⣿⣿⠠⢄⠠⠄⠤⢏⠤⠤⣿⣿⣿⣿⣽
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣧⣤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣾⣿⣿⣿⣗⣼⣿⣥⣤⣽⣭⣤⣤⣿⣦⡀⠻⡟⢣⣶⣿⣷⡖⣿⣿⣿⣿⣼
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣭⣟⣿⣿⣿⣿⣇⣑⣦⣉⣐⣒⣐⣀⣤⣷⣦⣀⣐⣆⣸⣟⣿⣟⣛⣿⣿⣿⣿⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣂⣀⣐⣀⣀⣀⣀⣺⣸⣿⣇⣢⣂⣀⣀
⡟⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠂⠀⠲⠂⠐⠷⠀⠺⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠶⠀⣸⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠐⠀⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡟⣻⡿⣿⡿⠿⡿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠄⣵⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣭⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣾⣿⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣻
⢻⣿⣿⡟⠻⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣩⣽⣴⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠁⠒⠐⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⠿
⢸⠀⠉⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣴⣷⣴⣷⣬⣭⣤⣭⣶⣶⣶⣶⣶⡶⠖⠂⠀⠀⠀⣿⣈⣰⣿⡏⠉⠩⠉⠩⠉⠉⠽⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⡞⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣶⡷⣶⣿⣿⡛⠛⠛⢷⡋⡉⠁⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡿⣿⣿⣿⣿⣍⠍⣉⣥⢉⣽⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⣿⣛⣛⣻⠀⠠⠤⠄⠀⠤⠤⠀⠀⠤⠠⠠⠤⠤⠀⠀⠤⠤⠀⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠉⠉⣉⣉⡉⢉⣉⣉⣉⣉⣉⣙⣉⣉⣉⣉⣉⣉⣉⣋⣙⣉⣉⣹⣟⣉⣉⣉⣉⣙⠛⣉⣉⣉⣉⣙⣿⣿⣿⣿⣿⣾⣿⡇⠛⠀⢸⣿⣿⣿⣺⣿⣿⣟⢿⣿⣿⣟⣿⣿⣿⠠⢄⠠⠄⠤⢏⠤⠤⣿⣿⣿⣿⣽
⠀⠀⠀⢠⠶⠾⣿⣿⣧⣤⣧⣤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣾⣿⣿⣿⣗⣼⣿⣥⣤⣽⣭⣤⣤⣿⣦⡀⠻⡟⢣⣶⣿⣷⡖⣿⣿⣿⣿⣼
⠀⠀⠀⢸⠀⢀⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣭⣟⣿⣿⣿⣿⣇⣑⣦⣉⣐⣒⣐⣀⣤⣷⣦⣀⣐⣆⣸⣟⣿⣟⣛⣿⣿⣿⣿⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠲⠷⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⢘⠂⠀⡾⠆⠐⠿⠀⡺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢠⣠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⢉⠉⣉⣿
⡇⠈⠀⠶⠀⣾⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⡇⠀⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⠐⠂⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠀⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣤⣾⣮⡄⠀⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣛⣛⣋⡉⡉⢛⣻⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⣉⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⡀⢀⠀⠀⠀⠀⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠊⠒⠒⠒⠒⠒⠒⠒⠈⠀⠀⠀⢀⡈⢸⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⡒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡁⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠀⠒⠒⠒⠒⠂⢠⡿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⡿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣻
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣭⣽⣴⡄⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠀⢸⡅⠒⠐⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣥⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⡉⠛⠻⠿⠛⢻⣿⣟⣟⣟⣿⣿⣛⣿⣿⣿⣿⣿⣿⣷⣖⣲⣖⣿⣿⣴⣷⣶⣷⣜⢀⣀⣉⣒⣒⣂⠘⣶⡶⠖⠒⠀⠀⠀⣿⣈⣰⣿⡏⠉⠭⠭⠭⠉⠉⠽⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠾⠀⣶⣿⣋⣉⠉⠐⣿⣋⡉⠩⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠠⢰⣤⣦⣶⣶⡶⣶⣴⣶⣶⢶⡆⣶⣶⣶⣶⣶⠦⢆⣲⣶⣦⣴⣴⣦⠦⣤⣴⢀⠀⠭⠭⠤⢤⡤⠀⣿⣿⣿⣿⡧⠀⠄⣿⣛⣛⣻⠠⣦⣶⡄⢠⢤⣦⠄⣴⣦⣦⠠⠤⠴⠄⠤⠶⠤⠀⣿⣿⣿⡟⣠
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣁⣀⣉⣉⣰⣉⣀⣉⣉⣹⣉⣉⡀⣭⣍⣹⣯⣉⣉⣉⣉⣉⠉⣉⠀⣀⣀⣙⣿⡿⠀⣿⣿⣿⣿⡇⠛⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠺⢌⠫⠕⢿⢟⠷⠶⣿⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠖⣿⣿⣿⣿⣿⡄⠉⠀⢀⢨⠀⠀⠀⠀⢨⠀⠀⠀⣤⡅⣀⠀⠀⠀⢀⣀⣸⣶⣿⠁⠶⠶⠶⠶⠖⠀⣿⣿⣿⣿⣧⣤⣤⣾⣿⣿⣿⣷⣿⣿⣯⣬⣽⣿⣥⣭⣿⣯⡄⠻⡿⢳⣾⣿⣿⡗⣿⣿⣿⣿⣼
⠀⠀⠀⠀⠀⠀⢉⣽⣿⣿⣿⣿⣯⣿⣽⣿⣿⣿⣭⣾⣿⣿⣿⣿⣄⣭⣽⣽⣿⣷⣬⣿⣯⣿⣭⣯⡜⣛⣛⣛⣛⣛⠸⣿⣿⣿⣿⣬⣭⣟⣿⣿⣿⣿⣏⣙⣯⣉⣒⣚⣛⣀⣥⣷⣶⣀⣐⣆⣸⣿⣿⣿⣛⣿⣿⣿⣿⣼
⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠲⠷⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⢘⠂⠀⡾⣆⠐⠿⠀⡺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢠⣠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⢉⠉⣉⣿
⡇⠈⠀⠶⠀⣾⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⡇⠀⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⠐⠂⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠚⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣤⣾⣮⡄⣄⡿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣾
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣛⣛⣭⡿⡿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⣉⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣶⣶⣦⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⡀⢀⠀⠀⠀⠀⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠊⠒⠒⠒⠒⠒⠒⠒⠈⠀⠀⠀⢀⠈⠸⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠂⠒⠒⠂⠀⠒⢤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⠿⠉⠁⠀⠾⠿⠿⠿⠶⠶⠶⠶⠦⠀⠂⠐⠀⠀⠀⠂⠐⠸⡿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⡿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣻
⠀⠀⠀⠀⠀⠀⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣭⣽⣴⡄⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠅⠀⠑⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣥⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⡉⠻⠻⠿⠛⢻⣿⣟⣟⣟⣿⣿⣛⣿⣿⣿⣿⣿⣿⣷⣖⣲⣖⣿⣿⣴⣷⣶⣷⣜⢀⡃⣁⣀⣀⣀⠀⣲⢠⡗⠒⠀⠀⠀⣿⣈⣰⣿⡟⠉⠭⠭⠭⠉⠉⠽⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠾⠀⡆⣭⣉⣉⠉⠀⢽⠸⡏⠩⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠠⢰⣤⣦⣶⣶⡶⣶⣴⣶⣶⢶⡆⣶⣶⣶⣶⣶⠦⢆⣲⣶⣦⣴⣴⣦⠦⣤⣴⢄⠀⠅⠩⠤⢤⡤⠀⠽⠀⣿⣿⡧⠀⠄⣿⣛⣛⣻⠠⣦⣶⡄⢠⢤⣦⠄⣴⣦⣦⠠⠤⠴⠄⠤⠶⠤⠀⣿⣿⣿⡟⣠
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣁⣀⣉⣉⣰⣉⣀⣉⣉⣹⣉⣉⡀⡭⢍⣹⣯⣉⣉⠉⣉⣉⠉⣉⠀⠀⠀⠙⠛⠛⠀⣻⠀⣿⣿⡇⠛⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠺⢌⠫⠕⢿⢟⠷⠶⣿⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠖⣿⣿⣿⣿⣿⡄⠈⠀⢀⢮⠀⠀⠀⠀⢨⠠⠀⠀⡄⡅⣀⠶⠆⠀⠀⣀⣸⣶⣿⠁⡆⠒⠒⠒⠒⠀⣿⠀⣿⣿⣧⣤⣤⣾⣿⣿⣿⣷⣿⣿⣯⣬⣽⣿⣥⣭⣿⣯⡄⠻⡿⢳⣾⣿⣿⣗⣿⣿⣿⣿⣼
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣾⣽⣿⣿⣿⣥⣿⣿⣿⣿⣿⣄⣆⣼⣽⣿⣿⣬⣦⣶⣶⣤⣦⡜⡃⡋⠉⠉⠁⠀⢭⠀⣿⣿⣬⣭⣟⣿⣿⣿⣿⣏⣙⣯⣉⣒⣚⣛⣀⣥⣷⣶⣀⣐⣆⣸⣿⣿⣿⣛⣿⣿⣿⣿⣾
⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠲⠷⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⢘⠂⠀⡾⣆⠐⠿⠀⡺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢠⣠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⢉⠉⣉⣿
⡇⠈⠀⠶⠀⣾⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⡇⠀⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⠐⠂⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠚⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣤⣾⣮⡄⣄⡿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣾
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣛⣛⣭⡿⡿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⣉⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠉⠉⠉⠉⠉⠉⠙⠋⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣶⣶⣦⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⡀⢁⠀⠀⣀⡤⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠊⠒⠒⠒⠒⠒⠒⠒⠈⠀⠀⠀⢀⠈⠸⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠂⠒⠒⠂⠀⠒⢤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⠿⠉⠁⠀⠾⠿⠿⠿⠶⠶⠶⠶⠦⠀⠂⠐⠀⠀⠀⠂⠐⠸⡿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⡿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣭⣽⣴⡄⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠅⠀⠑⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣥⣤⣤⣤⣥⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⡉⠻⠻⠿⠛⢻⣿⣟⣟⣟⣿⣿⣛⣿⣿⣿⣿⣿⣿⣷⣖⣲⣖⣿⣿⣴⣷⣶⣷⣜⢀⡃⣁⣀⣀⣀⠀⣲⢠⡗⠒⠀⠀⠀⣿⣈⣰⣿⡟⠉⠭⠭⠭⠉⠉⠽⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠾⠀⡆⣭⣉⣉⠉⠀⢽⠸⡏⠩⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠠⢰⣤⣦⣶⣶⡶⣶⣴⣶⣶⢶⡆⣶⣶⣶⣶⣶⠦⢆⣲⣶⣦⣴⣴⣦⠦⣤⣴⢄⠀⠅⠩⠤⢤⡤⠀⠽⠀⣿⣿⡧⠀⠄⣿⣛⣛⣻⠠⣦⣶⡄⢠⢤⣦⠄⣴⣦⣦⠠⠤⠴⠄⠤⠶⠤⠀⣿⣿⣿⡟⣠
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣁⣀⣉⣉⣰⣉⣀⣉⣉⣹⣉⣉⡀⡭⢍⣹⣯⣉⣉⠉⣉⣉⠉⣉⠀⠀⠀⠙⠛⠛⠀⣻⠀⣿⣿⡇⠛⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠺⢌⠫⠕⢿⢟⠷⠶⣿⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠖⣿⣿⣿⣿⣿⡄⠈⠀⢀⢮⠀⠀⠀⠀⢨⠠⠀⠀⡄⡅⣀⠶⠆⠀⠀⣀⣸⣶⣿⠁⡆⠒⠒⠒⠒⠀⣿⠀⣿⣿⣧⣤⣤⣾⣿⣿⣿⣷⣿⣿⣯⣬⣽⣿⣥⣭⣿⣯⡄⠻⡿⢳⣾⣿⣿⣗⣿⣿⣿⣿⣼
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣾⣽⣿⣿⣿⣥⣿⣿⣿⣿⣿⣄⣆⣼⣽⣿⣿⣬⣦⣶⣶⣤⣦⡜⡃⡋⠉⠉⠁⠀⢭⠀⣿⣿⣬⣭⣟⣿⣿⣿⣿⣏⣙⣯⣉⣒⣚⣛⣀⣥⣷⣶⣀⣐⣆⣸⣿⣿⣿⣛⣿⣿⣿⣿⣾
⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠲⠷⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⢘⠂⠀⡾⣆⠐⠿⠀⡺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢠⣠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⢉⠉⣉⣿
⡇⠈⠀⠶⠀⣾⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⡇⠀⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⠐⠂⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠚⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣤⣾⣮⡄⣄⡿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣾
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣛⣛⣭⡿⡿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⣉⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠉⠉⠉⠉⠉⠉⠙⠋⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣶⣶⣦⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⡀⢁⠀⠀⣀⡤⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠊⠒⠒⠒⠒⠒⠒⠒⠈⠀⠀⠀⢀⠈⠸⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠂⠒⠒⠂⠀⠒⢤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⠿⠉⠁⠀⠾⠿⠿⠿⠶⠶⠶⠶⠦⠀⠂⠐⠀⠀⠀⠂⠐⠸⡿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⡿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣭⣽⣴⡄⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠅⠀⠑⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣥⣤⣤⣤⣥⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⡉⠻⠻⠿⠛⢻⣿⣟⣟⣟⣿⣿⣛⣿⣿⣿⣿⣿⣿⣷⣖⣲⣖⣿⣿⣴⣷⣶⣷⣜⢀⡃⣁⣀⣀⣀⠀⣲⢠⡗⠒⠀⠀⠀⣿⣈⣰⣿⡟⠉⠭⠭⠭⠉⠉⠽⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠾⠀⡆⣭⣉⣉⠉⠀⢽⠸⡏⠩⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠠⢰⣤⣦⣶⣶⡶⣶⣴⣶⣶⢶⡆⣶⣶⣶⣶⣶⠦⢆⣲⣶⣦⣴⣴⣦⠦⣤⣴⢄⠀⠅⠩⠤⢤⡤⠀⠽⠀⣿⣿⡧⠀⠄⣿⣛⣛⣻⠠⣦⣶⡄⢠⢤⣦⠄⣴⣦⣦⠠⠤⠴⠄⠤⠶⠤⠀⣿⣿⣿⡟⣠
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣁⣀⣉⣉⣰⣉⣀⣉⣉⣹⣉⣉⡀⡭⢍⣹⣯⣉⣉⠉⣉⣉⠉⣉⠀⠀⠀⠙⠛⠛⠀⣻⠀⣿⣿⡇⠛⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠺⢌⠫⠕⢿⢟⠷⠶⣿⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠖⣿⣿⣿⣿⣿⡄⠈⠀⢀⢮⠀⠀⠀⠀⢨⠠⠀⠀⡄⡅⣀⠶⠆⠀⠀⣀⣸⣶⣿⠁⡆⠒⠒⠒⠒⠀⣿⠀⣿⣿⣧⣤⣤⣾⣿⣿⣿⣷⣿⣿⣯⣬⣽⣿⣥⣭⣿⣯⡄⠻⡿⢳⣾⣿⣿⣗⣿⣿⣿⣿⣼
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣾⣽⣿⣿⣿⣥⣿⣿⣿⣿⣿⣄⣆⣼⣽⣿⣿⣬⣦⣶⣶⣤⣦⡜⡃⡋⠉⠉⠁⠀⢭⠀⣿⣿⣬⣭⣟⣿⣿⣿⣿⣏⣙⣯⣉⣒⣚⣛⣀⣥⣷⣶⣀⣐⣆⣸⣿⣿⣿⣛⣿⣿⣿⣿⣾
⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠲⠷⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⢘⠂⠀⡾⣆⠐⠿⠀⡺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢠⣠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⢉⠉⣉⣿
⡇⠈⠀⠶⠀⣾⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⡇⠀⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⠐⠂⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠚⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣤⣾⣮⡄⣄⡿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣾
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣛⣛⣭⡿⡿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⣉⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠉⠉⠉⠉⠉⠉⠙⠋⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣶⣶⣦⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⡀⢁⠀⠀⣀⡤⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠊⠒⠒⠒⠒⠒⠒⠒⠈⠀⠀⠀⢀⠈⠸⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠂⠒⠒⠂⠀⠒⢤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⠿⠉⠁⠀⠾⠿⠿⠿⠶⠶⠶⠶⠦⠀⠂⠐⠀⠀⠀⠂⠐⠸⡿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⡿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣭⣽⣴⡄⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠅⠀⠑⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣥⣤⣤⣤⣥⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⡉⠻⠻⠿⠛⢻⣿⣟⣟⣟⣿⣿⣛⣿⣿⣿⣿⣿⣿⣷⣖⣲⣖⣿⣿⣴⣷⣶⣷⣜⢀⡃⣁⣀⣀⣀⠀⣲⢠⡗⠒⠀⠀⠀⣿⣈⣰⣿⡟⠉⠭⠭⠭⠉⠉⠽⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠾⠀⡆⣭⣉⣉⠉⠀⢽⠸⡏⠩⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠠⢰⣤⣦⣶⣶⡶⣶⣴⣶⣶⢶⡆⣶⣶⣶⣶⣶⠦⢆⣲⣶⣦⣴⣴⣦⠦⣤⣴⢄⠀⠅⠩⠤⢤⡤⠀⠽⠀⣿⣿⡧⠀⠄⣿⣛⣛⣻⠠⣦⣶⡄⢠⢤⣦⠄⣴⣦⣦⠠⠤⠴⠄⠤⠶⠤⠀⣿⣿⣿⡟⣠
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣁⣀⣉⣉⣰⣉⣀⣉⣉⣹⣉⣉⡀⡭⢍⣹⣯⣉⣉⠉⣉⣉⠉⣉⠀⠀⠀⠙⠛⠛⠀⣻⠀⣿⣿⡇⠛⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠺⢌⠫⠕⢿⢟⠷⠶⣿⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠖⣿⣿⣿⣿⣿⡄⠈⠀⢀⢮⠀⠀⠀⠀⢨⠠⠀⠀⡄⡅⣀⠶⠆⠀⠀⣀⣸⣶⣿⠁⡆⠒⠒⠒⠒⠀⣿⠀⣿⣿⣧⣤⣤⣾⣿⣿⣿⣷⣿⣿⣯⣬⣽⣿⣥⣭⣿⣯⡄⠻⡿⢳⣾⣿⣿⣗⣿⣿⣿⣿⣼
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣾⣽⣿⣿⣿⣥⣿⣿⣿⣿⣿⣄⣆⣼⣽⣿⣿⣬⣦⣶⣶⣤⣦⡜⡃⡋⠉⠉⠁⠀⢭⠀⣿⣿⣬⣭⣟⣿⣿⣿⣿⣏⣙⣯⣉⣒⣚⣛⣀⣥⣷⣶⣀⣐⣆⣸⣿⣿⣿⣛⣿⣿⣿⣿⣾
⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠲⠷⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⢘⠂⠀⡾⣆⠐⠿⠀⡺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢠⣠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⢉⠉⣉⣿
⡇⠈⠀⠶⠀⣾⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⡇⠀⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⠐⠂⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠚⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣤⣾⣮⡄⣄⡿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣾
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣛⣛⣭⡿⡿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⣉⠙⠋⠉⠛⠋⠛⠙⠉⠉⠙⠉⠉⠩⠉⠉⠉⠉⠋⠙⠛⢛⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣶⣶⣦⣤⣤⣤⣤⣤⣤⣀⣑⣀⣀⣀⡀⢁⠀⠀⣀⣤⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠊⠒⠒⠒⠒⠒⠒⠒⠈⠀⠀⠀⢀⠈⠸⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠂⠒⠒⠂⠀⠒⢤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⠿⠉⠁⠀⠾⠿⠿⠿⠶⠶⠶⠶⠦⠀⠂⠐⠀⠀⠀⠂⠐⠸⡿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⡿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣭⣽⣴⡄⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠅⠀⠑⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣥⣤⣤⣤⣥⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⡉⠻⠻⠿⠛⢻⣿⣟⣟⣟⣿⣿⣛⣿⣿⣿⣿⣿⣿⣷⣖⣲⣖⣿⣿⣴⣷⣶⣷⣜⢀⡃⣁⣀⣀⣀⠀⣲⢠⡗⠒⠀⠀⠀⣿⣈⣰⣿⡟⠉⠭⠭⠭⠉⠉⠽⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠾⠀⡆⣭⣉⣉⠉⠀⢽⠸⡏⠩⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠠⢰⣤⣦⣶⣶⡶⣶⣴⣶⣶⢶⡆⣶⣶⣶⣶⣶⠦⢆⣲⣶⣦⣴⣴⣦⠦⣤⣴⢄⠀⠅⠩⠤⢤⡤⠀⠽⠀⣿⣿⡧⠀⠄⣿⣛⣛⣻⠠⣦⣶⡄⢠⢤⣦⠄⣴⣦⣦⠠⠤⠴⠄⠤⠶⠤⠀⣿⣿⣿⡟⣠
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣁⣀⣉⣉⣰⣉⣀⣉⣉⣹⣉⣉⡀⡭⢍⣹⣯⣉⣉⠉⣉⣉⠉⣉⠀⠀⠀⠙⠛⠛⠀⣻⠀⣿⣿⡇⠛⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠺⢌⠫⠕⢿⢟⠷⠶⣿⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠖⣿⣿⣿⣿⣿⡄⠈⠀⢀⢮⠀⠀⠀⠀⢨⠠⠀⠀⡄⡅⣀⠶⠆⠀⠀⣀⣸⣶⣿⠁⡆⠒⠒⠒⠒⠀⣿⠀⣿⣿⣧⣤⣤⣾⣿⣿⣿⣷⣿⣿⣯⣬⣽⣿⣥⣭⣿⣯⡄⠻⡿⢳⣾⣿⣿⣗⣿⣿⣿⣿⣼
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣾⣽⣿⣿⣿⣥⣿⣿⣿⣿⣿⣄⣆⣼⣽⣿⣿⣬⣦⣶⣶⣤⣦⡜⡃⡋⠉⠉⠁⠀⢭⠀⣿⣿⣬⣭⣟⣿⣿⣿⣿⣏⣙⣯⣉⣒⣚⣛⣀⣥⣷⣶⣀⣐⣆⣸⣿⣿⣿⣛⣿⣿⣿⣿⣾
⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠲⠷⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⢘⠂⠀⡾⣆⠐⠿⠀⡺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢠⣠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⢉⠉⣉⣿
⡇⠈⠀⠶⠀⣾⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⡇⠀⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⠐⠂⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠚⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣤⣾⣮⡄⣄⡿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣾
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣛⣛⣭⡿⡿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⠉⣉⠙⠋⠉⠛⠋⠛⠙⠉⠉⠙⠉⠉⠩⠉⠉⠉⠉⠋⠙⠛⢛⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣶⣶⣦⣤⣤⣤⣤⣤⣤⣀⣑⣀⣀⣀⡀⢁⠀⠀⣀⣤⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠊⠒⠒⠒⠒⠒⠒⠒⠈⠀⠀⠀⢀⠈⠸⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠂⠒⠒⠂⠀⠒⢤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⠿⠉⠁⠀⠾⠿⠿⠿⠶⠶⠶⠶⠦⠀⠂⠐⠀⠀⠄⠂⠐⠸⡿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⡿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣭⣽⣴⡄⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠅⠀⠑⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣥⣤⣤⣤⣥⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⡉⠻⠻⠿⠛⢻⣿⣟⣟⣟⣿⣿⣛⣿⣿⣿⣿⣿⣿⣷⣖⣲⣖⣿⣿⣴⣷⣶⣷⣜⢀⡃⣁⣀⣀⣀⠀⣲⢠⡗⠒⠀⠀⠀⣿⣈⣰⣿⡟⠉⠭⠭⠭⠉⠉⠽⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠾⠀⡆⣭⣉⣉⠉⠀⢽⠸⡏⠩⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠠⢰⣤⣦⣶⣶⡶⣶⣴⣶⣶⢶⡆⣶⣶⣶⣶⣶⠦⢆⣲⣶⣦⣴⣴⣦⠦⣤⣴⢄⠀⠅⠩⠤⢤⡤⠀⠽⠀⣿⣿⡧⠀⠄⣿⣛⣛⣻⠠⣦⣶⡄⢠⢤⣦⠄⣴⣦⣦⠠⠤⠴⠄⠤⠶⠤⠀⣿⣿⣿⡟⣠
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣁⣀⣉⣉⣰⣉⣀⣉⣉⣹⣉⣉⡀⡭⢍⣹⣯⣉⣉⠉⣉⣉⠉⣉⠀⠀⠀⠙⠛⠛⠀⣻⠀⣿⣿⡇⠛⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠺⢌⠫⠕⢿⢟⠷⠶⣿⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠖⣿⣿⣿⣿⣿⡄⠈⠀⢀⢮⠀⠀⠀⠀⢨⠠⠀⠀⡄⡅⣀⠶⠆⠀⠀⣀⣸⣶⣿⠁⡆⠒⠒⠒⠒⠀⣿⠀⣿⣿⣧⣤⣤⣾⣿⣿⣿⣷⣿⣿⣯⣬⣽⣿⣥⣭⣿⣯⡄⠻⡿⢳⣾⣿⣿⣗⣿⣿⣿⣿⣼
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣾⣽⣿⣿⣿⣥⣿⣿⣿⣿⣿⣄⣆⣼⣽⣿⣿⣬⣦⣶⣶⣤⣦⡜⡃⡋⠉⠉⠁⠀⢭⠀⣿⣿⣬⣭⣟⣿⣿⣿⣿⣏⣙⣯⣉⣒⣚⣛⣀⣥⣷⣶⣀⣐⣆⣸⣿⣿⣿⣛⣿⣿⣿⣿⣾
⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠲⠷⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⢘⠂⠀⡾⠆⠐⠿⠀⡺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢠⣠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⢉⠉⣉⣿
⡇⠈⠀⠶⠀⣾⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⡇⠀⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⠐⠂⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠚⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣤⣾⣮⡄⣄⡿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣾
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣛⣛⣭⡿⡿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⠉⡭⠽⠿⣿⣿⡿⠿⠿⠽⠽⠿⠯⠭⠿⠭⠽⠯⠭⠿⠟⠻⢛⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣯⣿⣶⣶⣦⣥⣤⣤⣤⣤⣤⣀⣑⣀⣀⣀⡀⢁⠀⠀⣀⣤⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠊⠒⠒⠒⠒⠒⠒⠒⠈⠀⠀⠀⢀⠈⠸⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠂⠒⠒⠂⠀⠒⢤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⠿⠉⠁⠀⠾⠿⠿⠿⠶⠶⠶⠶⠦⠀⠂⠐⠀⠀⠄⠂⠐⠸⡿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⡿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣭⣽⣴⡄⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠅⠀⠑⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣥⣤⣤⣤⣥⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⡉⠻⠻⠿⠛⢻⣿⣟⣟⣟⣿⣿⣛⣿⣿⣿⣿⣿⣿⣷⣖⣲⣖⣿⣿⣴⣷⣶⣷⣜⢀⡃⣁⣀⣀⣀⠀⣲⢠⡗⠒⠀⠀⠀⣿⣈⣰⣿⡏⠉⠭⠭⠭⠉⠉⠽⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠾⠀⡆⣭⣉⣉⠉⠀⢽⠸⡏⠩⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠠⢰⣤⣦⣶⣶⡶⣶⣴⣶⣶⢶⡆⣶⣶⣶⣶⣶⠦⢆⣲⣶⣦⣴⣴⣦⠦⣤⣴⢄⠀⠅⠩⠤⢤⡤⠀⠽⠀⣿⣿⡧⠀⠄⣿⣛⣛⣻⠠⣦⣶⡄⢠⢤⣦⠄⣴⣦⣦⠠⠤⠴⠄⠤⠶⠤⠀⣿⣿⣿⡟⣠
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣁⣀⣉⣉⣰⣉⣀⣉⣉⣹⣉⣉⡀⡭⢍⣹⣯⣉⣉⠉⣉⣉⠉⣉⠀⠀⠀⠙⠛⠛⠀⣻⠀⣿⣿⡇⠛⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠺⢌⠫⠕⢿⢟⠷⠶⣿⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠖⣿⣿⣿⣿⣿⡄⠈⠀⢀⢮⠀⠀⠀⠀⢨⠠⠀⠀⡄⡅⣀⠶⠆⠀⠀⣀⣸⣶⣿⠁⡆⠒⠒⠒⠒⠀⣿⠀⣿⣿⣧⣤⣤⣾⣿⣿⣿⣷⣿⣿⣯⣬⣽⣿⣥⣭⣿⣯⡄⠻⡿⢳⣾⣿⣿⣗⣿⣿⣿⣿⣼
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣾⣽⣿⣿⣿⣥⣾⣿⣿⣿⣿⣄⣆⣼⣽⣿⣿⣬⣦⣶⣶⣤⣦⡜⡃⡋⠉⠉⠁⠀⢭⠀⣿⣿⣬⣭⣟⣿⣿⣿⣿⣏⣙⣯⣉⣒⣚⣛⣀⣥⣷⣶⣀⣐⣆⣸⣿⣿⣿⣛⣿⣿⣿⣿⣾
⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠲⠷⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⢘⠂⠀⡾⠆⠐⠿⠀⡺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢠⣠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⢉⠉⣉⣿
⡇⠈⠀⠶⠀⣾⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⡇⠀⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⠐⠂⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠚⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣤⣾⣮⡄⣄⡿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣾
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣛⣛⣭⡿⡿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⠉⡭⠽⠿⣿⣿⡿⠿⠿⠽⠽⠿⠯⠭⠿⠭⠽⠯⠭⠿⠟⠻⢛⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣯⣿⣶⣶⣦⣥⣤⣤⣤⣤⣤⣀⣑⣀⣀⣀⡀⢁⠀⠀⣀⣤⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠊⠒⠒⠒⠒⠒⠒⠒⠈⠀⠀⠀⢀⠈⠸⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠂⠒⠒⠂⠀⠒⢤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⠿⠉⠁⠀⠾⠿⠿⠿⠶⠶⠶⠶⠦⠀⠂⠐⠀⠀⠄⠂⠐⠸⡿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⡿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣭⣽⣴⡄⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠅⠀⠑⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣥⣤⣤⣤⣥⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⡉⠻⠻⠿⠛⢻⣿⣟⣟⣟⣿⣿⣛⣿⣿⣿⣿⣿⣿⣷⣖⣲⣖⣿⣿⣴⣷⣶⣷⣜⢀⡃⣁⣀⣀⣀⠀⣲⢠⡗⠒⠀⠀⠀⣿⣈⣰⣿⡏⠉⠭⠭⠭⠉⠉⠽⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⢲
⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠾⠀⡆⣭⣉⣉⠉⠀⢽⠸⡏⠩⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠠⢰⣤⣦⣶⣶⡶⣶⣴⣶⣶⢶⡆⣶⣶⣶⣶⣶⠦⢆⣲⣶⣦⣴⣴⣦⠦⣤⣴⢄⠀⠅⠩⠤⢤⡤⠀⠽⠀⣿⣿⡧⠀⠄⣿⣛⣛⣻⠠⣦⣶⡄⢠⢤⣦⠄⣴⣦⣦⠠⠤⠴⠄⠤⠶⠤⠀⣿⣿⣿⡟⣠
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣁⣀⣉⣉⣰⣉⣀⣉⣉⣹⣉⣉⡀⡭⢍⣹⣯⣉⣉⠉⣉⣉⠉⣉⠀⠀⠀⠙⠛⠛⠀⣻⠀⣿⣿⡇⠛⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠺⢌⠫⠕⢿⢟⠷⠶⣿⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠖⣿⣿⣿⣿⣿⡄⠈⠀⢀⢮⠀⠀⠀⠀⢨⠠⠀⠀⡄⡅⣀⠶⠆⠀⠀⣀⣸⣶⣿⠁⡆⠒⠒⠒⠒⠀⣿⠀⣿⣿⣧⣤⣤⣾⣿⣿⣿⣷⣿⣿⣯⣬⣽⣿⣥⣭⣿⣯⡄⠻⡿⢳⣾⣿⣿⣗⣿⣿⣿⣿⣼
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣾⣽⣿⣿⣿⣥⣾⣿⣿⣿⣿⣄⣆⣼⣽⣿⣿⣬⣦⣶⣶⣤⣦⡜⡃⡋⠉⠉⠁⠀⢭⠀⣿⣿⣬⣭⣟⣿⣿⣿⣿⣏⣙⣯⣉⣒⣚⣛⣀⣥⣷⣶⣀⣐⣆⣸⣿⣿⣿⣛⣿⣿⣿⣿⣾
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠲⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⢘⠂⠀⡾⠆⠐⠷⠀⡺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢠⣠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⢉⠉⣉⣿
⡇⠈⠀⠶⠀⣾⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⡇⠀⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⠐⠂⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⠀⠚⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣤⣾⣮⡄⣄⡿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿⣿
⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣾
⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣛⣛⣭⡿⡿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⠉⡭⠽⠿⣯⣿⡿⠿⠿⠽⠽⠿⠯⠭⠿⠭⠽⠯⠭⠿⠟⠻⢛⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣯⣷⣶⣶⣦⣥⣤⣤⣤⣤⣤⣀⣑⣀⣀⣀⡀⢁⠀⠀⣀⣤⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠊⠒⠒⠒⠒⠒⠒⠒⠈⠀⠀⠀⢀⠈⠸⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠂⠒⠒⠂⠀⠒⢤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⠿⠉⠁⠀⠾⠿⠿⠿⠶⠶⠶⠶⠦⠀⠂⠐⠀⠀⠄⠂⠐⠸⡿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⡿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣭⣽⣴⡄⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠅⠀⠑⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣥⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⡉⠛⠻⠟⠛⠻⣛⣟⣛⣛⣛⣛⣛⣻⣛⣛⣛⣻⣛⣓⣒⣒⣒⣻⣛⣐⣳⣐⣓⣘⢀⡃⣁⣀⣀⣀⠀⣲⢠⡗⠒⠀⠀⠀⣿⣈⣰⣿⡏⠉⠭⠭⠭⠝⠹⠽⠍⠉⠉⠙⠉⠉⠉⠛⠉⠉⠉⣿⣿⣿⣿⣳
⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠾⠀⡆⣭⣉⡉⠉⠀⢽⠘⡏⠩⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⢉⣛⣉⠉⡍⢻⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠠⢰⣤⣦⣶⣶⡶⣶⣴⣶⣶⢶⡆⣶⣶⣶⣶⣶⠦⢆⣲⣶⣦⣴⣴⣦⠦⣄⣴⢀⠀⠅⠩⠤⢤⡤⠀⠽⠀⣿⣿⡧⠀⠄⣿⣛⣛⣻⠠⣦⡶⡄⢠⢤⣦⠴⣶⣧⣦⠠⠤⠼⠧⠥⣶⠤⠈⣿⣿⣿⡿⣦
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣀⣀⣉⣉⣰⣈⣀⣉⣉⣹⣉⣉⡀⡭⢍⣹⣯⣉⣉⠉⣉⣉⠉⣉⠀⠀⠀⠙⠛⠛⠀⣻⠀⣿⣿⡇⠛⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠪⢌⠹⠕⢭⣿⠷⠷⣿⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠖⣿⣿⣿⣿⣿⡄⠈⠀⢀⢮⠀⠀⠀⠀⢨⠠⠀⠀⡄⡅⣀⠶⠆⠀⠀⣀⣸⣶⣿⠁⡆⠒⠒⠒⠒⠀⣿⠀⣿⣿⣧⣤⣤⣾⣿⣿⣿⣷⣿⣿⣭⣬⣽⣿⣥⣭⣿⣯⡄⠻⡟⢻⣾⣿⣿⡷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣾⣽⣿⣿⣿⣥⣾⣿⣿⣿⣿⣄⣆⣼⣽⣿⣿⣬⣦⣦⣶⣤⣦⡜⡃⡋⠉⠉⠁⠀⢭⠀⣿⣿⣬⣭⣟⣿⣿⣿⣿⣏⣙⣯⣉⣒⣒⣛⣀⣥⣷⣶⣀⣘⣦⣸⣿⣿⣿⣛⣿⣿⣿⣿⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠲⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⢘⠂⠀⡶⠂⠐⠷⠀⡺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢠⣠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⢉⠉⣉⣿
⡇⠈⠀⠶⠀⣾⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⡇⠀⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⠐⠂⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⠀⠚⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣤⣾⣮⡄⣄⡿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿⣿
⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣾
⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣛⣛⣭⡿⡿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⠉⡭⠽⠿⣯⣿⡿⠿⠿⠽⠭⠿⠯⠭⠿⠭⠽⠯⠭⠿⠟⠻⢛⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣼⣿⣯⣷⣶⣶⣤⣥⣤⣤⣤⣤⣤⣀⣑⣀⣀⣀⡀⢁⠀⠀⣀⣤⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠊⠒⠒⠒⠒⠒⠒⠒⠈⠀⠀⠀⢀⠈⠸⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠂⠒⠒⠂⠀⠒⢤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⠿⠉⠁⠀⠾⠿⠿⠿⠶⠶⠶⠶⠦⠀⠂⠐⠀⠀⠄⠂⠐⠸⡿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⡿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣭⣽⣴⡄⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠅⠀⠑⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣥⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⡉⠛⠻⠟⠛⠻⣛⣟⣛⣛⣛⣛⣛⣻⣛⣛⣛⣻⣛⣓⣒⣒⣒⣻⣛⣐⣳⣐⣓⣘⢀⡃⣁⣀⣀⣀⠀⣲⢠⡗⠒⠀⠀⠀⣿⣈⣰⣿⡏⠉⠭⠭⠭⠝⠹⠽⠍⠉⠉⠙⠉⠛⠉⠛⠉⠉⠉⣿⣿⣿⣿⣳
⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠾⠀⡆⣭⣉⡉⠉⠀⢽⠘⡏⠩⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⢩⠉⠉⢍⠉⢉⣛⣉⠉⡍⢻⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠠⢰⣤⣦⣶⣶⡶⣶⣴⣶⣶⢶⡆⣶⣶⣶⣶⣶⠦⢆⣲⣶⣦⣴⣴⣦⠦⣄⣴⢀⠀⠅⠩⠤⢤⡤⠀⠽⠀⣿⣿⡧⠀⠄⣿⣛⣛⣻⠠⣤⡶⡄⢠⢤⣦⠔⣦⡧⣦⠠⠤⠼⠧⠥⣶⠤⠈⣿⣿⣿⡿⣦
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣀⣀⣉⣉⣰⣈⣀⣉⣉⣹⣉⣉⡀⡭⢍⣹⣯⣉⣉⠉⣉⣉⠉⣉⠀⠀⠀⠙⠛⠛⠀⣻⠀⣿⣿⡇⠛⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠪⢌⠹⠕⢬⣿⠿⠷⣿⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠖⣿⣿⣿⣿⣿⡄⠈⠀⢀⢮⠀⠀⠀⠀⢨⠠⠀⠀⡄⡅⣀⠶⠆⠀⠀⣀⣸⣶⣿⠁⡆⠒⠒⠒⠒⠀⣿⠀⣿⣿⣧⣤⣤⣾⣿⣿⣿⣷⣿⣿⣭⣬⣽⣿⣥⣭⣿⣯⡄⠻⡟⢻⣾⣿⣿⡷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣾⣽⣿⣿⣿⣥⣾⣿⣿⣿⣿⣄⣆⣼⣽⣿⣿⣬⣦⣦⣶⣤⣦⡜⡃⡋⠉⠉⠁⠀⢭⠀⣿⣿⣬⣭⣟⣿⣿⣿⣿⣏⣙⣯⣉⣒⣒⣛⣀⣥⣷⣶⣀⣘⣦⣸⣿⣿⣿⣛⣿⣿⣿⣿⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠲⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⢘⠂⠀⡶⠂⠐⠷⠀⡺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢠⣠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⢉⠉⣉⣿
⡇⠈⠀⠶⠀⣾⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⡇⠀⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⠐⠂⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⠀⠚⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣤⣾⣮⡄⣄⡿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿⣿
⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣾
⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣛⣛⣭⡿⡿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⠉⡭⠽⠿⣯⣿⡿⠿⠿⠽⠭⠿⠯⠭⠿⠭⠽⠯⠭⠿⠟⠻⢛⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣼⣿⣯⣷⣶⣶⣤⣥⣤⣤⣤⣤⣤⣀⣑⣀⣀⣀⡀⢁⠀⠀⣀⣤⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠊⠒⠒⠒⠒⠒⠒⠒⠈⠀⠀⠀⢀⠈⠸⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠂⠒⠒⠂⠀⠒⢤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⠿⠉⠁⠀⠾⠿⠿⠿⠶⠶⠶⠶⠦⠀⠂⠐⠀⠀⠄⠂⠐⠸⡿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⡿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣭⣽⣴⡄⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠅⠀⠑⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣥⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⡉⠛⠻⠟⠛⠻⣛⣟⣛⣛⣛⣛⣛⣻⣛⣛⣛⣻⣛⣓⣒⣒⣒⣻⣛⣐⣳⣐⣓⣘⢀⡃⣁⣀⣀⣀⠀⣲⢠⡗⠒⠀⠀⠀⣿⣈⣰⣿⡏⠉⠭⠭⠭⠝⠹⠽⠍⠉⠉⠙⠉⠛⠉⠛⠉⠉⠉⣿⣿⣿⣿⣳
⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠾⠀⡆⣭⣉⡉⠉⠀⢽⠘⡏⠩⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⢩⠉⠉⢍⠉⢉⣛⣉⠉⡍⢻⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠠⢰⣤⣦⣶⣶⡶⣶⣴⣶⣶⢶⡆⣶⣶⣶⣶⣶⠦⢆⣲⣶⣦⣴⣴⣦⠦⣄⣴⢀⠀⠅⠩⠤⢤⡤⠀⠽⠀⣿⣿⡧⠀⠄⣿⣛⣛⣻⠠⣤⡶⡄⢠⢤⣦⠔⣦⡧⣦⠠⠤⠼⠧⠥⣶⠤⠈⣿⣿⣿⡿⣦
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣀⣀⣉⣉⣰⣈⣀⣉⣉⣹⣉⣉⡀⡭⢍⣹⣯⣉⣉⠉⣉⣉⠉⣉⠀⠀⠀⠙⠛⠛⠀⣻⠀⣿⣿⡇⠛⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠪⢌⠹⠕⢬⣿⠿⠷⣿⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠖⣿⣿⣿⣿⣿⡄⠈⠀⢀⢮⠀⠀⠀⠀⢨⠠⠀⠀⡄⡅⣀⠶⠆⠀⠀⣀⣸⣶⣿⠁⡆⠒⠒⠒⠒⠀⣿⠀⣿⣿⣧⣤⣤⣾⣿⣿⣿⣷⣿⣿⣭⣬⣽⣿⣥⣭⣿⣯⡄⠻⡟⢻⣾⣿⣿⡷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣾⣽⣿⣿⣿⣥⣾⣿⣿⣿⣿⣄⣆⣼⣽⣿⣿⣬⣦⣦⣶⣤⣦⡜⡃⡋⠉⠉⠁⠀⢭⠀⣿⣿⣬⣭⣟⣿⣿⣿⣿⣏⣙⣯⣉⣒⣒⣛⣀⣥⣷⣶⣀⣘⣦⣸⣿⣿⣿⣛⣿⣿⣿⣿⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠲⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⢘⠂⠀⡶⠂⠐⠷⠀⡺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢠⣠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⢉⠉⣉⣿
⡇⠈⠀⠶⠀⣾⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⡇⠀⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⠐⠂⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⠀⠚⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣤⣾⣮⡄⣄⡿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿⣿
⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣾
⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣛⣛⣭⡿⡿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⠉⡭⠽⠿⣯⣿⡿⠿⠿⠽⠭⠿⠯⠭⠿⠭⠽⠯⠭⠿⠟⠻⢛⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣼⣿⣯⣷⣶⣶⣤⣥⣤⣤⣤⣤⣤⣀⣑⣀⣀⣀⡀⢁⠀⠀⣀⣤⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠊⠒⠒⠒⠒⠒⠒⠒⠈⠀⠀⠀⢀⠈⠸⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠂⠒⠒⠂⠀⠒⢤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⠿⠉⠁⠀⠾⠿⠿⠿⠶⠶⠶⠶⠦⠀⠂⠐⠀⠀⠄⠂⠐⠸⡿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⡿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣭⣽⣴⡄⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠅⠀⠑⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣥⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⡉⠛⠻⠟⠛⠻⣛⣟⣛⣛⣛⣛⣛⣻⣛⣛⣛⣻⣛⣓⣒⣒⣒⣻⣛⣐⣳⣐⣓⣘⢀⡃⣁⣀⣀⣀⠀⣲⢠⡗⠒⠀⠀⠀⣿⣈⣰⣿⡏⠉⠭⠭⠭⠝⠹⠽⠍⠉⠉⠙⠉⠛⠉⠛⠉⠉⠉⣿⣿⣿⣿⣳
⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠾⠀⡆⣭⣉⡉⠉⠀⢽⠘⡏⠩⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⢩⠉⠉⢍⠉⢉⣛⣉⠉⡍⢻⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠠⢰⣤⣦⣶⣶⡶⣶⣴⣶⣶⢶⡆⣶⣶⣶⣶⣶⠦⢆⣲⣶⣦⣴⣴⣦⠦⣄⣴⢀⠀⠅⠩⠤⢤⡤⠀⠽⠀⣿⣿⡧⠀⠄⣿⣛⣛⣻⠠⣤⡶⡄⢠⢤⣦⠔⣦⡧⣦⠠⠤⠼⠧⠥⣶⠤⠈⣿⣿⣿⡿⣦
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣀⣀⣉⣉⣰⣈⣀⣉⣉⣹⣉⣉⡀⡭⢍⣹⣯⣉⣉⠉⣉⣉⠉⣉⠀⠀⠀⠙⠛⠛⠀⣻⠀⣿⣿⡇⠛⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠪⢌⠹⠕⢬⣿⠿⠷⣿⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠖⣿⣿⣿⣿⣿⡄⠈⠀⢀⢮⠀⠀⠀⠀⢨⠠⠀⠀⡄⡅⣀⠶⠆⠀⠀⣀⣸⣶⣿⠁⡆⠒⠒⠒⠒⠀⣿⠀⣿⣿⣧⣤⣤⣾⣿⣿⣿⣷⣿⣿⣭⣬⣽⣿⣥⣭⣿⣯⡄⠻⡟⢻⣾⣿⣿⡷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣾⣽⣿⣿⣿⣥⣾⣿⣿⣿⣿⣄⣆⣼⣽⣿⣿⣬⣦⣦⣶⣤⣦⡜⡃⡋⠉⠉⠁⠀⢭⠀⣿⣿⣬⣭⣟⣿⣿⣿⣿⣏⣙⣯⣉⣒⣒⣛⣀⣥⣷⣶⣀⣘⣦⣸⣿⣿⣿⣛⣿⣿⣿⣿⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠲⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⢘⠂⠀⡶⠂⠐⠷⠀⡺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢠⣠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⢉⠉⣉⣿
⡇⠈⠀⠶⠀⣾⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⡇⠀⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⠐⠂⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⠀⠚⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣤⣾⣮⡄⣄⡿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿⣿
⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣾
⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣛⣛⣭⡿⡿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⠉⡭⠽⠿⣯⣿⡿⠿⠿⠽⠭⠿⠯⠭⠿⠭⠽⠯⠭⠿⠟⠻⢛⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣼⣿⣯⣷⣶⣶⣤⣥⣤⣤⣤⣤⣤⣀⣑⣀⣀⣀⡀⢁⠀⠀⣀⣤⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠊⠒⠒⠒⠒⠒⠒⠒⠈⠀⠀⠀⢀⠈⠸⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠂⠒⠒⠂⠀⠒⢤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⠿⠉⠁⠀⠾⠿⠿⠿⠶⠶⠶⠶⠦⠀⠂⠐⠀⠀⠄⠂⠐⠸⡿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⡿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣭⣽⣴⡄⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠅⠀⠑⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣥⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⡉⠛⠻⠟⠛⠻⣛⣟⣛⣛⣛⣛⣛⣻⣛⣛⣛⣻⣛⣓⣒⣒⣒⣻⣛⣐⣳⣐⣓⣘⢀⡃⣁⣀⣀⣀⠀⣲⢠⡗⠒⠀⠀⠀⣿⣈⣰⣿⡏⠉⠭⠭⠭⠝⠹⠽⠍⠉⠉⠙⠉⠛⠉⠛⠉⠉⠉⣿⣿⣿⣿⣳
⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠾⠀⡆⣭⣉⡉⠉⠀⢽⠘⡏⠩⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⢩⠉⠉⢍⠉⢉⣛⣉⠉⡍⢻⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠠⢰⣤⣦⣶⣶⡶⣶⣴⣶⣶⢶⡆⣶⣶⣶⣶⣶⠦⢆⣲⣶⣦⣴⣴⣦⠦⣄⣴⢀⠀⠅⠩⠤⢤⡤⠀⠽⠀⣿⣿⡧⠀⠄⣿⣛⣛⣻⠠⣤⡶⡄⢠⢤⣦⠔⣦⡧⣦⠠⠤⠼⠧⠥⣶⠤⠈⣿⣿⣿⡿⣦
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣀⣀⣉⣉⣰⣈⣀⣉⣉⣹⣉⣉⡀⡭⢍⣹⣯⣉⣉⠉⣉⣉⠉⣉⠀⠀⠀⠙⠛⠛⠀⣻⠀⣿⣿⡇⠛⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠪⢌⠹⠕⢬⣿⠿⠷⣿⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠖⣿⣿⣿⣿⣿⡄⠈⠀⢀⢮⠀⠀⠀⠀⢨⠠⠀⠀⡄⡅⣀⠶⠆⠀⠀⣀⣸⣶⣿⠁⡆⠒⠒⠒⠒⠀⣿⠀⣿⣿⣧⣤⣤⣾⣿⣿⣿⣷⣿⣿⣭⣬⣽⣿⣥⣭⣿⣯⡄⠻⡟⢻⣾⣿⣿⡷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣾⣽⣿⣿⣿⣥⣾⣿⣿⣿⣿⣄⣆⣼⣽⣿⣿⣬⣦⣦⣶⣤⣦⡜⡃⡋⠉⠉⠁⠀⢭⠀⣿⣿⣬⣭⣟⣿⣿⣿⣿⣏⣙⣯⣉⣒⣒⣛⣀⣥⣷⣶⣀⣘⣦⣸⣿⣿⣿⣛⣿⣿⣿⣿⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠲⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⢘⠂⠀⡶⠂⠐⠷⠀⡺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢠⣠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⢉⠉⣉⣿
⡇⠈⠀⠶⠀⣾⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⡇⠀⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⠐⠂⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⠀⠚⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣤⣾⣮⡄⣄⡿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿⣿
⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣾
⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣛⣛⣭⡿⡿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⠉⡭⠽⠿⣯⣿⡿⠿⠿⠽⠭⠿⠯⠭⠿⠭⠽⠯⠭⠿⠟⠻⢛⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣼⣿⣯⣷⣶⣶⣤⣥⣤⣤⣤⣤⣤⣀⣑⣀⣀⣀⡀⢁⠀⠀⣀⣤⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠊⠒⠒⠒⠒⠒⠒⠒⠈⠀⠀⠀⢀⠈⠸⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠂⠒⠒⠂⠀⠒⢤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⠿⠉⠁⠀⠾⠿⠿⠿⠶⠶⠶⠶⠦⠀⠂⠐⠀⠀⠄⠂⠐⠸⡿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⡿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣭⣽⣴⡄⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠅⠀⠑⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣥⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⡉⠛⠻⠟⠛⠻⣛⣟⣛⣛⣛⣛⣛⣻⣛⣛⣛⣻⣛⣓⣒⣒⣒⣻⣛⣐⣳⣐⣓⣘⢀⡃⣁⣀⣀⣀⠀⣲⢠⡗⠒⠀⠀⠀⣿⣈⣰⣿⡏⠉⠭⠭⠭⠝⠹⠽⠍⠉⠉⠙⠉⠛⠉⠛⠉⠉⠉⣿⣿⣿⣿⣳
⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠾⠀⡆⣭⣉⡉⠉⠀⢽⠘⡏⠩⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⢩⠉⠉⢍⠉⢉⣛⣉⠉⡍⢻⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠠⢰⣤⣦⣶⣶⡶⣶⣴⣶⣶⢶⡆⣶⣶⣶⣶⣶⠦⢆⣲⣶⣦⣴⣴⣦⠦⣄⣴⢀⠀⠅⠩⠤⢤⡤⠀⠽⠀⣿⣿⡧⠀⠄⣿⣛⣛⣻⠠⣤⡶⡄⢠⢤⣦⠔⣦⡧⣦⠠⠤⠼⠧⠥⣶⠤⠈⣿⣿⣿⡿⣦
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣀⣀⣉⣉⣰⣈⣀⣉⣉⣹⣉⣉⡀⡭⢍⣹⣯⣉⣉⠉⣉⣉⠉⣉⠀⠀⠀⠙⠛⠛⠀⣻⠀⣿⣿⡇⠛⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠪⢌⢹⠕⢬⣿⠿⠷⣿⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠖⣿⣿⣿⣿⣿⡄⠈⠀⢀⢮⠀⠀⠀⠀⢨⠠⠀⠀⡄⡅⣀⠶⠆⠀⠀⣀⣸⣶⣿⠁⡆⠒⠒⠒⠒⠀⣿⠀⣿⣿⣧⣤⣤⣾⣿⣿⣿⣷⣿⣿⣭⣬⣽⣿⣥⣭⣿⣯⡄⠻⣟⣻⣾⣿⣿⡷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣾⣽⣿⣿⣿⣥⣾⣿⣿⣿⣿⣄⣆⣼⣽⣿⣿⣬⣦⣦⣶⣤⣦⡜⡃⡋⠉⠉⠁⠀⢭⠀⣿⣿⣬⣭⣟⣿⣿⣿⣿⣏⣙⣯⣉⣒⣒⣛⣀⣥⣷⣶⣀⣰⣧⣸⣿⣿⣿⣛⣿⣿⣿⣿⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠲⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⢘⠂⠀⡶⠂⠐⠷⠀⡺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢠⣠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⢉⠉⣉⣿
⡇⠈⠀⠶⠀⣾⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⡇⠀⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⠐⠂⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⠀⠚⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣤⣾⣮⡄⣄⡿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿⣿
⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣾
⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣛⣛⣭⡿⡿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⠉⡭⠽⠿⣯⣿⡿⠿⠿⠽⠭⠿⠯⠭⠿⠭⠽⠯⠭⠿⠟⠻⢛⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣼⣿⣯⣷⣶⣶⣤⣥⣤⣤⣤⣤⣤⣀⣑⣀⣀⣀⡀⢁⠀⠀⣀⣤⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠊⠒⠒⠒⠒⠒⠒⠒⠈⠀⠀⠀⢀⠈⠸⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠂⠒⠒⠂⠀⠒⢤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⠿⠉⠁⠀⠾⠿⠿⠿⠶⠶⠶⠶⠦⠀⠂⠐⠀⠀⠄⠂⠐⠸⡿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⡿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣭⣽⣴⡄⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠅⠀⠑⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣥⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⡉⠛⠻⠟⠛⠻⣛⣟⣛⣛⣛⣛⣛⣻⣛⣛⣛⣻⣛⣓⣒⣒⣒⣻⣛⣐⣳⣐⣓⣘⢀⡃⣁⣀⣀⣀⠀⣲⢠⡗⠒⠀⠀⠀⣿⣈⣰⣿⡏⠉⠭⠭⠭⠝⠹⠽⠍⠉⠉⠙⠉⠛⠉⠛⠉⠉⠉⣿⣿⣿⣿⣳
⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠾⠀⡆⣭⣉⡉⠉⠀⢽⠘⡏⠩⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⢩⠉⠉⢍⠉⢉⣛⣉⠉⡍⢻⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠠⢰⣤⣦⣶⣶⡶⣶⣴⣶⣶⢶⡆⣶⣶⣶⣶⣶⠦⢆⣲⣶⣦⣴⣴⣦⠦⣄⣴⢀⠀⠅⠩⠤⢤⡤⠀⠽⠀⣿⣿⡧⠀⠄⣿⣛⣛⣻⠠⣤⡶⡄⢠⢤⣦⠔⣦⡧⣦⠠⠤⠼⠧⠥⣶⠤⠈⣿⣿⣿⡿⣦
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣀⣀⣉⣉⣰⣈⣀⣉⣉⣹⣉⣉⡀⡭⢍⣹⣯⣉⣉⠉⣉⣉⠉⣉⠀⠀⠀⠙⠛⠛⠀⣻⠀⣿⣿⡇⠛⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠪⢌⢹⠕⢬⣿⠿⠷⣿⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠖⣿⣿⣿⣿⣿⡄⠈⠀⢀⢮⠀⠀⠀⠀⢨⠠⠀⠀⡄⡅⣀⠶⠆⠀⠀⣀⣸⣶⣿⠁⡆⠒⠒⠒⠒⠀⣿⠀⣿⣿⣧⣤⣤⣾⣿⣿⣿⣷⣿⣿⣭⣬⣽⣿⣥⣭⣿⣯⡄⠻⣟⣻⣾⣿⣿⡷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣾⣽⣿⣿⣿⣥⣾⣿⣿⣿⣿⣄⣆⣼⣽⣿⣿⣬⣦⣦⣶⣤⣦⡜⡃⡋⠉⠉⠁⠀⢭⠀⣿⣿⣬⣭⣟⣿⣿⣿⣿⣏⣙⣯⣉⣒⣒⣛⣀⣥⣷⣶⣀⣰⣧⣸⣿⣿⣿⣛⣿⣿⣿⣿⣼
⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠲⠷⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⢘⠂⠀⡾⣆⠰⠿⠀⡺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢠⣠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⢉⠉⣉⣿
⡇⠈⠀⠶⠀⣾⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⡇⠀⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⠐⠂⣿
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠚⣿
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣤⡆⠀⠁⠁⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣤⣤⣤
⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣛⣛⣭⡿⡿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⠉⡭⠽⠿⣿⣿⡿⠿⠿⠽⠽⠿⠯⠿⠿⠽⠿⠯⠭⠇⠀⠀⠀⠀
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣯⣿⣶⣶⣦⣥⣤⣤⣤⣤⣤⣀⣑⣠⣀⣀⡀⣁⠀⠀⠀⠀⠀
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀
⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠊⠒⠒⠒⠒⠒⠒⠒⠈⠀⠀⠀⢀⠈⢸⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠂⠒⠒⠂⠀⠒⢤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⠿⠉⠁⠀⠾⠿⠿⠿⠶⠶⠶⠶⠦⠀⠂⠐⠀⠀⠄⠂⠐⠸⡿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⡿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣭⣽⣴⡄⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠅⠀⠑⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣥⣤⣤⣤⣥⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⡉⠻⠻⠿⠻⢻⣿⣟⣟⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⣖⣲⣖⣿⣿⣴⣷⣶⣷⣜⢀⡃⣁⣀⣀⣀⠀⣲⢠⡗⠒⠀⠀⠀⣿⣈⣰⣿⡟⠉⠭⠭⠭⠝⠹⠽⠍⠉⠉⠙⠉⠛⠉⠛⠉⠉⠉⣿⣿⣿⣿⣳
⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠾⠀⡆⣭⣉⣉⠉⠀⢽⠸⡏⠩⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⢩⠍⢉⢍⠉⢉⣛⣉⢉⡍⢻⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠠⢰⣤⣦⣶⣶⡶⣶⣴⣶⣶⢶⡆⣶⣶⣶⣶⣶⠦⢆⣲⣶⣦⣴⣴⣦⠶⣤⣴⢄⠀⠅⠩⠤⢤⡤⠀⠽⠀⣿⣿⡧⠀⠄⣿⣛⣛⣻⠠⣦⣶⡄⢠⢤⣦⠔⣶⣧⣦⠠⠤⠼⠧⠥⣶⠤⠨⣿⣿⣿⡿⣦
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣁⣀⣉⣉⣸⣉⣀⣉⣉⣹⣉⣉⡀⡭⢍⣹⣯⣉⣉⠉⣉⣉⠉⣉⠀⠀⠀⠙⠛⠛⠀⣻⠀⣿⣿⡇⠛⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠺⢌⢻⠗⢿⣿⠿⠷⣿⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠖⣿⣿⣿⣿⣿⡄⠈⠀⢀⢮⠀⠀⠀⠀⢨⠠⠀⠀⡄⡅⣀⠶⠆⠀⠀⣀⣸⣶⣿⠁⡆⠒⠒⠒⠒⠀⣿⠀⣿⣿⣧⣤⣤⣾⣿⣿⣿⣷⣿⣿⣯⣬⣿⣿⣥⣽⣿⣿⡄⠻⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣯⣾⣽⣿⣿⣿⣥⣿⣿⣿⣿⣿⣄⣆⣼⣽⣿⣿⣬⣦⣶⣶⣴⣦⡜⡃⡋⠉⠉⠁⠀⢭⠀⣿⣿⣬⣭⣟⣿⣿⣿⣿⣏⣙⣯⣉⣒⣚⣛⣀⣥⣷⣶⣀⣰⣧⣸⣿⣿⣿⣛⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠒⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⢘⠂⠀⡶⠂⠐⠷⠀⡺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢠⣠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⢉⠉⣿⣿
⡇⠈⠀⠶⠀⣾⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⡇⠀⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡂⢀⣶⡟⠛
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⣿⡇⠀
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣤⡆⢘⣿⡏⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢠⣿⡇⠀
⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢘⣿⡇⠀
⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠿⣧⣤
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣛⣛⣭⡿⡿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⠉⡭⠽⠿⣯⣿⡿⠿⠿⠽⠭⠿⠯⠭⠿⠭⠽⠯⠭⠇⠀⠀⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣼⣿⣯⣷⣶⣶⣤⣥⣤⣤⣤⣤⣤⣀⣑⣀⣀⣀⡀⢁⠀⠀⠀⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣿⣿
⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠊⠒⠒⠒⠒⠒⠒⠒⠈⠀⠀⠀⢀⠈⠸⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠂⠒⠒⠂⠀⠒⢤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⠿⠉⠁⠀⠾⠿⠿⠿⠶⠶⠶⠶⠦⠀⠂⠐⠀⠀⠄⠂⠐⠸⡿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⡿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣭⣽⣴⡄⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠅⠀⠑⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣥⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡉⠛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣻⣛⣛⣛⣛⣛⣓⣒⣒⣒⣛⣛⣐⣓⣐⣓⣘⢀⡃⣁⣀⣀⣀⠀⣲⢠⡗⠒⠀⠀⠀⣿⣈⣰⣿⡏⠉⠭⠭⠭⠝⠹⠽⠍⠉⠉⠙⠉⠛⠉⠛⠉⠉⠉⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠶⠀⡆⣭⣉⡉⠉⠀⢽⠘⡏⠩⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⢩⠉⠉⢍⠉⢉⣛⣉⠉⡍⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⢰⣤⣤⣴⣴⡶⣶⣴⣶⣶⢶⡆⣶⣶⣶⣶⣶⠦⢆⣲⣶⣦⣴⣴⣦⠦⣄⣴⢀⠀⠅⠩⠤⢤⠤⠀⠽⠀⣿⣿⡧⠀⠄⣿⣛⣛⣻⠠⣤⡶⡄⢠⢤⣦⠔⣦⡧⣦⠠⠤⠼⠧⠥⣶⠤⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣶⣿⣶⣿⣷⣀⣀⣉⣉⣰⣀⣀⣉⣉⣹⣉⣀⡀⠍⢍⣹⣯⣉⣉⠉⣉⣉⠉⣉⠀⠀⠀⠙⠛⠛⠀⣻⠀⣿⣿⡇⠛⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠪⢌⢹⠕⢬⣿⠿⠷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠖⣿⣿⣿⣿⣿⡀⠈⠀⢀⢮⠀⠀⠀⠀⢨⠠⠀⠀⠄⡄⣀⠶⠆⠀⠀⣀⣸⣶⣿⠁⡆⠒⠒⠒⠒⠀⣿⠀⣿⣿⣧⣤⣤⣾⣿⣿⣿⣷⣿⣿⣭⣬⣽⣿⣥⣭⣿⣯⡄⠻⣟⣻⣾⣿⣿⡷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣾⣽⣿⣿⣿⣥⣾⣿⣿⣿⣿⣄⣆⣼⣽⣿⣿⣬⣦⣤⣴⣤⣦⡜⡃⡋⠉⠉⠁⠀⢭⠀⣿⣿⣬⣭⣟⣿⣿⣿⣿⣏⣙⣯⣉⣒⣒⣛⣀⣥⣷⣦⣀⣰⣧⣸⣿⣿⣿⣛⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣃⣀⣐⣀⣀⣀⣀⣺⣼⣿⣇⣢⣂⣀⣀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠒⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⢘⠂⠀⡶⠂⠐⠷⠀⡺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢠⣠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⢉⠉⣿⣿
⡇⠈⠀⠶⠀⣾⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⡇⠀⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡂⢀⣶⡟⠛
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⣿⡇⠀
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣤⡆⢘⣿⡏⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢠⣿⡇⠀
⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢘⣿⡇⠀
⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠿⣧⣤
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣛⣛⣭⡿⡿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⠉⡭⠽⠿⣯⣿⡿⠿⠿⠽⠭⠿⠯⠭⠿⠭⠽⠯⠭⠇⠀⠀⣿⣿
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣼⣿⣯⣷⣶⣶⣤⣥⣤⣤⣤⣤⣤⣀⣑⣀⣀⣀⡀⢁⠀⠀⠀⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣿⣿
⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠊⠒⠒⠒⠒⠒⠒⠒⠈⠀⠀⠀⢀⠈⠸⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠂⠒⠒⠂⠀⠒⢤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⠿⠉⠁⠀⠾⠿⠿⠿⠶⠶⠶⠶⠦⠀⠂⠐⠀⠀⠄⠂⠐⠸⡿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⡿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣭⣽⣴⡄⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠅⠀⠑⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣥⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡉⠛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣻⣛⣛⣛⣛⣛⣓⣒⣒⣒⣛⣛⣐⣓⣐⣓⣘⢀⡃⣁⣀⣀⣀⠀⣲⢠⡗⠒⠀⠀⠀⣿⣈⣰⣿⡏⠉⠭⠭⠭⠝⠹⠽⠍⠉⠉⠙⠉⠛⠉⠛⠉⠉⠉⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠶⠀⡆⣭⣉⡉⠉⠀⢽⠘⡏⠩⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⢩⠉⠉⢍⠉⢉⣛⣉⠉⡍⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⢰⣤⣤⣴⣴⡶⣶⣴⣶⣶⢶⡆⣶⣶⣶⣶⣶⠦⢆⣲⣶⣦⣴⣴⣦⠦⣄⣴⢀⠀⠅⠩⠤⢤⠤⠀⠽⠀⣿⣿⡧⠀⠄⣿⣛⣛⣻⠠⣤⡶⡄⢠⢤⣦⠔⣦⡧⣦⠠⠤⠼⠧⠥⣶⠤⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣶⣿⣶⣿⣷⣀⣀⣉⣉⣰⣀⣀⣉⣉⣹⣉⣀⡀⠍⢍⣹⣯⣉⣉⠉⣉⣉⠉⣉⠀⠀⠀⠙⠛⠛⠀⣻⠀⣿⣿⡇⠛⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠪⢌⢹⠕⢬⣿⠿⠷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠖⣿⣿⣿⣿⣿⡀⠈⠀⢀⢮⠀⠀⠀⠀⢨⠠⠀⠀⠄⡄⣀⠶⠆⠀⠀⣀⣸⣶⣿⠁⡆⠒⠒⠒⠒⠀⣿⠀⣿⣿⣧⣤⣤⣾⣿⣿⣿⣷⣿⣿⣭⣬⣽⣿⣥⣭⣿⣯⡄⠻⣟⣻⣾⣿⣿⡷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣾⣽⣿⣿⣿⣥⣾⣿⣿⣿⣿⣄⣆⣼⣽⣿⣿⣬⣦⣤⣴⣤⣦⡜⡃⡋⠉⠉⠁⠀⢭⠀⣿⣿⣬⣭⣟⣿⣿⣿⣿⣏⣙⣯⣉⣒⣒⣛⣀⣥⣷⣦⣀⣰⣧⣸⣿⣿⣿⣛⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠃⣀⡐⠀⠀⠀⠀⡚⢸⣿⢇⣢⢂⡀⠀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠒⠶⠶⠂⠀⠀⠀⠀⠀⠀⠂⠀⠐⠐⠓⠐⠒⠒⠐⠂⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣉⣉⣁⣉⣀⣀⣀
⡇⢰⣤⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠃⠀⠀⠀⠘⠀⠀⠀⠀⠀⡀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠃⠁⠉⠉⠙⠉⠛⠙⡛
⡇⠈⠀⠶⠀⣺⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⣀⣛⣛⣛⣛⣀⣀⣀⣀⣐⣂⣒⣇⣀⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣑⣂⣀⣦⣄⠛
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣛⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢟⣥⠿⠟⠂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⢛⡏⢟⣁⡠⠀
⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠻⣿⣶⣿⣿⣿⣷⡆
⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣼⣿⣵⣿⣾⣿⣿⣿⣿⣿⣿⣇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣯⣿⣿⣿⡿⣿⣿⣟⠛⠥⢝⣉⣛⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣽⣿⡇
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣛⣛⣻⣙⣛⣛⣻⡻⠟⠛⣛⣷
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣿⣿
⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠊⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⢀⠈⠸⣿⣿⣭⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠂⠒⠒⠂⠀⠒⠠⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⠿⠉⠁⠀⠾⠿⠿⠷⠶⠶⠶⠶⠦⠀⠂⠐⠀⠀⠄⠀⠐⠘⡿⠿⠿⠿⠿⣿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣭⣽⣴⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠅⠀⠑⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡉⠛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣚⣛⣛⣛⣛⣛⣓⣒⣒⣒⣓⣛⣐⣓⣐⣓⣈⢀⡃⣁⣀⣀⣀⠀⣲⠀⡗⠒⠀⠀⠀⣿⣈⣰⣿⡏⠉⠭⠭⠩⠝⠹⠽⠍⠉⠉⠙⠉⠛⠉⠛⠉⠉⠉⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠶⠀⡆⣭⣉⡉⠉⠀⢵⠀⡏⠉⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠩⠉⠉⠍⠉⢉⣙⡉⠉⡍⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⢠⣄⣤⣄⣰⠶⠶⣴⣶⣶⢶⠆⢶⣶⣶⣶⣶⠦⠆⣲⣶⣦⣴⣴⣦⠤⣄⣤⢀⠀⠅⠉⠤⠤⠤⠀⠽⠀⣿⣿⡧⠀⠄⣿⣛⣛⣻⠀⠠⠦⠄⠠⠤⠦⠐⡦⠧⠢⠠⠤⠬⠧⠁⣤⠤⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⣷⣀⣀⣀⣀⣰⣀⣀⣀⣀⣰⣀⣀⡀⠄⢌⣹⣍⣉⣉⠉⣉⣉⠉⣉⠀⠀⠀⠘⠛⠛⠀⣻⠀⣿⣿⡇⠛⠀⢸⣿⣿⣿⣻⣿⣿⣟⣿⣿⣿⣟⣿⣿⣿⠢⢌⢹⠄⢤⣯⠼⠧⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠒⣿⣿⣿⣿⣿⡀⠈⠀⢀⢬⠀⠀⠀⠀⢨⠠⠀⠀⠀⡀⣀⠶⠆⠀⠀⢀⣸⡶⠿⠁⡆⠒⠒⠒⠒⠀⣿⠀⣿⣿⣧⣤⣤⣾⣿⣿⣿⣗⣽⣿⣥⣤⣽⣯⣤⣬⣿⣦⡀⠻⣟⣫⣾⣿⣿⡶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣴⣾⣶⣷⣾⣧⣾⣽⣿⣿⣿⣥⣾⣿⣿⣿⣿⣄⣆⣸⣽⣿⣿⣨⣦⣤⣤⣤⣤⠘⡃⡋⠉⠉⠁⠀⢍⠀⣿⣿⣬⣭⣟⣿⣿⣿⣿⣇⣑⣦⣉⣐⣒⣐⣀⣥⣷⣦⣀⣰⣧⣸⣟⣿⣟⣛⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠃⣀⡐⠀⠀⠀⠀⡚⢸⣿⢇⣢⢂⡀⠀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠒⠶⠶⠂⠀⠀⠀⠀⠀⠀⠂⠀⠐⠐⠓⠐⠒⠒⠐⠂⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣉⣉⣁⣉⣀⣀⣀
⡇⢰⣤⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠃⠀⠀⠀⠘⠀⠀⠀⠀⠀⡀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠃⠁⠉⠉⠙⠉⠛⠙⡛
⡇⠈⠀⠶⠀⣺⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⣀⣛⣛⣛⣛⣀⣀⣀⣀⣐⣂⣒⣇⣀⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣑⣂⣀⣦⣄⠛
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣛⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢟⣥⠿⠟⠂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⢛⡏⢟⣁⡠⠀
⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠻⣿⣶⣿⣿⣿⣷⡆
⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣼⣿⣵⣿⣾⣿⣿⣿⣿⣿⣿⣇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣯⣿⣿⣿⡿⣿⣿⣟⠛⠥⢝⣉⣛⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣽⣿⡇
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣛⣛⣻⣙⣛⣛⣻⡻⠟⠛⣛⣷
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣿⣿
⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠊⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⢀⠈⠸⣿⣿⣭⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠂⠒⠒⠂⠀⠒⠠⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⠿⠉⠁⠀⠾⠿⠿⠷⠶⠶⠶⠶⠦⠀⠂⠐⠀⠀⠄⠀⠐⠘⡿⠿⠿⠿⠿⣿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣭⣽⣴⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠅⠀⠑⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡉⠛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣚⣛⣛⣛⣛⣛⣓⣒⣒⣒⣓⣛⣐⣓⣐⣓⣈⢀⡃⣁⣀⣀⣀⠀⣲⠀⡗⠒⠀⠀⠀⣿⣈⣰⣿⡏⠉⠭⠭⠩⠝⠹⠽⠍⠉⠉⠙⠉⠛⠉⠛⠉⠉⠉⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠶⠀⡆⣭⣉⡉⠉⠀⢵⠀⡏⠉⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠩⠉⠉⠍⠉⢉⣙⡉⠉⡍⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⢠⣄⣤⣄⣰⠶⠶⣴⣶⣶⢶⠆⢶⣶⣶⣶⣶⠦⠆⣲⣶⣦⣴⣴⣦⠤⣄⣤⢀⠀⠅⠉⠤⠤⠤⠀⠽⠀⣿⣿⡧⠀⠄⣿⣛⣛⣻⠀⠠⠦⠄⠠⠤⠦⠐⡦⠧⠢⠠⠤⠬⠧⠁⣤⠤⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⣷⣀⣀⣀⣀⣰⣀⣀⣀⣀⣰⣀⣀⡀⠄⢌⣹⣍⣉⣉⠉⣉⣉⠉⣉⠀⠀⠀⠘⠛⠛⠀⣻⠀⣿⣿⡇⠛⠀⢸⣿⣿⣿⣻⣿⣿⣟⣿⣿⣿⣟⣿⣿⣿⠢⢌⢹⠄⢤⣯⠼⠧⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠒⣿⣿⣿⣿⣿⡀⠈⠀⢀⢬⠀⠀⠀⠀⢨⠠⠀⠀⠀⡀⣀⠶⠆⠀⠀⢀⣸⡶⠿⠁⡆⠒⠒⠒⠒⠀⣿⠀⣿⣿⣧⣤⣤⣾⣿⣿⣿⣗⣽⣿⣥⣤⣽⣯⣤⣬⣿⣦⡀⠻⣟⣫⣾⣿⣿⡶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣴⣾⣶⣷⣾⣧⣾⣽⣿⣿⣿⣥⣾⣿⣿⣿⣿⣄⣆⣸⣽⣿⣿⣨⣦⣤⣤⣤⣤⠘⡃⡋⠉⠉⠁⠀⢍⠀⣿⣿⣬⣭⣟⣿⣿⣿⣿⣇⣑⣦⣉⣐⣒⣐⣀⣥⣷⣦⣀⣰⣧⣸⣟⣿⣟⣛⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠃⣀⡐⠀⠀⠀⠀⡚⢸⣿⢇⣢⢂⡀⠀
⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠒⠶⠶⠂⠀⠀⠀⠀⠀⠀⠂⠀⠐⠐⠓⠐⠒⠒⠐⠂⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣉⣉⣁⣉⣀⣀⣀
⡇⢰⣤⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠃⠀⠀⠀⠘⠀⠀⠀⠀⠀⡀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠃⠁⠉⠉⠙⠉⠛⠙⡛
⡇⠈⠀⠶⠀⣺⣿⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⣀⣛⣛⣛⣛⣀⣀⣀⣀⣐⣂⣒⣇⣀⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣑⣂⣀⣦⣄⠛
⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣛⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢟⣥⠿⠟⠂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⢛⡏⢟⣁⡠⠀
⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠻⣿⣶⣿⣿⣿⣷⡆
⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣼⣿⣵⣿⣾⣿⣿⣿⣿⣿⣿⣇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣯⣿⣿⣿⡿⣿⣿⣟⠛⠥⢝⣉⣛⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣽⣿⡇
⣧⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣛⣛⣻⣙⣛⣛⣻⡻⠟⠛⣛⣷
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣿⣿
⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠊⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⢀⠈⠸⣿⣿⣭⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠂⠒⠒⠂⠀⠒⠠⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⠿⠉⠁⠀⠾⠿⠿⠷⠶⠶⠶⠶⠦⠀⠂⠐⠀⠀⠄⠀⠐⠘⡿⠿⠿⠿⠿⣿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣭⣽⣴⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠅⠀⠑⠂⢒⣀⠂⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡉⠛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣚⣛⣛⣛⣛⣛⣓⣒⣒⣒⣓⣛⣐⣓⣐⣓⣈⢀⡃⣁⣀⣀⣀⠀⣲⠀⡗⠒⠀⠀⠀⣿⣈⣰⣿⡏⠉⠭⠭⠩⠝⠹⠽⠍⠉⠉⠙⠉⠛⠉⠛⠉⠉⠉⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠶⠀⡆⣭⣉⡉⠉⠀⢵⠀⡏⠉⡀⠶⣀⣹⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠩⠉⠉⠍⠉⢉⣙⡉⠉⡍⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⢠⣄⣤⣄⣰⠶⠶⣴⣶⣶⢶⠆⢶⣶⣶⣶⣶⠦⠆⣲⣶⣦⣴⣴⣦⠤⣄⣤⢀⠀⠅⠉⠤⠤⠤⠀⠽⠀⣿⣿⡧⠀⠄⣿⣛⣛⣻⠀⠠⠦⠄⠠⠤⠦⠐⡦⠧⠢⠠⠤⠬⠧⠁⣤⠤⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⣷⣀⣀⣀⣀⣰⣀⣀⣀⣀⣰⣀⣀⡀⠄⢌⣹⣍⣉⣉⠉⣉⣉⠉⣉⠀⠀⠀⠘⠛⠛⠀⣻⠀⣿⣿⡇⠛⠀⢸⣿⣿⣿⣻⣿⣿⣟⣿⣿⣿⣟⣿⣿⣿⠢⢌⢹⠄⢤⣯⠼⠧⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠒⣿⣿⣿⣿⣿⡀⠈⠀⢀⢬⠀⠀⠀⠀⢨⠠⠀⠀⠀⡀⣀⠶⠆⠀⠀⢀⣸⡶⠿⠁⡆⠒⠒⠒⠒⠀⣿⠀⣿⣿⣧⣤⣤⣾⣿⣿⣿⣗⣽⣿⣥⣤⣽⣯⣤⣬⣿⣦⡀⠻⣟⣫⣾⣿⣿⡶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣴⣾⣶⣷⣾⣧⣾⣽⣿⣿⣿⣥⣾⣿⣿⣿⣿⣄⣆⣸⣽⣿⣿⣨⣦⣤⣤⣤⣤⠘⡃⡋⠉⠉⠁⠀⢍⠀⣿⣿⣬⣭⣟⣿⣿⣿⣿⣇⣑⣦⣉⣐⣒⣐⣀⣥⣷⣦⣀⣰⣧⣸⣟⣿⣟⣛⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3616

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/Today_in_Techrights.shtml
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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Today in
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posted by Roy Schestowitz on Jan 13, 2025


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


⚓  Updated This Past Day⠀⇛


   1. ⚓ Gemini_Links_12/01/2025:_No_Country_For_Old_Men,_Burned_Homes,_and
      "Planet_P_is_Clean"⠀⇛


           Links for the day


   2. ⚓ Slopwatch:_Brittany_Day_and_Brian_Fagioli_Are_Still_at_It,
      Googlebombing_"Linux"_With_LLM_Slop_(Taking_Away_Traffic_From_the
      Articles_They're_Plagiarising)⠀⇛


           Some more sites that used to cover GNU/Linux have turned into
           slopfarms


   3. ⚓ [Meme]_Being_High_on_Drugs_Isn't_Happiness_(Likewise,_Being_a_"Star"_in
      Social_Control_Media_is_Temporary)⠀⇛


           Many entities - or people - will regret telling everybody
           "follow me on Twitter"


      ⚓  New⠀⇛


   4. ⚓ Bots_Covering_Debian_Releases⠀⇛


           It would be quite safe to guess that chatbots were at least
           partly leveraged for that text


   5. ⚓ Links_12/01/2025:_Microsoft_Admits_It's_Laying_Off_Staff_Only_Where
      Staff_is_"Expensive"_(Race_to_the_Bottom)⠀⇛


           Links for the day


   6. ⚓ [Meme]_They_Say_That_RMS_Says_the_"F"_Word_(Freedom)_Too_Much...⠀⇛


           About 32.7k US dollars are now left for the FSF to raise (in 6
           days)


   7. ⚓ Links_12/01/2025:_More_Sanctions_Against_Russia,_SCOTUS_Signals
      Fentanylware_(TikTok)_Ban_Will_Stay⠀⇛


           Links for the day


   8. ⚓ [Meme]_A_Jihad_Against_Servers_the_User_Controls⠀⇛


           We need to strive for and work towards greater control by users
           over "their" servers


   9. ⚓ Microsoft_Azure-Only_Bugs_in_"Linux"_Can_"Compromise_the_System."⠀⇛


           From ubuntu.com and linux.org a few days ago


  10. ⚓ Over_at_Tux_Machines...⠀⇛


           GNU/Linux news for the past day


  11. ⚓ IRC_Proceedings:_Saturday,_January_11,_2025⠀⇛


           IRC logs for Saturday, January 11, 2025


  12. ⚓ Gemini_Links_12/01/2025:_DHL_Express_Does_Not_Deliver,_Oddmuse_Update⠀⇛


           Links for the day


      =========================================================================
      The corresponding text-only bulletin for Sunday contains all the text.
      Top-read articles (excluding bot/crawler visits):


                          Span from 2025-01-06 to 2025-01-12
      2678 /n/2025/01/06/Fedora_Seems_to_be_Dying_of_Neglect_by_IBM.shtml


      2066 /n/2025/01/08/
           Communications_Assistance_for_Law_Enforcement_Act_CALEA_is_a_Fa.shtml


      1948 /n/2025/01/07/Microsoft_Continues_to_Attack_Users_Choice.shtml


      1533 /n/2025/01/11/
           Microsoft_in_Trouble_as_Azure_Breaks_and_Only_Days_After_Promis.shtml


      1189 /n/2025/01/10/More_IBM_Layoffs_2025.shtml


      944  /n/2025/01/08/
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      791  /n/2024/12/21/
           On_BetaNews_Latest_Technology_News_We_are_moderately_confident_.shtml


      760  /n/2025/01/07/
           In_Europe_Russia_s_Yandex_About_to_Become_Bigger_Than_Microsoft.shtml


      717  /n/2025/01/06/
           British_Police_Register_a_New_Account_With_Unscrupulous_America.shtml


      679  /n/2025/01/09/Computers_as_a_Heat_Source.shtml


      669  /n/2025/01/07/
           All_the_Latest_Articles_in_This_Fake_News_Site_Are_SPAM_LLM_Slo.shtml


      666  /n/2025/01/09/
           Free_Software_Cannot_Rely_on_Politicians_They_Don_t_Even_Care_A.shtml


      590  /n/2025/01/09/
           Sometimes_the_EFF_Prefers_to_Talk_About_Sex_Not_Tech_or_Unneces.shtml


      584  /n/2024/12/30/
           In_2024_Under_Linux_Foundation_Management_Linux_com_Produced_an.shtml


      578  /n/2025/01/10/
           Guardian_Digital_Inc_linuxsecurity_com_is_Again_Spamming_or_Goo.shtml


      575  /browse/latest.shtml


      553  /n/2025/01/08/
           Amid_Mass_Layoffs_at_Microsoft_2025_Executives_Flock_to_Google.shtml


      535  /n/2025/01/08/
           Engagement_in_Microsoft_GitHub_Falls_Expect_More_Layoffs_and_Of.shtml


      531  /n/2025/01/04/
           What_Would_Dennis_Ritchie_Say_About_the_Memory_Safe_Hype_or_Car.shtml




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⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠴⢕⠂⠁⣴⡄⠀⠀⠀⠀⢈⠀⢀⡀⣾⣯⢼⣷⡇⠀⠀⡙⢋⣖⠂⠀⠀⠀⠠⢗⡙⢇⢷⢴⡽⢳⣧⣶⣀⠛⠙⢋⠕⣒⣹⣆⣙⣿⣤⣰⣶⠸⠟⣏⠇⠀⠒⢏⣤⣶⣿⣿⣷⣿⣳⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢨⡁⠠⢷⠄⣚⢡⣽⡇⠀⠀⠀⠀⠄⠀⠀⣵⣿⡟⠉⢁⠠⠰⣶⡖⡿⢫⠀⠀⠠⣼⣹⣼⣇⡘⡻⣾⣧⣷⡏⠁⢔⣷⡚⠥⠸⣉⣴⡿⣿⣿⢓⢿⡯⠁⡤⠀⠀⣤⣶⠅⢉⠋⢴⣿⣶⣷⢶⡂⢘⣁
⠀⠀⡀⠀⠀⠀⠙⠰⠍⣯⢦⡷⠀⠈⠵⡅⠀⢒⣀⠀⠸⢆⣈⣥⣿⣷⣦⣿⣶⣿⣿⣛⣤⣂⣘⡀⡀⠙⣛⢟⣿⣿⣽⣥⣶⢠⢳⣖⠈⠁⢂⣦⠰⠏⣻⡧⠽⡋⢀⠙⢻⣟⢃⣶⡢⢄⢙⣀⢴⡼⠿⣿⠿⢿⡿⠃⠎⠉
⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⣹⢿⣧⣴⣷⢿⣺⣿⣼⣇⠑⠀⠛⢛⣻⣿⣿⣿⣿⣿⣿⣟⠿⠸⠿⠙⠀⠀⢀⣼⠋⠩⠈⠛⣇⣼⣾⣻⣾⣿⡟⣿⣿⣶⢽⢟⣿⣷⣿⣲⠉⠀⢺⣿⣧⡶⠟⠃⠚⣿⡏⠶⢒⡠⢤⣶⣿⣛
⠀⠀⠀⠀⠀⡀⠄⠀⢀⠀⣜⣅⠖⡖⣄⢸⣽⠻⢿⡿⣗⣷⣄⣔⣿⣿⣿⣿⣿⣿⣿⣿⣗⣦⣬⠷⣤⡶⢾⣅⠒⠖⢳⣌⣽⣹⠿⡯⣿⣿⣿⠟⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⢶⡒⢓⣷⢷⡶⣾⣜⣖⢁⣛
⢀⣤⠤⠀⡀⠀⠀⠠⡬⠛⠾⠿⠿⢽⣨⠀⠠⣦⡉⠀⠋⠛⠛⠄⠁⠘⠿⢿⣿⣿⣿⣯⣿⣿⠇⢰⣟⣁⣜⠈⢏⡀⣾⣿⣿⣿⣦⣠⡿⢧⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⢻⣿⣿⣿⡋⢻⢳⢺
⠁⠀⡄⠁⠢⠒⡎⡀⠁⠑⠁⠀⠈⠁⠈⠁⢄⣁⠀⠂⠀⠀⠀⠀⠀⠈⠀⠐⠃⠛⠻⣿⡿⣿⣷⣿⣿⣿⣶⡤⢀⢨⠶⠷⠟⠉⠉⠉⣰⣿⣿⣋⡔⣻⠻⢋⣿⣿⠛⠻⣿⣟⢿⣿⣛⣿⣷⣿⣿⣿⣿⣿⣿⡟⠏⠰⢽⡟
⠉⠀⠀⢖⠶⠒⠓⠁⠀⠀⠀⠀⡀⢀⠠⣠⡔⠔⠛⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢿⣿⢽⣿⣿⡟⢙⣿⣡⡠⣴⡆⠲⠂⠀⣰⣿⣿⣿⣁⢳⣟⣢⣿⠏⣴⣿⣷⣶⣿⣦⡈⠻⣏⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣾
⠂⠀⠮⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⡙⠂⠴⢄⣄⠀⡫⢦⠀⠂⠄⣀⠀⠀⡀⣀⡀⠈⠿⣐⠚⠉⠙⠽⢭⢿⠫⡿⠴⠘⠉⣀⣤⣾⣿⣿⣾⣿⣿⣿⣿⡟⢁⣰⠿⠿⠿⣿⣿⡿⢿⡀⢹⣷⣿⣾⣿⣿⣿⢿⣿⣿⠾⠟⡿
⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠆⣤⣌⡀⠐⠉⠈⠁⠀⠰⢀⠀⠀⡨⣽⡛⠉⢩⣿⣄⣠⡀⠐⢖⢢⣄⢠⣤⠀⢍⣀⣰⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣷⣤⣾⣿⣿⣾⣿⡷⠀⣿⣿⣿⢿⣿⣿⣿⣩⣷⣾⣯⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣴⡥⠤⠀⠀⠀⠀⡀⠀⠀⠈⢡⣧⣀⣀⣀⣉⣿⣹⣿⣷⣼⣿⣷⣾⢷⣴⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣧⠀⠩⣿⣿⣟⠿⢿⣿⡿⠇⢸⣿⣟⣿⣿⣏⣚⣿⣿⣿⣹⠿⢻
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣤⣤⣵⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣦⢻⣿⣿⣿⣷⡄⠘⡯⠙⠓⠐⠻⢃⣴⣿⣿⣿⣿⢺⠯⢿⣽⣿⡏⣿⡇⢹
⠀⢴⡀⠀⠀⡀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣧⠀⢠⣴⣶⣶⡄⢼⣿⣿⣿⣿⣷⣼⣩⠈⢛⡶⡏⡟⠀⠠
⠀⠘⠀⠉⠀⠀⠀⠀⠈⢵⣾⣿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣇⠂⠀⠛⡟⠛⠙⣿⣿⣿⢿⢛⡏⢿⣿⣦⢹⢯⣹⡷⣤⣝
⠄⢠⠄⠄⠄⠒⣤⣀⢰⣿⣟⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣠⣷⡇⠀⠀⣧⣿⢯⡝⢶⣿⣿⢶⣙⣬⣺⣿⡵⠟⠥
⠀⠀⠀⠠⢦⢠⡁⠀⣿⣿⡏⠀⣰⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠏⢹⣿⡷⢿⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⡃⠀⢐⢹⢻⣷⡄⡧⠳⢻⣿⣿⠓⠍⠁⣉⠀⠒
⠂⠀⠀⠈⠁⠀⠀⠀⣿⣿⠀⢀⡿⠀⣼⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠓⠀⠉⠉⠛⠛⠿⠟⠟⠚⠠⢀⠉⠉⠛⠛⠀⣿⣿⣿⣿⣟⠙⣿⣿⣮⢹⣿⣿⣿⣿⣷⣿⡆⣺⣧⣿⣿⣻⣶⣿⣿⣟⣤⢦⡘⠱⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢼⠁⠀⠺⡇⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠶⠒⠶⠿⣿⣿⣿⣿⣷⣌⡛⢿⣷⡙⣿⡇⢻⣯⡟⢾⣿⣙⣿⣿⣟⢻⣿⢿⠟⠋⠇⢭⠉⠄⠀
⠀⢀⠀⠀⠀⠀⠀⠀⣿⣿⠆⣃⠀⠀⠀⠀⠀⠈⠙⠃⢹⣿⣿⣿⣿⣏⠋⠀⣀⠀⠘⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡛⠁⣄⠙⠛⢾⡇⢺⠋⢀⠈⢹⣿⢿⣿⣗⣴⣦⣴⣦⠰⠬⣠⣼⡆⠣
⠀⠀⠠⢀⣶⣶⠴⠠⣿⣿⡷⠋⠀⠀⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠯⠀⠀⠂⠀⠀⠀⠀⠀⠈⠁⠀⠒⠒⠐⡀⠐⠒⢤⡀⢰⣿⡿⢿⣿⣿⣿⣿⣷⣤⠀⠀⢀⠇⠉⠀⢶⡰⢞⣿⢾⣿⣿⣿⣿⣿⣇⠟⠀⠉⠀⠁⠞
⢂⡀⣠⣼⣭⠁⠀⠈⣿⣿⠁⠀⠀⠀⠀⠀⢀⡠⣒⣿⢻⣿⣿⣿⣟⣤⣴⣤⣀⣀⠀⣀⢀⠀⠀⠀⡀⠀⣠⣾⣿⡀⠀⠀⠀⠉⢉⣠⣼⣿⣿⣿⣿⣿⣿⣧⠀⢒⣆⣐⣿⣼⣷⡶⢻⣿⡿⠿⢿⣛⣛⡋⢆⢤⣄⠀⠀⠀
⠀⠀⠀⠁⡉⠁⠐⠈⣿⣿⠋⠀⠀⠀⠀⢰⠞⠿⣿⣿⣿⣿⢁⠀⠘⠂⠐⠭⠿⠟⠘⠋⠽⡤⠉⠈⡛⠂⠀⠁⣿⡆⠀⠀⠀⣠⢊⣡⡟⢻⡿⣿⣿⣿⣿⣿⢄⡝⠟⣾⣿⡏⠀⠈⠉⠙⠃⠀⡉⢿⠉⡣⢞⢙⠏⠃⠀⠀
⠀⢀⠀⠰⣕⡊⠓⢸⣿⡟⠀⢠⣾⡢⢻⣡⣠⣁⣹⣿⣿⣿⣿⣷⡵⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠠⢸⣿⣆⠀⠀⡴⠁⠆⡀⠄⡀⠻⠹⠿⣿⣿⣿⣆⠙⣛⣥⣼⣶⣆⠀⠀⠀⠀⠈⠀⠀⢁⠀⡳⡟⠙⠻⠀⢲
⠞⠒⠲⠞⠩⢘⣷⣿⠟⠁⢀⡞⢸⣾⣿⣵⣮⠍⠁⠙⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠰⡰⢆⣾⣿⠃⠀⠰⢃⠀⠀⠀⠀⠄⠀⠐⠄⢺⣿⣿⣿⠈⠈⠁⠂⠄⠈⠀⠀⠂⠀⠀⠀⠄⠘⠀⠻⢮⡌⠀⢐⠸
⡁⢱⣾⣛⣿⣿⢟⣡⢤⠀⠺⠿⠿⢷⡧⠈⠛⠀⠀⠀⠈⠛⠿⣿⣿⣿⣶⣶⣶⣦⡤⣀⣥⣤⡶⣾⠐⠀⠠⢹⠛⢿⣻⣍⣁⠉⠀⠈⠀⠀⠀⠀⢸⠿⣿⣿⣿⣦⣀⣄⡀⠀⠀⠀⠉⡙⠀⠄⠀⠀⠀⠀⠀⠀⠕⢅⡐⠀
⠈⠙⠃⢐⠒⠒⡚⠶⠿⠶⠶⠶⢶⣶⣧⣴⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣅⣠⠀⠀⠀⠀⢘⠁⠱⠞⡂⠘⢋⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠞⣇⢠
⠀⠀⠁⠉⠁⠈⠉⠀⠁⠉⣭⣝⣛⣗⣳⣾⣿⣶⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⡀⡠⡠⢀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣍
⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠟⠿⠿⠿⠏⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠠⠴⣧⣅⠀⠘⠘⣇⠠⠐⠂⠉

                    ䷩ 𝚕𝚒𝚗𝚎 3831

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/today_s_howtos.1.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/today_s_howtos.1.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ today's
howtos⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 13, 2025


    * ⚓ The New Stack ☛ Linux:_How_To_Install_Apps_From_the_Source⠀⇛


           When I first started using Linux, there was one way to install
           applications… from the original source code.


    * ⚓ Linux Capable ☛ How_to_Install_DeaDBeeF_on_GNU/Linux_Mint_22,_21_or
      20⠀⇛


    * ⚓ Barry Kauler ☛ Partial_fix_for_JWM_blurry_wallpaper⠀⇛


           The problem was reported by SteveS:


           https://forum.puppylinux.com/viewtopic.php?t=13561


           I do get this blurry-wallpaper problem at shutdown, when a
           window asks whether you want to save the session. That happens
           because ROX-Filer has exited and fallback is to the wallpaper
           provided by JWM. I have fixed that, so I get nice JWM wallpaper
           at shutdown: [...]


    * ⚓ Peter N M Hansteen ☛ That_grumpy_BSD_guy:_Harvesting_the_Noise_While
      it's_Fresh,_Revisited⠀⇛


           After a while I started extracting the potential new spamtraps
           from the greylist — actually dumping data from there once per
           hour as part of the script that also generated the exported
           blocklist. The basic process is described in the July 25 2007
           article Harvesting the noise while it's still fresh; SPF found
           potentially useful (also available trackerless but with links
           to tracked articles).


           Then today it struck me that while that method is useful, by
           extracting only from the greylist we will only ever collect the
           address from the initial connections. Any addresses attempted
           after the miscreants enter the blocklist will simply not be
           recorded there.


           This of course lead to the question: What did we miss?


    * § idroot⠀➾


          o ⚓ ID Root ☛ How_To_Install_Enlightenment_Desktop_on_Fedora_41⠀⇛


                 Enlightenment Desktop, sometimes called the “E Desktop”
                 or Enlightenment Window Manager, is a lightweight and
                 highly customizable desktop environment best known for
                 its speed, versatility, and visually stimulating
                 interface. For Fedora 41 (F41) users seeking a full-
                 featured yet resource-efficient environment, installing
                 Enlightenment can help transform daily computing into a
                 faster and more responsive experience.


          o ⚓ ID Root ☛ How_To_Install_OpenCV_on_Manjaro⠀⇛


                 OpenCV (Open Source Computer Vision Library) is a
                 powerful tool for computer vision and image processing.
                 It provides a comprehensive set of functionalities for
                 real-time computer vision applications. This guide will
                 walk you through the process of installing OpenCV on
                 Manjaro, a popular user-friendly GNU/Linux distribution
                 that is based on Arch Linux.


          o ⚓ ID Root ☛ How_To_Install_Enlightenment_Desktop_on_Ubuntu_24.04
            LTS⠀⇛


                 Ubuntu 24.04, often referred to by its codename “Noble
                 Numbat,” is a powerful and user-friendly GNU/Linux
                 distribution that arrives with numerous performance
                 improvements. Although it comes with GNOME 46 by default,
                 users who want an alternative window manager or desktop
                 environment often explore Enlightenment.


          o ⚓ ID Root ☛ How_To_Install_Gitea_on_openSUSE⠀⇛


                 In this tutorial, we will show you how to install Gitea
                 on openSUSE. Gitea is a lightweight, self-hosted Git
                 service that provides a convenient way to manage and
                 collaborate on software development projects.


          o ⚓ ID Root ☛ How_To_Install_Calibre_on_Linux_Mint_22⠀⇛


                 Calibre is an essential tool for e-book enthusiasts,
                 offering a powerful suite of features for managing and
                 organizing digital libraries. This guide will walk you
                 through the process of installing Calibre on Linux Mint
                 22, ensuring you have access to this versatile e-book
                 management software.


    * ⚓ The New Stack ☛ Linux:_How_To_Install_Apps_From_the_Source⠀⇛


           The most reliable and easiest methods for installing
           applications are the default package managers — such as APT for
           Debian — and universal package managers, such as FlatPak.
           Following that would be AppImage, which allows you to install
           Linux apps on any platform.


           That leaves installing from the source.


           Why is the oldest method of installing Linux applications at
           the bottom of the list? It’s not just the simplicity offered by
           package managers. In fact, there’s a very good reason why you
           should go with a package manager installation over source. When
           you install via a package manager, your system is aware of that
           application.


    * ⚓ Sahilister ☛ Sahil_Dhiman:_Prosody_Certificate_Management_With_Nginx
      and_Certbot⠀⇛


           I have a self-hosted XMPP chat server through Prosody. Earlier,
           I struggled with certificate renewal and generation for Prosody
           because I have Nginx (and a bunch of other services) running on
           the same server which binds to Port 80. Due to this, Certbot
           wasn’t able to auto-renew (through HTTP validation) for domains
           managed by Prosody.





                    ䷩ 𝚕𝚒𝚗𝚎 3991

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/today_s_howtos.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/today_s_howtos.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ today's
howtos⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 13, 2025


    * ⚓ LinuxBuz ☛ How_to_Use_Tags_in_Ansible_Playbooks_with_Examples⠀⇛


           Playbooks often include many tasks, some of which may not be
           necessary every time you run the playbook. Ansible tags provide
           a powerful way to manage which tasks run and …


    * ⚓ University of Toronto ☛ IMAP_clients_can_vary_in_their_reactions_to
      IMAP_errors⠀⇛


           For reasons outside of the scope of this entry, we recently
           modified our IMAP server so that it would only return 20,000
           results from an IMAP LIST command (technically 20,001 results).
           In our environment, an IMAP LIST operation that generates this
           many results is because one of the people who can hit this have
           run into our IMAP server backward compatibility problem. When
           we made this change, we had a choice for what would happen when
           the limit was hit, and specifically we had a choice of whether
           to claim that the IMAP LIST operation had succeeded or had
           failed. In the end we decided it was better to report that the
           IMAP LIST operation had failed, which also allowed us to
           include a text message explaining what had happened (in IMAP
           these are relatively free form).


    * ⚓ Tom's Hardware ☛ How_to_rip_your_audio_CDs_to_MP3_from_the_Linux
      terminal_with_abcde⠀⇛


           Ripping CDs was a popular activity around 15 to 20 years ago.
           Heck, I remember ripping audio CDs to MP2 (not a typo!) on an
           AMD K6-2 333. It took plenty of computing power back then, but
           now even a Raspberry Pi can rip an audio CD and convert the
           output to MP3 without breaking a sweat.


    * ⚓ Daniel Estévez ☛ Tianwen-1_second_apoapsis_raise⠀⇛


           Some weeks ago I reported about an apoapsis raise manoeuvre
           done by Tianwen-1, the Chinese Mars orbiter. This has now
           happened again. Using state vectors from the telemetry decoded
           with the 20 m antenna in Bochum observatory by AMSAT-DL, we
           have detected an apoapsis raise manoeuvre done on 2025-01-08.
           This new apoapsis raise is much larger than the previous one. I
           have done the same kind of calculations as in the previous
           post, and also corrected a bug in my Keplerian elements plots
           (the periapsis and apoapsis passings were being paired
           incorrectly, which caused the SMA and eccentricity not to
           change in the plots I did in the previous post).


    * ⚓ University of Toronto ☛ The_problem_with_combining_DNS_CNAME_records
      and_anything_else⠀⇛


           A famous issue when setting up DNS records for domains is that
           you can't combine a CNAME record with any other type, such as a
           MX record or a SOA (which is required at the top level of a
           domain). One modern reason that you would want such a CNAME
           record is that you're hosting your domain's web site at some
           provider and the provider wants to be able to change what IP
           addresses it uses for this, so from the provider's perspective
           they want you to CNAME your 'web site' name to
           'something.provider.com'.


    * ⚓ Medium ☛ Automating_Users_Creation_and_Configuration_Alerts_on_Amazon
      Linux_via_EC2_by_using_python_script⠀⇛


           This project automates the creation of new users on an Amazon
           Linux server, restricting execution to administrators only. It
           offers customizable options, such as specifying the username,
           group, and home directory for the new user. After creating the
           user, the script sends an email to the administrator via
           Postfix, a widely used mail transfer agent. The email includes
           details about the new user’s configuration.





                    ䷩ 𝚕𝚒𝚗𝚎 4090

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

(ℹ) Images, hyperlinks and comments at https://tuxmachines.org/n/2025/01/13/today_s_leftovers.shtml
    Gemini version at https://tuxmachines.org/n/2025/01/13/today_s_leftovers.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ today's
leftovers⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 13, 2025


    * § GNU/Linux⠀➾


          o ⚓ Linuxiac ☛ Linuxiac_Weekly_Wrap-Up:_Week_2_(Jan_6_–_12,_2025)⠀⇛


                 Catch up on the latest GNU/Linux news: Plasma 6.3 Beta,
                 Budgie Desktop in 2025, COSMIC Desktop Alpha 5, Debian
                 12.9, Tails 6.11, Raspberry Pi 5 16GB, and more.


          o § Audiocasts/Shows⠀➾


                # ⚓ Jupiter Broadcasting ☛ Cache_My_OS_|_LINUX_Unplugged_597⠀⇛


                       We're taking on some of the toughest critiques of
                       the GNU/Linux desktop, then taking a look at
                       CachyOS and what makes it feel like a million
                       bucks.


          o § Applications⠀➾


                # ⚓ OMG Ubuntu ☛ VLC_Developers_Working_on_AI-Powered_Real-Time
                  Subtitles⠀⇛


                       Real-time Hey Hi (AI) subtitling is in the works
                       for VLC, the phenomenally popular open-source media
                       player. VideoLAN, the non-profit in charge of VLC
                       development, demoed automatic subtitle generation
                       in VLC during CES 2025 —where not using Hey Hi (AI)
                       made you stand out this year— and shared a clip of
                       the feature in action at their CES booth on X last
                       week. No cloud service or internet connection is
                       needed for VLC to auto-generate subtitles with AI.


    * § Distributions and Operating Systems⠀➾


          o § Debian Family⠀➾


                # ⚓ DEV Community ☛ Divine_Attah-Ohiemi:_My_30-Day_Outreachy
                  Experience_with_the_Debian_Community⠀⇛


                       Hey everyone! It’s Divine Attah-Ohiemi here, and
                       I’m excited to share what I’ve been up to in my
                       internship with the Debian community. It’s been a
                       month since I began this journey, and if you’re
                       thinking about applying for Outreachy, let me give
                       you a glimpse into my project and the amazing
                       people I get to work with.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ Ubuntu Studio ☛ Ubuntu_Studio:_Support_and_Help_Updates⠀⇛


                       We have always strived to give our users the best
                       support options. After asking the community via a
                       thread_on_Ubuntu_Discourse and being given positive
                       feedback, we have decided to move our primary
                       support channel from Ask Ubuntu to Ubuntu
                       Discourse.


                       Ask Ubuntu, which was run outside of the Ubuntu
                       Governance, was a great idea in its time, but as
                       time has gone on, it has become difficult for the
                       moderators to moderate as its host, StackExchange,
                       has made questionable decisions, including
                       shutting-down OpenSSO, which effectively disabled
                       many accounts which were exclusively linked to
                       Launchpad without recovery. StackExchange has been
                       uncooperative with re-enabling this link to
                       Launchpad, leaving many users, who had higher
                       privileges due to their participation, having to
                       start over.


          o § Open Hardware/Modding⠀➾


                # ⚓ It's FOSS ☛ ArmSoM_AIM7:_A_Promising_Upcoming_Rockchip
                  Device_for_Hey_Hi_(AI)_Development⠀⇛


                       Harness the power of RK3588 Rockchip processor for
                       Hey Hi (AI) development with ArmSoM AIM7 Hey Hi
                       (AI) kit.


                # ⚓ Hackaday ☛ Fraens’_New_Loom_And_The_Limits_Of_3D_Printing⠀⇛


                       [Fraens] has been re-making industrial machines in
                       fantastic 3D-printable versions for a few years
                       now, and we’ve loved watching his creations get
                       progressively more intricate. But with this nearly
                       completely 3D-printable needle loom, he’s pushing
                       right up against the edge of the possible.


                # ⚓ Hackaday ☛ Second_CNC_Machine_Is_Twice_As_Nice⠀⇛


                       [Cody Lammer] built a sweet CNC router. But as
                       always, when you build a “thing”, you inevitably
                       figure out how to build a better “thing” in the
                       process, so here we are with Cody’s CNC machine
                       v2.0. And it looks like CNC v1.0 was no slouch, so
                       there’s no shortage of custom milled aluminum here.


                # ⚓ CNX Software ☛ Seeed_Studio_XIAO_Plus_series_adds_more
                  GPIOs_through_castellated_holes⠀⇛


                       In response to community feedback for more I/
                       O options, Seeed Studio has recently launched the
                       Seeed Studio XIAO Plus series with 23 castellated
                       mounting pins (20 GPIOs, 3 power pins) and improved
                       back solder points, improving compatibility with
                       carrier boards for complex projects. The new series
                       includes the XIAO ESP32S3 Plus, XIAO nRF52840 Plus,
                       and XIAO nRF52840 SensePlus which are direct
                       upgrades of the XIAO ESP32S3, XIAO nRF52840 BLE,
                       and XIAO nRF52840 Sense boards.




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