2025年4月2日 2025年4月2日
この記事ではかわいいシナモンくんや仲間たちのアスキーアートやドットアートをまとめていきます₍ᐢ◍ට ⩊ ට◍ᐢ₎🍒☆彡
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⚠️文字サイズ・使用環境・デバイスなどにより見え方が異なったり、ズレが生じる場合があります(◞ ̫◟)💭🌀⚠️
シナモン
. _ – ､
/ ) _ – 、
_ノ - ￣｀´、ー一’´ }
{ ,:’´ ､ ／
Ч , – _ ⌒ ,, }｀ ｰ–‐ ´
乂＿_ヽﾉ_ - ´
{ 、) /⌒Y
_ゝ __ ＞r′
｀ｰ ´ ｀´
⠀⠀ ,ー､_－ーーー－_,ー-､
/ ／ ＼
／ / ● ● ヽ ヽ＿
( ( ⊃ ’-‘ー′⊂⊃ ) ヽ 丶
`ヽ_ノ`(⌒)ーーーー＜′ ヽ＿＿_ノ
(_ｒ ／￣￣~丶_)
. ∇
[> 〇 <]
( （：） )
[二二二]
／ ＼
／ / o o ＼
（ 人○ ∀ ○人 ）
￣ (つ ﾉつ ￣
し-Ｏ
⠀⠀ ⠀⣀⡤⣤⠶⠛⠉⠉ ⠀⠉⠉⠛⠲⣤⣤⣄
⠀⠀⠀⡼⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢧
⠀⠀⡼⢁⡆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢰⡈⢧
⢀⡞⠁⣸⠁⠀⢠⠬⠓⠀⣀⠀⠀⢀⠀⠛⠥⣄⠀⠀⡇⠈⢳
⡞⠀⠀⠹⣆⠀⠀ ⠀⠀⠓⠊⠙⠚⠁⠀⠀⠀⠀⣰⠇⠀⠀⢻⠀
⣇⠀⠀⠀⠈⣹⠶⠦⠤⠤⣤⣤⣤⡤⠤⠤⠴⠶⣏⠁⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠖⡽⠉⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀
⠀⠀⢀⣠⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠦⡀
⡴⠉⠀⠀⠀⠀⠀⡏⠤⠴⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠓⢤⣀
⠀⠀⠀⠀⠀⠀⣀⡄⠬⠀⠘⠒⠦⠂⠀⠀⠉⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲
⠙⠤⣤⠤⠶⠋⠀⣈⡶⠴⠶⠤⣤⡀⠀⠀⠘⠘⠀⢀⡼⢦⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠏⠉⢦⠋⠀⠀⠀⠀⣀⠀⠀⠀⠉⠉⠉⠉⢦⠀⠀⠈⠲⣄⡀⠀⠀⣠⠁
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣾⠀⠉⠆⠀⠀⠀⠘⡀⠀⢳⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠙⠤⠖⠓⠲⠤⢤⣸⡀⠀⣀⣤⠴⠚⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠔⠊⠉⢳
⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉⠉⠃⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⡔⠚⠀⠀⠀⠀⠸⢆⣬⡖⠒⠒⠚⠁⠀
⠀⠀⡠⠊⠀⡄⠲⠀⠲⡿⠀⣨⢙⣀⢀
⡞⠁⠀⠀⢠⠳⠛⡡⠄⠒⠉⠀⠙⣅⡆⡃
⠣⣀⣀⠔⠁⠀⠘⢲⣀⠀⠀⠀⡀⠗⠒⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣨⠄⠒⠊⠀⠁
⠀⣠⠔⠛⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡍⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⣧⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⣆⠀⠀⠀⡸⠏⠑⢢⡴⠶⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠷⣄⠀⣸⡤⣤⠏⠀⠀⠀⠀⠀⠈⠛⡖⠊⠳⠀⠀⠀
⠀⠀⠀⠀⢈⡟⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣀⡴⣏⠀⠀
⠀⠀⠀⠀⣾⠁⠀⠞⠙⠂⠀⠀⠀⠀⠀⢀⣄⡀⠁⣄⢹⡆⠀
⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠻⠤⠤⣤⠀⠉⠀⠃⢀⣼⠀⢷⠀
⠀⠀⠀⠀⠀⠈⠙⠒⠶⢤⣤⣄⣀⣀⠀⠄⠀⢀⡡⠋⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠻⣏⠀⠀⠀⢠⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠾⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣤⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢋⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠉⠓⠦⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀
⠀⠀⣠⠞⠁⠀⠀⣀⣠⣏⡀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⡃⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⢀⡞⠁⠀⣠⠶⠛⠉⠉⠉⠙⢦⡸⣿⡿⠀⠀⠀⡄⢀⣀⣀⡶⠀⠀⠀⢀⡄⣀⠀⣢⠟⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⡞⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⢳⢀⣠⠀⠀⠀⠉⠉⠀⠀⣀⠀⠀⠀⢀⣠⡴⠞⠁⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⣀⣤⠞⠁⠀
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠁⠀⢀⣀⣀⡴⠋⢻⡉⠙⠾⡟⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠀⠀⠀⠀
⠘⣦⡀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢉⣹⣯⣍⣿⠉⠟⠀⠀⣸⠳⣄⡀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠙⠒⠒⠒⠒⠚⠋⠁⠀⡴⠋⢀⡀⢠⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⡾⠋⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠉⠋⠻⣄⠀⠀⠀⠀⠀⣀⣠⣴⠞⠋⠳⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⠤⠶⠋⠙⠳⣆⣀⣈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣠⠴⠒⠒⠒⠦⢄⡀⠀⠀⠀⠀
⠀⠀⢠⢊⠘⠀⠀⠀⠀⠀⠀⠀⠃⠉⡄⠀⠀
⠀⣠⢋⡏⠀⠿ ⢠⣀⢄⡦ ⠿⠀⠀⠙⣄⠀
⢸⡇⠀⠳⢆⡀⠀ ⠀⣠⡾⠀⠀⢘⡄
⠀⠳⣆⡶⠟⠙⠛⠛⠛⠛⠛⠁⠻⢶⣰⠾⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⠾⠛⠋⠉⠁⠀⠀⠈⠉⠉⠛⠳⢦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣶⠿⢉⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡉⠹⣷⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡾⠋⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⢻⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣾⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢻⡄⠀⠀⠀⠀
⠀⠀⠀⢀⡾⠃⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠈⢿⣄⠀⠀⠀
⠀⠀⣠⡟⠁⠀⣿⠁⠀⠘⣟⠛⠛⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠛⢋⡟⠇⠀⠀⣿⡄⠀⠻⣦⡀⠀
⠀⣸⠏⠀⠀⠀⢿⡄⠂⠀⣿⠀⠀⢹⠃⠀⣿⣠⡴⠦⣤⣻⠆⢠⡇⠀⣸⠃⠀⠀⠀⣿⠀⠀⠀⠘⣷⠀
⢀⣿⠀⠀⠀⠀⠈⢿⣤⡀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢸⠇⠀⣠⡾⠃⠀⠀⠀⠀⢹⡇
⠈⣿⠀⠀⠀⠀⠀⠀⠈⢿⣷⣷⣆⣹⣄⣀⣀⣀⣀⣀⣀⣀⣇⣀⣸⣇⣶⣿⡿⠉⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠹⣦⡀⠀⠀⠀⢀⣠⡾⠃⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠉⠀⠈⠻⣦⣀⠀⠀⠀⢀⣠⡟⠀
⠀⠀⠈⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠱⠊⡱⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠒⠤⢄ ⣑⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⣢⠐⡄⠀⠉⠑⠒⠒⠒⣄
⠀⠀⠀⣀⠴⠋⠀⠀⠀⡎⠀⠘⠿⠀⠀⢠⣀⢄⡢⠉⣔⣲⢸⠀⠀⠀⠀⠀⠀⢘
⡠⠒⠉⠀⠀⠀⠀⠀⡰⢅⠫⠭⠝⠀⠀⠀⠀⠀⠀⢀⣀⣤⡋⠙⠢⢄⣀⣀⡠⠊
⢇⠀⠀⠀⠀⠀⢀⠜⠁⠀⠉⡕⠒⠒⠒⠒⠒⠛⠉⠹⡄⣀⠘⡄⠀⠀⠀⠀⠀⠀
⠀⠑⠂⠤⠔⠒⠁⠀⠀⡎⠱⡃⠀⠀⡄⠀⠄⠀⠀⠠⠟⠉⡷⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠤⠴⣄⡸⠤⣄⠴⠤⠴⠄⠼⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠛⠻⢿⣶⡀⠀⠀⣠⣶⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠙⣿⣀⣾⠟⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠀⠀⠀⢐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣤⣾⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣷⣄⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀
⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀
⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀
⠀⠀⠐⣿⡀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣼⡿⠀⠀
⠀⠀⠀⠘⣿⣤⡀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⣠⣾⡿⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠿⣿⣿⡏⠀⠀⠀⠀⢴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⢹⣿⣿⠿⠛⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣝⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣋⠁⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⣶⠆⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠢⢊⢌⢅⢨⢅⠀⠀⠀⠀⣿⣤⣴⡿⠿⢿⣶⣶⠟⠀⠀⠀⠀⢑⢡⡊⢌⢕⠆⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡈⠔⠑⠑⠑⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠑⠑⠨⠐⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣷⣶⣿⡿⠁⢸⣿⠀⠻⣿⣶⣶⣾⣷⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠻⢿⣷⣿⠁⠈⠀⠀⢀⣿⣿⣆⠀⠀⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⢠⣦⠀⢈⣿⠀⠀⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣇⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠈⠿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣦⣤⣤⣾⣿⡇⠀⢀⣤⣄⣀⣀⣀⣤⣄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠘⣿⣄⠀⣽⡿⠋⠛⠻⣿⣅⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠋⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀
⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣰⣿⠟⠉⠀⠀⠀⠀⠉⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀
⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⢀⣴⡿⠛⠛⣻⣿⣶⣶⣶⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡄⣰⣿⡿⠇⠐⣻⡟⠋⠁⢠⣶⠀⠀⠈⢿⣿⣶⣶⣤⣀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⣤⣾⡿⠟⠛⠛⠛⠻⣿⣷⣄⠀⠀
⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠏⠀⠀⢸⣟⠀⠀⠀⠈⠻⠷⣦⣴⠿⠁⠹⣯⠉⠛⠿⣿⡿⠛⠻⣿⣦⣠⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠟⠛⠛⠛⠛⠛⠛⠛⠷⢶⣤⣄⡀⠀⠀⠀⣿⠇⠀⠀⠀⠙⠧⣀⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⣤⣾⠟⠀⢀⣀⣤⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⠀⠀⢀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣀⣄⣀⡈⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡲⣌⢧⡛⢷⡄⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⢹⣷⣶⣶⣶⠶⠶⠿⠿⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣮⣒⠹⠚⠁⣀⡀⣀⣽⡷⠖⠲⣤⣸⡇⠀⠀⠀⠀⠙⠿⠟⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⢶⣾⣿⣻⢟⣯⣿⣿⣶⣄⠀⠀⠀⠀⠀⢠⡖⢯⣛⠳⡶⣄⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⣻⣧⣿⣿⣿⣟⣿⣿⣦⣤⣄⣀⣀⣈⣉⣳⣌⣻⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣛⣿⣛⣿⣿⠈⠉⢉⣩⣿⡿⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣾⣟⣿⣟⣿⣿⣿⣶⣾⠿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣤⣴⣶⡿⠿⠿⠛⠛⠛⠟⠛⠻⠶⢤⣤⣿⣟⣿⠟⠋⠁⠀⣀⣀⡀⠈⠉⠛⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠿⠛⣩⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⣀⣴⠟⠋⠉⠙⢳⡄⠀⠀⠙⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⢶⣦⣌⠃⠀⠀⢀⣿⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣤⣶⣾⢿⣿⣽⠏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉⠀⠀⠙⢿⣦⠀⠀⠀⠀
⠀⠀⠀⢀⣀⣀⣠⣴⠟⠁⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠈⢿⣦⠀⠀⠀
⢀⣴⣿⠟⠛⠋⠉⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⢸⣿⠀⠀⠀
⣾⡿⠁⠀⠀⠀⠀⠀⠀⣼⡏⠀⣠⣤⣤⣶⣶⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠂⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⢸⣿⣆⠀⠀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣏⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠷⣦⣤⣀⡀⠀⣀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⠉⢻⣷⡀
⢻⣿⣄⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⣠⡇⠀⠀⠀⠀⠀⣿⣇⣀⣤⣤⣄⡀⠠⣦⠀⠀⠀⣀⣀⣉⣙⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⣠⣿⡇
⠀⠙⢿⣶⣤⣀⣀⡀⣀⣀⣘⣿⣿⣧⣤⣀⡀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠛⠛⠋⢠⡏⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣴⣶⡿⠟⠋⠀
⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠋⠉⠀⠉⠙⠛⠿⠿⢶⣦⡤⠤⣦⣄⣀⣀⣀⣀⣀⣏⣀⣀⡀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⠿⡿⣶⣶⣶⣦⢒⢛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⠶⠶⠶⠶⠦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠾⠟⣿⣿⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣤⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉⠀⠀⠸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣀⠈⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⢀⡿⠁⠀⠀⣰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠐⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣄⡀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠉⠁⠉⠈⠉⠀⠀⠀⠀⠀⠀⣠⢤⣀⠀⠀⠀⠀⠀⠉⠿⠿⠁⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⠀⠀⠀
⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠤⠠⠐⢀⡀⠀⠀⠀⠀⠀⠋⠁⠉⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⢁⠀⠀⣼⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀
⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠻⢶⣤⣴⡾⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣤⠀⠜⣀⣴⠟⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⣿⠃⠀⠀⢸⡟⠳⠶⠶⠶⢦⣶⣴⣶⣴⣶⣶⣿⠉⠀⠹⣷⣿⣿⣥⣄⡀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢿⣆⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠀⢀⣿⠟⠉⠉⠉⠛⣷⡄⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠃⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠿⣷⡀⠀⠀⣀⠀⠈⣿⡄⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⣀⣼⠏⠀
⠀⠀⠉⠛⠷⠶⠶⠶⠶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣤⣴⠏⠀⠀⣽⡇⠀⠀⠀⠈⠛⠿⠶⠶⠶⠶⠿⠋⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡾⠋⠀⠁⠀⠀⠀⠀⠀⢀⣾⠛⠉⠙⠓⠀⠀⢀⣴⠟⠛⠿⠾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠐⢶⣶⣶⣶⣶⣾⣿⡀⠀⠀⢶⡶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⣠⡿⠁⠀⠀⠀⠀⢹⣇⡀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠉⣉⡉⠉⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡾⠋⠀⣠⡾⠛⠛⠻⣷⡀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠖⠿⠋⠉⠁⠀⠀⠀⠀⠀⠉⠉⠛⢷⣶⣿⣤⣤⣀⠀⠘⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠙⢷⣄⠀⠀⣠⣾⣇⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⣤⣤⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡋⠀⠈⠻⣦⡀⠀⠀⠀
⠀⢀⣴⠾⠋⠉⠁⠀⢀⣀⣀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠈⢿⡶⣤⡀
⢠⡾⠁⠀⠀⠀⠀⠀⠈⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡷⠦⢤⡄⠀⠀⠀⠀⠙⢷⡄⠈⣧⠈⣿
⢸⠁⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣋⣰⠟
⢸⣆⠀⠀⠀⠀⠀⠀⠀⢸⣇⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠟⠁⠀
⠀⠙⠷⣤⣄⣀⣀⣀⣀⣀⣻⣮⡉⡉⠉⠀⠀⠀⠀⠀⠀⠀⠛⠲⠶⣤⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠈⠉⠛⠒⠒⠷⠴⠶⠤⠶⠤⠤⣤⣦⣤⣤⣤⣿⣦⣀⣀⣀⠀⢀⣀⣀⣀⣀⣤⣤⠶⠛⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
おともだち
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣶⣿⣟⠛⠛⠿⢷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠟⠛⠋⠉⠉⠉⠁⠀⠉⠉⠉⠛⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣀⣠⣶⡾⠿⠿⣶⣤⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡟⠁⠀⠀⠀⠀⠙⢿⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⢠⣄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣄⠀⠀⠀⠉⠛⠿⠟⠁⠀⠀⠀⣿⠇
⠀⠀⣼⠙⠷⢾⡿⠃⣀⣀⣤⣤⣤⣤⡄⢀⣴⡿⠟⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀
⠴⣾⣯⡀⣀⣘⣷⡈⠉⠁⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡆⠀⠀⠀⠈⢿⣧⣀⣀⣀⣀⣤⣶⡿⠋⠀⠀
⠀⠀⠸⣷⡟⠉⠉⠋⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠁⢀⣀⣀⣀⣀⣸⣿⣛⣛⡛⠛⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⢿⣛⡉⠉⢉⣩⣭⣟⣿⣏⣳⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡇⠀⠀⢀⡟⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⢉⣉⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡾⠿⠿⠿⣶⣄⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢾⣶⡿⠛⠉⣿⡇⠀⠀⠘⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣶⡿⠛⠛⢿⣦⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⣿⡇⠀⠀⠀⠀⠙⢿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠙⠿⠶⠾⠟⠁⠀⠀⣀⣽⠀⠀⠉⠉⠉⠉⠉⠉⣽⡟⠀⠀⠀⠀⣿⡇⠀⠀
⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⢿⡿⠦⠤⣤⣤⣤⣤⣤⣤⣼⣿⣄⠀⠀⣠⣿⠃⠀⠀
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣠⣤⣾⠿⠁⠀⠀⢈⣿⣧⣠⣶⠿⠿⠿⢷⣶⣦⣄⣀⠀⣀⣀⣤⡴⣶⣟⣿⣏⡹⣷⢛⣐⣿⠀⠀⠀⣴⣾⣿⣿⣦⡀⠻⠿⣿⣾⠿⠃⠀⠀⠀
⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⣼⡿⠹⣿⣇⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣟⠉⠁⠀⠙⢿⣿⠿⠟⠛⠛⢻⠄⠀⠸⣿⣿⣷⣿⣯⡽⠀⠀⣽⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠀⠀⠈⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⣰⣶⠟⠁⠀⠀⠀⠀⠸⣶⣸⣿⣿⡿⢿⢿⣻⣯⣧⣠⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠻⢷⣶⣤⣤⣤⣤⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠉⠻⢿⣶⣤⣀⡀⠀⠀⠀⠀⠹⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⢿⣿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠛⠛⠒⠶⣄
⠀⠀⢀⡴⠋⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠉⠳⡀
⠀⠟⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⡙⡄
⠘⡀⠙⠁⡏⠀⢰⣷⠀⠀⠀⠀⠀⠀⢠⣷⠀⠈⡆⠛⠁⣿
⠀⠻⣤⣤⠀⠀⠈⠁⠀⣤⣀⣀⢰⠀⠀⠋⠀⠀⣯⣠⡴⠁
⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣿⣿⣥⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⣿⣿⢿⣿⣽⣽⣯⣷⣿⣿⣿⣿⣯⣿⣿⣿⣽⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⠟⠛⠉⠁⠀⣿⣿⠀⠀⠀⣀⣄⣠⣀⠀⠀⠉⠉⠛⠿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⠀⣠⣾⣿⣻⣾⠛⠃⠀⠀⠀⠀⠀⠀⢸⣿⡇⢠⣾⣿⣿⠿⠿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣧⣀⢀⣀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣽⣿⣿⣻⣿⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⢿⡿⠁⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣟⣟⢿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⠿⠋⠀⢀⣼⣟⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⣿⠀⠀⠀⠀⠀⠀⠀⣽⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣾⣥⠀⠁⠛⢷⣯⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠿⠁⠀⠀⠀⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⢿⣄⠀⠀⠀⠀⠀⣠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠀⠀⠀⠙⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠻⣿⣿⣶⣶⣶⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠁⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠩⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠃⠀⠀⠀⣿⣽⡟⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣿⠀⠀⠀⠹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⠋⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⡆⠀⠀⠀⠹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣴⣟⣿⠋⠀⠀⠀⠀⣿⣺⠁⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣟⣟⣿⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣿⠀⠀⠀⠀⠹⣟⣿⡆
⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠄⠀⠀⠀⠀⠙⣿⣿⣆
⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⡿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣯⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡇⠀⠀⠀⠀⠀⠘⣿⡿⣷
⠀⠀⠀⣿⣻⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠉⢿⣻⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿
⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣧
⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⡄
⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣿
⠠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣀⠀⠀⠀⠀⣀⣾⠟⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿
⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣷⣿⣿⣷⣾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣽⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⠁
⠀⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣽⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣦⣴⣶⣾⣿⣿⣿⣿⣿⣯⣿⣯⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠀⠈⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣷⣿⣿⣿⣿⠿⠿⠛⠋⠉⠀⠀⠀⣿⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇
⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⡟
⠀⠀⠀⠻⣷⡿⣷⣤⣀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⡿⠋
⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠉⠉⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡄⢀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⡞⡴⠁⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀
⣸⢠⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⠉⠀⠀⠀⠀⠈⣦
⡇⠾⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠁⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠞⠛⢉⡟⠉⠉⠉⠉⠛⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢀⣴⠛⠁⠀⠀⠀⠀⣿⣰⠟⠛⢳⣄⠀⠀⠀⠀⠀⠙⢿⡞⠶⠶⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⢸⠀⠀⠀⠀⠀⡾⠉⠀⠀⠀⠀⠀⠀⠀⣟⣇⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠷⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⢿⡀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠃
⠀⠀⠀⠀⠀⠻⣴⠃⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⡟⢣⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠷⠀⠀⠀⠀⠸⡄⠉⠙⠛⠛⠛⠛⠉⠁⠀⡀
⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢷⣧⠃⠀⠀⠀⠀⡟⠁⠈⢿⣆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠐⠒⠛⣉⡴
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⣸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣶⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠇⠀⠙⣦⣀⣀⣀⡀⢀⡀⢀⣀⣀⣀⣤⣤⣴⣲⡾⠽⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠈⠂⠀⠀⠁⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢀⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢻
⠀⠀⠀⠀⠀⠀⠀⢸⠅⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⢀⣤⠛⠿⠶⣤⣤⣄⣀⣀⣀⣀⣀⣄⣤⣤⡶⠾⣤⡀⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⡖⢺⢻⡫⣅⣘⣛⣲⠶⡶⡤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢞⣻⣫⣵⣭⡭⣭⣏⣛⢟⠶⡖⣻⠿⠖⠛⠉⠉⠁⠀⡇⡟⠀⣀⣤⣤⣄⡉⠉⠛⠳⠶⣭⣻⡶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⣛⣭⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⡯⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⠱⢰⣏⡶⠚⠛⠷⣭⢷⡄⠀⠀⠀⠀⠉⠛⢯⣛⣦⡀
⠀⠀⠀⣀⡴⡻⣭⣪⠴⠦⢴⣮⣫⣏⠻⢖⠶⠶⠶⡖⡖⠶⢟⣏⣍⡵⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣷⠁⠀⠀⠀⠀⠀⢿⢾⠀⠀⠀⠀⠀⠀⠀⠀⠛⣭⠷⡴⣤⣤⣀⡀
⠀⢀⡞⢸⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠙⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣸⢻⡀⠀⠀⠀⠀⠀⣾⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⡉⠛⠲⠮⣝⡳⢶⣄
⠀⡟⣳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢺⠀⠳⣝⣦⣀⣀⣠⢞⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠈⠛⠾⣝⠻⣤⡀
⢸⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠈⠛⠾⠶⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣎⢷⣄
⣾⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣙⠷⣤⣀
⢸⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣬⣏⣍⣩⢏⢩⢝⣩⣹⣫⣝⣋⣝⣫⡛⢲⣤
⠸⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢧⡏⢦
⠀⢷⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠁⠀⠀⠀⠀⣠⣟⠷⠚⠛⠓⢮⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡕⣷
⠀⠈⣯⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡾⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⢯⡳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠹⡆
⠀⠀⠈⣧⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡍⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠈⢷⡛⣄⠀⠀⠀⠀⠀⠀⠀⠿⠾⠛⠛⠛⠺⣬⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻
⠀⠀⠀⠀⠻⣇⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⠏⣱⠮⠱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⢽
⠀⠀⠀⠀⠀⠀⠛⣮⡝⠻⢶⣤⣤⣠⣀⣀⣄⣤⣤⡶⡺⡋⣑⡼⠗⠋⠀⠀⣧⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⣼⠇⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠷⠶⣦⣴⣧⣬⡼⠷⠞⠛⠉⠀⠀⠀⠀⠀⠀⠘⡜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣤⣀⠀⣀⣾⠟⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⡚⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠣⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣭⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠉⠳⢼⣵⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡜⣜⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⡻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢁⡀⠛⣦⠶⠶⣧⣤⡀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣱⠀⠀⠳⣎⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠮⣭⡻⠶⣤⣀⡀⠀⠀⠀⢷⣌⠀⠀⠀⢀⠧⣠⠂⠉⠋⣴⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣫⠏⠀⠀⠀⠀⠳⣌⡻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⣱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⣮⢬⣭⣛⡻⢶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢫⡼⠁⠀⠀⠀⠀⠀⠀⠀⠙⠳⣵⣛⢗⢦⣤⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡞⣙⣼⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣼⢢⠃⣀⣀⡀⠀⣷⠀⠿⠇⠀⢠⣄⠀⠀⣿⠇⠀⡿⣛⢻⡞⠲⠶⠶⢶⠶⢶⢦⡴⢦⠶⡶⠶⢖⣛⣯⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠛⠶⠦⣬⣭⣍⣙⣫⣍⣴⡦⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡹⡟⠀⠀⠙⠻⢽⣙⣤⡀⠀⠀⠐⠙⠀⠀⡀⠀⢀⢧⣤⣵⠷⠉⠉⠉⠉⠉⠉⠉⣎⣝⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣾⠀⠀⠀⠀⠀⠀⠈⠻⡪⡀⠀⣠⣀⠀⠀⡶⣺⡷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢼⠃⠀⠀⠀⠀⠀⠀⠀⠀⡟⡿⠀⠓⠚⠀⢀⡇⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡓⡟⠀⠀⠀⠀⠀⣀⣤⡶⢩⠞⠀⠀⠀⠀⠀⠀⡦⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠀⠀⠀⠛⠿⠾⠓⠋⠁⣿⠀⢀⣤⣤⣄⠀⠀⡿⠙⠷⢼⣻⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠘⢶⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣀⡴⣛⣣⡦⠵⠼⣏⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡪⡵⠋⠀⠀⠀⠀⠀⠀⢻⡛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡀⠀⠀⠀⠀⠀⠀⢀⡾⣪⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡧⣬⣛⠶⢶⢶⢶⢟⣹⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢔⠁⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠛⡽⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⡿⠟⠁⠀⠀⠀⡾⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⣎⣳⡀⠀⢀⡴⣃⠞⠛⠺⠾⠵⣽⣝⣝⣏⣹⣭⣭⣭⣭⠵⠶⠓⠓⣦⡻⣄⠀⠀⣠⢟⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣭⣝⡵⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣭⣥⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⢶⡶⣤⣤⣀⣀⠀⢀⣠⣴⣶⣻⣻⣽⣯⠽⢻⣹⠷⢮⣿⣻⣶⡶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢶⣟⡵⠞⠛⠉⠉⠉⠉⠛⠛⢼⣭⠾⠙⠉⠀⠀⠀⠀⠀⢀⣟⠃⠀⢀⣀⠀⠀⠈⠙⠛⠷⣽⡶⣄
⠀⠀⠀⣠⡖⣛⣭⢭⡭⢽⣝⣛⡻⠶⢶⡦⢴⢴⣦⡶⢶⢶⣟⣽⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡴⣿⠗⠚⠺⣽⣶⠀⠀⠀⠀⠈⠓⢽⣳⣄
⠀⢠⢻⡾⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢎⠏⠀⠀⠀⠀⠀⢳⣻⠀⠀⠀⠀⠀⠀⠈⠳⡯⣻⣟⡲⢦⣤⡀
⢁⢏⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢳⢧⠀⠀⠀⠀⠀⡯⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠉⠛⢮⣹⢶⣄
⣼⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠛⣽⣲⣤⡴⣞⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣝⢶⣄
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡷⢦⣀
⢻⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⣯⣳⡶⢶⡦⣤⣤⣤⡦⡦⡴⡤⣤⣤⣄⡀
⡈⣎⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠛⠛⠛⠛⠛⠛⠛⠛⠷⣯⡳⣤
⠀⢹⡺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡾⠀⠀⠀⠀⠀⠀⠀⣠⢾⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡮⢷
⠀⠀⠹⡻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⠃⠀⠀⠀⠀⠀⠀⢰⢪⡕⠪⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡱⡇
⠀⠀⠀⠙⢮⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢹⢯⢽⠀⠀⠀⠀⠀⠀⠀⢺⢼⣇⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢶⣄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠙⢶⣝⢻⠶⣤⣄⣀⣀⣀⣠⣤⢴⡞⢫⣕⡾⠞⠉⠀⡧⡆⠀⠀⠀⠀⠀⠀⠈⠷⠾⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠉⠉⠺⡳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢸⡧⣻⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢗
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠚⠺⠶⢶⢼⠷⠞⠛⠉⠁⠀⠀⠀⠀⠀⢻⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⣿⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣟⡸⢏⣿⠀⠀⠀⠀⠀⠀⠀⢸⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣝⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⠵⠃⠀⠀⠀⠀⠀⠀⠀⣞⢌⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⢶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⢀⣶⠏⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠇⠙⣝⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠾⣭⣝⡷⡦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢵⣧⣶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠻⣝⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣎⡞⠯⢽⣻⣗⢶⡦⣤⣤⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣻⠟⠀⠀⠀⠀⠀⠀⠙⠧⣻⢷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡞⣕⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡽⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠷⠮⠽⣽⣽⣯⣟⣟⣳⡞⢶⡶⠶⢶⠶⠶⢶⢶⣟⣫⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣮⣏⡝⣓⡺⡗⢺⣏⣍⣼⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣼⠀⠀⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⡮⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⢤⣄⢠⢣⠃⠀⠀⠀⠙⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠟⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⠗⠁⠉⠻⡪⡾⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⡏⣺⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠀⠀⠀⠀⠸⣗⠀⣀⠀⠀⠀⠀⣹⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⠀⠀⠀⠀⠀⠀⠀⣠⣻⠛⠀⠀⠙⣮⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⡂⠀⠀⠀⠀⠀⠁⠀⠉⠻⣿⣶⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣄⡀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢸⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣼⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢷⣀⠀⣀⣠⣞⡷⠛⠛⠯⢿⣿⣟⣺⣶⣶⣶⡶⡦⣤⣤⣤⣤⣤⢴⢶⣶⣶⣛⣯⡫⣶⠀⠀⠀⠀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠾⠷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠛⢯⣻⣟⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠶⢶⡖⡲⢖⡲⢖⠶⡶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⡴⡶⡶⡦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⢞⣏⣩⡦⠶⠚⠛⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠺⠵⣵⣝⡗⢦⣀⢀⡾⣕⠾⠛⠉⠉⠓⠺⣍⠷⡄⠀⣀⣤⡤⢤⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢖⡻⡟⡲⡦⣀⠀⠀⣀⡴⡻⣣⠵⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡪⠼⣀⠀⠀⠀⠀⠀⠀⠀⠳⡑⣪⠼⠓⠚⠛⠚⠺⢼⣙⢷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡫⡼⠚⠉⠀⠀⠉⠳⡮⢗⡫⣼⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣵⠷⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣝⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡾⣪⠋⠀⠀⠀⠀⠀⠀⡴⢕⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣕⢧⡤⠶⠲⢖⡲⡶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢏⣱⠧⠚⠳⠼⣵⠁⠀⠀⠀⠀⠀⠀⢈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠵⠚⠉⠉⠉⠉⠙⠚⢵⡝⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣕⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣪⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣪⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣮⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻
⠀⠀⠀⠀⣤⡞⢹⣧⢮⢼⣍⡱⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡚⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣈
⠀⠀⣴⣏⡾⠋⠀⠀⠀⠀⠀⠙⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠶⠶⠶⡲⠶⢶⠶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢽
⠀⡾⢼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠀⠀⠀⠀⢀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⡼⣮⠃
⢰⡑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡟⠀⠀⠀⠀⢀⣀⣤⡶⣚⣏⡭⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡴⢛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡢⡎
⣾⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡘⡇⠀⠀⠀⠀⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿
⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢢⠅⠀⠀⠀⠐⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣋⣤⣭⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡕⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⣽
⢻⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣓⢣⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢱⠇
⠈⣝⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢶⡎⣫⡝⣶⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢟⣪⠋⠘⣆⣧⠀⠀⠀⠀⠀⠀⡴⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢣⡞
⠀⠈⢷⣪⡗⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠫⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢟⣪⠛⠁⠀⠈⣆⣇⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢴⡺⣭⠶⠋⠀⠀⠀⠘⢮⠝⡲⢶⢶⡞⢹⡧⣼⠻⢤⣀⣀⡀⣀⣀⣤⡖⢫⣼⠋
⠀⠀⠀⣰⣘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡺⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣵⠋⠀⠀⠀⠀⠀⢏⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⠶⢲⡻⢏⣍⡵⠷⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠉⠀⠀⠀⠉⠚⠧⢴⣬⡴⠮⠶⠛⠁
⠀⠀⠀⣟⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡆⢹⢶⣤⣄⣀⣀⣀⣀⣀⣀⣀⢞⣼⠁⠀⠀⠀⠀⠀⡾⢆⡲⠶⢖⣛⡛⢹⣫⣍⣵⡦⠼⠷⠒⠛⠙⠚⠧⣜⡫⠶⢤⣀
⠀⠀⠀⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⢴⣕⠞⠈⠉⠛⠚⠷⠷⠼⠼⡸⢇⢕⣺⠁⠀⠀⠀⠀⠀⡾⣮⠙⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢼⣫⢗⣤⡀
⠀⠀⠀⠘⣜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢢⣵⣎⣵⠷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⢕⠏⠀⠀⠀⠀⠀⠀⠀⡞⣲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣫⢷⡀
⠀⠀⠀⠀⠙⣜⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡫⣵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⢳⢛⡀
⠀⠀⠀⠀⠀⠀⠓⣬⣏⢗⠶⡴⠶⢲⡻⣣⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡴⡖⡛⢛⢻⡻⠶⢖⣦⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣽⠉⠁⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠽⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⢹⡧⠴⣮⡟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⠀⠀⠀⠙⡢⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢪⠀⠀⠀⠀⡷⢞⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢪⠀⠀⠀⠀⠋⠈⣎⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⠀⠀⠀⠀⠀⠀⢸⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡕⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣱⠃⠀⠀⠀⠀⣦⣀⢏⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⡕⣏⠀⠀⠀⠀⠀⡿⢵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡑⠁⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⠷⠋⢕⢎⡲⢤⣤⢤⡺⣮⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠀⠀⠀⠙⢦⢜⡫⣛⢗⡲⡲⠶⠶⠶⠶⠶⢖⡲⢞⣛⣛⣛⢻⣏⣹⣝⣩⣣⡩⡵⠃⠀⠀⠀⢸⢨⠀⠙⠚⠓⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢺⠀⠀⠀⢀⡞⣪⠁⠀⠀⠀⠀⠁⠈⠁⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡕⡇⠀⠀⠀⠀⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡧⣠⢴⡏⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣇⣀⣀⣤⡞⣪⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⠦⠵⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣤⣶⣺⡿⠿⠿⠿⠿⠿⠿⠿⣿⣶⣶⣤⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣻⣿⠿⠿⡿⣗⢶⣶⡿⠛⠉⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⢿⣶⣄⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⡿⠛⠉⠀⠀⠀⠀⠈⠀⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⢖⢶⣶⣦⢥⣄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⡴⣾⣯⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠈⠙⠺⢽⢶⣤⣂⠀⠀⠀⠀⠁
⠀⠀⠀⣀⣤⢶⣶⣶⣶⣶⡶⢶⣤⣤⣤⣶⣶⣲⣿⠽⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⣽⣳⣦⣀⠄
⠀⣠⣟⠗⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠮⣟⣻⢶⣬⣭⣭⣭⣭⣭⣭⣭⢭⢴⡶⢶⣬⣭⣥⣀⠀⡀
⢠⣫⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠙⠻⣟⣦
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣻⡀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠠⢠⢿⣟⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡽⡀
⢻⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠁⠀⠀⠀⠀⠀⠀⣿⡗⢪⣿⠀⠀⠀⠀⠀⠀⡀⠔⠉⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠐⠂⣞⡸⡏⡆⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷
⠀⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣼⣸⠀⠀⠀⠀⠀⠀⠀⣿⠮⡪⡏⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⡎⠱⡜⡇⠀⠀⠀⠀⠀⠀⢸⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼
⠀⠘⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣠⢞⣽⠗⣽⠀⢀⠀⠀⠀⠀⠁⠀⠉⠉⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠉⣷⠀⠀⢂⠀⠀⠀⠿⣪⡼⠁⠀⠀⠀⠀⠀⠀⠀⣎⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣸⣽
⠀⠀⠈⢿⣳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣺⡷⠟⠁⠀⠀⣯⡆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠘⠷⣤⣀⠀⢸⠀⣀⣀⡿⠀⠀⠀⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠹⣻⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⡏
⠀⠀⠀⠀⠙⢾⣻⢶⣤⣀⣀⡀⢀⣀⣀⣤⡴⡲⣯⡼⠞⠋⠀⠀⠀⠀⠀⠀⠈⢾⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠛⣿⡦⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢟⡞
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠷⠾⠷⠓⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢽⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣵⠁⠀⠀⠀⠀⠈⠛⣽⣻⡦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⢾⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠯⣟⣖⣤⣤⣀⣀⠀⠀⠀⠀⠈⠃⠐⠒⠐⠠⠄⠠⢂⠐⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⢴⣻⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠮⣝⣛⣗⣲⢶⢶⡴⠶⠶⢲⣖⣻⣽⠷⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢧⠒⠺⠷⠯⢯⡽⣽⣟⣻⣗⣲⣶⣶⢶⣶⢶⢶⡶⢶⡶⢶⢶⢲⣲⣲⣻⡽⠾⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡏⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⠀⠀⠀⠈⠂⣷⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⣟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠐⠀⠈⣿⡀⠂⠀⠀⠀⠀⠐⠀⣰⡳⠁⠀⠀⠀⠀⠀⠀⠸⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠈⢰⡽⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⣤⡀⠁⠂⣰⣾⠀⠀⠀⠀⠀⠂⢿⡆⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⡇⠀⣠⡴⢶⣲⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠄⠛⠾⢷⡿⠿⠀⠀⠀⠀⠀⠸⢝⡿⠋⠁⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣹⣄⡀⠀⠀⢀⣠⣺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢼⠀⠉⠚⠾⠿⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠐⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⢛⣛⣲⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⢶⣟⠟⠁⠀⠀⡾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣳⠴⣾⠗⠁⠀⠀⠉⠉⠙⠛⠛⠛⠛⠉⠉⠉⠀⠈⠷⣳⣤⢴⣯⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⣠⣤⣤⣤⣄⣀⣄⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠉⠀⠀⠙⢿⣿⣶⣠⣤⣤⣀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡿⡿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⣀⣦⣦⣤⣴⣿⡿⠉⠀⠈⠙⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢻⣿⠟⠛⠿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠿⠻⡛⠉⡉⠁⡁⡐⡁⢂⠢⡂⢐⡂⢐⡂⠄⢄⠢⠅⠌⠄⠉⠉⠙⠟⢟⢿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⠿⠟⠻⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠟⠋⡀⡀⢄⡂⡐⡅⢂⠔⠅⠅⡑⢊⡊⠡⠌⡡⠌⡁⠔⠅⢐⠆⠄⡄⠡⡂⠔⢂⡐⠠⠄⠜⠛⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⢄⡡⠅⡨⡂⢄⡊⠡⠕⢂⠔⢅⠌⡑⢂⡢⢅⠌⡁⠔⢅⡐⠕⢂⠔⠅⡁⡄⢂⠌⡡⡊⠢⠅⡡⠌⠠⡠⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡇⠀⡑⡂⠅⡑⠢⢅⡢⠅⢄⡊⠆⡑⠊⡑⢂⡢⠕⠊⡁⠔⢅⡂⢄⡊⠆⡡⠅⡑⢂⠌⡡⡊⠢⠅⡑⠅⢌⠆⠂⣺⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠀⢄⡢⠅⠌⡑⠢⢅⡢⠅⢄⡂⠌⡑⠊⡑⠢⡢⠕⠊⡁⠔⢅⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⠅⡄⠂⠐⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⠠⡢⠅⠌⡑⠢⢅⡢⢅⢄⡂⠌⡑⠊⡑⠊⡡⠕⠊⡁⠔⢅⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⠅⡡⡂⢱⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡇⢂⡢⠅⠌⡑⠢⢅⡢⠕⢂⡂⠌⡑⠊⡑⠊⡑⠕⠊⡁⠔⢅⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⢅⡣⡐⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠏⢀⠄⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⢅⡢⠅⠌⡑⠢⢅⡢⠕⠢⡂⠌⡑⠊⡑⠊⡁⠔⠊⡁⠔⢅⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⠅⡈⢐⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⡀⢻⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠄⢘⠅⣻⣿⣆⠀⠀⠀⠀⠀⣰⣿⣶⣀⣀⣶⣿⣿⠏⢄⡂⠢⢅⠌⡑⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢌⡊⡁⠔⢅⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⢅⡃⢐⡂⠿⣿⣿⣦⣀⣠⣶⣿⡄⠀⠀⠀⠀⠀⣰⣿⡏⢈⡑⠂⢛⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡃⡂⡢⠌⡠⠨⢿⣿⣧⣤⡄⣠⣶⣿⡿⠿⣿⡿⠿⠛⠁⠐⠑⠌⠆⡑⠊⡑⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢄⡊⡁⠔⢅⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⢅⡊⠂⡐⠔⡉⠟⢿⣿⡿⠿⣿⣿⣦⣤⢄⣤⣾⣿⡿⡀⠡⢌⠆⠆⢛⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠇⠄⠡⠕⢂⡂⠐⢀⠙⠿⣿⣿⣿⠟⠋⠀⠠⠄⠠⠔⢁⡐⠢⢑⡢⠅⡑⠊⡑⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢄⡢⠅⢐⢅⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⢅⡊⢊⡂⠄⡨⡑⠠⢄⢄⠄⠠⠛⠿⣿⣿⣿⠟⠓⠄⡑⢂⢌⠆⠢⠌⠽⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⢐⡂⠔⠊⡡⡊⠢⠅⡡⠄⡀⢄⢄⡢⡢⢅⡐⡅⢂⠔⢅⡊⢂⠨⢅⡐⠕⠊⡑⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢄⡢⠕⢂⢄⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⢅⡊⢂⡂⠌⡡⡃⡁⠔⡅⡑⠅⡁⢄⢄⢄⢄⡂⠡⢅⡊⠡⡊⠆⢐⢅⠀⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣯⠄⠌⡑⢂⠌⡡⡊⠢⠅⡑⠢⢅⡊⠂⡨⠕⢅⡢⠕⢂⠔⢅⡊⢂⠔⢅⡂⠔⠊⡑⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢄⡢⠕⢂⢄⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⢅⡊⢂⡂⠌⡡⡊⡁⠌⡡⡂⢌⡢⠕⢂⠔⢂⠅⢐⡂⠢⠅⡁⢄⡊⢂⠌⠈⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠃⡐⢅⡊⠆⢌⡅⡌⠆⡡⠕⠢⢅⡊⠊⡁⠔⠢⡢⠕⢂⠔⠅⠊⢂⡐⢅⡂⠔⠊⡑⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢄⡢⠕⢂⢄⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⢅⡊⠢⡂⠌⡡⡢⠅⠌⠡⠢⢂⡢⠕⢂⢄⡊⠢⠌⡑⢂⠡⡁⠂⠨⠢⠅⡂⠸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡃⡐⢂⠨⠠⣺⣿⣿⣆⡐⡅⡑⠢⢅⡊⠊⡁⢌⡂⠢⠅⠂⠁⠐⠅⠡⢂⢄⡂⢌⡊⡑⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢄⡢⠕⢂⢄⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⢅⡊⠊⡁⠌⠡⡂⠐⡂⢐⡢⠌⡡⠕⢂⢄⡊⠢⠅⡑⠢⣺⣿⣿⣆⠀⡌⠆⡀⢿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣟⠀⡑⢂⠀⣶⣿⣿⣿⡟⡁⢕⠌⠆⡡⡊⠊⡁⡄⠊⢁⣤⣶⣷⣶⠄⠐⠈⢄⡂⢄⡊⡑⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢄⡢⠕⢂⢄⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⢅⡊⢊⠆⠡⡠⣴⣷⣶⡤⠁⠢⠕⠕⢂⢄⡊⠢⢅⡃⠠⣿⣿⣿⣿⡦⠂⢅⡢⠐⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡏⠠⠌⡡⠨⣰⣿⣿⣿⢿⠁⢄⡊⠢⠅⡡⡊⠆⡑⠅⢠⣿⣿⣿⣿⣿⣿⣆⠐⢄⡂⢄⡢⠕⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢄⡢⠕⢂⢄⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⢅⡊⠢⠅⣺⣿⣿⣿⣿⣿⣷⠄⠌⡑⢂⢄⡊⠢⠕⠪⡢⠀⣿⣿⣿⣿⡅⠡⠢⢅⡂⢿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠀⠡⠌⡁⢀⣿⣿⣿⣿⡀⡂⠡⡊⠢⠅⡡⡂⠌⢐⠢⣻⣿⣿⣿⣿⣿⣿⣿⠅⡂⢂⢄⡢⠕⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢄⡢⠕⢂⢄⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⢅⡐⡈⢸⣿⣿⣿⣿⣿⣿⣿⣧⠌⠕⢂⢄⡊⠢⢅⡊⡁⡌⢈⣿⣿⣿⣷⠁⡂⠄⠢⠈⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡟⠀⠨⢂⠄⠠⣲⣿⣿⣿⠇⠄⢄⡂⠔⠢⠅⡡⡂⡄⠢⢘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⡐⢂⡢⠕⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢄⡢⠕⢂⢄⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⢐⠅⢐⠨⢼⣿⣿⣿⣿⣿⣿⣿⣿⠄⡑⢂⢄⡊⠢⢅⡊⠡⡣⠅⢹⣿⣿⣿⣂⠁⢂⠄⡨⠈⢿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⢀⠄⠌⢑⡂⠀⣿⣿⣿⣟⡁⡢⢅⡂⠔⠢⠅⡡⡢⡃⠐⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠕⢅⡢⠕⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢄⡢⠕⢂⢄⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⢅⡃⠔⢂⠌⠠⢺⣿⣿⣿⣿⣿⣿⣿⣿⠄⢅⠢⢅⡊⠢⢅⡂⠌⠡⡠⠰⣿⣿⣿⣿⠀⠌⠨⢅⡐⠘⢿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠟⠠⡈⢐⡂⠨⠑⣡⣿⣿⣿⡗⡀⡂⠡⡂⢌⡢⠅⡡⡊⡑⠌⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⡂⠔⢅⡢⠕⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢄⡢⠕⢂⢄⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⢅⡂⠌⡑⠨⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⡂⡂⢐⢅⡊⠢⢅⡂⢐⠢⢑⡪⢿⣿⣿⣿⡁⢌⡂⠨⠅⡈⡀⢿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⡇⡠⡊⠂⡨⠅⠔⠂⣳⣿⣿⣿⡃⠂⡢⠅⡁⢄⡢⠅⡡⡊⡑⢊⠨⣿⣿⣿⣿⣿⣿⣿⠗⠠⡂⠔⢅⡢⠕⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢄⡢⠕⢂⢄⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⢅⡂⠌⡑⢂⠌⠂⣻⣿⣿⣿⣿⣿⣿⡗⡀⢃⠔⠂⡨⡢⢅⡊⠢⡰⡇⠡⢜⣿⣿⣿⡆⢑⠆⢐⢅⡃⢂⡂⠻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⣀⣿⣿⣿⡿⠁⡈⢅⠌⠊⡁⠔⢌⠆⣽⣿⣿⣿⠠⠨⠅⢌⡢⢅⡢⠅⡡⡢⡃⠢⡃⠄⠿⣿⣿⣿⡿⠋⢄⢘⠅⢐⢅⡢⠕⠢⢅⡢⡃⢔⠂⡐⡑⠢⡊⠊⡁⢄⡢⠕⢂⢄⡂⢄⡂⢌⠆⢐⢊⠅⡐⠡⡊⠢⢅⡂⠌⡑⢂⠔⠆⡀⠟⢿⣿⣿⣿⡟⠠⠪⠕⢂⠌⡡⡢⠕⢂⡰⢕⡪⠌⢱⣿⣿⣿⡇⠨⡂⠔⠢⢌⡢⡂⠄⠫⣿⣿⣿⣿⡀
⠀⠀⠀⢠⣿⣿⣿⣿⠁⡌⠢⠕⢊⡊⡁⠔⡅⠄⣻⣿⣿⣿⠅⢁⡐⡅⠢⢅⡢⠅⡡⡊⡑⠊⡁⠔⠂⢁⡉⡁⢐⢌⡃⠢⠕⢂⢄⡢⡑⠢⠅⠨⠁⣰⣷⣾⣿⢄⠅⠨⡂⠡⠌⡡⠄⡠⢐⠢⡂⠄⡰⣿⣷⣾⣁⢌⠕⠢⢅⡂⠌⡑⢂⠔⡅⠡⠂⢈⡉⡁⢈⢄⡂⠔⠕⠂⡠⢌⡃⠡⡃⢸⡇⢸⡕⢡⣿⣿⣿⡇⠠⢐⡊⠢⢅⡊⡁⠔⡅⠩⣿⣿⣿⣿⡄
⠀⠀⢠⣿⣿⣿⡿⠁⠨⠕⠢⠕⠂⡨⠅⠌⢑⠅⣝⣿⣿⣿⡆⠅⡡⡊⠢⢅⡢⠅⡡⡊⡑⠊⡁⠔⠊⠡⠌⠡⡊⠂⡨⡢⠕⢂⢄⡊⢑⡂⠐⠂⣼⣿⣿⣿⡿⠂⠑⠈⠁⡠⣤⣤⣤⣤⠤⠂⠁⠐⠍⣿⣿⣿⣿⡅⠂⡐⢅⡂⠌⡑⢂⠌⡑⢅⡊⠡⡂⠃⡨⢅⡂⠔⠕⠊⡑⠨⡢⢪⡕⢪⡕⢪⢕⣮⣿⣿⣿⠅⠡⢌⡃⠔⢅⡊⡁⢌⡂⢄⠈⣿⣿⣿⣿
⠀⠀⣿⣿⣿⡿⠀⡢⡢⠕⠢⠕⠊⡁⠔⠢⠕⠔⠐⣿⣿⣿⣷⡀⠨⠕⠢⢅⡢⠅⡡⡢⠕⠊⡁⠔⢂⡐⢂⡐⠕⢅⡊⠡⠕⢂⢄⠆⡡⠌⠄⠀⣻⣿⣿⣥⣀⣔⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⣠⣼⣿⣿⡧⠠⡂⢄⡂⠌⡑⢂⠌⡁⢄⡂⢌⡂⠌⠡⢅⡂⠐⢑⠊⡅⢢⡜⢣⡜⢣⡜⡣⢥⣿⣿⣿⣿⠀⠢⢅⡂⠔⢅⡢⠅⢄⡂⠄⡀⠘⣿⣿⣿⣿
⠀⣰⣿⣿⣿⡉⢌⠕⠂⡑⠢⠕⠊⡁⢌⡊⠆⡡⡀⢹⣿⣿⣿⣃⠐⠕⡢⢅⡢⠅⡡⡢⠕⠊⡁⠌⡡⡊⢂⡂⠔⢅⡢⢅⠌⡑⢂⠌⡁⠔⠂⡂⠸⢿⣿⣿⣿⣿⣿⣿⢿⡟⠫⠍⠉⠙⠿⢿⣿⣿⣿⣿⣿⣿⡿⢅⡂⢂⢄⡂⠌⡑⢂⠌⡁⢄⡂⢄⡂⢐⠢⢌⡣⢂⡰⢎⡱⢇⡪⢕⡪⢕⡪⢕⣺⣿⣿⣿⡃⠄⠂⠨⢅⡐⡅⠢⢅⢄⡂⢌⠆⠂⢝⣿⣿⣿⡆
⠀⣿⣿⣿⣿⠀⠔⢂⠌⡑⠢⠕⠊⡁⢄⡂⠌⡡⡂⠐⣿⣿⣿⣿⣔⠈⠕⢅⡢⠅⡡⡢⠕⠊⡁⠌⡡⡊⢂⡂⠔⢅⡢⠕⠊⡑⢂⠌⡁⠔⠊⡁⠄⠐⠉⠛⠛⠏⠁⠀⠂⠢⠕⠢⡐⠌⢐⠄⠈⠋⠛⠛⠏⠁⢐⡊⠕⢂⢄⡂⠌⡑⢂⠌⡁⢄⡂⡄⠊⠁⡐⡆⢪⡣⢎⡑⢪⡕⢪⡕⢪⡕⡢⣴⣿⣿⣿⡏⠀⢂⡐⠢⢅⡢⠕⠢⠕⢂⡂⠔⢂⠌⠀⣿⣿⣿⣿
⢸⣿⣿⣿⠁⡂⠡⠕⠅⡨⡢⠕⠊⡁⢄⡂⠌⡡⢅⢂⠌⣿⣿⣿⣿⣇⡀⢨⠅⠐⠡⡢⠕⠊⡁⠌⡡⡊⠢⡂⠔⢅⡢⠕⠊⡑⢂⠌⡁⠔⠊⡁⠔⠅⠌⡡⠌⡑⠢⠅⢐⡢⠕⠊⡁⡄⠆⢐⡢⠌⡡⠌⡑⠢⠌⡁⡄⠆⡡⡂⠌⡑⢂⠌⠢⢅⡂⡡⢢⡇⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡅⢨⣷⣿⣿⣿⡿⡂⠨⡂⠨⡢⢅⡢⠕⠢⠕⠢⡂⢄⠆⠡⡂⠫⣿⣿⣿⡄
⢸⣿⣿⣿⠀⡃⠢⢅⠌⡡⡢⠕⠊⡁⢄⡂⠌⡡⠕⠂⡀⠈⣿⣿⣿⣿⣿⣄⠈⠌⡂⠡⠕⠊⡁⠌⡡⡊⠊⡁⠔⢅⡢⠕⠊⡑⢂⠌⡁⢌⡊⡁⠔⢅⠌⡁⠔⠕⠢⠕⢂⡢⠕⠊⡡⠅⡑⢂⡢⠅⡁⠔⠕⠢⠅⡡⢅⡐⡅⢂⡐⢂⠐⡈⢅⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⠪⣅⣖⣾⣿⣿⣿⡏⠀⠸⠌⡁⠔⡅⠡⡢⠕⠢⠕⠊⡁⠔⢅⢄⡂⢈⣿⣿⣿⡇
⢿⣿⣿⡯⠀⡐⠢⠕⠊⡡⡢⠕⠊⡁⢄⡂⠌⡑⠕⢊⡢⡃⢈⠹⣿⣿⣿⣿⣾⣤⡂⠂⡐⡊⠅⠌⠡⠌⠨⠅⢐⢅⡢⠕⠊⡑⢂⠌⡁⢄⡊⡁⠔⠕⠊⡁⠔⠕⠢⠕⢂⡢⠕⠊⡁⠔⠕⢂⡢⡑⠅⢐⠕⠅⠐⠅⠡⡂⡁⡔⢡⡕⢣⡜⢣⡕⢪⡕⢣⡜⢣⡜⢣⡜⢓⠣⢘⢦⣬⣿⣿⣿⣿⣿⠋⡁⢄⡢⢅⡂⠌⡑⠢⠕⠕⠢⠕⠊⡁⠔⠅⡈⠄⠀⣿⣿⣿⣗
⣽⣿⣿⣗⠀⠔⠢⠕⠊⡡⡢⠕⠊⡁⢄⡂⠌⡁⢄⡊⠡⡊⡂⡂⠈⠻⣿⣿⣿⣿⣿⣯⣧⣂⡀⠁⠐⠑⠂⡑⢂⠄⡂⡑⠊⡑⢂⠌⡁⢄⡢⠅⠐⢑⡊⡁⠔⠕⠢⠕⢂⡢⡃⠨⡢⠅⠄⠊⠃⡐⠕⠢⡂⠠⢕⡢⡬⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⠕⣂⣌⣧⣼⣿⣿⣿⣿⣿⡿⠛⢀⡊⠢⢅⡢⢅⡂⠌⡑⠢⠅⢐⡢⠕⠊⡁⠔⠅⡁⠐⠐⣿⣿⣿⡗
⢸⣿⣿⣿⠀⠅⠔⠕⠊⡡⡢⠕⠊⡁⢄⡂⠌⡁⢄⡢⢅⡃⠨⠅⡡⠄⢈⠫⢿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣂⣀⣂⡈⠁⠊⠊⠑⠂⠌⠅⢄⠢⠅⢂⢄⡊⠅⡐⡑⠂⠃⢄⣈⡂⡐⣑⡌⢎⡣⢕⡪⡕⢪⡕⢣⡜⢣⡎⢱⡎⢱⡎⠱⢪⢕⢎⢕⡜⢱⣃⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⡐⡂⠊⡑⠢⢅⡢⢅⡂⠌⡑⠢⠕⢂⡢⠕⠊⡁⠔⡅⠣⡅⠀⣿⣿⣿⡇
⢸⣿⣿⣿⠄⡂⡐⠨⡊⠡⡢⠕⠊⡁⢄⡂⠌⡁⢄⡢⢅⡢⠅⠌⡑⢂⡊⢑⡂⢀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣴⣤⣦⣢⣔⡖⢱⣖⡣⣴⢇⡕⢱⠮⡪⢕⢆⢨⡕⠃⡌⠡⣜⡃⣵⢇⣵⡱⣲⣵⣵⣶⣶⣬⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢐⡁⠔⠅⡑⠢⡃⠔⢅⡢⢅⡂⠌⡑⠢⠕⢂⡢⠕⠊⡁⠌⡑⠊⡁⢔⣿⣿⣿⡇
⠀⣿⣿⣿⣷⡀⡐⠨⠅⠌⡡⠕⠊⡁⢄⡂⠌⡁⢄⡢⢅⡢⠅⠌⡑⠢⢌⠆⡄⢀⣿⣿⣿⣿⠋⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠛⣿⣿⣿⣇⠈⢅⡁⠌⡑⠊⡁⠔⢅⡢⢅⡂⠌⡑⠢⠕⠢⡢⠕⠊⡁⠌⡑⠅⢀⣿⣿⣿⡿
⠀⠺⣿⣿⣿⣗⠀⠁⢐⠅⡡⠕⠊⡁⢄⡂⠌⡁⢄⡢⢅⡢⢅⠌⡑⠢⡑⠊⣁⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠋⠝⠟⠿⠿⠿⠿⢿⣿⡿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠿⠿⠿⠿⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⡂⠐⡢⠌⠨⢅⡐⡅⠢⢅⡂⠌⡑⠢⠕⠊⡡⡑⠨⢂⡐⡅⢀⣾⣿⣿⣿⠇
⠀⠀⠻⣿⣿⣿⣾⠀⠂⢌⠕⠕⠊⡁⢄⡂⠌⡁⢄⡢⢅⡢⢃⠌⠡⠂⠢⣴⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣦⠀⠈⢂⢄⡢⠕⠢⢅⡂⠌⡑⠢⠕⠊⡁⢐⠅⢈⠀⣐⣿⣿⣿⣿⠟
⠀⠀⠀⠸⣿⣿⣿⣿⣧⣂⢀⠑⠊⢁⢄⡂⠈⡡⡐⡢⠅⠂⢁⣀⣮⣽⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣮⣅⣀⠠⠕⠢⢅⠆⠨⢕⠢⠃⠨⠂⠄⢀⣡⣾⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣧⣔⣀⣀⣀⣁⣀⣥⣗⣾⣷⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣾⣕⣡⣁⣁⣈⣀⣀⣒⣼⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⢿⡿⢿⣿⡿⣿⡿⠟⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠿⡿⡿⣿⣿⣿⣿⡿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⡿⠿⢿⣿⣾⣶⣦⣤⣀
⠀⠀⠀⠀⠀⣤⣾⠿⠋⠈⠄⡐⡂⠔⡂⠐⠆⠔⠄⡠⠉⠛⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⠿⠿⠿⠿⠿⢿⣷⣦⣄⡀
⠀⠀⢀⣶⠿⢉⢄⢅⡢⠅⠂⡂⠅⢂⠨⠅⠂⡂⡂⠅⠅⢂⢂⠄⠉⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠉⡀⡄⢄⡡⠌⠁⡂⡈⢐⢂⡀⠉⠿⣿⣄
⠀⢠⣿⠁⡐⠅⠅⢈⠅⠅⠂⠌⠄⠐⠡⠂⠅⠌⠅⠐⡂⠂⠅⠌⠐⠠⠉⣿⣦⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⡀⠅⠅⡂⠅⠅⠂⠅⠂⠅⠐⡂⠅⡂⠂⡂⢀⠙⣿⡀
⢠⡿⠀⠅⠅⡂⠡⠡⠡⠁⡁⡂⡁⠠⠄⠢⡃⡂⠅⠄⡂⠡⠡⠄⡂⠠⠕⢂⠛⣷⠀⠀⠀⢀⣾⠛⠠⡁⡀⠄⠂⡄⠆⡀⡐⠢⠄⡂⡄⡂⠡⠄⠅⠅⠌⡁⠅⠀⣿⡄
⣿⠁⡆⢊⠂⠁⠅⢈⠄⡂⡁⢁⡂⠠⠊⠈⡁⠁⠁⠌⠅⠅⡄⡈⢅⢄⡂⡂⡂⠙⣷⠀⣠⡿⢁⡊⡁⡈⢁⢃⠆⣿⠈⡁⠅⢂⠠⠂⠅⢊⡁⡂⡂⡃⠨⢅⡂⡈⠈⣿
⣿⠀⠅⢂⠅⡂⠔⢂⠅⠅⠅⢊⠀⣿⠛⠛⠛⠛⠛⠟⠿⠿⣷⣦⣤⣁⠈⠢⠀⣄⣽⡗⣻⠀⠁⣁⣤⣤⣶⣾⠿⠿⣥⠁⠅⠆⠡⠂⠂⡂⠂⠅⠅⠆⠡⡊⡑⡁⡂⣿⡆
⣿⠀⡑⠅⠅⠅⠄⡂⠅⠢⠅⠌⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣯⠁⠀⠀⠈⣿⠛⠉⠀⠀⠀⠀⠀⠀⠻⣦⠀⡂⠠⠂⡂⠡⠄⡂⡂⡄⠢⠅⡡⠄⠀⣿⠇
⢻⣧⠂⡈⠅⡂⡈⠌⡁⠅⢅⡆⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣧⠈⡃⡀⡂⡁⠅⠁⠅⠁⡀⡨⢅⢅⠀⣿
⠀⠛⣿⣄⠂⠢⠢⢂⡂⠢⠂⠂⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠶⠶⠶⠶⣿⠀⠀⠀⠀⣿⠛⠙⠉⠉⠉⣷⠀⠀⠀⠀⠈⡿⣤⠁⠇⠂⠈⡀⠄⠂⠅⡀⠑⢀⣾⠏
⠀⠀⠀⠙⠿⡿⣷⣷⣶⣿⡿⠟⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣇⣀⡀⣠⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣗⣤⣀⣀⣀⣂⣀⣥⣮⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡾⠛⡀⠁⣧⣽⡁⡀⠋⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡉⠛⠛⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣴⡷⠛⡁⡐⠆⠁⣾⠛⠈⢿⣢⠑⠃⠠⠌⠙⠛⢷⣶⣄⡀⠀⠀⠀⠠⡯⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣧⣀⣀⣀⣤⡾⠟⢉⠀⢈⣁⣤⣶⠷⠿⠾⠟⠻⠛⠟⠻⠿⠿⣶⣤⣄⡀⠠⢄⡉⠛⠿⠷⠿⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⢀⡋⠉⢉⡄⠀⣀⣦⠿⠋⡁⠀⠀⡠⢂⡈⢁⡂⡊⠈⠅⡨⡅⢄⡀⠉⠛⠿⣦⣀⠢⠌⠡⠂⡂⡀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⡀⠐⡂⠅⢁⣴⠟⠃⠄⢐⡂⠌⠄⠄⠐⡈⠅⡂⢂⠅⠄⡂⢊⡃⡃⠂⡊⠐⠂⡀⠙⣿⣆⠀⡂⠅⠔⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⡁⠠⠢⠄⠛⠄⡂⡁⡂⢅⠄⠄⡂⡄⡂⡁⠠⠂⠅⠔⠆⡡⠅⡄⡂⡁⠡⠂⡂⠅⠄⠄⠙⣿⠀⡀⡌⡁⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡡⠡⡂⡃⡂⡃⡁⡈⡁⢅⡂⠂⠅⡁⡈⡁⠅⡂⡂⢂⡂⡊⡂⡈⡁⠅⡁⡂⠅⠄⡂⠨⢑⢄⡂⠅⡁⡃⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⡿⠂⠂⢂⠅⠅⠐⠁⠌⠄⠂⡂⡂⠅⠄⡂⠅⠌⢁⠄⠅⡂⠅⠅⠄⠐⡑⠂⠅⠄⠨⠕⢊⠄⠄⢦⠈⢸⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣽⠟⡠⠄⠄⢅⠄⠐⡂⠐⠠⠂⡂⠅⡡⠄⡂⠡⠅⠌⡂⠅⡂⠡⠅⠄⡂⠄⠅⠅⡁⡁⠂⠅⠅⠅⠄⡄⢿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⡀⡈⠌⠆⠡⠀⣯⢫⢿⠀⠅⠂⡂⠅⢁⠅⡁⠅⡂⡈⠄⡊⡂⡁⠅⠂⢈⠄⢠⡿⡷⡄⠅⡂⠂⡂⢂⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠃⠌⠐⠆⠅⡰⡇⡣⢾⠀⠔⠔⠅⠔⠂⠅⠅⡂⠐⠡⠂⡂⢑⠆⡄⠂⡂⠅⣾⡺⡗⣻⠐⠪⡂⡂⠔⠅⢚⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⢐⠄⡐⡂⡃⠢⠐⣧⣮⢟⠠⠅⠅⡂⡡⠄⢄⠅⠅⠔⠊⡂⠅⠄⡂⠅⠅⠌⠅⢚⣎⣜⡿⠠⠌⡂⡂⠄⠄⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠨⠅⠡⠊⡁⠄⠄⠠⠄⠢⠄⡂⠂⠅⢊⡂⣮⠀⠊⣂⡂⠃⢿⠠⠣⠅⡂⡈⠌⠁⡈⠁⠄⡌⠡⠂⡂⡂⡡⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⡐⡐⠂⠄⡂⠄⠐⢂⠔⠢⡂⡂⠂⠔⠢⡉⠛⠋⢉⡉⠛⢋⡀⠅⠄⠄⠅⠄⠐⡂⡂⠂⠆⠡⠂⠅⠅⠂⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⠠⠌⡊⡂⠅⠅⡁⠅⠄⡂⠅⠅⡂⠠⠅⠄⠄⡂⡂⠄⠅⠌⠢⠅⠢⠅⠅⠄⠅⠅⠄⡂⠠⠂⠄⠨⣀⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣷⣀⠁⠈⠄⢈⠔⡅⡀⡂⡂⡂⢊⡁⠅⢂⡈⡁⡊⡁⡂⠢⡅⢅⡁⠌⠄⡂⡃⡀⠌⢃⠅⠂⣀⣲⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⢶⣤⣤⣁⣈⡁⠑⠂⠀⠐⠂⠊⠌⠑⠅⠅⠂⠂⠁⠈⠐⠐⡁⣀⣄⣤⣶⣾⡽⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⡀⡀⢈⡉⠋⠛⠛⠛⠛⠻⠟⠻⠟⠟⠻⠟⠛⠛⠛⠛⠛⠋⠙⠛⡮⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠿⢁⡄⠌⣦⡁⠌⡁⠅⠅⡑⠅⡨⡃⠂⠄⡂⠊⠅⡂⢅⡃⠅⠂⡠⡂⠂⠈⡀⡈⠛⣿⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠢⢊⠁⣴⠇⡂⢂⠄⠄⠄⠅⠐⡁⠅⠅⢂⡊⠄⡂⢂⠔⠂⡂⠐⣤⠁⠂⠂⠌⢈⠀⠀⣾⠉⠻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠂⠐⢂⣁⡿⢐⠅⠅⡃⡂⡀⠅⠄⠅⠄⡂⠅⠌⠄⠅⠡⡅⡂⡁⠐⠈⠟⣶⣤⣤⣦⡶⠟⢁⠂⡠⡉⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠿⠿⠛⣗⠁⡃⡁⡨⡃⡂⡂⢂⡈⠄⠅⠁⢂⡂⡂⢂⡁⠅⠂⡂⡁⠅⠂⠄⠺⡆⠠⠄⠁⠂⡀⡀⢨⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⡂⢑⡂⡂⠅⠔⠂⡂⠔⠂⡈⠅⠅⠂⡊⠆⠅⠄⠅⠐⠂⠔⠂⣿⠀⠠⠢⠀⡇⡃⡁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠠⠂⠅⡄⡂⡀⠅⠄⠅⠄⠄⠐⡊⡂⡂⠔⠅⡃⡀⠅⠄⠂⠄⠆⢹⡆⣈⣤⡿⠁⡂⠄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢁⢂⡂⡂⠂⡂⡂⢂⡈⠄⠅⡂⠨⠕⠅⡊⡡⡂⠆⠁⡂⢂⡁⡂⡑⣸⡏⢉⡁⠄⢅⢈⠀⣮⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠅⠐⡑⠅⠅⠄⡂⠂⡂⠔⠅⢑⡢⡂⡂⢑⠆⠄⡂⠅⠐⢂⠅⠁⣿⠀⠌⠄⠐⠈⡡⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣷⠀⠔⠅⠅⠅⡂⡡⠄⡂⠄⡂⠢⢅⠡⠂⣈⣀⣁⣈⠂⠠⠢⠁⣮⣽⣶⣶⣶⣯⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠦⡊⠑⡁⠁⠅⠃⢕⡑⢅⡁⡁⠅⣺⡋⡉⠀⡡⠂⠨⠅⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⡂⢄⡉⠛⢿⡿⣾⣶⣶⣶⣶⣶⣿⣆⠀⠄⠊⠢⠄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠠⠅⠔⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠄⠌⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣈⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣠⡾⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⢤⣄⣀⡟⠉⠀⣸⣄⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠈⣹⣇⣀⣴⠿⣏⠁⠀⠀⠈⠙⢶⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠁⠀⣿⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣤⣤⡴⠟⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀
⠀⠀⠀⠀⢠⡴⠾⢷⡄⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢦⡀⠀
⠀⠀⠀⢠⡏⠀⠀⣸⡿⠀⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⠀
⠀⠀⠀⠈⣧⠀⠘⠋⠁⠀⣿⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡀⠀⠀⢀⣼⠁
⠀⠀⠀⠀⠘⠳⣤⣤⣤⡾⠻⢷⣤⣿⡼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠉⠛⠷⣶⡛⠁⠀
⠀⠀⠀⠀⠀⢰⠏⢠⡿⠀⠀⠀⠈⠉⠁⠈⠻⣦⣄⣀⠀⠀⢀⣀⣤⡶⠟⠁⠀⠀⠀⢹⡀⠀⠀
⠀⠀⠀⠀⠀⣸⠀⢸⡇⠀⠀⠀⢀⣀⡀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠁⠀⠀⠀⢀⣀⠀⢸⡇⠀⠀
⠀⠀⠀⠀⠀⠸⣆⢸⡇⠀⠀⢰⠻⢶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢳⣎⡆⢸⡇⠀⠀
⠀⠀⠀⠀⠀⢰⠋⠸⣧⠀⠀⢯⢷⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣾⡇⢸⠃⠀⠀
⠀⠀⠀⠀⠀⢺⣶⠷⢿⡄⠀⠈⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⢡⡟⠀⠀⠀
⠀⠀⠀⠀⢰⠏⠁⡀⠈⢻⣦⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀
⠀⠀⠀⠀⢿⡄⠀⠙⠳⠟⢉⣿⠷⣦⣤⣀⣸⣧⡀⠀⠀⠀⢀⣠⣿⣤⣴⡞⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢹⣶⣤⣤⣴⣿⠃⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⣇⢿⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢿⢸⡇⣼⡇⠀⢠⡀⠀⣠⡾⠛⠛⢿⣆⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀
⠀⣠⠶⣛⣟⣓⣾⣿⡇⢸⣇⠀⣾⠁⣴⠏⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀
⢰⡏⠸⣯⣉⣽⡿⣸⡇⣾⠛⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⢰⣾⠁⠀⠀⠀⠀⠀⠀
⠸⣇⠀⠈⠉⣁⣴⠟⣰⡏⠀⠀⢹⣇⢠⡟⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀
⠀⠙⠻⢿⣿⣭⡴⠾⡿⠀⠀⠀⠀⠻⢾⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡏⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⣼⡇⢻⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢠⡏⠻⣄⣀⣤⠴⡿⠋⠀⠀⠀⠀⣿⠁⢸⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠻⣤⣄⣀⣤⠴⠞⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢿⠶⠞⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡶⠦⠤⠤⠶⠛⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠟⠻⠿⢿⣿⣧⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⡟⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠉⠛⠿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣇⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣶⣶⣶⣿⣿⠃⠀⠀⠀⠀⢀⣴⠟⠛⣦⠀⠀⠀⠀⠀⣸⣿⣿⣿⠿⠿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠙⠛⠛⠛⠻⠿⣿⣿⣆⡀⠀⠀⠀⠘⣧⣀⣠⡿⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣶⣴⣶⣴⣿⣿⠛⠉⠀⠈⠙⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣿⣿⡿⠟⠛⠻⡿⢇⠀⠀⠀⠀⠀⢸⣿⣿⣶⣤⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠂⠀⠀⠀⢠⣦⠰⠆⠀⠀⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⣦⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⣤⣤⣶⣿⣿⣿⣶⣶⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⣴⠟⠋⠻⣦⠀⠀⠀⠀⠀⢈⣿⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣭⣿⣿⣿⣟⡁⠈⠉⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣷⠄⠀⠀⠀⢿⣆⣀⣠⡿⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀
⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⠿⢿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠸⣿⣶⣾⣿⣿⣿⣷⣦⡀
⠀⣰⣿⣿⣋⣸⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⣿⣿⡏⠈⠙⠿⣿⣿
⣰⣿⠟⠛⠿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣦⣤⣶⣿⣿⣦⡀⠀⠀⢀⣴⣿⣿⠁⠀⠀⠀⠈⠻
⣿⢿⣦⣄⣼⣿⣿⠿⠀⠀⠀⠀⣠⣴⣶⠿⢶⡄⠀⠀⠀⠀⠈⣿⣿⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠿⠟⠛⠛⠛⠻⠿⠿⢿⣿⣷⣶⣦⣤⣀⠀⠉⠛⠛⠛⠛⠋⠻⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢀⣼⠟⠉⢠⣤⣾⣿⠀⠀⠀⠀⠀⢸⣿⡿⠿⠿⢿⣿⣿⣶⣤⣄⢀⣾⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣸⣿⣿⠇⠀⠀⠀⠀⣾⣿⢀⣴⣾⣿⣿⡟⡄⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⠏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⣿⣿⣿⡏⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠃⠃⠀⠀⢠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡟⠀⠀⠀⢠⣶⠟⠉⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢹⣿⣿⣧⡀⠀⠀⠀⠀⠹⢿⣿⣿⡿⠟⠁⠀⠀⣠⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢠⡴⠟⠁⣴⣶⡾⠛⠛⠋⣽⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⡿⣿⣷⣦⣤⣄⣀⣀⣀⣀⣀⣠⣤⣶⣿⣿⣿⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⠈⠻⠟⠿⠶⢶⣾⣿⣿⣿⣾⡁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣦⣄⢹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⣿⣿⣧⠀⠉⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉⠀⢿⣿⣧⣤⣤⣶⣶⣤⣀⠀⠀⠀⣴⣦⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⠈⠉⠛⠿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠟⠛⠛⠿⣿⣿⣶⣴⣿⣿⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠋⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠈⠻⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢨⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣶⣶⣶⣤⣤⣤⣶⣶⣾⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧⡀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⡿⠻⢿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢿⣿⣷⡀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣧⠀⠀⠈⠙⠻⢿⣿⣿⣿⣷⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠁⠈⢿⣿⣷⡄⠀⠀
⠀⠀⠀⠀⠸⣿⣿⣷⣤⡀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣷⣶⣦⣄⣀⣠⣴⣿⣿⡿⠋⠀⠀⠀⠀⠻⣿⣿⣆⠀
⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣷⣦⣀⠀⠀⠀⠀⢀⣄⠀⠈⠉⠙⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣀⣀⣀⣀⣀⣠⣶⣿⣿⣿⠿⠟⠛⠛⠋⠉⠛⠛⠿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣷⣄⢀⣴⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣤⣶⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣏⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⢻⣿⣿⡄⣠⣴⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠋⠀⠀⢿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠉⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀
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