2025年5月9日 2025年5月9日
この記事ではかわいいハム太郎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
プレビュー画像の下にある枠内をクリックすると簡単にコピーできるので、お気に入りが見つかったらコピペしてお使いください🐾
⚠️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(◞ ̫◟)💭🌀⚠️
アスキーアート🐹☆彡
`／￣＼ ／￣ヽ
//⌒ヽr “”””ﾂｯｯ ／⌒ヽ
Y ミ/⌒＼ `彡 |
ヽ_｜＿ ＼ ＿ヽ_ノ
/(⚫) `(⚫)｜
工 ￣(_人_)￣ 工
＼ ヽノ ／
_＞- ＜
(ﾐ) (ﾐ)
~( 厂
(_＞―-＜_)
ドットアート⭐️
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⡒⡒⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⢡⢆⢢⢌⡘⡪⠱⢢⢔⡢⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⢅⡨⡕⠸⢕⢸⡪⡕⡣⢢⢎⡣⢆⡙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡐⢣⢆⡔⢎⡘⠱⢢⢌⡑⡪⢱⡪⢜⡱⢢⢌⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢇⢪⢌⡨⡜⡪⡜⡱⢢⢌⡑⠘⣁⡬⠥⠤⣌⠈⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⢕⡆⡐⡪⢸⡪⢌⡨⣠⠞⠁⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⣠⢚⢅⡐⢊⡑⠢⢄⡙⢦⠀⠀⠀⠀⢀⣄⢀⡤⣤⡤⣤⣘⣐⢊⡅⡨⡕⠸⢕⠆⠞⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢀⠋⢘⢪⡱⢢⢔⡊⠡⠔⠸⢕⡙⡀⠀⢠⢋⠟⠴⡉⠢⠔⠢⢌⡰⢢⢌⡑⡣⢌⡕⣼⢡⠥⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢀⢃⡃⢐⡸⠕⢊⡡⠔⠪⠇⠪⢱⠊⡞⡝⢄⢡⢜⢪⢇⢢⡌⠕⢘⡱⢜⡑⠢⢎⡘⢡⢅⣒⠉⠀⠀⠀⠀⠀⠀⠀⡼
⠀⡏⢕⡊⠨⢜⡊⢑⡊⠡⢌⡡⢌⣑⢸⢨⡢⢔⢸⡣⢆⡔⡢⡔⡘⠱⢣⡪⡅⠨⢕⢱⡣⠱⢪⢍⢦⡀⠀⠀⢀⠴⠟
⢰⢈⠨⣑⣐⣘⣑⠜⢇⢢⢌⡡⢌⣕⢧⢆⢌⡑⠢⢌⡘⢑⢪⡌⡨⡌⢕⡸⠪⠱⢪⡸⢕⡘⠱⢢⡸⢪⡚⢭⠚⠁
⢸⡴⠉⠀⠀⠀⠀⠀⠙⠦⠑⡢⠞⠀⠀⠙⠧⡢⢌⡑⢱⢕⡊⠡⢌⡘⠱⠜⢁⣴⣶⣷⣶⣦⡈⠱⢢⢌⡜⡑⠳
⢸⠀⠀⠀⠀⠀⠀⠀⠀⣒⣍⠎⠀⠀⠀⠀⠀⠀⠉⠚⢼⣱⢢⡌⡘⡊⡑⣴⠟⠁⠀⠀⠙⣿⣿⣷⠘⡪⡕⢎⡔⠹⡀
⠈⡀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠳⠅⡟⠀⠀⠀⠀⠀⢸⡟⠛⣷⠸⢕⢣⡱⢪⠹
⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⣿⢿⣿⠴⣢⢔⡎⢜⡑⢳
⠀⠀⠀⠲⣄⣀⠀⠀⢀⣈⠀⠀⣠⣿⠋⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣤⣄⣤⣾⣿⡀⠀⡟⠀⠀⠈⠛⢑⣁⠂⡄
⠀⠀⠀⠀⠀⠈⠉⠛⠉⢹⠀⢰⣿⡏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⠋⠀⢀⠴⠊⠁⠀⠈⢮⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣷⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠛⣿⣶⣶⣿⠇⠀⠰⠭⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠳⣤⣿⣿⡿⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠓⠒⠦⣄⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢠⡀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡗⠒⠒⠂⠀⠀⠀⠀⠳⡀⠀⢀⢯⠢⡍⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡠⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⣌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡡⢜⢢⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣦⡎⢜⢱⢅⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⢆⡌⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⣀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢵⡕⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⠈⢷⣈⡄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢕⡎⢜⠀⠀⣠⠉⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢸⢕⡽⠀⢰⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣀⠤⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠁⠉⠉⠉⠒⠒⠒⠒⠒⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⠶⠶⣤⣀
⠀⠀⠀⠀⠀⢀⠶⡋⢰⡎⢱⡎⢱⡎⢱⡎⢢⡌⠳⣄
⠀⠀⠀⢀⡾⡅⢱⡎⢱⡎⢱⡎⢱⡎⢱⡎⢱⡎⢱⡦⠙⣄
⠀⠀⢠⢋⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⢠⢃⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢆⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡛⢅⡰⢖⡣⢔⡢⢌⡙⠲⣄
⠀⡟⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢕⡣⢜⡣⢜⡣⢜⡣⢜⡣⢜⡣⢆⡉⢦⡀
⢠⢀⡸⢃⣤⠶⠒⠒⠲⠦⣬⡃⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⣷⢀⣠⡤⣤⠶⢙⢀⣠⣤⣄⠀⠀⠀⠀⠀⢠⢋⡣⢜⡣⢜⡣⢜⡣⢜⡣⢜⡣⢜⡣⢜⡳⢗⡉⣦
⢸⠨⡼⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⣬⠣⢜⡣⢜⡣⢜⡣⢜⡣⣠⠟⠅⣊⠞⣡⠞⢩⢒⣨⡥⠶⠓⠒⢦⠀⢀⠏⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢢⢷
⢸⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⢕⡪⢕⡪⢕⡪⢌⡰⢕⡌⢔⡣⢆⡸⢇⡸⢎⡹⢇⡸⢇⢾⣀⣼⡸⢇⡸⢇⡸⢇⡸⢇⡸⢇⡸⢇⡸⢇⡸⢇⡸⢇⡸⢇⡱⢷
⠀⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠉⠓⣦⠾⠛⠉⣮⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢢⡅⢱⡎⢱⡎⢱⡎⢱⡎⢱⡎⢱⡎⢱⡎⢱⡎⢱⡎⢱⡎⢱⡆⡆
⠀⢹⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡟⠀⠀⠀⠀⠀⠈⣎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢊⡥⠶⠛⠛⠛⠛⠲⢬⣑⢎⡱⢮⢹
⠀⠀⢳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⡱⢎⢁⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⢕⠈
⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣮⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢅⡛⢛⡒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠈⠾⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⠶⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢰
⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡾
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⢷⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣰⠁
⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⢠⣿⣿⣿⡿⠉⠀⠀⠉⠻⣆⠀⠀⠀⠀⠀⠀⠙⣮⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢽⠀⠀⠀⠀⠀⠀⠀⢀⡞⣴⠁
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠙⣧⢜⡣⢜⡣⢜⡣⠜⣡⣴⣶⣶⣤⣈⠱⡎⢱⡎⢱⡎⢳⠀⠀⠀⠀⣀⠶⣩⠛
⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⣾⡁⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡕⢪⡕⣴⣿⣿⠿⠿⠿⣿⣿⣿⣦⠘⢣⡜⢣⢬⢒⣒⣫⠭⠖⠉
⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⣿⣿⡶⠿⢿⣄⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣼⣿⠋⠀⠀⠀⠀⠀⠻⣿⣿⣿⡘⡣⢜⡣⢸
⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⢹⣿⣶⣶⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠪⢕⡪⠅⡆
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⣸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢸⣇⡆⡇
⠀⠀⢨⠉⠉⠛⠲⢤⣀⠀⠀⠀⠈⠒⠿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⠀⠀⠀⠀⢀⣾⠁⠀⢘⣿⠀⢌⡸⢧⣿
⠀⠀⣸⠀⠀⠀⠀⠀⠀⠉⠶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣶⡿⠋⠉⠙⢶⣿⣿⡰⢎⡱⠮⢻
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠁⠀⠀⠀⠀⣿⠁⠉⠓⢮⣱⢸
⠀⠀⣿⠀⣀⣀⣤⣤⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣀⠀⠀⠚⠀⠀⠀⠀⠀⠀⢸
⠀⠶⢻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠁⠀⠈⠉⠉⠛⠶⠄⡿
⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⢀⣀⡴⢧⠀⠀⠀⢀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⣄⡀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⣠⠋⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤⠀⣠⠁
⠀⠀⠀⠀⠀⠀⣧⠀⠀⢀⠃⠀⠀⠀⠠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⣸⡰⡟⠀⢸⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⢀⠾
⠀⠀⠀⠀⠀⡏⠟⠀⠀⠀⢧⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⢴⢅⣧
⠀⠀⠀⠀⣸⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢻⡘⡀
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⠾⠀⠀⠀⠀⠀⠀⠀⢳⣧
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣀
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠛⠄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡞
⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠋
⠀⠀⡤⠋⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠠⣋⡤⠀⢀⠉⠲⠤⢤⣤⣤⣤⠤⠤⠤⠶⠶⠒⠚⠛⠛⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠒⠒⠶⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢯⡀
⠀⠿⠴⢻⡁⣀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠳⡛⠋⠁⠀⢀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⣀⢶⣄⠙⡦⠇
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⣠⠖⡉⡀⢈⡁⠔⡢⡂⢉⠲⡀
⠀⠀⢀⠞⠠⠢⠕⠆⢊⠐⠂⠂⢐⠅⠑⠌⣆
⠀⢀⠃⢅⡂⢐⡂⢔⡢⢀⡐⢂⡐⢂⡐⡑⡘
⠀⡟⠋⠉⠛⠦⡑⠊⢐⢄⡐⢂⡀⡂⠀⠂⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠒⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠳⡁⠠⠢⠢⠐⠂⠀⠑⣸⢔⡶⣋⡾⢒⣋⣭⣁⣀⠀⠀⠀⠀⢠⢋⠆⡑⡀⠠⠄⡠⠄⠄⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣌⠄⡂⣸⠮⠅⠌⡐⡀⠐⡠⢂⠠⢘⢛⠛⣭⣓⡄⠀⢠⢁⢌⡐⡁⢄⡂⢅⢄⡨⢀⠠⠄⢦
⠀⢧⠀⠀⠀⠀⠀⠀⢘⡚⡰⠊⠀⠀⠹⢂⠎⠐⢂⡑⠁⢀⡐⠁⢈⢌⡠⡉⠳⣏⠑⢑⢊⡑⢂⡑⠑⠂⢑⡂⢀⡑⡀⡄
⠀⠀⠳⣀⠀⠀⠀⠀⡀⠛⠀⠀⠀⠀⠀⠳⢅⡐⢂⡐⢂⢐⢕⡂⡐⢂⡐⢅⢡⡰⡂⢌⢨⢕⠢⢑⡂⢐⠨⢐⡂⠨⠐⢹
⠀⠀⠀⠈⠻⣶⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠙⡕⡠⢑⡈⠀⢅⡈⢈⢨⡑⢅⡨⢈⢅⢕⡨⢄⢌⡈⠁⠊⢁⡨⠢⢈⢌⡈
⠀⠀⠀⠀⠀⠀⢀⠃⢚⣿⣶⠖⠒⢿⡉⠀⠀⠈⢧⠘⢁⠅⠨⢅⠅⠡⠨⠅⡨⢅⡢⠔⢀⣤⠒⠛⠉⠉⠉⠓⢦⡁⢈⢰
⠀⠀⠀⠀⠀⠀⡏⣰⣿⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⣆⢐⢢⠅⠐⢐⠰⢊⠅⠨⠢⡢⠠⣕⠍⠀⠀⠀⠀⠀⠀⠈⡆⡾
⠀⠀⠀⠀⠀⣸⠀⣷⣀⣿⡄⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠙⢕⠂⠨⣂⣙⣄⠢⢐⠕⠪⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⢀⣀⡀⠀⣠⠁⠀⢿⠏⠀⢹⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠈⢻⣦⣈⠁⢄⠅⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠉⠳⣄⠀⠀⠳⠤⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⠶⢨⡴⢽⣦⣤⣠⠤⠚⠁
⠀⠀⠀⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⠄⠀⠀⠀⠀⠀⣿⣦⡀⠀⣀⣾⠀⢻⠰⣨⡏
⠐⠉⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠉⠀⢻⣿⡟⠀⠀⡇
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⣀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢤⣤⠾⠋⠀⠀⠀⠁
⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠦⠤⣄⢸
⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⡏⠈⠓
⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡼
⠀⠀⠀⠀⠀⠀⣰⠈⠀⠀⠤⠒⠚⠋⢹⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠓⣀
⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⡼⠒⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⣠⡤⡞⠁
⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⡤⠧⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⢸⠳⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⠀⠀⡇
⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠈⡾⠀⣿⠛
⠀⠀⠀⠹⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠁⠀⡏⠎
⠀⠀⠀⠀⠑⣄⢳⣤⠤⠤⠶⠶⠒⠒⠒⠶⠶⠤⠤⣤⣀⣀⡀⠀⠀⢀⠏⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⢉⡉⢉⢙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢤⣍⡛⣟⣍⠍⣍⢭⡭⢥⡌⢩⡭⢭⣍⣙⡛⠻⠿⣿⣿⣿⣿⣿⣿⠟⡀⡐⡐⠪⠪⢕⢅⡊⡊⢐⡈⠢⢉⠻⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡯⢮⢗⣌⠺⣶⣇⠪⢮⢵⡹⡪⣝⡳⢯⢦⠳⣙⣳⢦⣍⡛⢿⡀⠨⠡⠅⠡⠄⠠⠅⠡⠄⠨⠅⠨⠌⡑⠡⢀⠻⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣝⡶⠶⡒⣒⡫⠺⣗⡮⣙⠙⡩⢮⣝⣕⣪⢦⠳⡙⡽⢮⡽⣲⣙⠦⣀⠪⠅⠨⠅⡨⡑⠈⢁⡤⡆⢑⠌⠌⠡⠹⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣕⡺⡵⢯⢵⢮⣝⡦⣙⠺⣝⡲⢥⣙⡫⠝⣝⣌⢦⢪⣪⣝⣝⡽⡲⡑⢄⠁⣀⡤⢖⣫⣮⠖⡀⠨⢐⡊⢑⠀⢻⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠉⠉⠉⡛⠻⣿⣌⢮⣞⣝⣝⣑⡥⠶⣚⡭⢮⣖⡭⣙⡒⠯⢭⣛⣓⣓⣒⣒⣒⣚⣛⣩⣭⠶⠒⡋⢉⠄⢂⡑⢂⡐⠢⢐⠂⠐⠸⣿⡇
⣿⣿⣿⣿⣿⣿⠛⠁⠐⠢⠐⠢⠄⠠⠄⠨⠕⠕⠢⢈⢦⠯⢽⡳⢮⣕⡪⢝⡳⢮⣕⡪⢝⣝⡝⣊⢖⣥⢖⡲⣖⣲⢖⠳⡴⠁⠑⣈⡥⠴⠒⠒⠒⠒⠒⠤⣌⠢⡢⠀⣿⡇
⣿⣿⣿⣿⠟⢀⡐⢊⡂⢐⡑⢂⡁⢐⡑⢂⡐⢐⡂⢈⡀⠙⢜⢗⣗⣗⡺⢽⣗⡪⢕⠪⣡⢖⢭⢮⣞⡽⡫⡫⡪⠝⣣⠋⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⢸⣿⡇
⣿⣿⣿⠃⢂⠅⡊⡑⠨⠡⠪⢕⢌⠅⡊⡑⠨⠡⠪⢕⡢⢂⢂⢉⠮⣙⢺⢽⣳⢮⣋⣕⣝⣝⣝⡽⣳⢮⠮⣊⠴⠋⡐⠁⡊⡂⠰⢤⠤⠶⠚⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇
⣿⣿⠇⡨⡐⠠⠄⠠⠄⠠⠄⠠⠄⠠⠄⠠⠄⠠⢔⡂⣴⢲⠠⠄⡑⢂⡉⠒⠥⣬⣊⣙⣙⣙⣙⡥⠴⠚⢉⡠⡢⠄⠠⠄⠠⢂⠠⠓⠤⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⣿⣿⠀⠠⠄⠨⠄⠠⠅⠨⠄⠠⠅⠨⠄⠠⠅⠨⠨⡾⠀⠀⠈⢦⠨⠅⠠⠄⠐⠐⠠⠐⠐⠐⠠⠅⠐⠨⠅⠠⠄⠨⠄⠠⠅⠡⠄⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇
⣿⣿⡈⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡵⠋⠀⠀⠀⠀⠀⠈⢦⣐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⢐⡂⠝⡄⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⡇
⣿⣿⠀⢅⡊⢑⡈⢁⡊⢑⡈⠅⠊⠑⣁⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠅⠊⡑⢈⡁⢊⡑⢈⡁⢊⡑⢈⡁⠊⠑⠀⠂⠊⠅⠂⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⠀⢁⠌⠡⢈⡁⡈⠁⠀⣨⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠉⠪⣡⠈⠡⠌⡁⢈⡁⢈⡁⠨⠅⣠⡾⠿⠿⣿⣿⣶⡀⡂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣦⠥⠥⠬⠥⠶⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁⠀⠀⠀⠉⢦⠀⠀⠀⠈⠓⠮⣬⣅⠨⢐⢕⠊⣾⠃⠀⠀⠀⠀⢿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣼⢟⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢡⣿⠀⠀⠀⠀⠀⠈⣿⣽⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣶⣤⣀⣀⡀⢀⣀⡤⣒⣡⠀⠀⠀⢀⣿⣸⣇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⢰⣿⠀⣿⡠⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⡀⠀⣿⡀⠀⠀⠀⠀⠀⣠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⠀⣠⠋⠛⣠⠇⠈⣄⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⠏⠀⠀⠱⣤⣤⣤⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠿⢷⠀⠀⠃⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⣛⣽⣿⡿⠁⠀⠀⠀⠀⠀⠒⠤⠚⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠤⠤⣤⣀⣀⣀⠀⠀⠙⠛⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣀⡤⠤⠒⠒⠒⠒⠂⢰⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣀⣠⠤⠴⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⣠⠋⠉⠒⠒⠊⠀⠀⠀⠀⠀⠀⠒⠒⠦⢤⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡹⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⡀⠉⢶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡀⠀⠀⠀⠀⠀⠀⢀⠋⠈⠁⡿⢻⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⢆⠈⠀⠱⠀⠀⠀⢤⠀⠀⠀⠀⠀⢀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠙⢄⠀⢀⡀⠀⠇⠀⠀⠀⠇⣼⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠑⠶⣒⡭⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢧⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⣾⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⣮⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠋⠉⠙⠒⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠛⠓⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠉⠉⠙⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠈⣸
⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡞⠘⠀⡤⠚⠁⢙⣠⠤⠶⣄⠀⡇⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⣼⠀⠀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡠⠞⠀⡤⠁⠀⡤⠋⠀⠀⠀⠖⠓⠒⠺⠆⠀⠀⠀⠀⢸⠞⢉⠃⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⡇⢠⠋⠀⠀⠀⠀⠀⠉⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠞⢁⠎⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢉⠟⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⢀⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣄⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠲⣷⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⢯⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⢳⢚⡛⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠉⠀⠀⠈⠻⣿⣿⣷⠀⠀⠀⠀⠀⠀⣆⢎⡸⢇⣐⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻⣿⠟⢷⠀⠀⠀⠀⠀⠘⠈⢱⡎⠑⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⡾⠀⠀⠀⠀⠀⢀⣿⣿⣿⠟⠉⠀⠈⠛⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣼⣿⣦⣼⡇⠀⠀⠀⠀⠀⣇⢇⠈⡾⠉⠀⠀⠉⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⡰⢇⡐⠹⡇⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣀⠀⠀⢀⣴⣿⡿⠿⣿⡇⠀⠀⠀⠀⠀⢸⢚⠙⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠏⢔⡪⢕⡪⢕⠁⠀⠀⠀⠀⠀⣸⣄⣀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢋⢦⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⢧⠃⢸⡇⢸⡇⢠⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣄⠀⠀⠀⣀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⢐⡪⢕⠹⠲⡀⠀⠀⠀⡀⠀⢸
⠀⠀⠀⠀⣠⠴⠒⠒⠳⡈⢱⡎⢱⢸⠀⠀⠀⠀⠀⢹⣿⠛⠙⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠔⠒⣠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢕⡪⠕⡇⠙⡀⠀⠀⣷⠀⡎
⠀⠀⡴⠉⠀⠀⠀⠀⠀⠈⠳⠤⠴⠋⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠶⠶⢼⠤⠅⢈⠞⠀⠀⣷⠀⠀⣟⡜
⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠶⠋⡆⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⡞⠒⠋⠀⠀⠀⠀⡿⠀⢠⠁
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⡜⠣⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢃⡴⠁
⣼⠀⠀⠀⠀⠀⠀⠀⢀⠋⣼⢕⡪⢕⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡼⠀⠀⠀⠀⠀⠛⠉
⣇⠀⠀⢀⠋⠁⠀⢀⠃⠀⢻⢪⡕⢪⡕⢷⠀⠀⣀⡤⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣰⠁⠉⠒⠦⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠶
⠸⠀⠀⡟⢸⠀⠀⡞⠀⠀⠀⠙⠦⣥⡤⠃⣦⠋⠀⠀⠀⠀⠀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⠶⠋⠀⡄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠙⠦⣜⣬⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⢧⠀⠀⠀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠚
⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⣸⡆⢳⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡊⡇⡇⠄⣆⠷⡚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠃⠀⠀⠀⠀⠀⠐⠋⠉⡆⢀⣞⡇⡇⠸⣠⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡴⡇⡇⢺⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡇⠇⡇⡎⢾⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢉⡞⣇⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠞⡄⡆⣇⢎⡱⠀⠙⡖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⠀⠁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢹⢘⡃⡇⢹⠸⢇⣸⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡆⢆⢷⠀⠦⠶⣡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠖⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⣸⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠒⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠈⠲⠤⢤⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⠀⡀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠋⠧⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠙⠉⠙⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠉⠲⣀
⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⢰⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠸
⠀⠀⠀⣏⠋⠀⠂⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣣⠔⡩⣅⠤⣊⠼⣖⣲⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠈⢦
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢄⠀⠀⠀⠀⠀⠐⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡥⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠺⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⡀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠄⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠈⣢⣶⣿⡀⣀⡼⠀⠀⠀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⠀⠀⠘⣀⠀⣰⣶⣦⣊
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣯⡽⠀⠀⣴⣿⠟⠉⠉⠉⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⠛⣿⣿⡄⠀⠘⢁⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠘⣿⣿⣿⣿⢿⣾⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⢹⣿⢿⣿⣿⣿⡟
⠀⠀⠀⣀⠤⣌⣿⣿⣷⣗⡟⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣞⣯⣿⣟⣋⠤⣤⡀
⠀⡴⠁⠀⠀⠀⠀⠙⣿⢼⠇⠀⠀⢿⣦⣼⣄⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⠀⢀⣾⣤⣿⠃⠀⠀⣿⣽⡿⠁⠀⠀⠀⠀⠑⡀
⢠⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠻⣀⠈⣿⣿⣿⣿⠋⠀⠀⠀⠀⡤⡤⠀⠀⠀⠀⠻⣿⣿⣿⠏⠀⣸⠃⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹
⢸⠀⠀⢠⠚⠁⠀⡤⣲⣭⡦⣤⣀⣀⠀⠀⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⠀⣀⣀⡤⣿⣷⡲⡀⠀⠉⢦⠀⠀⢸
⠈⡀⢠⠁⠀⢀⠃⣼⣿⢼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⣿⣿⡀⢣⠀⠀⢳⠀⡼
⠀⠙⢼⠀⠀⠇⢰⣿⣿⡺⢟⣆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⠾⣿⣿⢿⠀⡆⠀⢈⠔
⠀⠀⠈⡀⢸⠀⣿⣿⣟⣽⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠶⠚⠀⠙⠶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣾⣯⣝⣾⡿⡀⢸⠀⡼
⠀⠀⠀⠈⠪⠀⠙⠿⣿⣻⣿⣿⠃⠓⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢿⣿⣿⣿⡿⠛⠁⠼⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠤⠤⢤⣤⣤⣤⣤⠤⠤⠤⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣫⣶⣿⣿⣿⣿⣿⣿⣯⡳⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⠶⠚⠛⠶⠶⠶⢦⣾⣚⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢷
⠀⠀⠀⠀⢀⡶⣫⣶⣿⣿⣿⣿⣶⣭⡲⣄⠀⠀⢀⣤⠶⣛⣭⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣭⣙⠷⣭⡻⣿⣿⣿⣿⣿⣿⣷⢷
⠀⠀⠀⣴⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣯⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠳⣞⠛⠛⠶⣭⡻⡞
⠀⠀⡾⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡳⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢷⠀⠀⠀⠈⣆
⠀⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠹⡀⠀⠀⣸
⢀⡏⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣱⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠹⡀⢠⠃
⠘⡇⣿⣿⠿⣯⠶⠛⠉⠉⠉⠉⠉⠙⠲⠭⡻⢏⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⠁
⠀⢷⣿⣱⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⢭⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡇
⠀⠀⢷⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣡⣿⣿⣿⣿⣿⠿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⠀⠀⠀⠉⠶⣄⡀⠀⠀⠀⠀⠀⠀⣠⢞⣾⣿⣿⠿⣉⠴⣛⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⡛⠛⠻⠿⠿⣿⣿⣿⢸
⠀⠀⠀⠀⢀⠇⣦⣭⣍⣛⣛⣭⣵⣾⣿⠟⣩⢖⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣉⡥⠶⠚⠋⠉⠉⠀⠀⠀⣰⠀⠀⠈⠻⣿⣶⣍⣼
⠀⠀⠀⠀⢸⣸⣿⣿⠟⣴⣸⣿⠟⣡⢚⣵⣿⣿⣿⣿⣿⣿⣿⠿⣋⣭⠶⠛⠉⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸⣿⣷⠁
⠀⠀⠀⠀⣿⢣⢸⠏⢯⢡⢋⠖⠥⣩⠯⣿⣿⣿⣿⡿⢛⣡⣶⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣸⡤⣿⣆
⠀⠀⠀⠀⡇⠇⠌⣘⢃⢞⠕⡵⣫⣾⣿⣿⠿⣉⡴⢛⣿⡯⢿⣿⡀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣤⣠⡴⠛⠳⣿⠘
⠀⠀⠀⠀⡇⡟⡞⡀⡗⢦⢫⣿⣿⡿⢋⡴⠋⠀⠀⠈⣿⣄⣠⣿⣿⣤⣀⣤⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣇⣀⠰⠁⠀⣇
⠀⠀⠀⠀⠹⠃⢨⢄⡐⡀⣇⠟⣡⠞⠀⠀⠀⠀⠀⠀⢻⣿⣷⠀⠀⠀⡟⣻⣿⠟⠀⠀⠀⠀⠀⠀⠀⣖⣉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⠖⠚⠉⠁
⠀⠀⠀⠀⢸⠈⠲⣌⣑⢈⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⣀⣴⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⠀⠀⠀⠘⠁⢸⡳
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⣆⠀⠀⢀⣀⣤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⢺⢓⠧⠤⣤⣀⡀
⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⡟⢀⠃
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⢀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠳⣤⣀⣀⣀⣤⠖⠉⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⣼⣱⠁
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⠁
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢀⠇
⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢠⠀⣸
⠀⠀⠀⠀⠀⠀⠀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣶
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⢠⠶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⢸⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⣸⡼⡇
⠀⠀⠀⠀⡆⡇⠀⠀⠀⠀⣤⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⠄⡁⢠
⠀⠀⠀⠀⠈⣷⠀⠀⡾⣿⢸⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡐⡂⠅⢀⠇
⠀⠀⠀⠀⠀⠸⡀⢰⠀⡂⢌⡑⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠠⠢⠢⢠⠋
⠀⠀⠀⠀⠀⠀⠹⣸⠠⠢⠪⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢊⠈⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⡀⢌⢌⠄⡏⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠶⠶⠶⠶⠶⠤⠤⠤⢤⠤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠶⠚⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠐⡑⣰⠦⠤⠶⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣩⣶⣶⣾⣿⣿⣿⣿⣶⣍⠻⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣫⣵⣶⣶⣴⣴⣦⣬⣭⡛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢟⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣦
⠀⠀⠀⠀⠀⠀⠀⣰⠫⢛⣭⣴⠶⠶⠶⢶⣍⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣷
⠀⠀⠀⠀⠀⠀⢀⠏⡾⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡙⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠜⡄
⠀⠀⠀⠀⠀⠀⣼⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠽⣛⣭⣥⠶⠶⠛⠛⠶⣦⣥⠣⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢑⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢹
⠀⠀⠀⠀⠀⢸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⣿⣿⣿⣿⣿⡿⠟⣋⣤⡧⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠳⠶⣤⣀⣧⢿⣿⣿⣿⣿⣿⣿⣿⢋⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣄⢿⢻⣿⠟⣋⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣬⡛⢿⣿⣿⣿⢃⣿⠶⣛⢛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽
⠀⠀⠀⠀⠀⠀⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣮⣭⣦⡻⢆⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣬⡻⡏⣿⢬⣴⠾⠿⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡟
⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄⣚⡛⢉⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣃⣙⣩⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣱
⠀⠀⠀⠀⠀⠀⠈⣞⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⠃
⠀⠀⠀⠀⠀⠀⠀⠹⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣣⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢷⡀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⣠⣿⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣮⡻⣦⡀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⣀⣤⠶⣛⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣬⠛⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⠶⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠿⠋⠉⠉⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠿⠿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣿⣿⠋⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣿⣿⡀⢀⣿⣿⣦⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⣼⣿⣦⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⢹⡟⠙⣿⣿⣿⣿⣿⣶⣤⣴⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⡀⣀⣠⣾⠿⠛⠿⣧⣠⡿⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠉⠉⠁⠈⠉⠉⠙⠛⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⣀⡴⠟⠛⠛⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢠⢧⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠶⠶⠛⠛⠛⢶
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⣀⣀⣠⡴⠋⠈⢷⣀⡀⠀⠀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠨⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⢿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⣆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⡀
⠀⠀⠀⠀⠀⠀⣠⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢻
⠀⠀⠀⠀⣠⠟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⣤⠟⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⢠⠟⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄
⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠶⠶⠶⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞
⠀⠀⠀⠉⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⢀⣀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠉⠀⠀⠀⡿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠁⠀⢉⡷⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣩⣤⣤⣤⣤⣤⣤⠶⠶⠶⠶⠦⣤⣤⣤⣤⣀⣀⣀⣀⡉⠛⠓⠶⠶⠶⠛⠉⠀⠀⠀⠀⠀⠀⣀⣾⠟⠁⠈⠻⣤⡀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⣤⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⢻⡛⠛⠉⠉⠀⠀⢷⠀⠀⠀⠀⠈⠛⠓⠶⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⢀⠀⠀⠀⠄⠀⣴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⣿⡴⢻⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⢲⣄⢻⢦⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠆⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠒⠛⠛⠒⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠛⠉⠉⠀⠀⠉⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠉⠀⠀⠠⠈⠨⠨⠡⠨⠄⠄⠀⠙⠶⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠶⠋⠀⠀⢈⢈⢈⢑⠅⢐⠁⡂⠀⠅⡂⠈⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠈⢐⠀⠠⢈⢈⢈⡂⠁⢈⠨⢐⡀⠻⣄
⠀⠀⠀⠀⠀⠀⡴⠁⠐⠀⠀⠀⠀⠀⠀⢐⡂⠀⠀⠀⠀⡂⡂⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠈⢦
⠀⠀⠀⠀⢀⠟⠠⢔⠄⠀⠀⠀⠄⠄⠄⠨⠅⠠⠄⠄⠂⡁⡣⠢⠄⠂⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠠⠄⠀⠄⠠⠠⠠⠀⠨⠠⠠⠄⠀⠄⠐⠠⠄⠠⠔⠄⢀⢷
⠀⠀⠀⠀⠟⢀⢈⢌⠠⢀⠀⠀⠀⠀⠄⠑⠂⢀⠀⡀⠀⠅⠅⡂⠁⡀⠀⠈⡄⠀⠀⠀⠀⢀⡴⢻⠀⢀⣀⡤⠴⣤⠀⠀⠀⠀⠀⢸⠀⠀⠁⠁⠈⠀⠀⠁⡁⠈⠠⠀⠡⠀⡀⠄⢀⠠⠠⢈⢄⢌⠨⠀⢷
⠀⠀⠀⣾⠀⠀⢐⢐⠐⠀⠀⠀⢀⢂⠀⢐⡂⢀⠀⠀⠀⡂⡂⠀⠀⠀⠀⠀⣷⢀⡴⢛⡽⠁⠀⠿⠛⠁⢠⠶⠛⠉⡉⠉⢙⠄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⢀⡀⠀⠀⢐⠂⠀⠀⠀⠀⠀⠈⡄
⠀⠀⢀⠃⠀⠀⠐⠈⣠⠤⠶⠶⠶⠶⣤⣀⠂⠐⠀⠀⠀⠅⠅⡂⠀⠀⠠⢀⠿⠁⠀⠋⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠉⠉⠙⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢐⠀⠐⠁⣀⣤⠶⠒⠛⠛⠛⠶⣤⠀⠀⣇
⠀⠀⢸⠀⡂⢂⡶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠂⡂⡂⡂⠀⡂⠀⡀⠄⡂⡂⡂⡊⡐⡂⠁⠁⠀⡂⡐⢐⡀⠀⠀⠀⠀⠈⡊⡂⠀⠀⡀⠀⠈⠀⠀⡐⢁⠐⢁⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⢹
⠀⠀⢸⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠂⡀⡁⠂⠐⠀⠐⠂⡂⠂⠐⠂⠐⠐⠂⠂⠂⠀⠐⠀⠐⠂⠀⠐⠂⠐⠂⠐⠂⠐⠐⠀⠀⠐⠐⠐⢐⠂⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠉⠉⠛⠆⡂⡂⡂⠀⠀⠀⠀⡂⡂⠂⡂⠀⠐⠂⠐⠂⠀⠀⠂⠐⠂⠀⠐⠀⠀⠀⡂⡂⠀⠀⠀⠐⠀⠀⠐⠀⣼⠴⠒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞
⠀⠀⠀⢻⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⡂⠁⠀⢅⠅⠅⠀⡂⠀⠀⠅⠅⡂⠅⡂⡁⢀⠀⠀⡁⡂⡁⢀⡁⠀⠀⠀⠀⠀⠅⠅⠀⠀⠁⢀⠀⠀⡀⠅⠀⠴⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⢳⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡁⠀⡂⡂⠅⠀⠁⠀⠀⠢⠅⡡⡁⡁⢁⡈⠀⠀⠀⡁⠁⢈⠁⡀⠠⠀⠀⠀⡁⡁⠀⠀⡀⠈⠀⠀⠀⢁⠄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠏
⠀⠀⠀⠀⠀⠙⣍⢦⠀⠀⠀⠀⠀⠀⠀⠀⡔⠠⠀⠄⠀⠅⠅⠄⠀⠄⠀⠀⠅⠄⠌⠄⠄⠄⠠⠀⠀⠀⠄⠄⠠⠄⠀⠈⠀⠈⠀⠄⠄⠀⠀⠀⠠⠀⠀⠀⠄⠠⢀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣫⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢬⡲⣤⣀⠀⠀⠀⠎⠅⠨⠄⠅⠀⠢⡂⡂⠠⠅⠀⠄⡂⡂⡁⠅⠁⠠⠄⠠⠄⡀⠡⠠⠨⠁⠀⠠⠄⠄⠄⠅⠅⠀⠀⠅⠠⠀⠀⠠⠨⠀⠨⠨⠪⡀⠀⠀⠀⠀⢀⡤⣛⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠬⣭⠁⢈⡀⢈⠀⡁⠁⡊⡁⠁⠂⠁⠀⠀⡁⠅⠁⠁⠁⠈⠑⠀⠂⠂⠁⠈⢈⠀⠁⠀⠀⠀⠀⠁⠂⠀⠀⠂⠈⠀⠀⠀⢈⠀⢐⠈⠈⠹⠒⠒⠛⣉⡴⠛
⠀⠀⡟⣍⠍⡆⠀⠀⠀⠀⠀⠀⠀⡇⠄⠠⠅⠠⠀⠀⠀⠄⠄⡀⠀⠀⠀⠀⡀⡁⠀⠀⠀⠀⠀⠀⠀⣄⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⢹
⠀⠀⣿⣟⣕⣷⠀⠀⠀⠀⠀⠀⢰⠀⢀⢘⡂⢐⠀⡂⠀⡃⡃⡂⠀⡂⠠⠄⠅⡂⡢⡁⡂⢐⡂⢀⡼⠀⠀⠛⣄⠀⠀⠠⠀⠀⠀⡂⡂⠀⠀⠀⠀⠀⠀⠀⢐⠀⢈⢐⢐⢐⡁⠀⡄
⠀⠀⢻⢺⣟⣿⠀⠀⠀⠀⠀⠀⣼⠀⠈⠐⠅⠈⠀⠁⠀⠂⠅⠁⠀⠁⠀⡀⡂⠅⠁⠁⠁⠁⣬⠋⠀⠀⠀⠀⠀⠳⣄⢀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⠐⠈⠈⠈⠁⡀⣧
⠀⠀⢸⢸⣯⢸⠀⠀⠀⠀⠀⠀⡏⠀⠀⠠⠄⠀⠀⠀⠀⠄⠄⠀⠀⠀⠂⠂⡁⠂⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠈⠨⡿⠸⠀⠀⠀⠀⠀⢀⠃⢀⢀⠨⠑⢤⣶⣿⣿⡶⢤⣀⠀⡂⠀⠀⡁⡀⣔⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄⠀⡀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣥⡐⢀⡀⠅⠈⡄
⠀⠀⠀⡇⡿⠅⡆⠀⠀⠀⠀⣸⠀⠈⠈⢐⠚⠛⠿⢿⣧⠀⠀⠀⢹⣦⡀⢠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠁⣠⡞⠀⠀⠀⣸⣿⠿⠿⠿⠄⡂⠀⠄⣇
⠀⠀⠀⣇⣗⡆⡇⠀⠀⠀⠀⡏⢀⠐⢐⡈⡁⢐⠀⡂⠀⡘⡒⠒⠿⣟⠉⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢻⡿⠒⠲⡊⢀⠀⢐⢐⢈⢐⡂⡀⠀⢻
⠀⠀⠀⣿⡻⢇⣿⠀⠀⠀⢰⠀⢐⠐⢐⠨⠅⢐⠀⡂⢀⣠⠗⠋⠀⠀⠉⠻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠋⠀⠈⠓⣤⡂⠢⠀⠨⢐⠔⢐⡂⡀⠀⠘⡀
⠀⠀⠀⢹⢪⣝⢿⠀⠀⠀⡟⠀⠨⠨⠨⡑⣄⡬⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡨⠡⠨⠅⠌⠨⠄⡇
⠀⠀⠀⢸⠨⢽⢸⠀⠀⢸⢀⣤⠬⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣀⣀⣠⣤⣿⣀⡀
⠀⠀⠀⠀⡄⣿⠸⠀⠶⣾⠶⠶⠦⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣁⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠦⡠⢹
⠀⠀⠀⠀⡇⣽⡂⡇⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣧⣿⡇⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣤⣤⣀⣀⠀⠀⠀⢸
⠀⠀⠀⠀⣿⣻⣏⣿⠀⠀⣧⠀⣀⣤⠶⠚⠛⠉⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⣾⣄
⠀⠀⠀⠀⢸⢸⣽⢻⠀⠶⠋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⢀⣤⠋⠀⠙⠦⣀⣀⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⣸⠶⠛⠛⢦⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⣧⠀⣧⣤⣼⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠃⠀⠀⠀⠀⡋⠉⠉⠉⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⡀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⢳⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿
⠀⠀⠀⠀⣠⢼⠳⠶⣶⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢁⢸
⠀⠀⠀⢰⠁⣴⢸⡇⢯⣦⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⡄
⠀⠀⠀⣿⠀⣧⠀⠀⠀⢿⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣧
⠀⠀⠀⠈⣦⣀⠀⠀⢀⣠⣾⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⢀⣯⠒⠶⠶⢒⣩⢧⠀⠀⠀⠙⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⡀
⠀⠀⢀⠋⢠⠃⠉⠉⢳⢷⠀⣧⠀⠀⠀⢸⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠛⠶⠤⣤⣤⣿⢶⣞⣟⡯⡇
⠀⠀⡏⠀⡟⠀⠀⠀⠀⢿⠀⠈⡆⠀⠀⣾⣻⣗⡺⡯⡯⢽⣯⣝⣽⣿⣟⣻⣟⣻⣟⣳⣖⣲⣖⣲⣖⣲⣖⣲⢶⣞⣻⣟⣻⣟⣻⣟⣻⣯⣽⣯⢯⣿⣠⣀⡿⢴⣻⣛⣹⣽⠷⠛⢻⡀
⠀⢸⠀⠀⣃⡞⠀⠀⠀⠀⡇⠀⢻⠀⠀⡇⠀⠀⠉⠉⠉⠉⣿⢿⣟⣻⢷⡾⢶⡶⢶⡶⢶⡶⢶⡾⣗⣻⣟⣻⣟⣻⢟⣻⣟⣻⣟⣻⣟⣟⣻⣟⣻⣽⣯⣽⡯⡇⠀⠀⠀⠀⠀⠀⢸⠈⠶⣀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣬⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣮⣷⣛⣣⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⡀⢠⠃
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⡷⠁
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡄⠀⠀⠀⠀⠀⢀⠃
⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⣿⡿⢿⣿⢿⡿⢿⡿⢿⡿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⡿⠿⠿⢻⣟⣓⣧⠀⠀⠀⠀⠀⡾
⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢷⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣠⠟⣦
⠀⣠⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⡶⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠒⠶⠤⠤⠤⣤⠶⠚⠉⠀⠀⠀⢷
⣰⠁⠀⢀⣠⠶⠃⣠⠞⣠⣃⠟⠀⢀⠋⣤⠀⠀⠀⠉⣉⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠻⣈⣶
⠈⠉⠉⠳⠶⠖⠙⠴⠋⠀⠀⠀⠀⠀⠉⠤⢾⣤⠶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠤⠴⠔⠶⠦⠴⠦⠶⠤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢖⣛⣛⣛⡳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠫⠿⠿⣿⣿⣿⣿⣷⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠉⠳⡻⣿⣿⣿⣿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⣻⣿⣿⣿⠿⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣸⠽⠯⣭⡻⣾⣭⠶⡚⣻⣽⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣀⣤⠼⠒⣋⣁⠀⠀⠀⠀⠈⣞⣿⣿⣿⣿⣝⣓⠿⣤⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⣤⠤⡀⠀⠀⠀⠉⠳⠀⠀⠀⠹⠶⠶⠭⣙⠿⣿⣭⢿⣀⡶⣫⣶⣾⣷⣮⡻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠛⠟⠒⠶⠳⣬⡼⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⢮⢿⣵⣣⣿⣿⣿⣿⣿⣿⣿⣮⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⣠⠶⠂⠀⠀⠈⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄⠀⠀⠀⠈⣎⣿⣛⡭⠶⠾⣭⡛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⣀⠀⠀⠀⠀⠀⠀⠉⢛⠛⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⡄⠀⠀⢸⢽⣷⣤⠟⠀⠀⠈⢳⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢷⠂⠀⠀⠈⣆⠀⠀⠀⠀⠀⢼⠞⠳⣄⠀⢀⠏⠀⠀⠀⢀⣤⡀⠈⢦⠀⠀⣞⢸⠉⠀⠀⠀⠀⠀⣇⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⣠⣯⣄⣀⠉⠙⢤⡴⢃⡉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠰⣌⠀⠀⠃⠀⢟⢸⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⣠⣛⣵⣿⣿⣿⠟⡴⣫⣝⢦⠀⠀⠀⡾⣘⠿⣿⣾⣶⣭⣓⠦⣌⠃⠢⡌⢄⡛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠉⠙⣄⠀⢰⣼⣸⣀⣀⣀⣤⠞⠁
⠀⠀⠀⢀⢞⣶⣿⣿⣿⣿⣣⠏⠓⢭⡻⣷⡝⣲⢛⠦⣀⠉⠛⠮⣝⠿⣿⣿⣷⣭⡳⣄⠑⢨⡑⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠳⡏⣿⣙⣿⠁
⠀⠀⣴⣣⣿⣿⣿⣿⡿⣴⣩⡳⣤⠐⠌⢓⠞⣾⣿⣿⣷⣭⣓⢤⡀⠉⠓⢬⡻⣿⣿⣷⣭⠶⣀⠑⠣⠢⠙⢤⣠⠤⣄⡀⠀⠀⠀⣧⠀⡾⣾⢣⠃
⠀⣼⣴⣿⣿⣿⣿⣿⣴⣵⣿⣿⣿⣮⢓⠏⠙⠶⣝⠿⣿⣿⣿⣿⣶⣝⢦⣁⠌⠛⣬⠻⣿⣿⣶⡻⣄⠨⡘⡁⢦⠄⠀⠈⣦⠀⠀⢀⢞⣾⣣⠋
⣸⣼⣿⣿⣿⣿⣿⢡⡑⣿⣿⣿⣿⠏⡏⣮⣝⠦⣀⠉⠶⣙⢿⣿⣿⣿⣿⣶⣝⢦⡀⢉⠶⣙⢿⣿⣷⣝⣦⠑⡈⠲⢦⠀⣸⣠⢶⣵⠿⣴⠁
⡇⣿⣿⣿⣿⣿⡿⡿⡈⠓⣬⡻⣿⣸⣾⣿⣿⣿⣶⣛⣤⠀⠙⢦⡛⣿⣿⣿⣿⣿⣮⡳⣄⠨⠳⣝⢿⣿⣿⣝⣄⠂⡐⡠⠙⡝⠿⣡⠟
⠨⣿⣿⣿⣿⣿⠇⢟⢦⣁⠂⡈⠳⣭⡻⣿⣿⣿⣿⣿⣿⣮⡳⣌⠈⠳⣍⢿⣿⣿⣿⣿⣷⡝⣄⠠⠛⣭⢿⣿⣷⡳⡐⡢⠪⠙⠛
⡇⣿⣿⣿⣿⣿⣸⣼⣿⣶⣝⠶⣄⠂⢈⠳⣭⡻⣿⣿⣿⣿⣿⣷⣝⢦⠂⠙⣮⠿⣿⣿⣿⣿⣧⡳⣄⠄⠻⡹⣿⣿⡝⡌⢌⠄⡇
⢿⢻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣮⣓⣤⡐⢈⠳⣍⢿⣿⣿⣿⣿⣿⣝⢦⡀⡙⣮⢿⣿⣿⣿⣿⣮⠷⡀⠈⣎⢿⣿⡸⠀⣰⠁
⠀⣧⣿⣿⣿⣗⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢤⡀⡙⢦⡻⣿⣿⣿⣿⣿⣭⢦⡀⠹⣜⢿⣿⣿⣿⣿⡝⣄⠄⣧⣿⡇⡶⠁
⠀⠈⣦⢿⣿⣿⣧⠙⠶⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠶⡁⠌⠶⣛⢿⣿⣿⣿⣿⣝⢦⠀⠳⡹⣿⣿⣿⣿⣌⣆⠄⣎⡾
⠀⠀⠀⠳⣝⠿⢸⢙⠦⣄⠉⠳⣭⠻⣿⣿⣿⣿⣿⣿⣿⣮⡳⣌⠈⠳⣝⢿⣿⣿⣿⣿⡝⣄⠘⣮⢿⣿⣿⣿⣎⣄⠟
⠀⠀⠀⠀⠀⠛⢦⣧⢿⣷⣭⡳⣄⠉⠲⣍⠿⣿⣿⣿⣿⣿⣿⣷⣝⣄⠀⠳⣝⣿⣿⠿⠿⠲⢳⡀⢳⠻⣿⡿⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣍⡻⢷⣭⠶⣄⠉⠳⣍⠿⣿⣿⣿⣿⣿⠷⣙⡤⠶⢓⣛⣩⣭⣵⣶⣶⣶⣭⠳⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡙⣷⣝⠦⣀⠙⢮⡻⡿⢋⡴⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⠿⣶⣛⣤⢉⢞⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡛⢣⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠾⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢮⣍⣛⣛⣛⣉⣥⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢶⣶⠶⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣀⢖⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⣠⢾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣶⣿⣿⡶⣶⣤⣀
⠀⠀⠀⠀⡴⣩⢟⣭⣶⣶⣶⣭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⡾⣥⣵⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⣸⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣤⣤⣤⣴⣿⣿⣤⣶⣤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣻⡀
⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣷
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣻⣿⣿⣿⣿⣿⣿⣿⣞⣿⡄
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠙⢿⣟⡻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀⣠⣶⣿⣿⣿⣿⣷⣤⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣟⡿⠿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢀⠇⠀⢀⣾⣿⣿⣿⠛⠉⠁⠙⢿⣿⠀⠀⠀⠀⠈⠉⠛⠛⠉⠀⠀⠀⠀⠀⣤⣶⣿⣷⣶⣦⣀⠀⠀⠀⠀⠙⣿⣿⣿⣟⠉⠉⠁
⠀⠀⠀⠀⠀⠀⣼⠀⠀⣿⠋⠻⣿⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠉⠀⠀⠙⢿⣿⣿⣷⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⣠⠃⠀⢸⣿⣤⣴⣿⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⣿⣿⢿⣿⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⢀⠇⠀⠀⢸⣿⣿⠛⠛⣷⣄⣀⣀⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⣿⡄⠀⣽⡆⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⡿⠀⠀⠀⠀⢿⡇⠀⠀⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⣤⣀⣤⣾⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿
⠐⠛⠒⢲⣷⣤⣀⠀⠀⠀⠻⣶⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⠁⠀⠀⠀⢸⣿⣿⡄
⠀⠀⠀⠘⠀⠀⠀⠉⠛⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣄⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⣀⣠⣿⠋⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⣀⣠⣤⣤⣄
⠀⠀⣀⡤⢿⠛⠛⢉⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠶⠿⠿⠻⠷⠶⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠰⠉⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣤⡶⠟⢷⣀⠁⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⣤⣀⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡆
⠀⠀⠀⠀⠀⠀⣸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⣄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠉
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠉⠉⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠈⠉⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⣿⣤⠀⣠⠆⠀⠀⠀⠀⠀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠙⠷⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣶⣥⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣫⢻⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣭⢿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣯⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢮⣼⠷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⣠⣶⣟⣽⣾⣿⣿⣿⣿⣿⣷⣯⡿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣾⣿⣿⣿⣿⣿⣾⣯⣟⣷⣄
⠀⠀⠀⠀⣠⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢿⣄
⠀⠀⢀⣾⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣷⡀
⠀⢀⣿⠾⣛⣿⣷⣾⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡇⠀⠀⠀⠀⢀⡤⠚⢉⣧⣠⣤⡀⠀⠀⠀⠀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣫⣽⣷⣾⣯⣛⢷⢿⡀
⠀⡿⣵⠿⠉⠀⠀⠀⠀⠙⢿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⣠⠞⢉⠟⠁⡤⠚⠁⢀⠴⠚⠉⠉⠉⢓⡄⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣾⠛⠁⠀⠀⠀⠀⠉⠻⣎⣷
⣼⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣵⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣱⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⣿⣺⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣿⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⠛⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⢿⣄⠀⠀⠀⠀⠀⢀⣀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⡀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠈⠛⠿⢿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣿⣿⣿⣿⣿⠛⠀⠀⠀⠉⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣿⣿⠿⢿⣿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⠉⠛⣿⣿⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⣸⣷⡀⢀⣿⣿⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣟⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣷⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⣿⡟⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠈⣯⣿⣷⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣾⣿⣾⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠈⠿⣽⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠙⠶⠞⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⣻⡿⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣼⣀⡀⠀⠀⠀⠀⠀⠉⠙⠓⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠛⠛⠉⠀⠀⠀⣀⣀⣀⣇⣀⣀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠙⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⣠⠞⠀⠈⠦⣄⣀⣀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠘⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣼⡀
⠀⠀⠀⠀⠀⡴⠋⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠈⠳⣄
⠀⠀⠀⠀⠋⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢳⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⣿⣿⣿⣷⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⡏⣇⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠻⣿⣿⣿⣿⢟⣾⠟⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⢻⣎⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢸⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢷⣽⢯⡿⠁⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠹⣷⣿⣿⢿⣿⠋⠀⠀⠀⠀⢸⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠻⣄⠀⣤⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢿⣬⡾⠛⠀⠀⠀⠀⠀⠀⣾⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠉⠀⠀⠉⢛⡶⠲⠶⠖⠒⠚⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠿⣛⠉⠁⠀⠉⠛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⣶⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⢶⠈⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠷⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⢿⣟⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⣿⣿⡿⣸⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢀⠀⢀⣴⣶⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢝⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⣿⣷⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣿⣟⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢿⣿⡿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⣾⣿⣿⣿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣳⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢮⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠟⣋⣭⣭⣙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⣶⣿⣿⣿⠿⠛⠿⣦⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⣿⣿⣿⣿⠁⠀⠀⠀⠈⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⣤⣶⣤⣍⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢰⣿⠁⠙⣿⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⠛⡉⠙⠻⣿⣿⣿⣆⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡌⣿⣶⣾⣿⣷⣄⣀⣤⣾⣿⢸⣿⡇⠀⠀⢀⠀⠉⠙⠻⣿⣿⢰⠁⠀⠀⠀⠀⢹⣿⣿⣿⣇⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⢿⣿⠹⣿⣿⠀⠀⠉⣿⣿⣿⠋⣿⣿⠀⠰⣄⠀⠀⠀⠀⠐⣿⣿⣿⣆⠀⠀⠀⠀⣼⣟⠀⢙⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣀⣤⣿⣿⣿⣉⡀⠀⠹⣿⣍⠻⠆⠀⣼⡿⠛⣥⣿⡿⠁⠀⠀⠛⠟⠃⠀⠀⠀⣿⣿⢹⣿⣷⣤⣴⡾⠿⣿⣿⣿⡏⣿⣿⣿⣿⡇
⠀⠘⠉⠉⣼⣿⣿⠁⠉⠙⠛⠀⠈⠻⣿⣿⣿⣷⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⣿⣧⠻⣿⣿⡏⠀⠀⢸⣿⠟⣼⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠙⣿⣿⣌⠛⠿⠆⠀⣛⣥⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⣤⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠿⠛⠀⠻⣿⣿⣿⣿
⠀⠀⣾⣷⡀⣇⡶⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⢻⣿⣿⣿⣿⣷⣀⠀⠀⠀⣠⠇⠰⠀⠀⠀⠀⠀⠂⣀⣤⣶⣿⣿⣿⣿⣶⣤⡀
⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠛⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⣿⣿⠀⠀⠀⠁
⢸⣿⣿⡿⠁⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⢻⡟⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣶⣄⠀⣾⠁
⠀⠀⣷⠀⠀⠀⠀⠀⠙⡆⠠⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇
⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠈⣷
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠟⠁⢈⠉⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡀
⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠙⠟⠿⠋⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇
⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣀⠀⠀⣠⡿⠀⠀⠀⠀⠻⣿⣿⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣾⠋⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠹⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶
⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏
⠀⠀⠀⠀⠀⠀⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟
⠀⠀⠀⠀⠀⠀⣠⣿⣷⣤⣤⣤⣤⣤⣶⠿⠿⠛⠛⠉⠉⠀⠀⠈⠉⠛⠛⠛⠻⠿⠿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣤⠟
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⣿⠉
⠀⠀⠀⠀⠀⠙⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣒⣛⣛⡒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⠴⢥⡋⢿⡿⣿⣷⣟⢶⣍⢦⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⢄⣀⣾⣿⣬⢧⢺⣞⣿⣿⣿⣿⢯⢝⣄⠀⣧⢸⢀⣿⠀⠀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⡪⢰⣿⣿⣿⣿⣆⣇⣿⣿⣿⣿⣿⣿⣯⡚⢀⣿⣿⣿⣿⣾⣿⡿⢀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢐⠢⣿⣿⣿⣿⣿⣿⢹⢻⣻⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣠⣤⣶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢈⡕⢿⣿⣿⣿⣿⣿⢸⢸⣿⣿⣿⣿⣿⣟⠍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢣⡈⣿⣿⣿⡇⣦⢻⢨⣽⣟⣻⡯⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠣⠈⢿⣿⣇⡏⠜⠉⠉⠀⠀⠈⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⠉⠉⠛⠻⠿⣿⣿⠿⣍⡾⣝⣿⣿⣽⣲⢍⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢾⠀⠀⠀⠀⠻⣹⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⡯⣷⣿⣺⣿⣿⣿⣿⡮⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠉⢦⠀⠀⠀⠀⠉⠚⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢽⢿⢿⣿⣽⣿⣿⣿⣿⣿⣷⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣺⣻⣟⣻⣿⣿⣿⣿⣿⣽⢮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣩⡵⠶⠶⢦⣕⠛⡽⣿⣯⣗⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⡄⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⢶⡃⣿⣿⣿⣷⣍⢷⡙⣟⢯⡇
⠀⠀⠀⠀⠀⠀⣠⣾⣶⣦⣹⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣽⣾⣿⣿⣿⣿⣿⣯⡝⡔⢵
⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⡸⢷⣿⣿⣿⣿⣿⣿⣿⡿⢁⣿⠏
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢻⣿⣿⣿⣀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣿⣿⠆⠀⠀⠀⠀⢠⣆⠢⡄⠙⠿⠿⠿⠛⢉⠆⢁⠏
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣽⣤⡈⠔⠘⠱⠆⣨⠖⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠟⠋⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⠀⠀⠀⠀⣴⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠉⢦⢀⣾⠋
⣼⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⣀⣴⠟⠁
⣿⡧⣝⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡶⠲⠶⠤⠶⠒⣿⡿⠛⠁
⠘⣜⣺⠅⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠈⠛⠋⠐⡀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣠⡾
⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⣠⠤⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢞⡺⡪⠄⣇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡺⡳⡺⠇⡼⣠⣿⠿⠉⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠿⠗⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢀⠴⣚⣭⣭⣭⣭⡒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣚⣭⣭⣭⣝⡒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⣒⣛⣛⡒⠦⣄
⠀⠀⠀⢀⢞⣶⣿⣿⣿⣿⣿⣿⣿⣿⣎⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣱⣿⣿⣿⣿⣿⣿⣿⣷⣬⠳⡀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣵⣿⣿⣿⣿⣿⣿⣿⣷⣌⢦
⠀⠀⢀⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⡄⠀⠀⠀⠀⠀⢠⢃⣛⣛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠹
⠀⠀⡏⣩⠶⡒⠒⠦⣙⠿⣿⣿⣿⣿⣿⣿⣧⡇⣤⣄⣞⣧⣶⣦⣀⡀⡏⣿⣿⣿⣿⣿⣿⡿⣋⡥⠶⠶⢬⣙⢹⠀⠀⠀⠀⠀⡿⡁⢸⡇⢠⡙⣌⢿⣿⣿⣿⣿⣿⣿⣧⡇
⠀⠀⡼⢄⡸⢇⡸⢎⡠⠻⡙⣿⣿⣿⣿⣿⣘⣿⣿⢩⢰⣿⣿⢋⡍⣿⣷⣍⣿⣿⣿⣿⢑⠞⡔⢣⡜⢣⡜⢂⢧⠀⠀⠀⠀⠀⡇⢎⡱⢎⡱⢎⡀⣆⣿⣿⣿⣿⣿⠿⠏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣒⣚⣛⣒⠤⣀
⠀⠀⡇⢕⡪⢕⡪⢕⢂⣯⢿⢹⣿⣿⣿⣿⣿⣿⣿⢸⢸⣿⣿⢸⡃⣿⡿⣿⣿⣿⣿⡇⣯⣲⠪⡕⢪⡕⢪⡕⠈⠀⠀⠀⠀⠀⡇⢎⡱⢎⡱⠎⢰⣼⢸⣿⣿⡏⣻⣿⡿⣛⣿⣷⣶⡿⠀⠀⠀⠀⢀⢞⡖⣿⣿⣿⣿⣿⣿⣶⡙⣄
⠀⠀⢷⢊⡱⢎⡱⢎⠐⣭⣕⣿⣿⣿⣿⣿⣿⣿⣿⣼⢸⣿⣿⣽⢰⣿⡇⣿⣿⣿⣿⢰⠿⡽⢃⡕⢪⡕⢪⡕⣸⠀⠀⠀⠀⠀⠸⣄⠪⢕⡪⢅⢮⡞⢸⣿⡟⣾⣿⢟⡞⣴⣿⣿⡿⠷⠶⣿⡀⢀⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢦
⠀⠀⠀⢷⡈⠕⠪⣡⣻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢸⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣦⠑⡪⢕⠊⣴⠃⠀⠀⠀⠀⠀⠀⠙⣷⣀⢾⣿⣿⣿⣿⣿⣸⣿⢏⡯⣼⣿⣿⢏⣺⠏⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡄
⠀⠀⠀⠀⠙⠿⢲⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡌⣿⡟⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⣖⠽⠁⠀⠀⠀⠀⠀⠀⠀⠀⡞⣾⣿⣿⣿⣿⣿⡇⣿⣿⣾⣰⣿⣿⣣⣿⢋⣿⣿⡿⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣛⠻⢿⣷⡇
⠀⠀⠀⠀⠀⢸⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⢻⡇⣿⡇⠏⣿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⣿⣿⣿⡇⣿⢇⠇⣿⣿⣱⣿⢁⣿⣿⢟⣾⣿⣿⣿⣿⣿⣿⠟⣡⠞⢩⡆⢰⡌⠛⡜⡇
⠀⠀⠀⠀⠀⣾⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⣸⣇⣿⢨⢰⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⢏⣴⣿⣿⣿⣶⡙⣇⣿⣸⢸⣿⣡⡿⣠⣿⡿⢥⣾⣿⣿⣿⣿⣿⣿⢅⠿⣲⢐⡪⢕⡪⢕⡪⢸⠇
⠀⠀⠀⠀⢀⠻⠿⠦⣿⣿⡿⠛⠉⠉⠉⠉⠙⠻⢿⣿⣿⠿⣿⠿⠋⠉⠀⠀⠉⠉⠺⣿⣿⣿⣿⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣷⢂⡿⣿⠋⠀⠀⠀⣿⢸⣹⣿⣿⢃⠏⣴⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⠡⠭⠟⡨⢕⡪⢕⡪⠕⡼
⠀⠀⠀⠀⣾⣷⡍⢖⣿⣿⠟⠛⠶⣦⣄⠀⠀⠀⠀⠀⠛⠟⠀⠀⠀⠀⠀⠀⣀⣤⣤⠤⣭⣭⣙⠛⣩⣿⠀⠀⠀⠀⠀⠀⠀⣯⠿⣿⣷⣿⠀⠀⠀⠀⣿⠘⣿⡇⡟⡇⢛⢥⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⠕⢪⡕⢪⡕⠊⡜
⠀⠀⠀⢠⣬⡛⡇⣭⠿⠛⠋⠉⠉⠙⠓⠿⣶⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⠷⠿⠶⠶⠶⢿⣿⣿⢰⢂⡄⠀⠀⠀⠀⠀⡾⠁⠀⢿⠀⣿⡀⠀⠀⣰⠟⠀⠀⢷⠾⠿⠿⠿⣟⣴⠿⠛⠻⣿⣷⣌⢿⣿⣿⣿⣿⢃⣁⣨⣥⠖⠁
⠀⠀⠒⣾⠭⣤⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣜⢻⣇⠀⠀⠉⠉⡹⠢⣀⠀⠀⠻⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣿⣿⣧⣿⣿⣿⠟⣼
⠀⠀⠀⡏⣿⣿⠀⠉⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⢲⣒⣿⠒⠤⠀⠀⠇⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⢹⠛⣡⣿⣿⡆
⠀⠀⠀⢿⠟⣇⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠀⠠⠒⠒⡒⠤⣄⠀⠀⠀⠀⢀⠄⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠹⣧⣀⠀⢀⡴⢿⣼⡿⣣⣛⣫⡭⣢⣷
⠀⠀⠐⠉⡱⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠢⣅⠃⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡀⢀⡿⠀⢻⣋⣤⣾⡿⢻
⠀⠀⠀⠀⠹⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⢿⣿⣿⠓⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡞⠈⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⣄⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣿⡶⠞⣡⣿
⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠉⠉⠉⣿⣷⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠤⠶⠒⠒⠶⠤⢭⣛⣛⢛⠃
⠀⠀⠀⠀⠀⠀⣏⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣡⠋
⠀⠀⠀⠀⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⣰⢻⣇⣛⣶⢷⠤⣄
⢀⠞⣇⡖⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡉⢿⣿⣿⢸⠨⣸
⣇⢫⣡⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠔⢿⠠⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢦⠀⣠⠖⢻⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢸⣰⠁
⠀⡄⠁⠀⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠉⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠙⠤⠓⠁⠀⠀⠀⠀⠀⢀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿
⠀⠈⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣙⣤⡠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⢑⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠲⠤⢤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⢾⡴⢙⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⢭⠉⢦⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠥⠧⠖⠉⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⠛⢒⠒⣲⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠖⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⣠⣶⠶⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣶
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠉⢷⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣱⠃
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠛⠁⢻⡀⣼⣵⣿⣿⣿⣄⠀⠀⠀⠀⠀⢿⠀⢠⣿⣿⣿⣿⣿⣿⡿⠁⠀⠉⠀⣼⣥⠶⠿⠛⢻⣀
⠀⠀⡾⠻⣿⣿⣿⣿⡿⠋⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⣇⣯⣀⠀⢸⣿⣿⠀⠀⠀⠀⣀⣠⣇⣿⠘⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⣼⠁⣠⠶⠛⠛⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠉⠙⠻⣦⠈⣇
⠀⡏⣾⠁⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠿⣿⣿⡿⠛⠛⢛⠛⠉⠉⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢻⣹
⢠⢱⠃⠀⠀⠀⠀⠀⠀⢠⣦⣷⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣤⣀⣀⣀⣴⠋⠙⢶⣤⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠈⣿⠀⠀⠀⠀⠀⠀⠀⠸⣆⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣷⠂⠀⠀⠀⠀⠀⠀⢴⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣉⣽⠇⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠻⣶⣶⡶⠶⠶⠿⠃⠀⠀⠀⠶⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠶⠀⠀⠀⠀⠛⠿⠶⢶⣶⣶⡶⠋
⠀⠀⠀⠀⠀⠀⠉⠙⠛⣿⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢸⡉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣾⣿⣿⡿⠉⠀⠀⠻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠀⠀⠈⠻⣿⣿⣿⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣼⡿⠿⣿⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⠀⠀⠀⠀⠀⣿⠉⢻⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣦⣴⣿⣄⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⣠⣿⣿⣿⣿⠂⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢿⣿⠏⠀⢹⣿⣿⣿⣿⣿⠁⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠈⣿⣿⠀⠀⢿⠀⠀⠀⡀
⠀⠀⠀⠈⣆⣤⢿⠀⣏⣄⠀⠀⠿⣧⣀⣼⣿⣿⣿⠿⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠻⣿⣿⣿⣿⣤⣤⡿⠀⠀⠀⣼⣆⠀⣸⠉⠳⣤
⠀⠀⠀⠀⠙⠀⠀⢻⠁⠘⣦⣤⣀⠀⠉⠛⠛⠉⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠈⠉⠉⠉⣀⣴⠾⢶⣤⡇⣇⠉⠋
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠈⠉⠛⠷⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠸⠛⠁⠀⠀⣀⣤⣴⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢹⣀⠀⠀⣀⣠⣤⣤⡄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢀⣀⣀⣾⢛⢭⣲⢽⣪⢮⢞⡢⠻⡄
⠀⠀⠀⠀⢀⡶⣀⣸⡏⢷⡿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⡌⡮⡹⠚⠹⡺⣝⣝⡅⡇
⠀⠀⠀⠀⣾⠀⠈⠁⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⣤⣾⣿⣿⢸⡪⢕⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⢃⣝⡵⠏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣄⠳⠋⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣴⣿⣿⡿⣿⠀⠉⠻⣿⣿⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠏⢻⣿⣿⠋⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠠⠔⣰⠃⠉⠗⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⣈⣼⠋⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣧⢀⠿⣄⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡌⠉⠉⣿⣿⡅⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣦⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⣤⠈⢿⣿⣦⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠻⣤⠀⠀⠻⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⡩⡌⠛⢻⣿⠿⠿⠛⠛⠛⠋⠉⠉⠉⠉⠉⠛⠛⠛⠛⠿⠿⠿⠿⣿⡿⠛⠛⠛⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢡⡟⣠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⣿⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⣤⠶⠛⠉⠁⠀⠀⠀⠉⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⣀
⠀⠀⢀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟⠉⠀⠀⠀⠀⠀⣠⣿⠷⣤
⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣶⡻⣦
⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣠⣤⣤⣾⣤⡶⠿⣷⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣮⣷
⣸⣴⠟⠉⠉⠉⠛⠛⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣶⢿⣾⢟⣵⣿⣛⣻⣭⣿⣗⣸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣷⣮⣽⡇⠀⠀⠀⠀⠀⢸⣿⣻⣵⡾⠿⠛⠛⠻⠿⣾⣹
⢸⡄⠀⠀⠀⠀⠀⠀⠀⣿⣛⠻⣷⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⣾⣏⡀⠀⠀⠀⠀⠈⠀⠀⣻
⠀⣿⡀⠀⠀⠀⠀⠀⠀⠘⠿⠶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠋⠴⢾⡁⠀⠀⠀⠀⠀⠈⠀⣿
⠀⠈⢿⣄⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⠀⠀⠀⠀⠀⠈⣼⠃
⠀⠀⠀⠻⣷⣄⠀⠀⡘⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠛⠿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢀⣴⣿⠃
⠀⠀⠀⠀⠀⠳⣝⡟⠀⠀⠀⠀⣠⣿⣿⣿⠿⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣷⣤⠀⠀⠀⠀⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⢰⣿⣿⣿⠁⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠁⠀⠉⣿⣿⣿⡀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠛⣿⣇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣿⠿⠿⣿⣄⠀⠀⢀⣿⣿⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⢻⣿⡀⠀⠀⠀⣼⣿⣠⣿⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠛⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠈⣿⣿⣶⣶⣿⠛⠉⣿⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠶⣿⣿⣿⡿⠛⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⢿⣿⣿⣿⡀⠀⠈⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⣶⣻⣭⣻⣿⡆⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⣸⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠘⣿⣿⣯⣽⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠉⠁⣿⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠙⢻⠦⣄
⠀⠀⠀⠀⣿⢻⢿⣶⣶⢛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣤⣴⣾⠁⠀⣿⡷⠶⠶⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠉
⠀⠀⠀⠀⢸⣶⢿⣯⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣤⡀⠀⠀⡏
⠀⠀⠀⠀⠉⢿⡹⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾
⠀⠀⠀⠀⠀⠀⢿⡽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠉⡦
⠀⠀⠀⠀⠀⠀⠀⣿⣹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣽⠃
⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⢰⣇⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣸⣼⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⣱⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⣿⣿⡇⠀⣽⢟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠁⠀⢉⠿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣿⣻⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡏⠀⠀⠀⠻⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣯⡇
⠀⠀⠀⠀⠀⠹⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣼⠁
⠀⠀⠀⠀⢀⡾⡻⣷⣽⣛⣻⣿⣻⣛⣯⣭⡶⠟⠛⠉⠉⠉⠉⠉⠉⠉⠓⠒⠒⠲⠦⠤⣶⣾⣛⠿⢿⣿⣿⣿⣿⣿⡿⢛⣵⡟
⠀⠀⠀⢠⣿⠹⡚⢇⣩⡿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢿⣿⡿⠿⡛⢥⢿
⠀⠀⠀⠀⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣰⣷⣼⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⣼⣿⡿⠉⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠈⠻⣿⣿
⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣾⡄⠀⣀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠈⠈⣿⣧
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣴⣿⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿
⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⡟
⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣤⡿
⠀⠀⠀⠈⠿⣶⣶⣤⣤⣄⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⣀⣤⣤⣴⣶⣷⡿⠉
⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⣀⣴⣶⣿⣶⣦⣀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣤⣶⣶⣶⣶⣤⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢀⣾⣿⣿⠟⠉⠀⠉⢿⣷⠀⠀⠀⠀⠈⣿⣿⠏⠀⠀⠀⠀⢠⡟⠁⠀⠀⠙⣿⣿⣿⣄⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠿⣿⠃⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠙⢿⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⣇⣀⣾⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⢀⣿⣤⣼⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢻⣿⣿⠛⠻⣄⣀⣀⣠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣤⣴⠟⠉⠛⣿⣿⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⣿⠀⠀⠀⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⣿⠃⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠳⣤⣴⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣶⠾⠁⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢀⣀⣀⣀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠶⢺⠒⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠙⠻⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⣾⣄
⠀⠀⠀⠀⠀⠀⣀⠶⠋⠁⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⣠⡴⠋⠀⠙⠶⣤⣀⣤⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⣠⣼⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡐⡆⡙⢷⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢈⡐⢰⡆⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠶⣬⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠅⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠶⠶⣶⣤⣴⠶⠶⠚⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠒⠶⣶⡶⠶⠶⠛⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡥⢘⢊⡘⣡⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡁⠠⣄⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢿⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣾⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣾⣿⣇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣵⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣽⡻⡇⡟
⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⠤⠤⠤⣄⣀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⣿⣿⣿⣳⠇⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⢀⣟⣟⡻⣏⣠⣤⣤⣤⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣧⣹⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⢸⣿⣿⣿⠿⢛⠉⠉⠛⣿⠟⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⠻⠿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⢸⣿⡿⢁⠂⠀⢀⢂⡾⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⠀⠀⠀⢀⢀⠟⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠙⢿⣿⣿⣿⣟⠋⠍⠀⠀⠠⢉⠛⢿⣿⣿⣿
⠀⠹⡀⠄⢀⢀⡟⠀⠀⣠⣿⣿⣿⣿⠿⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠈⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠢⠙⣿⣿
⠀⠀⠙⣄⠂⣾⠀⢀⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠙⠻⣿⣿⣿⣿⣦⠈⢿⠉⠄⠀⠀⠀⠀⠀⠀⠀⢹⡿
⠀⠀⠀⠀⢙⠃⢠⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣦⠙⣄⠢⠀⠀⠀⠀⠀⠜⣼⠁
⠀⠀⠀⠀⣸⢀⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⡈⣧⠢⢀⡀⠰⣀⡾⠁
⠀⠀⠀⠀⣿⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣄⠷⠷⠟⠋⡆
⠀⠀⠀⠀⢳⣿⡏⢤⣶⣶⣶⠚⠛⣿⣿⣛⣻⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⠤⣤⣤⣤⣤⣀⣀⠀⠈⣿⣿⣄⠀⠀⠀⢿
⠀⠀⠀⠀⢾⣿⠀⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠂⠀⢀⣿⣿⣿⣄⢿⣿⡀⠀⠀⢸
⠀⠀⠀⠀⠸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⣿⣿⠀⠀⣺
⠀⠀⠀⢀⣀⣱⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⢸⣿⡆⠀⡟
⠀⠉⠉⠀⠀⠘⠛⠉⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⣿⣷⢀⠃
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠉⠉⠉⠉⣿⣿⣼⡇
⠀⠀⠀⠀⠀⣧⠶⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢰⣿⣷⠁⢿
⠀⠀⠀⠛⠁⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠖⣿⣿⣿⣷⣤⣀⣠⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣾⣿⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠙⣿⠀⠘
⠀⠀⠀⠀⠀⠀⠀⣿⡳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⣖⣻⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣦⣭⣛⣓⣒⣖⣦⣤⣄⠀⠀⠀⠀⠈⠿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⣺⣭⣷⣶⣿⣿⣿⣿⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠛⠉⠉⠉⠉⢧⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡟⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⡗⣼⠁
⠀⠀⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⣄⠀⠀⣀⣠⡶⢛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣤⣀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡿⡇
⠀⠀⠀⠀⠀⠀⠀⣏⠉⠙⠛⠒⠚⠛⠶⡴⠳⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣦⣠⣌⣩⠿⠿⠿⠭⠭⠭⠗⣶⣿⣁⡇
⠀⠀⠀⠀⠀⠀⢀⡾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣃⣤⠶
⠀⠀⣀⣤⣶⣶⣏⡾⣀⠙⠶⣤⣤⣀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣤⣀⣀⠀⠀⠀⠀⠀⢀⣠⠶⣷⣶⣤⣀⠁
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠄⣰⠹⡌⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠚⠛⠋⠉⠉⠁
