Island Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠄⠘⣸⠁⠀⢸⠧⡄⠀⠀⠀⢀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠄⠀⠈⠀⢶⣇⡀⠀⠀⠀⠀⠀⠀⠀⠋⢻⡷⠆⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠠⢿⡵⠀⠀⠀⠀⠀⢋⣠⣄⣴⣤⣤⣤⣦⣴⡀⠀⢡⡄⠈⢉⠋⠀⠀⢠
⠀⠀⠀⠚⠿⣤⣤⡀⠀⠰⣾⣰⠼⠄⠘⠛⠃⠀⢈⣁⠀⠁⠉⠛⠀⠼⠅⠀⠸⢶⣰⠄⠘⠀⣸⠖
⠀⠀⠀⠀⠀⠘⠿⢷⣶⣄⠀⠉⠁⠀⣀⣀⣴⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣤⣤⣤⡤⠶⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⡿⠿⠟⠁⡀⢿⣧⡀⠚⠛⢿⣛⡛⠛⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠐⠚⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢀⠤⠀⠠
⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇
⠀⠀⠀⠀⠴⠀⠀⢠⣤⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⡄
⠀⠀⠀⠰⠁⠀⠀⠛⠟⢫⠁⠀⠀⠀⠀⠀⠀⠀⣤⣿⠂⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠲⠃⠠⣆⠉⠋⢩⡀⣀⠈⢂
⠀⠀⠀⠀⠀⠀⠄⡄⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⡧⠂⠀⢫⠁⠬⢴⣏⡠⢰⠤
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⠈⢥⠀⠀⠁⠉⠀⠾⢤⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠉⢩⠁⠴⢻⠓⡀⠀⠀⠀⠀⠀⠀⠘⠀⠉
⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⠗⠷⢽⣿⠤⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣥⡄⠀⠀⠉
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣧⡰⠈⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢐
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⡉⠉⠀⠀⠒⠒⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠒
⠀⢀⠉⠀⠀⠀⠀⠀⠀⢀⠰⠀⡀⠈⠁⠀⠤⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠴⠓⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⡀
⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠢⠤⣤⡀
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠒⠀⠀⠀⠀⠀⠀⠁
⢤⢶⣆⠀⠀⠀⠀⠉⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠘⠒⠒⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠠⠄⠠
⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠢⠀⢨⡦⠀⢀⠄⠢⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡞⠢⠀⠀⣠⡶⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣢⡄⢲⣄⣦⠀⣤⠎⢀⡲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡘⣢⡔⠵⡄⢁⡔⢨⡡⠂⢑⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠍⠶⠬⠑⠄⣀⡡⢊⠴⢂⡉⠉⡥⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⢀⡉⠲⡐⢈⢁⠋⢠⠶⠅⣤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠂⠐⠶⢂⠈⢣⡿⡿⣭⢀⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣆⢀⣩⠀⣙⢾⣿⠥⢄⠛⠛⠁⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢷⠖⢉⣠⢺⡇⡛⣄⢢⡉⠣⡁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⡤⢊⡰⠋⣽⡅⠠⣌⠫⡀⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡠⠪⠉⠍⢁⡆⢸⣄⡓⠠⢔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠗⠂⠘⡤⡏⢠⡑⢻⠸⢶⠈⠛⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢠⠃⢿⡼⢿⣄⢸⢹⡷⢂⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢀⡘⠱⡎⠄⠇⠱⢖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢨⡁⣙⠲⣹⣯⣍⠰⡍⠶⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠃⡇⢘⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⡺⢾⠝⢓⣽⢿⠿⣥⡞⢇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠧⡸⢻⠟⡎⣷⢳⠙⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢸⠀⡔⡡⠾⠛⣤⠎⠏⠙⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⠎⢰⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡉⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠇⠀⡗⠚⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⠀⠓⠂⠠⢄⣀
⠀⠀⠀⠀⢀⠀⡠⠋⠉⠀⠀⠀⠓⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⡸⠀⠀⠀⣀⡨⠉⢰
⠀⠀⠀⠐⠁⠀⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠅⠐⢀⠩⠄⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢔⡀⠉⠒⠠⢀⡀
⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡻⠀⠀⠀⠈⠁⠂⢄
⠀⠀⠀⠀⠈⠒⠤⠀⣀⣀⠀⠈⠂⠀⠀⠉⠀⠈⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠰⠶⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠹⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠰⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡎⠀⠀⠀⠀⠀⢀⡴⠂⠉⠀⠀⠈⠉⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⢢⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠧⡀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠞⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠒⠈⠉⠁⠀⠀⢀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠈⠉⠉


⣶⣶⣶⣶⣶⡷⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣿⣶⣿⢷⡶⢶⠿⠿⣶⣾⡿⠿⠿⠶⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠄⣀
⠀⠀⠀⠀⠀⠠⠠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⣄⠑⢧⡄⠀⠀⠀⠀⢀⢉⣀⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠈⠃⢆⢳⡄⡠⢨⣀⡬⡉⠉⠀⠁
⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⡄⠀⡄⠍⣑⢪⣾⡸⠾⠛⠑⠒⠛⠂
⠀⠀⠀⠀⠐⢀⡀⠀⠀⠀⠴⡀⠀⠀⠀⠀⠀⠀⠁⡠⣴⡾⢿⣯⣿⣿⡧⡴⠖⠒⢏⢲⡢⡲⡠⡄⡀⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡘⠻⠛⠟⣻⡏⣽⢁⣧⢀⠀⠀⠁⠀⠀⠈⠈⠃⠠⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠰⠋⠠⡢⠊⠨⠇⡏⢸⠁⢋⠀⠘⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡱⠁⠀⠀⢶⣇⠏⠀⠀⠘⠆⢠⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠈⠋⠀⠀⠀⠀⠈⠳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⠄⠀⠀⠀⠀⠀⡤⠤⠠⠤⠤⢤⣄⣤⣤⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠒⠀⢰⡆⣸⡤⠄⠀⣀⡀⠀⠂⠋⠉⢉⣛⣉⣉⣉⣉⡩⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠁⠁⠉⠁⠈⠀⠀⠀⠁⠒⠢⠀⠀⠈⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠰⠶⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⢹⠗
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠒⠀⠀⠂⠀⠤⠤⠤⠄⠶⠒⠚⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⢠⡀⣠⣶⠶⢤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢐⡖⢾⣿⣿⣫⣤⣤⣤⣀⡈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⠿⣿⣟⠶⠲⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠐⣡⣾⠼⡈⢳⣄⠈⠙⠆⠳⡅⠀⠀⠀⣠⣼⣶⠒⠲⠦⠀⠀⣦⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣡⣠⢹⣿⡀⠛⢾⡿⢦⠀⠀⠀⠰⠀⠀⣩⢖⢻⣷⣄⠙⠦⣴⢞⣻⢿⠛⡛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⠈⢿⠃⠀⠀⢿⡊⠀⠂⠀⠀⠀⢰⠛⠀⠀⡿⣽⣧⠀⠏⠸⠏⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⢦⡄⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠓⠦⣀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣄⠀⠀⠀⠀⠀⠈⠙⠒⠤⣄⡀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠒⠒⢒⠂⢒⣒⣀⡀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⡀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠶⠷⠶⢷⠷⠶⠾⠷⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⠀⠀⠀⠉⠲⣄⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣔⠀⠀⠈⠙⢦⣄⠀⢈⡷⢂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⢄⠉⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠳⣷⡀⠀⠀⠻⡡⣌⡁⠻⣆
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠤⢴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠦⢤⡵⠦⡙⣿⣤⢴⣎⣀⠚⠓⡦⣭⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣠⠴⠾⠛⠉⢀⠄⠠⠞⠓⠲⢵⣬⣣⣿⠚⠻⢴⣿⣇⠨⠟⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢶⣛⠂⠀⡰⠀⢠⡿⠋⡄⡆⣠⣿⣄⣻⣿⣮⣷⣄⣠⠀⣽⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠏⣉⣴⢏⣴⣿⠅⣘⡁⡥⣸⣷⡿⣿⠿⠻⠿⠿⠿⠿⠟⢿⣶⡈⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠟⠛⠿⠿⡷⠾⠿⠷⠿⠋⠋⠀⠀⠀⠀⠀⠀⠑⠀⠐⠁⠀⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣟⣛⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⣰⠃⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⢀⣴⠖⢣⣼⢋⣠⠟⣰⡇⣠⣄⠀⠠⣄⡀⣶⣤⡀⠀⠀⠀⠀⠀⠀⢸
⣀⣤⠀⣤⣤⣤⣤⣤⣶⣿⣿⣿⣾⣿⣧⣾⣿⣵⠟⢃⣶⡿⣹⣏⣉⡠⡴⣠⢥⣭⣿⣿⣷⠶⣶⣶⠶⣦⢸
⠘⠛⠛⠒⠒⠲⠚⠇⠬⠭⠭⠯⠍⠿⢉⣙⣓⣛⢒⣛⣿⣅⡠⠤⠽⠿⠿⠿⠛⠛⠻⠛⠛⠛⠛⠉⠉⠉⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢢⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣤⣴⣟⡁⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠁⠀⠀⠀⠙⣿⣿⣿⠿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⡟⢉⣝⣿⣿⠙⠂⣄⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡤⠞⠋⢹⣿⡟⣦⡌⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⡁⢈⡼⢇⣻⣟⢧⡄⠘⢿⣄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣰⠟⠀⣰⡶⢀⢻⡏⠙⢇⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠐⢊⣷⢀⣿⣏⢣⠙⣦⡀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣴⢿⠇⢨⣿⠃⠀⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⢸⡟⠈⡎⠛⠷⡌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠁⠀⠠⠂⠛⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠁⠀⠀⠀⢀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡁⠀⠀⣤⠴⠒⠃⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⡀⠀⡀⠀⠀⠼⢷⠔⠁⠀⠀⠀⠄⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣠⠉⠀⠀⠠⠙⠂⠀⠀⢀⡀⠀⠀⡀⠀⠀⡄⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠇⣿⣏⠀⠰⣆⣴⣶⠶⠀⠄⠼⢇⡀⠀⠠⡄⠀⣧⡧⠀⠂⢴⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⣧⣴⡶⠉⢀⣀⠹⡟⠋⡁⠀⠀⠀⠠⢨⣧⠀⣰⡷⠿⣿⠟⠀⢶⣬⠁⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢦⣄⢴⣦⣄⣼⣧⣤⣤⣠⣦⣾⣿⣿⣟⣀⣤⣧⡤⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠒⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⣀⠤⠤⠤⠤⠤⠤⠔⢊⣠⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠒⠒⠺⠳⠦⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣀⣀⣀⢀⣀⣀⣤⠴⢋⣁⣋⣈⣉⡙⠋⠁⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠉⠀⠙⠚⠛⠉⠀⣠⣀⡉⠩⠤⠤⠚⠷⠤⠍⣉⠉⠉⠉⠁⢒⣪⣭⣩⠩⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢩⣭⣥⡤⠖⠠⣬⡍⠁⠀⠈⠉⠁⠒⠒⠂



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠙⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡸⢴⢔⡁⠃
⠀⠂⣄⠀⣧⡐⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣦⠄⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⡀⡀⠀⡀⠀⠍⢰⢟⠈⠉⠂
⠀⠐⠡⠈⡿⠙⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠻⠛⠀⠀⠤⠠⠀⢿⠴⡄⠀⠀⠂
⠀⠈⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⣾⣯⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠁⢰⠀⣠⡄⠌
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⢾⣯⠀⠀⠀⠀⠈⠊⠙⠟⠿⠟⠛⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠨⠀⠟⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡀⠀⢠⠄
⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⡀⠀⠀⠀⠀⠐⠒⠀⠀⠉
⠀⠀⠄⠈⠁⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠄⠀⠀⠀⠒⠂⠀⠠⠄⠀⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠉⣄⠀⠀⠀⠀⢠⣤⠀⠤⠤⠄⠀⠀⡀⠄⠠⠄⠤⠤⣤⣀⡤⠤⠀⣤⠀⣀⣠⣒⠀⠀⠀⠀⢀⣂⠀⠀⠀⠀⠉⠁
⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠁⠈⠀⠀⠈⠙⠛⠦⠀⠀⠀⠀⠀⢀⣉⣀⠀⠀⠃⠀⠀⠉⠉⠀⠀⠀⠘⠋⠛⠉⠀⠀⠀⠀⠠⠤
⣤⠒⠀⠈⠉⠑⠂⠀⣀⠀⠀⠈⠉⠉⢀⠀⠀⠀⠀⠀⢤⣤⡄⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⢀⡀⠤⠤
⣀⣀⣉⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣐⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣃⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀
⣿⣿⢛⡻⢛⡛⢻⡻⣻⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣤⡎⠤⠄
⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢻⣶⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⡀⠀⠀⠇
⠀⠀⢩⠒⣾⠬⡀⠀⠀⡂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⢄⣖⢂⠀⠂⠃
⠀⠀⠀⠀⡆⠀⠀⠀⢰⠀⠀⠠⣤⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⠀⠀⠀⡆
⠀⠀⠀⠀⠆⠀⠀⠀⠎⠀⠀⠊⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⣀
⠐⠂⠀⣀⠀⡈⠶⠀⢀⠀⠀⠀⠀⠀⢀⣠⣀⣤⣤⣤⡀⠀⢠⣤⣀⣠⣤⣀⣀⣀⣀⠀⣠⣤⣠⡄⠀⣀⡀⠀⣀⡀⠬⠵⠄
⢠⡄⠀⠀⢤⡛⠃⠀⡁⠀⠀⠠⠄⠀⠀⠀⠈⠉⠉⠠⠍⡀⠀⠀⠻⠟⠒⣛⠉⠁⠀⠀⠁⠀⠀⠀⠌⠉⠙
⠀⠀⣀⣄⠀⠁⠀⠀⠀⠀⠰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠈⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀
⠀⠆⠘⠉⠓⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠁⠀⠀⠈⠭⣤⢤⠶⠆
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡉⠉⠀⠀⠀⠀⣀⣀⠤⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠌⠀⠀⠀⠀⠀⠨⠥⠀⡀⠀⠀⠀⠀⠋⠉⢀⠀⠀⠀⠀⠀⣰⠦⠄
⠐⠇⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣬⣏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠉⠏⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠒⠢⠤⣀⡻⣍⣙⡻⠖⣲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⡊⠭⠁⢒⣚⣉⣑⡒⠡⢴⠂⠘⠭⡀⣤⣉⡴⢊⣀⠬⠼⠓⠒⠢⢕⡌⢢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠡⠂⢁⡤⠒⡉⠍⠠⠆⠀⣠⢔⡒⠶⠿⠓⠚⠫⣄⡀⠛⠒⠖⠿⣀⣀⣤⠁⠋⡓⠉⣉⡒⡲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡽⢋⢔⡉⢠⡆⢀⡤⠚⠁⢸⠛⠦⣾⣀⣤⡀⠀⠉⠢⡀⠀⠀⢇⠀⠈⣹⠉⢹⠀⠢⡙⢦⡈⠒⠝⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⣁⠾⡥⠏⢹⠃⠀⡶⠴⣃⠀⣠⣧⣈⣩⡟⠛⠋⠉⠁⠀⠀⣴⠻⠟⢻⣄⢀⣧⠘⠀⠢⡙⣦⠷⣄⣙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⣞⣠⠔⠁⠀⠀⠉⠈⢫⠉⣩⠿⡀⠀⠀⠀⡤⠚⢉⠢⣤⠇⠀⠀⠀⠳⣄⣆⠰⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠂⢘⡆⢠⢎⠑⢬⣀⠞⠀⠀⠀⠀⠀⠀⠈⠘⠢⢄⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡔⢋⡱⡎⠢⣌⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠂⡠⢾⣀⣠⡇⢀⡀⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⠉⡐⢊⣇⣹⢀⠊⡆⠀⠀⠀⠈⡄⢀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠂⠀⣀⡱⠚⠉⢀⠸⣤⡚⠁⣳⢹⢑⣀⠘⡄⠀⠀⠀⠸⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠒⠋⠉⠡⠀⠀⠀⠀⠀⠀⠉⠁⠉⡛⠁⠀⠀⠁⠑⠀⠂⠀⠐⠀⠈⠉
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⢀⠀⠲⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠂⡠⠬⠤⠔⠒⠚⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠛⠛⠛⠉⠓⢄⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠚⠉⠀⠀⠉⠉⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⠤⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⠇⣀⣠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⢀⠰⠂⠀⠀⠀⠀⣀⡏⠀⠁⠀⠀⠙⠀⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡐⠻
⠀⠠⠦⠀⠀⡀⠀⠁⠀⠻⠃⠀⠀⠀⠆⠀⠀⠈⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠧⠀⠀⠀⢀⠤
⠀⠐⠂⠀⠀⢠⡀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠔⠂⠀⢀⠁⠀⠀⠀⡤⢃⡀⠂
⠀⠀⣧⠀⠒⡌⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡋⠁⠀⠸⠀⠀⠀⡜⢙
⠀⠀⡃⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡜
⠀⠀⢰⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⢰⠀⢠⣁⣀⣠⣤⡀
⢀⣀⢘⡆⣀⣀⢰⡿⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠂⠘⠘⠋⠉⣉⠉⠉⠁
⢀⢞⣄⣿⣫⢉⢸⣇⠀⠀⠀⢀⡀⠈⠉⠉⠀⠀⠀⠀⠠⠄⢈⣠⠀⠀⠀⠀⠀⠐⡂
⡏⣾⣿⣿⣿⣾⣿⡏⢸⡦⣀⡀⠀⠐⠀⠐⠸⠶⠶⠤⣤⣼⣿⣿⣶⣦⡐⠾⠶⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣧⣯⣥⣼⣿⣿⣿⠇⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠛⠉⠛⠋⠀⢠⣯⠁⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣐
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠐
⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀
⠀⠀⠀⠹⣝⠳⢰⣄⠀⠀⢀⠚⠉⣀⠐⠂
⠀⠀⠀⠀⠈⠦⣄⠈⢳⡀⢀⣀⠉
⠀⠀⠀⠀⠐⠂⠛⠢⣀⢠⡎⠀⠀⠄⠄⠓⠦⣤⡀
⠀⠄⠒⠛⠤⠶⠒⣲⣽⣿⣃⣈⡈⠒⠦⠀⠀⠈⠁
⠀⠀⠀⠀⢠⠎⠀⢿⣿⡍⢻⣿⣿⠀⠀⠀⠁⠄
⠀⠀⠀⠀⡄⢴⡟⠁⠁⡜⠀⠹⣿⡄⠀⠉⠢⣰
⠀⠀⠀⢀⠏⡟⠁⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⢐⠀⠀⡁
⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢛⡿⠿⣿⠂⢰⣤⡆⠀⠀⠀⠀⠀⢐⠀⠡⠄⠁⠀⠀⣰⣋⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⣬⠁⠸⠀⠀⠹⠛⠃⣤⣐⡶⢎⣯⣿⣮⣻⣽⠃⠀⣾⣱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠛⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠑⢄⠛⠄⡀⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⡁⠁⠀⡠⠾⢁⠠⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢖⡀⠳⡈⠓⡘⡠⣛⠩⠟⢩⢠⡀⠀⠀⠀⠀⠀⠀⠀⠢⡆⠙⠣⣙⠆⠸⢠⠖⢡⡔⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠴⠉⢠⡍⠡⠤⣷⣷⡒⠀⠶⢄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠑⢳⠈⠦⣽⣄⡂⠵⠤⠌⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣤⠜⢂⣽⡏⠳⣙⢌⠓⠘⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠋⡩⠙⣉⢜⢩⠟⣷⠈⣔⠲⡀⠐⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⣀⠐⠟⡸⠉⡆⢹⣌⠇⢬⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠆⢲⣡⠎⢠⠰⡧⢷⠌⠓⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠈⢸⣼⢿⣧⣌⣻⠆⣚⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡘⢰⡰⠠⠐⢖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠯⣬⡑⣽⣯⣅⡪⠑⠻⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠈⠁⠀⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡸⠻⠖⣩⣾⢻⣻⠺⣝⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠼⠛⠸⣱⣯⠇⢧⡧⣰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⢀⠈⡐⠉⠀⠖⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠇⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠐⠥⠥⠄⠀⠒⠒⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠐⠒⡆⠀⡦⠄⣀⣀
⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⢀⠁⠀⠀⠀⣙⠓⢀
⠀⠀⠀⠌⠁⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⢐⡉⠭⠀⠀⠁
⠀⠀⠸⠀⠀⠀⠀⠈⠒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⢦⡈⠀⠀⠀⢀
⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⢘⠀⠀⢀⡀⢀⡠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠼⠀⠀⠀⠀⠈⠒⠄⡀
⠀⠀⠀⠀⠈⠁⠒⠀⠤⠀⠈⠀⠀⠀⠀⢀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠠⠀⠀⠀⠀⠀⠀⣀⠤⠐⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠢⠄⡀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⡄⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠁⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠈⠒⠔⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠤⠤⠠⠤⠒⠂⠊⠀⠀⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⡀⢀⠀⠀⠀⣀⡀⢀⣀⠀⣀⣀⡀⢀⠀⠀⠀⢀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠶⠶⣿⣿⣶⡬⡽⠿⠿⢿⣛⡛⣻⣾⣿⣿⠶⢶⣶⣶⣆⣬⣍⣥⣤⣭⣭⣭⣥⢭⣭⣽⣿⣿⣷⣦⡚⢫⣭⣭⣿⣭⣿⣭⣿⣿⣷⣾⣿⣿⣿⣯⣭
⠠⠭⢷⣶⣶⣾⡿⠿⢿⣻⣿⣿⣿⢿⣿⣿⢓⣻⣿⣿⣟⣛⣫⣭⣿⢿⣿⡾⠿⣿⣿⣾⣽⣿⣿⢿⡿⣿⡿⠿⠛⠛⣩⣿⡿⢟⠻⠟⠛⠋⠛⢩⠶
⣒⣀⣉⠿⢭⡍⠥⠬⠯⠍⠛⠻⠿⠏⣉⢙⣿⣿⣯⠿⠷⢿⠗⠒⠊⢉⠤⡭⠛⠋⠈⠉⠙⠛⠷⠆⢀⠉⠉⠀⠘⠈⣭⠈⠉⠁⠀⠀⠀⠙
⣤⡀⠁⠀⠀⠀⠈⠉⠉⠉⢓⣂⣀⡀⠘⠛⠛⠓⠒⠀⣀⡀⠀⠐⠂⠀⠀⠀⠒⠒⠒⠀⡀⠀⠀⠈⠉⠁⠤⠠⠠⢀⣠⠤⠤⠀⠠⠤
⠉⠁⠀⠀⠀⠀⠐⠂⠤⠀⠉⠉⠉⠙⠃⠀⠀⠀⢀⡤⣉⢁⠀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠐⠲⠟⠿⠛⠋⠀⠠⠁⢀⣠⡶⠟⠉
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⣷⣤⣤⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣿⣿⣿⣿⣶⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀⣠⣴⣶
⠉⠉⠁⠀⢸⣿⣷⠄⠀⠀⠐⠀⡀⠀⠀⣀⣄⠀⠈⠛⠲⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⡀⠀⠀⠀⠺⠶⠀⢀⣄⣀⠀⠀⠈⣻⡿⠟
⠰⢷⡦⠄⠀⠶⠄⠀⠀⢤⣾⣦⣀⡀⠸⠿⠟⠀⠈⠀⠀⢀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣽⣄⠀⠈⠁⠀⠀⠀⠀⠉⠙⠛⠉⠭⢀⣤⣀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠺⠷⠦⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣠⠖⠀⠀⠀⢠⣦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣟⣿⡀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡷⠀⠀⡉⠀⠀⠀⠓⡄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣤⣀⠁⠙⠁⠶⠀⠀⠀⡇⠀⢠⣤⠀⢈⢠⡄⣉⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⣤⣠⠀⢤⢴⢦⠄⠀⠀⠁⠉⠙⠋⠐⠘⠠⣶⡤⠾⠿⢿⣿⣿⡿⢣⠦⠼⢷⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠐⠂⠸⠄⠀⠀⡈⢰⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣤⣧⠖⠂⢛⢻⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠸⣏⠿⠏⠙⠋⡉⡏⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⣈⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⢂⡠⢀⣿⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⣹⣿⣿⣿⣯⣿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠙⠛⣿⣅⣤⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⢀⣴⠖⠁⣼⠋⢠⡟⢠⡌⢀⣄⠀⠀⣀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⢸
⢀⣀⠀⢀⣀⣀⣀⣠⣤⣶⣾⣿⣧⣶⢿⣥⣶⣿⣥⠾⠋⣠⣿⢳⡿⠙⢀⣠⡄⣍⣈⣛⣿⣷⣦⣤⣤⣤⢤⣤⢸
⠙⠚⠂⠉⠩⠥⠤⠭⠉⠭⠛⠻⣛⢓⡟⠛⠻⠭⠿⠤⠚⣿⡃⣈⣁⣹⡿⢾⣾⠷⠿⠿⠿⠿⠷⠶⠓⠒⠂⠉⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠉⠃⠀⠉⠈⠉⠉⠉⠁⠈⠀⠁⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠠⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⣀⣀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⣤⣴⣶⣶⠂⠀⠀⠀⠀⣰⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⠀⠀⠀⠐⠤⣀
⠀⠀⣼⣿⣿⣿⡿⠃⣾⣶⡀⢠⣾⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⡀⠀⠈
⠀⣼⣿⣿⣿⠟⢀⣴⣿⠇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⢀⡄⣚⠿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⡄⠁
⠀⠀⠀⠀⠚⢙⣿⣿⣯⣜⡟⠊⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣿⠩⣦⠁⠁⠀⣴⣗⢂⣠⣦⠄
⠀⠀⠀⠀⠀⡾⠁⠋⢡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠝⠀⡀⠈⠀⠙⢇⠉⠘
⠀⠀⠀⠀⡐⠁⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⡀⠑⠠⡀
⠀⠀⣠⠞⠀⣠⠊⠀⠐⠀⠴⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⢄⡀
⠀⠘⠁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡗⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡄⠐⢺⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄
⠀⠀⠀⠀⠀⠀⣠⣄⢠⣠⣤⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄
⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠴⠛⠛⠉⠉⠁⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⢰⢤⣄⣴⠀⣦⡴⠀⣤⣤⣤⣠⢴⠆⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡫⠿⡼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠀⠀⠀⣰⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠘⢠⡧⠀⠀⠸⡿⢢⠄⠀⠀⠀⠀⠀⣠⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠃⠀⡴⣿⡁⠀⠀⠈⠀⠘⠒⡆⠀⠀⠀⠚⠿⣿⣶⣆⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⡋⠀⠀⠀⠀⠂⠀⠻⠞⢂⠀⠀⣀⢀⠀⠀⢠⠀⣄⢀⠀⢹⢡⠀⠀⠶⠿⠶
⠀⠀⠀⠀⢀⣀⡀⠀⠈⠙⠛⠃⢀⢠⠀⠀⢠⠀⠀⣼⣼⡶⠾⠿⣼⠞⠻⠿⠿⣿⣾⠀⠀⣼⡂⠀⠀⣰⢀⡄⣀⠀⢸⡄⢀⣀
⠀⠀⠀⠀⠉⠙⢳⣶⣶⡄⠀⠀⠺⢾⣤⠷⠾⠇⠀⠉⠉⠁⢀⣀⣀⣄⣀⠀⠀⠀⠋⠁⠈⠉⠛⠀⠐⠟⣿⣿⡿⠄⡙⢁⣤⣿⣿⠥⠄
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣦⡀⠀⠈⠛⠀⠀⠀⢀⣈⣠⣿⣿⣿⣿⣿⣿⣷⣶⣶⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⢶⣿⡿⠟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢶⣦⣴⣶⣿⢿⠿⠉⠉⣘⣿⡭⠉⠡⠿⠿⢿⢿⣿⠿⢿⣿⡟⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠈⠐⠠⢶⠛⠓⢀⡤⠀⠩⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢲⣄
⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣄⠀⠨⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣧⠀⣿⡇⠀⢀⣀⣀⣀
⠀⠀⠀⢀⣠⣴⡶⣶⣶⢦⣬⣽⣷⣿⣤⢾⡿⢟⠙⠉⠉⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠒⠛⠛⠛⠒⠶⢤⣀
⠀⠀⠀⠈⠈⠈⠀⠈⣁⣭⣾⡿⣟⣿⣿⡷⡶⣾⣤⣀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢀⠀⠀⠀⣶⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⣴⡿⠿⢉⡿⡙⢿⣿⢻⣧⡀⢈⠙⠹⢷⡄⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠈⠤⢬⣷⣉⣶⡥⠤⠁⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠼⠋⠁⢀⡟⠀⠈⢽⣿⠀⢿⣷⢸⠀⣰⠂⢉⡀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠈⠢⡀⢠⠴⢒⣿⣿⢿⡓⠶⡄⠀⡠⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠰⠤⢀⣿⠇⠲⠄⣿⠮⠤⣁⠰⠋⠀⡀⠠⠤⢸⡄⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠈⠳⠄⢟⣀⢿⣀⠻⠀⠠⠊⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠞⠁⢈⢡⠆⠘⠀⠈⠠⡑⡌⠉⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡇⠀⠑⠒⠒⠄⢀⠖⠉⢘⣛⡁⢍⠢⡀⢠⠤⠴⠂⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣈⣭⣈⣭⣉⣼⣀⣠⣄⣠⣄⣡⢧⣉⢥⣉⣷⣸⠁⠀⠀⠀⠀⠀⢷⠀⠠⣄⣀⣀⣮⠤⢤⣼⣈⣥⡤⠤⣧⣀⣀⣤⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡴⢤⠤⠦⡤⠦⠤⠦⠤⠦⠤⠴⠤⠴⠤⣴⠏⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⣀⣁⣠⡤⣤⣀⣀⣀⣤⠤⣀⣀⣀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⠶⠤⠶⠤⠖⠦⠖⠦⠴⠦⠴⢢⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠈⠁⢀⣠⣄⣀⠉⢀⣠⣤⡀⠉⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⢾⣦⣒⣲⣖⣳⣴⡷⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠉⠉⠉⠀⠀⣀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠲⠖⠖⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⣠⣤⣴⠆
⠀⠀⠀⠀⠀⠀⠶⢶⣤⡀⠀⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢀⣴⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⢸⣿⠃⣠⣾⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡸⣿⠀⣠⣴⡶⠶⠶⠶⣶⣤⡀⣿⣤⡿⠉⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣦⣜⣿⣾⣟⣂⣀⣤⣤⣀⡀
⠀⠀⠀⠀⢀⣤⣶⣶⡶⡶⣾⣿⣿⣿⣏⣁⣀⡀⣀⣤⣤⣼⣿⣿⣿⣻⠛⠙⠛⠛⠛⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⢾⣿⣿⣟⣻⠙⠋⠛⠛⠙⠻⠷⠄
⠀⠀⠀⠀⠉⠁⠀⠀⠀⡴⣟⠯⠙⢿⣏⠉⣻⠿⢿⣏⠁⣴⡿⠉⠛⢽⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠛⠋⠁⢡⣿⠿⠑⠛⣭⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡼⢴⠃⠀⠀⠈⢿⣷⡀⠀⠀⠀⣼⠟⠀⠀⠀⠀⢿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣰⣿⠋⠀⠀⠀⠘⣟⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠿⠀⠀⠀⣀⣀⣼⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣶⠄⠀⣿⠃⠀⠀⠀⠀⠀⢸⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣏⣻⣿⣫⠰⠶⠶⠚⠒⠒⠒⠒⠒⠚⠛⠋⣉⠽⣿⠿⡇⠀⠀⠀⠀⠀⠀⡤⠶⠚⢉⢀⠸⣇⠀⠀⣙⣀⣤⠤⠤⠤⠤⢤⣏⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢧⢈⣇⠈⠙⠒⠰⠶⠶⣶⣦⡠⠴⠔⠒⠉⠀⢀⡷⣼⠁⠀⠀⠀⠀⠀⠀⢧⠈⠀⣨⠤⣤⠈⠉⢉⡉⠀⠐⣀⣒⣒⣒⣀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⢙⣦⠤⠖⠒⠉⠉⠉⠉⠉⠉⠉⠙⠒⠢⠾⣠⠇⠀⠀⠀⠀⠀⠀⠀⠘⣦⠞⠁⢸⣁⣀⣁⡤⠶⠚⢉⣉⡀⠀⠀⠉⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠄⠈⣩⡴⣶⠄⠀⠀⣠⠴⠚⣻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣄⣀⠀⠀⠀⠀⢀⣀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢴⣃⡀⠳⠤⠖⣋⣑⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⢰⣾⣖⡀
⠀⣤⠆⠈⠛⠈
⣕⢾⢃⣼⠀⠀⠟⢠⠀⢲⠆
⠉⠉⢉⠿⢧⣐⠂⠀⠠⢀
⣶⣄⢸⣷⠀⠘⠷⣄⢘⡀⣁⣤⣤⣄
⣿⡈⣿⠿⠦⠤⠦⠌⠉⠁⠀⠀⠀⠀⠀⠀⠄⣀⣀
⠉⠙⠛⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠐⠐⠐⠠⠄⢤⣀⣀⣀⠀⠀⠀⠀⢀⢀⣀⣀⡀
⠀⢲⣿⣶⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠲⣤⣤⣤⣉⣉⡉⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠛
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣞⣿⣏⣰⢤⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤
⠀⡀⠀⠀⠀⠀⠀⣀⢠⠤⢌⠧⢻⣿⣶⣾⣿⠿⢼⠛⢪⠈⣿⠙⠠⢷⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠁⠀⠚⠂⠈⠉⠉⠉⠉⠉⠉⠃⠛⠛⠛⠓⠲⠶⠦⠛⠞⠒⠴⠿⠻⠯⠌⠶⠆⠰⠀⠀⠀⠀⠐⠓⠲⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠂⠀⠀⠠⠠⠀⠀⠴⣦⡤⣶⣄⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠐⠶⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⡈⠉⠁⢀⣀⡀⠀⣀⣀⢀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠉⠁⠁⠀⠀⠀⠀⠈⠀⣀⣀⣀⣉⣀⣭⠤⣤⣤⡄⠤⠥⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶⠐⠒⠤⠤⠤⠶⠮⠍⠛⠛⠛⠛⠋⢉⣉⣠⣤⣤⣴⣶⡶⠖⠒⠀⠒
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠠⣤⣤⠤⠄⠀⠐⠺⠓⠂⠶⠂⠀⠀⠀⠀⠉⠁⠉⠉⠉⠉⠁⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠋⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣶⣤⣄⠀⠀⠀⢽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠽⢷⣄⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣻⣆⠰⣿⠇⠀⣀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⢀⣤⡶⡿⣻⢟⣻⢶⣦⣶⣿⣿⣿⣴⡾⡟⠻⠛⠉⠈⠉⠁
⠀⠀⠀⠀⠀⠉⠈⠈⠀⠁⠈⣀⣩⣴⣿⢿⢿⣿⣿⡷⡶⣶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⢻⠓⣧⠟⢿⡏⢸⣿⣅⠘⠈⠏⠯⢻⢷⡄⢸⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠻⠈⠀⡼⠁⠐⠢⣄⠀⢋⣿⣎⢣⡀⠀⠈⡘⠻⠄⠀⠀⡎⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣸⠃⠀⠀⠀⠈⠁⠈⢞⣿⠀⠀⢀⠀⠳⠀⢰⠀⠀⠀⠀⠞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣠⣤⠖⣒⠒⠦⡄⢨⣿⠀⣀⠈⢣⡀⣆⢸⢠⠇⡰⠂⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢒⠀⣄⢀⣶⣋⠉⠐⠃⠤⣌⡑⠦⠙⣈⣈⣈⡚⡥⠊⡁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢉⢰⠣⢼⡑⡞⠣⠤⠤⠤⠤⠭⢀⡞⡥⠀⠀⠙⣆⠩⢄⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠊⠂⠠⡓⢷⣄⣀⣤⣴⣒⣒⣸⣇⡥⠴⢖⣒⠛⠒⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡤⠗⠚⠭⠍⣉⣐⣒⣠⠖⠋⠁⣚⣩⠭⠶⢲⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣖⠚⢉⠉⣡⢟⠕⣀⡴⠊⢝⣤⣶⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠾⣥⣤⣼⣥⣤⠴⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣀⣀⡄⠀⠀⠀⠀⣀⣤⣴⣶⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣪⣵⣶⣿⣿⣿⣷⣄⠀⠀⢀⡼⣦⡤⠖⠙⠉⢡⡞⢤⡶⠀⠀⣼⣿⣿⣿⣿⣿⣷⣮⡳⣄
⠀⠀⠀⠀⠀⠀⠀⡴⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⡤⠖⠉⠀⠃⠀⠀⠀⠀⠀⠀⠈⠈⠑⠺⢿⣿⣿⠿⠛⠛⢿⣿⣿⡌⢧
⠀⠀⠀⠀⠀⠀⢸⢡⣿⣿⡿⠋⠁⠈⠙⢿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣀⠀⠀⢹⣿⣿⠘⡇
⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⡇⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⣸⣿⣿⠀⡇
⠀⠀⠀⠀⠀⠀⢹⡘⣿⣿⣷⣄⠀⡜⠀⠀⠀⢠⣖⣽⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣤⣖⡢⣄⠀⠀⠀⠘⣤⣼⣿⣿⡟⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠳⣜⢿⣿⣿⣿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢰⣿⣿⡟⠿⣿⣷⡀⠀⠀⢹⣿⡿⠿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⡇⠀⠀⢠⣿⣿⣿⠿⠿⢿⣿⣇⠀⠀⠀⠀⣿⣿⠟⠛⠛⢮⣿⣷⡀⠀⢀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣾⣿⡟⢡⢶⡆⠀⢹⣿⠀⠀⠀⠀⣿⣧⣾⣀⡀⡄⢻⣿⣷⡀⠈⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡞⠀⣼⣿⣿⠁⢣⠻⣿⢟⣿⡿⠀⠠⠀⠀⢻⣯⡛⠿⣋⠇⢀⣿⣿⣷⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢻⣿⣿⣷⣤⣙⣒⡿⠋⢀⣴⣶⠿⢖⣦⠈⠛⠯⣥⣶⣿⣿⠿⠃⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠙⠻⡿⠛⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠒⠴⠶⠿⢖⠂⠁⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣦⣄⣀⠀⠀⢠⡀⠀⠈⠀⠀⠁⠀⢀⠄⠀⣀⣠⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣶⣿⠦⣄⣀⣀⣠⠴⠛⢾⣿⣿⣿⣿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⣿⣿⣿⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣧⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⡼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡝⣿⣿⣿⣿⣿⣮⣝⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣿⣿⣿⡎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣌⢳⡀⠀⠀⠀⠀⢀⣜⣵⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⣺⣥⣤⣉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣴⣾⡛⢲⡒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣾⠿⣿⣉⣹⣿⣿⣿⣿⡟⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⡿⠻⣿⠿⣿⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⢿⡶⠞⠉⠁⠀⠉⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠓⠚⠻⠤⣾⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡏⠀⠀⠀⠀⠀⠈⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣀⠀⠀⠀⠀⢀⣀⣠⡶⠿⠿⢿⣿⣇⠀⠀⠀⢀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⠤⠴⠾⠋⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒





⠀⠀⠀⠀⢠
⣷⣶⣶⣶⣾⣤⣾⣦⣤⣤⣼⣤⣄⡀⢀⣆⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣤⣿⣾⣾⣿⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠤⠤⣄⠀⣀⣰⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠓⠂⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠛⠉⠉⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠻⠛⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠉⠌⠀⢠⠆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⢿⣿⡿⡿⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠟⢛⣧⠀⠀⢀⣀⠀⠀⢂⠀⠀⠀⣀⠀⠤⠀⠈⢀⠄⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⢈⣁⢤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿
⠞⠋⠀⠀⠀⢀⡤⠆⢀⠈⣷⠖⣀⣀⠀⠠⠐⡀⠀⢀⠘⠀⢀⡈⠀⠀⣁⠀⠀⠀⠀⠀⠙⠀⠿⡋⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠐⠓⠀⠀⠀⠐⠀⠴⠒⠀⠀⠴⠍⠁⢀⣀⠀⠐⠀⢈⠁⣀⡀⠅⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⣼⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠛⠛⠛⠿⣿⣿⣿⣦⣇⣉⡟⠛⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠻⢯⣏⠁⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠟⠋⠉⠀⠈⢻⣿⣿⣷⣶⣶⣶⣾⣷⡶⠆⠄⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⡛⠁⠀⠀⠀⠀⠈⠙⠛⠛⠛⠁⠀⠈⠉⠉⠉⠁⠀⠀⠈⠙⠛⠛⠛⠛⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡷⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣆⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠉⠙⠛⠛⣛⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⣸⣦⣴⣶⣶⣾⣷⣿⣿⣶⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⡄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄⠻⣿⣿⣿⣿⣿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣴⣿⣿⣿⣿⣿⠿⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡅⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⣧⡟⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⢛⣼⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣇⢿⣛⣶⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣦⣛⡿⣸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡿⠋⣀⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣀⠙⢿⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣮⡹⣧⣾⣿⠛⠛⠉⣍⠙⢻⣿⣿⣿⣿⣿⣿⡿⠋⣉⠉⠻⠻⣿⣷⣜⢟⣵⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⡟⠃⣿⣿⠛⠛⣿⣽⣷⢸⣿⣿⣿⣿⣿⣿⡇⣾⣯⣿⠛⠛⣿⣿⠈⢻⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⣳⣝⡷⠿⠿⠶⣀⣀⠛⡿⠿⢛⣻⣿⣿⣟⡛⢻⢿⠟⣁⣀⡶⠿⠿⢾⣻⣾⣻⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⡿⢏⣽⣏⠀⠀⠀⠀⠉⠿⣶⣶⠀⠸⢿⣿⣿⡿⠇⠀⣶⣶⠿⠉⠀⠀⠀⢀⣹⣯⡹⢿⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡎⠙⠻⢷⣤⠀⠀⠀⠀⠉⠟⠀⠀⠸⠟⠟⠇⠀⠀⠻⠉⠀⠀⠀⠀⣠⡾⠟⠋⢹⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢫⣾⣿⣦⡀⠙⠛⣤⠀⢀⠛⠀⠀⢠⣴⣤⣤⣶⣄⠀⠀⠚⡀⠀⣤⠛⠋⢀⣴⣿⣷⣝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⣿⣿⣿⣀⠀⠀⠀⣿⣿⠀⢸⣿⣷⣴⣾⣿⣿⡇⠀⣿⣿⠀⠀⠀⣀⣿⣿⣿⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣽⣿⣀⣀⠀⠉⠿⠶⣨⣹⣿⣿⣿⣿⣏⣅⠶⠿⠉⠀⣠⣀⣿⣿⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠻⠻⣿⣤⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⣠⣿⠟⠛⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣦⣀⣀⣀⣀⣴⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣯⠟⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠠⣼⣿⣿⣧⠄⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠞⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠄⠀⠀⠀⠀⡼⠁⠊⠁⠰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠜⠁
⠀⠠⠀⠀⡀⠁⠀⠸⠗⠀⠀⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠈⠀⠀⠀⠠
⠀⢈⠀⠀⠠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⡈⠀⠀⢰⡎⠅
⠀⠘⠃⠈⠂⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡇⠀⠀⠁⠀⢀⠊
⠀⠀⡀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡆⠀⠎
⠀⠀⣣⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠇⠞⠛⠚⠛⠛
⢀⣮⣸⣏⠋⢹⡇⠈⠀⢉⠉⠙⠋⠉⠉⠉⠉⠬⢍⣡⠉⠉⠉⠉⠉⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣧⣿⣿⣿⣿⣿⠇⡿⣠⣄⠀⠀⠀⠐⠖⠒⠤⠤⠿⢿⣾⣦⡚⠗⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⠿⠻⡿⠀⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀
⠁⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⢀⡄⢀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣿⣾⣀⣾⣿⡯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢚⣽⣿⣿⢿⣿⡟⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠏⡼⡙⡄⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⣀⠀⠀⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣛⣩⣽⠿⠒⢶⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢈⡉⠉⠉⠉⠀⠀⠀⢀⡄⣀⣽⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢶⣿⣾⣿⣿⣿⣷⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠶⠶⠶⢶⣶⣶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉⠛⠛⠋⠋⠉⠉⠛⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⣿⡿⠻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠠⢄⡀⠀⡀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠻⠛⢉⠙⠳⣿⣾⠟⠁⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⣴⠟⡩⠄⠒⢿⣷⣿⣿⡯⢅⡈⢀
⠀⠀⠀⠀⡀⠀⢠⠆⢀⡀⠀⠟⡙⠡⡈⢀⣾⡾⣿⡿⣟⢶⣄⠻⣬⡀
⠀⠀⣀⣤⣼⣿⣿⡿⢦⣤⠀⢀⠊⢰⣷⣿⢿⢳⡟⢧⠸⡖⢿⣷
⠀⢰⠏⢠⢈⣼⠻⢵⣎⢿⣦⡆⠐⡿⢫⡟⣼⣼⠀⠈⠀⡰⠮⣿⠆
⠀⠘⠀⠀⢸⣿⡘⠘⠏⠀⠋⠈⠀⢠⡟⠀⠃⠸⠀⠀⠈⠀⠀⢸⠂
⠀⠀⠀⠀⠈⠘⣷⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠻⢆⠀⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⠈⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⢀⣀⣀⢀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡏⡇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⢀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⢣⠀⢀⣀⠈⣀⣋⣈⣉⡉⣋⠀⡀⣋⣈⣉⣃⡉⣁⣙⠈⢛⣉⣉⣐⣠⡀
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢸⢸⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⣿⠟⠛⠛⠛⠉⠙⠙⠋⠉⠉⠁
⠀⠀⠠⠀⠀⠀⢸⡧⠀⠀⣾⢸⠀⠀⢀⡄⢀⡠⢀⢄⠀⠀⠀⠀⢠⡏⠠⠠⠤⠀⠀⡀⠀⠀⠀⠄⡠⠀⠄⠀⠀⠄⠀⢤⢀⡄⠄
⠀⠀⠐⢠⠄⠀⢸⡇⠐⠄⣗⢸⠴⣞⣂⣐⣭⡭⠤⢒⡀⠈⣁⣀⡹⡇⠍⣉⣩⣤⠤⠀⣀⣈⠉⠧⠄⠒⠒⣛⣩⣤⡒⢒⣠⣤
⠀⠀⠐⠒⠒⠀⢻⡟⠛⠛⡟⢸⠃⠀⠒⠒⠀⠉⠓⠣⡈⠉⢂⠬⠽⣧⣴⣶⣾⣿⣭⣍⣽⣷⣶⠶⠶⠖⠈⠉⠛⠓⠠⠤⠤⠦⠄
⠀⠀⠀⠀⠀⠢⣜⠃⠀⠀⢡⢸⡀⠀⠀⠀⠀⠀⠀⠀⢣⠠⠀⠚⢡⡟⢦⡀⠈⢆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣸⣧⡦⠀⠀⠀⠀⠀⠀⠀⣣⣄⣘⣯⡇⠈⣷⠹⡞⣮⡁⡀⠔⠚⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠘⠛⠛⠋⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠉⠙⡇⠐⢺⣧⣼⣾⣿⣶⠞⠋⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠠⡤⠀⠀⠧⠀⠉⠀⠀⠈⠙⠉⠒⠲⢤⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠁⠀⢤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣛⣛⣛⣂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡷⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣤⣭⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢘⡻⢿⣿⡿⢛⣛⡛⢿⣿⣿⠟⣛⣿⣿⣿⢇⣿⣿⣿⣿⣿⠿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣾⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⠏⣼⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⠿⠻⢿⣿⣿⠿⢻⣿⣿⣿⢋⣼⣿⣿⣿⣿⣿⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣿⣿⣷⣶⣶⣿⣿⡿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣭⣭⣭⣭⡙⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⢛⣩⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢋⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣤⣾⣷⠦⠄⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⡟⢿⡟⠛⠶⡄⠴⣿⡟⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⠃⡀⠀⠁⠸⠁⠰⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⠀⠀⠀⠀⠰⡀⠀⠀⠀⠐⠀⢺⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⢺⠟⠿⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠢⣀⠀⢀⢀⡀⢸⣤⣤⣤⣿⣶⣷⣶⣶⣲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣔⣦⣴⣶⣶⣾⣿⣾⣯⣿⣿⣷⣿⣧⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠁⠑⠒⠚⠒⠦⠭⠍⠉⣉⣉⠉⢛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠒⠒⠒⠈⠀⣀⣠⠴⠶⠊⠐⠀⢀⣠⡤⠔⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⣀⣐⣢⣤⣤⣽⣿⣶⣶⠶⠶⠶⠴⠶⠶⠶⠶⠟⠛⠋⠁⠀⠖⢄⣀⡀⠐⠘⠒
⠀⠀⠀⠤⠦⠤⠶⠒⠂⠉⠉⠉⠉⠉⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣴⠟⠋⣹⠀⠀⠘⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠶⠶⠛⠛⠛⢋⣉⠉⠉⣉⠛⠉⠙⠙⠛⠉⠉⠉⠈⠀⣀⣠⠴⡃⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠠⠤⠐⠒⠒⠲⠒⢒⣛⣋⣩⣥⠶⠶⠟⠟⠛⠻⠻⠟⠛⠙⠻⢛⡾⠶⠶⠶⠶⢖⣒⠛⠿⠛⠥⠼⣗⠤⠤⠒⠊⠁⠀⢰⡀
⠒⠒⠒⠈⠉⠛⠛⠋⠉⠉⠁⠀⠀⢀⣀⣀⣠⡤⠤⠖⠒⠉⠩⠚⠋⠁⠐⢀⣠⠔⠊⠁⠀⠀⠀⠀⢀⠀⠀⠠⢽⣦⡴⣴⣛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣠⠤⠒⠀⠀⢀⣀⡤⠤⠒⡂⠀⠻⠀⠀⠀⠀⠀⠀⣀⠴⣙⣾⡷⢟⣪⡟⠁⣉⣭⠉
⠀⠀⠀⠀⠀⠈⠈⠉⠉⠐⠒⠒⠛⠋⠉⠀⢀⡤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠁⡚⠥⠼⠃⠀⠉⠉⠀⠛⡉⠉

⠀⠀⠀⢻⣿⣿⣿⠀⢀⣠⣼⣿⣿⣾⣿⠏⠁⠻⣄⠀⠀⣹⣿⣿⣶⣾⡷⠀⣀⠟⠩⠤⠄⠀⠀⠀⠀⠀⣾⣿⣿⣷⠂⠔⣡⢞⠁⣴⣿⣿⡎⠡⠖
⠤⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⡀⠀⢨⣶⣿⣿⣿⣿⣋⣠⣶⣦⠠⣚⣥⣶⣦⠀⠀⡀⠀⠈⠛⠛⠛⠋⢠⣊⡁⢋⣼⣿⣿⡿⠃⣠⣾
⠓⠦⣠⣴⣿⣿⣿⣿⣿⡿⠿⣿⡆⠀⠀⠀⠹⣆⠀⠉⣡⣤⣿⣿⣿⡟⠛⠋⠸⢿⣿⡏⠁⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣷⣾⣿⣿⠟⢠⡼⣿⡿
⡉⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⢻⣿⠀⠀⠀⠀⠹⣧⡀⠈⠿⠻⣿⣿⠀⠀⠀⠀⠘⠛⠀⠀⠈⠀⠀⠀⠀⣿⣿⣿⡿⠟⢩⣾⣿⡿⠁⣴⣿⡏⠏⠄
⠀⠘⢿⣿⡿⠏⠉⣿⡿⣧⠀⠘⠋⣀⡰⠄⠀⠀⠈⠳⣄⠀⠀⠻⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⠛⠉⠀⢀⣌⣙⠛⣡⣄⠈⠛⢁⣴⣿
⠀⠀⠈⠋⠀⠀⠀⠀⠻⠆⠀⠀⠀⠿⣤⣤⢶⣶⣤⠀⣈⠃⣄⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡏⢰⣿⡿⠃⣤⡸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠒⠀⠀⠀⠀⠀⠁⠉⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⢡⣾⣿⡇
⠀⠀⠀⠀⠠⠀⠄⠀⢼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣴⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢋⡀⣐⣆
⢀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⢙⡃⢿⠇
⢸⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⢀⡀⠀⠀⠀⠀⣶⣶⣄⣀⣶⣤⣶⣄⠨⠅⢈
⣾⡿⢶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠚⠯⠉⢻⣿⣿⣿⣿⣿⣷⠀⠸
⠋⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣤⣍⠿⣿⡿⠇⢹⣿⡀⡿⠂
⠀⠀⠀⠀⢪⡝⠃⢠⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⠛⢿⡿⠟⠓⡆⠈⠃⠀⠀⡂
⠁⠀⠀⠂⠀⠀⠐⠀⠀⢹⣿⣿⣷⡶⢻⣿⣶⣿⡿⢉⣿⠡⠟⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠠⠖⠉⠀⠀⢀⢠⡀⠾⠟
⣀⡄⠀⠀⠀⠀⠀⠀⡤⠀⢉⠉⠁⠀⠈⠉⠀⠉⢀⡈⠁⠀⡀⠀⠀⠀⠀⠈⠀⠀⠤⠀⠀⠀⠄⠀⠠⠀⡤⠀⠀⠊⠀⠀⠀⠀⣀⠀⠈⠀⠀⢃⣀
⣿⣇⣴⡖⠀⠀⠀⠀⠁⠀⠌⠈⠂⠀⠀⠀⠀⢠⣿⣿⣶⠆⠁⣀⠀⠀⡴⣖⠆⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠘⠀⣀⢰⣦⣠⣾⡟⠀⣼⣶⣴⣿⣿
⣿⣿⣿⣿⣿⣼⣿⣴⣦⣶⣶⣿⣦⣄⣀⡀⣄⡀⠀⠀⢈⡁⠀⣍⡀⠈⠉⠉⠀⠀⣀⣋⣀⣤⣀⣀⣂⠀⣀⣄⣠⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡉⢁⣀⣀⠀⠀⠀⠀⣀⣀⡉⠀⠀⠀⠀⠁⠈⠁⠀⠀⠉⠁⠉⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⢠⡀⠀⠀⣤⣤⣤⣤⣄⣤⣶⣟⣿⣿⣿⣯⣤⣾⣦⣠⣤⣤⢠⣶⡶⠛⣤⣤⡄⢀⠀⢠⣤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⣤⣤⣤
⢀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣷⢸⡿⠟⢺⣿⣿⡇⣼⠐⠻⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⣼⣿⣿⣿⣿
⠀⠁⠀⠀⠀⠰⡆⢰⠔⠶⠀⠀⢹⣿⣿⣯⠉⠿⣬⣿⣧⠜⢿⣿⣆⢰⣦⣿⣿⠘⣿⣿⢰⣤⠀⠀⠀⣤⡘⠓⠷⠶⠿⠦⡤⠤⣾⠇⢨⣿⣿⣿⣿
⢰⣦⡀⠀⠶⠦⢤⠀⠆⠶⠐⠒⢀⠿⣫⣾⠷⣶⣿⠙⣿⠔⢻⣿⣿⣦⣩⣿⣷⣴⣿⡇⠈⢉⣀⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠰⣇⠀⣞⣸⣿⣿⣿
⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣄⡹⠷⠈⣀⣿⣿⣿⣿⣉⠉⣉⣿⣿⣿⣿⣿⣿⠀⠘⠋⠏⠀⣿⣦⣄⡀⠀⠀⠀⠀⢦⠀⠀⠸⢿⣿⣿⣿
⠀⠛⠛⠃⠻⠂⠀⠀⠤⠐⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠉⠛⠛⠛⠳⠀⠀⠀⠀⠀⠀⠀⠛⠋⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠫⠀⠀⠀⢡⢹⡟⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⡀⠀⠈⣶⣦⡀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡄⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠈⠀⠠⠄⠀⠀⢿⠿⠷⠀⢰⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄⠀⠀⠸⠎⠀⠀⠀⠀⠀⣁⠈⣁⠀⠉⠁⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣧⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠤⠀⠤⠄⠀⠀⠉
⠀⠀⠀⠀⠀⠈⠀⠄⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣼⣿⢯⣄⣽⠶⠤⠤⢀⠀⠀⣤⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠤⢠⣤⡀⠀⢠⣤⠀⠀⠀⠈⠻⢷⣶⣶⠞⠉⠉⠛⠛⠀⠀⠀⠀⠤⣄⠀⠊⡄⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠰⣦⣄⠀⠀⠀⣤⠀⠀⠀⢀⠠⣶⡶
⠀⠀⠉⢻⡇⠈⠛⠂⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⢀⣴⡿⠳⣦⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣮⠹⢆⢠⣤⢿⣦⡄⢠⠿⠀⡄
⠠⢠⣄⣸⡇⠀⠘⠛⣷⠛⠘⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠛⡴⢋⠟⠀⠀⢀⣿⣆⠀⠀⣷⠠⠈⠀⠠⠂⠀⢀⣧⠴⣎⠁⠀⢀⠀⠈⢡⠖⠀⣿⡄
⠀⠀⠈⠉⠁⠀⠀⠀⠉⠁⠉⠀⠀⠢⡀⠀⠀⠀⠀⠀⡰⣿⣷⢾⣀⠠⢀⣼⣿⣿⡆⠀⠏⠠⣶⡖⠉⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⣀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠰⣦⣬⠅⠀⢡⣠⡾⠋⠉⣉⠀⠀⠠⠀⠈⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠀⣁⠉⠀⠀⠀⠄⠀⠨⣄⠉⠁⠀⠀⠙⠋⠁⠀⢠⠇⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⣀⣀⣀⠋⡀⠉⣀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⡄⡀⣁⠀⢤⡀⠄⠀⠀⣀⣄⣤⠈⢳⣀⠀⠀⠀⠀⠀⠀⠨⠦⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⠀⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠿⠈⠁⠈⠻⢆⠀⠂⣠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠐⠀⠓⠀⠐⠀⠐⠂
⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡛⠀⠀⠁⠀⠀⣤⠘⢻⡿⠁⠀⠀⢠⠀⠷⠲⠶⠦⣤⠤⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣬⡅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⢀⢀⣀⠀⡠⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠤⠤⢧⡜⠂⣀⣆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡄⡸⢶⡛⠚⢫⣵⢄⡴⠀⠀⠙⠑⠂⠇
⠀⠀⠀⠀⠁⠀⠀⠒⢆⠈⠢⡀⠀⠀⠀⠀⠀⡀⠀⠀⢄⡽⠓⠁⠁⠀⠃⡷⠆⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡢⢹⠇⠀⠀⠀⣤⠈⠀⠀⠊⠀⠀⠀⢠⠊⠀⣭⣗⠋⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣅⢁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢃⡗⠂⠀⠀⠁⠁⠀⢠⢧⡀⣀⡀⣈⢁⣀⢀⠀⠀⠀⣠⠀⠀⢀⣀⡀
⠀⠀⠀⣰⠖⠒⠒⣻⠯⣔⠟⠀⠤⠀⠀⠀⠀⢀⡞⠂⠋⢈⢀⡈⠉⡉⢉⢀⡀⣰⣿⠦⣤⣤⢞⣁⣄
⠀⠀⠀⠀⠀⠐⢶⠁⠀⠈⠀⠀⠀⠐⠀⠀⠤⠾⠧⠄⠀⠀⠄⠀⠀⠀⠘⠛⠛⠛⠻⢷⢽⡛⠛⢛⠙⠃
⠀⠀⠀⢰⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⢤⢀⣿⠈⠁
⠀⠀⠀⠈⠀⠠⠄⠀⠀⠀⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠠⠀⠀⠀⠀⢁⡀⢐⣰⠤⠆⠸⠗
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠒⠀⠐⠚⠐⠃⠤⠤⠤⠢⠐⠁⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠖⠾⢿⡖⢤⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣷⣶⣶⡤⣾⠤⣶⡷⠀⠗⠀⣲⣿⣿⣿⣿⣷⣿⣿⣿⣿⣉⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣿⣭⠿⠿⠟⠃⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⡏⣥⣀⠀⠀⠨⠰⠀⠀⠀⠈⠙⢯⡿⢽⣟⣿⣿⡿⠿⠿⠿⠿⠟⠃⠋⠘⠋⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁⠀⡐⢩⠑⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣶⣿
⠿⠿⠘⠛⠉⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣯⣿
⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣶⣾⢿⡿⢻⢿⣿⡛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣀⣄⣠⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣶⣿⣿⣿⣿⣿⣿⣧⣞⣷⠾⢿⠁⣇⣰⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⢿⣿⣿⡿⢻⣿⣿⡿⣿⣿⣿⣿⡟⢿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣟⠋⡛⠋⠉⠿⠟⢿⣿⣩⣿⣉⡙⠙⣛⠛⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠛⠿⠭⣿⣿⣿⣮⠿⣿⡕⠻⡽⣤⣴⣶⣆⣀⣀⠀⠀⠁⣶⣶⡍⠙⠙⠛⠿⢦⣤⡉⣰⠦⠀⠀⠉⣉⠙⠛⠿⠿
⠉⣿⡿⢛⣓⠛⠙⠁⠋⠁⠤⡦⠤⢬⢴⡆⠀⠀⠉⠉⠛⠿⢛⡛⠻⠿⢿⢿⣿⡾⠋⠵⣶⣖⣂⡐⠀⠀⠀⠀⠀⠀⠐⢀⠙⠻⠿⣶⣴⣀
⠈⢉⠙⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠀⠔⠂⠃⢶⣶⣾⣾⣼⡏⣶⠦⡙⢿⣷⣖⡰⠂⠀⠀⠖⠀⠀⠀⠀⠄⠀⠉⠻⣷⣆⡆⣤
⠀⡀⠀⠈⠁⠀⠀⠀⢀⣠⣤⣴⣶⣶⣿⣿⣿⣟⠥⠔⢊⡏⠀⠀⠄⢝⣋⣭⣼⢟⣩⠎⡠⠤⣿⣿⣿⡿⡜⠃⠁⠀⣀⣴⡆⠀⠀⢰⡤⣀⣼⣷⣉⡉⠁
⠀⡂⠀⠀⠄⢀⠀⠀⠈⠁⠀⠀⠈⠻⣛⣛⡿⢋⣄⡤⠶⠶⠆⠸⣿⣯⣭⣩⣽⢋⠁⢈⣭⣶⣿⡿⠛⣤⣵⣾⣿⡀⢉⡉⠀⠀⠀⠉⠀⠀⢹⡟⠛⠒⠈
⠀⠀⠀⠀⠘⢓⠂⠀⠒⠀⢐⣾⢛⣛⣏⣩⢬⡳⠋⣾⠏⣴⡼⣫⣽⣿⣿⣃⣽⣷⠞⠿⠛⠷⡾⠲⠰⠶⠃⠀⡀⠀⠚⠓⠀⢀⠀⣂⣴⡿⢛⠉⠓⣀⡃
⢀⣠⣈⢉⡙⠛⢋⣬⣥⣾⠗⠲⣿⣶⣶⣛⡛⢿⡿⢟⣉⣿⣿⣿⣿⣍⣹⡶⣇⢀⠀⢀⡀⢈⡈⢤⡔⣂⠰⠐⠆⠀⠐⠛⣡⣤⡾⠋⠭⢛⠛⣻⣭⡈⠆
⠈⠁⠁⠀⣀⣄⡈⠛⠡⣥⡤⠶⢿⣿⣿⣿⣯⣿⣯⢿⣿⣿⢿⣿⣽⣟⠿⠿⠴⠙⢯⡍⢩⣭⠉⡄⠜⠀⠀⠜⢶⣶⣶⢟⡩⣿⢿⣇⣂⣤⣌⢋⢋⣁⡀
⠜⠣⠤⢩⢏⣭⣿⡟⠲⡜⡷⣛⡺⢙⣩⣽⡆⢨⣥⣦⣼⡦⠨⡟⡛⢻⠗⢆⡙⣳⠦⣤⡈⠂⠀⣥⣤⣨⠟⢻⠛⢦⣛⠺⢥⠒⠀⠘⠋⠻⠁⠈⠉⠀⡀
⣀⣂⣄⣀⣤⣑⣚⣀⣙⣂⣐⣒⣃⣼⣯⣛⣛⣟⣛⣛⣋⣐⣁⣐⣀⣒⣂⣀⣀⣀⣀⣀⣁⣸⣂⣙⣉⣐⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⠀⢀⠤⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠢⠤⠤⠄⠀⠄⣀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠈⠀⠐⠢⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄
⠀⠀⠀⠀⠠⢄⣒⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⢄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠐⠠⠀⠀⠀⠤⢀⠤⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣽⣯⣮⣯⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣯⣿⣿⣿⣿⣿⣯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣦⣰⣴⠶⠛⠒⠦⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢴⣭⣿⣿⣗⣺⡛⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠻⢟⣽⢛⠺⡈⠛⠷⡀⠄⠀⠀⠀⢀⣤⡤⢤⣄⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢋⣄⢺⣿⠘⢦⣿⣦⠀⠀⠀⠀⠀⣲⣝⣿⣥⠐⠆⣠⢞⣿⡟⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠈⢿⠀⠀⢹⡊⠐⠀⠀⠀⠀⠛⠀⠸⢯⣷⠀⠋⠻⠁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠈⠢⣄⡀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠈⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡋⠑⠀⣀⠀⠀⠀⠀⠈⠉⠒⠤⣄⡀⠀⠀⠈⠓⢤⡀⠀⠀⠑⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣴⠦⢶⡴⠴⠼⠥⠤⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀⠀⠀⠈⠳⢄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠙⢦⣄⠀⣹⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡉⢳⣦⠀⠀⢙⠡⣍⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠲⠂⠀⡄⠀⠀⠀⠀⠀⣀⣤⠤⠒⠛⢒⣞⡢⡝⣷⢲⣳⡄⢉⣽⠲⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠖⠋⢉⠀⢀⡤⠀⠉⠀⣍⠻⣶⣏⣁⠉⠻⠻⣦⡉
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢛⣸⢂⣤⡏⠔⠘⡀⣦⣷⣾⡿⣿⣿⣿⣿⡷⣧⡌⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠺⠟⠳⠿⣿⢶⣿⡴⠞⠛⠀⠁⠀⠀⠀⠐⠀⠐⠈⠉

⠀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⢀⠐⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠤⣄⠀⠀⠄⠈⠀⠠⠂⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⠀⠀⠀⠀⠀⢠⠊⠀⠀⠠⠐⡌⢦⣜⠀⢀⣀⡀⠀⠄⠁⠀⠀⡀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⡀⠀⠈⠠⡀⠀⠀⠀⢸
⠀⣿⠀⠀⠀⠀⡴⡆⠀⠀⠀⢀⠂⡇⠸⡂⠀⠀⠡⡀⠀⠀⠀⠀⡎⣠⠟⠚⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠘⠡⠀⠀⠀⠀⢠⠀⠀⠀⢸
⠀⣿⠀⠀⠀⠀⢹⣧⠀⠀⢀⡌⠒⠁⠀⠉⡂⠀⠀⠙⠀⠀⢠⢊⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⢡⠀⠀⠀⠀⢀⣶⠀⠀⠀⢸
⠀⣿⠀⠀⠀⠀⠀⠙⢷⠶⠞⠽⠒⠀⣤⠚⣄⣀⡤⣄⠀⠀⠀⠛⠸⠏⠀⣀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠺⠶⠠⣖⡶⠟⠁⠀⠀⠀⢸
⠀⡇⠀⠀⢀⠄⡀⢴⠆⡶⠀⣠⠄⠚⡾⣯⣥⣽⣶⣶⣷⠤⠀⠀⢁⠖⡀⠀⠀⣸⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢀⠜⣹⣄⡀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠈⢦⡈⠐⠂⠀⠌⠀⠀⢸⢠⢸⢡⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠒⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠊⠛⠁⢌⠆⠀⠀⠀⢸
⠀⡇⠀⣀⣀⣀⣼⣿⣿⣿⠀⠀⠀⠈⠢⠜⠈⠰⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣛⡶⢤⣤⣴⣀⣁⣀⡀⠀⠀⢸
⠀⡇⠀⠉⠉⠉⠉⠉⠉⢻⢧⣀⠀⠀⣠⢤⣀⡠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠷⠾⠿⠾⠿⠿⠿⠛⠛⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⡿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠰⡒⠏⣻⡃⠧⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣇⣀⣀⣀⣀⣀⣀⣀⣓⣤⣄⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⠒⠒⠀⠒⠂⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣠⣶⢶⣣⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠠⠴⣶⣴⣿⣧⣾⣿⣿⠶⣤⠀⠀⣠⣤⣤⣄⢤⡄⢀⣀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢠⣾⣿⣿⣿⣿⣻⣿⣿⣿⠿⣿⡆⠘⢋⣭⣽⣷⡾⣿⣿⣋⣳⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢋⣴⣶⢾⣿⣿⣿⣿⣽⠿⢿⡆⠁⢠⡾⢿⣿⢿⣷⣿⣿⣿⢿⣷⣆⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣿⠟⣿⢿⣿⣿⣾⢿⣿⡆⠀⠁⠀⠈⢰⡿⢻⣿⣿⣿⣿⣿⡷⡝⡟⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⢸⠇⢾⡿⠙⣿⠄⠙⢧⡀⠀⠀⠀⠈⠀⢺⡿⢋⣿⠟⢿⡇⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠁⠈⠧⠀⠘⠃⠀⠈⢳⡀⠀⠀⠀⠀⡾⠁⢠⡿⠀⠈⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⢰⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⡀⠀⣀⢀⣿⡇⣧⣤⣀⣀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣶⠴⠶⢶⡞⠉⣹⡿⠗⣾⣿⠷⣿⠷⣽⡿⣽⣷⣺⣅⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠶⠿⠖⠒⠚⠛⣿⡿⠋⣀⣬⣿⠏⠀⢿⣷⡈⢁⣉⣭⡼⠟⣋⠙⢿⣏⠻⢶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⠶⠶⠶⣿⣤⣾⣟⣛⣁⣀⣀⣬⣿⣿⣟⣋⣩⣭⣿⣿⠷⠾⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠠⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⢠⡤⠄
⣶⣆⣄⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢲⠴⠄⣤⣶⡅⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠈⣿⣧⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠀⢤⣿⠁
⢀⣾⣷⠞⠉⠀⠤⠑⢾⣿⡁⣲⠀⠄⠀⢀⣂⣰⣶⠿⠂⠠⠀⠈⢳⣼⣿⠍⠀⠠⠴⠤⠴⣶⡀⠄
⢈⣿⣟⠁⠀⡀⣀⠀⠀⠙⠻⣽⡄⠀⠀⣻⡿⠗⠚⠁⣀⡄⡀⠀⣹⡿⢿⠉⠀⠀⣀⠀⠉⠓⢿⣷⠀⠀⠀⠐
⣏⣶⣺⣧⣶⡮⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⠁⢨⣶⣶⣿⣶⣠⣿⣾⡦⠀⠀⠀⠀⠀⠈⠁
⣿⠃⢠⣻⠷⢅⢄⢀⢀⠲⣄⠀⠀⠀⠀⠀⣀⠔⢂⢠⢄⣴⣿⣿⣿⠀⣿⡿⣿⠳⢄⢠⡀⠀⠲⣄⠀⠀⠀⠀⠀⠐
⣿⢡⠸⣿⠀⠀⠁⠁⠋⠷⣉⠿⣆⡀⢠⡾⢣⡢⡞⠋⠉⢺⣿⡟⢻⡄⡿⠛⢸⡇⠀⠁⠉⠞⠢⣚⢷⣄⣀⠀⠀⠀⡴⠄
⠁⡸⠒⣯⠀⠀⠀⠀⠀⠀⠉⠈⢈⣷⠏⠀⠀⠀⠀⠀⠀⢀⣿⠀⢸⠀⠁⠀⢸⣇⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠄
⡔⠁⠐⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡔⠀⠀⠸⣿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⡇⡦⠶⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠤⢸⡇⡄⠀⢀⡧⣿⡧⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⢀⢠
⣿⢁⢾⡏⠀⠀⠀⡎⠀⡢⢤⡀⠐⡄⢰⢁⠝⠃⣤⣀⣅⠀⠀⢰⣼⡇⡧⠆⠚⡇⠿⡀⠀⢀⢤⠒⠐⡊⠁⣠⠋⡑⠠⣆⣲
⠸⣜⠀⡅⠀⣀⠠⡍⠈⠤⠃⠐⠉⢳⢈⠁⠖⠁⣀⡁⠙⠏⠋⢉⢸⡃⣷⠀⢸⢃⠦⠉⠈⠀⢰⠄⢁⡁⠀⢳⢆⡀⠀⣀⠁
⠀⣿⠀⡇⠷⠀⢀⡄⠀⡧⠀⠘⠁⢀⡃⢴⢁⠀⢈⠀⠐⠆⠀⠉⣹⠀⠶⢨⠃⠎⢕⠀⠉⡁⢨⣇⠀⣠⠠⠞⡼⠧⣀⡆
⡴⡇⠀⡁⠀⡀⠀⠤⠤⠋⠂⠓⠎⠈⢀⠆⠀⠈⠈⠈⠀⠀⠉⠈⣽⡌⠤⠌⢠⠀⠀⠷⠴⠈⠁⠀⢄⣁⠀⡼⢁⣀⡈
⠀⠁⠠⠄⠀⠉⠈⢁⣀⠀⠀⠈⠈⠉⠁⠀⠀⠀⠀⣀⠐⠒⠂⠀⣿⠀⠈⠀⣾⠀⠀⠀⠀⠀⠈⠀⠀⠐⠒⣀⣀⣀⣀
⠀⢀⠈⠦⠁⠀⠀⣐⠂⠀⠀⠀⠀⠉⠀⡀⠐⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⡇⠒⠒⠒⢦⣁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⡠⠥⠮⠅⠀⠰⢒⣋⠁⣀⡀⣖⡒⠂⠀⠈⠛⠀⠌⠉⠐⠚⠀⣈⠀⢰⠀⠀⠠⠄⠤⠤⠤⢋⠈⠉⠤⡄⠀⠀⠀⠈⠭
⠒⠈⡠⠂⠒⠀⠠⡄⠀⠀⠂⠀⠀⠈⠉⠁⠂⠤⠀⠀⠁⠀⢨⣁⠂⠀⠐⡍⠁⠀⠐⠀⠀⠄⣀⠂⠀⠀⠀⠢⡄⠁⠚⠉⠍
⣉⣁⠀⡃⠠⠀⠂⢁⡀⠠⠤⠬⠀⠂⠂⣈⠀⡀⡀⠀⠄⠀⠀⠂⠨⠉⠅⠚⠀⢀⡢⠀⠀⠔⠁⠀⠀⠀⡄⠐⢁⢀⠠⠐
⠀⠁⠍⢄⡀⠀⠐⢐⠒⠒⠒⠀⡒⠈⠀⠠⠄⣐⣀⠀⠀⠈⢢⠐⠀⠒⠀⠅⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠤⠤⠀⠐⠂
⠀⠠⠀⡘⠂⣀⣀⣐⢒⣈⠭⠥⠭⠩⠭⣐⠬⠁⠀⠰⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠥⢐⠀⠀⠠⠭⠤⠀⢀
⠓⠒⠊⠓⠀⡀⢂⠀⠐⠀⡀⠆⠀⠀⠉⠉⠀⠈⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠚⠐⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠢⠀⡠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢹⣠⠊⠐⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠐⠀⠀⠀⠠⠐⠘⠁⠀⠛⠢⠸⠙⠀⠀⢀⠁⡂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢈⠀⢀⡀⠄⢄⡠⡪⠀⠀⠀⡄⠀⡠⠀⡰⠀⢤⣷⠀⠙⣔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠠⡤⢁⣇⠢⠒⠀⠀⠬⢼⢪⠤⠀⠀⠈⠉⢀⡁⢑⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠋⠓⠀⠀⠀⠀⢘⠐⠠⣴⣾⠀⡀⠈⠀⠈⠡
⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠉
⠀⡀⠀⢠⡼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠃⠀⠀⡄⠀⢀⠀⠀⠀⢠⠀⠀⢰⠀⠀⠀⠀⢠⡀
⠈⠀⠀⠋⠨⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣰⡇⠤⣾⡀⢀⠛⠿⠶⠶⠿⢛⡃⡠⢸⣿⠻⡾
⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡉⠁⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠒⠂⠄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⣀⠀⠁⠢⣀⠌⠀⠀⠈
⠀⠀⠀⢀⠊⠁⠀⠀⠈⠐⠀⠀⠠⠀⠀⠀⠐⠀⠂⠈⠸⠀⠀⠀⠀⠤⢀⣀⠀⠈⢢⡖⡀⠀⠀⠠⠤⠆⠠⠄⢀⣀
⠐⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⢈⠩⣦⣴⠼⢤⡶⠖⡀⠀⠀⠀⠀⠀⠀⠈⠂⠄
⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠄⠁⠠⠐⠀⠀⠄⠀⡘⠁⠀⠀⠁⠀⠀⠁⠀⠸⠀⠀⠠⡀⡀⠀⠀⠀⠐⠥⡀
⠀⠀⡀⠀⠓⠤⢀⡀⠠⠔⠁⠀⠀⠀⢀⠄⠀⠀⠀⠀⢀⡄⠐⠀⠄⠀⢣⡀⠀⡠⣇⠀⣠⣇⣀⠜⠀⠀⠀⠀⠀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢁⠀⠀⡠⠠⣀⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠘⠒⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⡌⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⡄⠀⣀⣤⡄⢠⣤⣤⡀⠀⣠⣤⠀⣤⡄⢠⣤
⠀⠀⠀⠀⠀⢸⡇⣰⣏⣼⡇⢸⣧⣼⠇⣾⣋⣿⠀⣿⢿⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄
⠀⠀⠀⠰⣦⡾⠃⠿⠋⠹⠇⠻⠇⠀⠸⠟⠉⠿⠀⠿⠈⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠉⠻⣧⡀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⠀⡆⢀⠀⡀⡀⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠙⠿⣶⣤⡾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠃⠃⠒⠂⠃⠂⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡟⠀⠀⠀⠀⠀⠉⠀⠿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠙⠃⠀⠀⠀⠀⢠⣤⣴⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⠰⣦⣶⣶⣤⣀⢰⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣠⡶⠿⣿⡟⠻⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠇⠛⠲⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣰⡿⠃⠐⠀⠠⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢫⣿⡿⠟⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠘⠁⠀⠀⠀⠁⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠾⢶⣶⣾⠿⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⠟⠉⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⢀⠠⣴⣏⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣉⡀⢀⣤⣤⡤⠒⢿⣷⠖⠀⠀⣹⣶⣶⣶⣿⣼⡿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠁⠀⠙⢹⣾⠃⠀⣀⡀⣤⣿⣄⢀⣼⡿⠟⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣵⠀⠀⣠⣿⣄⣸⣿⠿⠟⠉⠻⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⢠⣿⠋⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣒⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠁

⢼⣯⢛⣿⣷⣦⣤⡀
⠸⣿⠘⣿⣷⣧⣿⣿⣷⡶⣤⣀⠀⢀
⢤⣿⡇⢻⢹⡏⣿⣿⣿⠔⡹⣿⡟⡛⢿⣶⣤⣀
⢸⡅⢻⡿⣧⣰⣿⡟⢏⠈⠱⣿⣟⣌⢢⡙⣿⣿⣿⣧⣀
⢡⡞⣄⡳⢙⡿⣷⣿⣌⠆⠐⡹⣿⡞⣧⡱⣜⣿⣳⡉⠉⡁
⠀⢰⢹⡇⢉⡃⣿⣿⡿⣷⣄⣈⠿⣟⠸⣷⣜⣿⣷⣍⣦⢈⡢⣀
⠀⠘⣿⠃⠘⡇⢸⡟⣗⡇⣿⣻⢶⣄⣠⡈⠓⢍⠳⣝⠓⠻⣿⣿⣷⠆
⢘⠄⣿⣀⢠⡇⣿⣇⢹⢧⡇⣿⣧⣿⣝⠷⣶⣤⣀⡀⠙⠀⠀⠉⠛⠁
⡈⣗⠀⢿⣿⢷⣿⡏⣼⢸⡇⣿⣿⢧⢿⡇⡿⣿⢿⣿⡲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠒⠂⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠
⢹⡯⢶⣀⣿⠈⣿⢡⡏⣿⢰⡇⡇⢸⡸⡇⡇⠘⠀⠃⠃⠙⠀⠀⠀⠀⢠
⠈⣿⢀⠿⡣⡼⢃⡼⢁⠏⢈⢡⠃⠸⠇⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⣷⣿⣣
⠀⣱⣿⣶⢛⠛⠛⠁⣀⡀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠛⢇⠀⢀⣰⣿⣦⠂
⠈⡉⣉⢿⣅⠒⢂⣤⣀⡉⠣⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠷⡾⣆⢨⡎⢹⣿
⢠⠞⣡⠞⣹⣿⣋⣩⡭⣷⡄⠠⠤⠾⣟⣳⡦⣤⡀⠀⠀⠀⠠⠄⠒⠄⠀⠐⠟⣇⣹⣿⣿⣦
⠉⠀⡵⡌⣉⣿⣷⠴⠖⠊⣉⠡⠄⣰⢿⣷⣧⡄⣙⠫⠲⠆⡬⣲⣦⣤⡒⠈⠁⣉⣥⣿⣿⡏
⠀⠰⠉⣾⢟⣿⣿⣿⣿⣶⡭⢆⡀⠁⠋⢙⣿⡿⠋⠀⡠⢀⣴⢍⣻⢯⡙⢢⣙⢻⣿⣾⣟⣠⠆
⠀⠀⢈⡞⠁⠼⣿⣾⣿⠟⠛⠀⠀⠀⣠⠟⢋⡤⠐⢉⠴⢟⣷⡋⣤⡙⠋⢨⣯⡉⣹⣿⣯⣟⠀⢴⣶⣦⣔⣶⣶⣤⡀
⠀⠀⠘⣧⠞⢠⣿⠿⣥⠈⠃⠀⠀⠊⠁⡀⢡⠔⠀⢀⡐⣾⣷⣿⢷⣤⢌⡿⠿⠇⠉⣿⡿⢙⣷⣾⠿⡛⢉⣱⣿⠏⠻⡟
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢁⢠⡔⠁⠍⠓⣬⢙⣳⢀⠐⣄⣰⠳⢾⣽⣷⣿⢽⣏⣼⠃⣼⣿⠫⣶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡤⠿⢯⣁⠒⠤⢤⣈⣽⣿⡿⠟⢻⠟⢛⢿⡝⠉⢲⡟⢁⣿⣇⠀⠃⠻⠁
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠶⣄⡀⠐⣮⣑⣰⡾⣻⠉⠅⠀⠀⠌⣐⢫⠛⠀⠀⠀⣷⡾⢧⣿⣧
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡴⠤⣉⣠⣼⠟⣽⠘⢇⠰⠀⠀⢀⣸⣿⠋⠀⠀⠀⢀⣟⣿⣿⣿⡿⢧⡀
⠂⢠⠀⠀⠀⠀⠀⠀⠀⢴⣞⠓⠢⣿⣷⣚⣷⣾⣟⡀⠀⡿⠀⠀⠀⠀⠐⣭⠟⠁⠀⠀⠀⠀⡜⢡⣻⣿⠂⣸⣾⢻⣄
⢈⡅⠀⠀⠀⠀⠀⠀⠀⠠⣬⣉⣴⣿⣿⢿⡋⣾⢻⡅⠀⠀⠀⢀⠴⢁⡐⠉⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣇⠿⡇⢸⣿⡆
⠈⠓⠀⢤⡀⠀⠀⠀⠀⠀⢹⠏⣿⣿⣿⣀⠇⣼⠇⠅⠘⢀⡔⠛⠎⠈⠀⠀⠀⠀⠀⠀⠀⠐⢯⡽⢻⡿⣿⣆⠁⣿⣉
⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠈⠐⠁⠙⣍⠛⠀⠋⠀⠰⠖⢳⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⠼⢿⣿⣆⠉⢻⣦
⠀⠀⠀⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠁
⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠆⠀⣤⠥⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠄⠤⠤⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⠀⠀⢀⠎⠹⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠤⠤
⠀⠀⠐⠂⠀⠀⠢⠀⠚⠀⠀⠄⠀⠀⠎⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⣀⡀⠀⠀⠀⠐⣾⠤⡄⣦⡀⢠⡔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠋⠁⠀⠉⠀⠀⠀⠀⠆⠀⠘⢅⠈⢐⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡠⠄⠙⠋⠉⠀⠘⢧⡀⠀⠀⠘⣷⠄⠀⢀
⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⣘⡉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠠⠴⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠇⠒⠄⠀⠈⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠙⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠄⠀⢰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠁⠀⠀⠉⠐⠶⡬⣁⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠉⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠒⠋⠉
⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠒⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠩⠐⢄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢠⣰⡁⠀⢀
⠀⠀⠀⠀⠀⠀⠚⠋⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⠛⠉⠠⠀⡀⠀⠀⢀⢄⠒
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠂⠀⠀⠀⠀⡄⠆⠀⠀⠀⠀⠀⠁⠀⡀⠀⠈⠀⠀⢃⠀⠊⠐⠆⠁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠰⡄⢀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠞⠁⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢣⡀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢀⣰⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⢀⠠⣤⣤⣤⣤⠤⠤⠤⢴⣄⠀⠀⠀⣾⣿⣷⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⢀⣀⣠⢤⠈⠉⢹⣿⠟⠛⠉⠁⠀⠈⢉⠟⠀⠀⠀⠀⠠⣿⣦⣤⣤⣬⣋⣉⡀⠉⢉
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢻⠁⢹⣷⡢⣤⣀⢠⠂⠀⠀⣼⡤⠴⠞⠋⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠙⠈⠛⠿⢿⣭⣿⣷⡿⠶
⢀⡀⣠⣤⣤⣤⠀⣨⣿⣷⣉⣤⣶⣿⢇⣼⣿⣾⣀⣀⣸⠁⣀⣀⣀⣠⣤⠴⠖⠒⠚⠛⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠸⣷⣬⣿⣿⡇
⢀⣀⠀⣀⡐⣛⣛⣿⣿⣿⠿⠿⠿⠟⠛⠿⠿⣿⣿⣿⣯⣿⣿⣀⡀⢠⡶⣀⡔⠀⠀⠀⢹⣿⣿⣿⡄⢠⠄⣠⣀⠀⠀⣼⡏⠉⠻⢿⣥
⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⠶⠺⠷⢶⣦⣘⣉⠉⠩⢍⣛⡛⠿⢿⣿⢿⣿⣿⣿⣿⡿⠿⠿⢿⠟⠿⠿⠿⣿⣿⣿⣅⣀
⢸⣿⡛⣛⠟⡛⠘⠛⠘⠻⡿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣿⣿⣿⡿⠿⠿⠶⠶⢦⣞⣿⣿⣿⣀⣀⡀⠘⣇⡀⠀⠀⣯⡉⠉⠙⣍⠛⠶⣶
⢠⣤⣤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⢫⣤⣭⢿⣿⣿⣿⣿⣶⣦⣄⣩⣿⠓⠢⠬⣭⣉⡉⣛⠛⠻⠿⠿⢷⣄⣀⠈⣳⣄⡀
⠐⠂⣀⡒⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠻⠿⠭⠿⣟⡿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠜⢹⣷⣄⣀⠀⠈⠉⠉⠛⠛⠿
⢸⣿⡿⠭⠩⠅⠠⠤⠤⠤⠤⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⡿⣿⡿⣿⣿⣿⣷⣻⣿⣿⣿⣻⣿⣶⣬⣙⢳⣶⡦⣄⣀⡀
⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠠⠀⣤⣥⡴⠶⠿⠿⣿⡷⠼⣿⣿⣿⣯⣥⣎⣻⡿⣿⣿⣿⡿⣿⣿⣷⣶⣭⣿
⠸⠷⠶⠖⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠹⣿⣧⠤⠼⠿⠛⠻⣿⣿⣭⣟⣙⣷⡷⢿⣽⣽⡾⣽⢿⣻
⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠟⠿⠿⠿⠷⠛⢻⡃⠀⠀⠀⠀⣾⣿⣿⣇⣩⣟⣙⣿⣿⣿⢶⣏⣽⣞⣷
⠰⠶⠶⠶⠶⠶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠶⠶⠶⠶⠟⠛⠛⠛⢿⣿⠃⠀⠈⠈⠙⢿⠿⠟⠟
⠐⠒⠒⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣼⣄⠀⠀⠀⢀⣏⣀⡀⡀
⠘⠓⠀⣀⣠⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠀⠀⠀⠙⠓⢤⠀⠀⠑⢤⣀⣼⣯⣇⣱⡟
⢠⣤⣤⠤⠤⠤⠀⠨⠿⠿⠿⠿⠿⠿⠿⠷⠶⠤⠤⠤⠤⠤⠄⠐⠒⠒⠶⠶⠶⠶⣶⣶⣷⠀⣀⣀⣤⢄⣠⢳⢦⡄⠀⡙⣿⠟⠛⠋
⣴⣴⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣴⣶⣶⣶⣿⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣬⣭⣿⣿⣽⣭⣽⣯⣿⣭⣥⣥⣤⣥⣧⣤⣤⣤⣤
⣿⣿⣤⣬⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠋⠉⠉⠀⢀⠏⠉⠹⠍⠉⠉⠙⡛⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠍⠀⠀⠀⠀⠀⠀⠀⢘⠀⢀⠀⢀⣴⡶⢶⣦⣔⠀⣪⣻⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠀⢸⣯⠀⠀⠈⠙⢿⣄⡡⢹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⣀⣤⠶⠒⠒⠉⠁⠉⠉⠉⢻⡲⠦⢄⣀⠈⠻⡷⣤⣤⣤⣼⠿⢁⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠴⠊⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢶⠀⣀⠙⠉⠀⠀⣼⡟⠀⠀⠀⠀⣠⠞⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣀⠘⠁⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠊⠱⣆⠀⠀⠚⣳⣿⠃⠀⠀⢀⡔⠁⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡄⠀⠀⠀⠀⠀⢀⣤⣶⣶⡿⠿⠿⠿⣿⣿⣷⣤⣀⠀⠀⠙⠛⠈⠣⡀⢠⣿⣿⠀⢀⣴⢫⡂⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⣅⠀⠠⡀⣠⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⡻⠉⠙⠻⣦⣤⣶⣄⡐⠁⢸⣿⣧⣴⠿⢛⣁⣀⣤⡄⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢠⣤⣄⠁⢠⠟⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⣿⠟⠋⠛⣷⠀⠀⢠⣿⣿⠛⠛⠛⠉⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⠘⠷⠟⠀⠀⠀⠀⠈⠓⠦⣤⣄⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⠀⣶⡄⢸⡇⠀⢸⡇⣿⠶⠶⠤⢤⡤⠤⠄⠀⠐⣿
⠀⠀⠀⡤⠤⠤⠤⠖⠚⠉⠀⠀⠀⠐⣤⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠙⠁⣸⡇⠀⢸⡇⣿⢦⣤⣀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⢿⣉⠒⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⣿⣦⣾⠟⠀⠀⠈⠻⠷⣄⠈⠙⠻⠕⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠈⠉⠒⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⣠⣶⠏⠑⡈⠳⠦⡀⠀⠁⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⢴⠀⠀⢀⣠⠶⠋⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢏⢹⣿⠀⠀⠈⠢⡀⠈⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⣇⠉⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡘⢠⡀⠘⣿⠀⠀⠀⠀⠈⢢⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠐⠁⠰⠀⠀⠁⢻⡆⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⢤⡀⠀⠇⠂⠠⠄⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⢿⣶⣤⣀⠀⠀⠀⠀⠀⠖⠁⠱⠀⠀⠀⠀⠀⠨⡄⠀⢀⣽⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⣿⡿⣾⣷⠀⢤⣀⠀⡀⠀⠀⠄⠀⠀⠀⢀⣂⣠⣾⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣧⠀⠈⠉⠛⠳⠾⠿⠷⠶⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠈⡆
⠀⠀⠀⠀⡔⠊⠉⠉⠉⠉⠒⠤⡀⠀⠀⡸⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢀⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⡇⠀⠀⠀⢀⣜⡠⠤⠤⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⢆⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢣⠀⢀⠔⠉⠀⠀⠉⡆
⠀⠀⠀⠀⠀⠀⠑⠢⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢦⡎⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⣀⠤⠐⠒⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠙⠂⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠒⠒⠒⠂⠬⣣⡀⠀⠀⠀⠈⠀⠀⠀⢀⡔⠁
⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠒⢤⡀
⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⣠⢴⠃⠀⠀⠀⢰⠜⠲⢄⡀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⢨⠀⠀⠀⠀⠀⢀⡤⠊⠁⡎⠀⠀⠀⠀⢸⣆⠤⠐⠉⠹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⠔⡝⠁⠀⠀⡀⠀⠀⠀⠻⡢⢄⣀⠀⠀⣀⡴
⠀⠀⠀⠓⠤⠤⠔⠊⠁⠀⠀⠀⡅⠀⠀⠀⠀⢸⠘⡄⠀⢀⡠⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠓⠞⠀⠀⠀⠀⣧⠀⠀⠀⠀⢣⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⣠⠃⠀⢸⠊⠁⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠂⢼⠀⠀⠀⠀⢠⠉⡄⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⣧⠤⠒⠊⠉⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⠤⢀⡘⢄⠀⠀⢀⠜⠀⠘⢄⡀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣀⣀⠤⢵⠀⠀⠀⠀⠀⠀⠀⢠⣃⡀⠀⠀⠈⡝⠉⠀⠁⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠉⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢀⠇⠀⠀⠉⠑⢲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡠⠄⠒⠂⠉⠙⡀⠀⠀⠀⠀⡜⠉⠙⠛⠐⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢀⡠⠤⠒⠈⠉⠉⠉⠉⠉⠉⠁⠀⠒⠆⢀⣀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠈⠁⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠠⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⡀⠀⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠁⠤⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠁⢀⣈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠤⠤⠐⠒⠒⠢⠤⢀⣀⣀⣀⣁⣀⣀⣀⣀⠤⠒⠒⠐⠒⠒⠢⠤⠠⠤⠒⠊⠉⠀⠀⠀⠉⠐⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⠂⠤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢮⣀⣀⡉⠁⢠⡀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡚⠛⠀⠈⢉⣽⢿⣿⣤⣭⠿⠗⠚⠁
⠀⠀⠀⠀⠀⣀⠀⠈⠛⢟⠛⠿⠻⠃⠈⠀⡰⣦⣍⣍⣁⣢
⠀⠀⢠⡿⢾⣻⡿⠒⣺⣃⣀⣀⣢⠀⣀⠀⠸⢯⣤⣤⣤⣈⠆
⠀⠀⠈⠙⠉⠉⠁⠀⠀⠀⢠⣼⠃⠰⣤⣄⣴⣤⠀⠤⡆⠚⠢⣄
⠀⠀⠀⠀⢤⣀⡈⠙⢦⣄⠈⠁⠘⠛⠛⠋⠈⣿⠿⣦⣿⣿⣦⠤⠃
⠀⠀⠀⠳⠶⠞⠿⠿⣧⢼⠆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⢀⢠⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢀⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡉⣀⣴⡿⠋⠉⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠀⠀⠀⠀⠀⠋⢀⣾⠁⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠰⢛⡷⢁⣤⣶⡶⠀⠀⣴⡽⢀⣷⠊⢤
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠐⠄⠈⢉⠐⠒⢄⡀⢀⣰⡃⣤⣰⣈⣵⠾⠋⢠⠞⠁⠋⣠⠀⢀⣸⣷⠞⢻⣧
⠀⠀⠀⠀⠀⠀⠀⣠⢟⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⣡⣼⠾⠃⡤⠀⢸⣿⡆⠛⠉⠁⠰⣦⣿⣦
⠀⠀⠒⠒⠚⠛⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠐⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠀⠃⠀⠀⠀⠀⠐⢶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⢠⠀⠀⣀⣦
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣶⣄⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠻⢿⣿⣿⣿⣮⡷⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠄⠀⠀⠀⠉⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⢀⡀⠀⠀⡀⠀⢀⡀⣀⣤⣴⡄
⠀⠀⡀⡀⠀⡄⠀⡀⠄⢄⣦⡵⠊⠉⠉⠉⠁⠒⢄⠒⢠⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠀⣀⠈⠰⣷⡅⢈⣁⣠⢀⡀⢀⠈⠀⠠⡀
⠀⠀⠃⣹⣾⠗⠀⠀⠀⣠⠟⣶⢖⡴⢿⡢⠐⠀⠀⠀⠐⠓⢀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣠⣿⣶⣲⣿⣏⠀⢀⠉⠚⠅⠛⠁⢠⠀⠉
⠀⠀⢰⡝⡏⠀⣀⢄⠘⠻⠉⢿⡀⠻⡾⠀⠉⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠟⠚⠁⢙⡵⠻⡏⢻⣁⡤⠀⠈⠀⠀⠀⠒⠠⡀
⠀⠀⠸⠉⠁⠀⠉⠆⠀⠀⢀⣿⡏⠀⠀⢀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠛⡟⠁⠀⣿⡭⢹⣋⠀⠂⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢲⠄⠀⠀⠘⠷⠗⠚⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠀⠀⠨⠁⠀⠀⡽⠓⠴⠋⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢠⣠⣦⡴⠀⠀⠘⠀⠀⠐⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⠠⠄⢀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠞⠃⠐⠣⠈⠁⠀⠀⠀⠄⠀⠀⠄⠀⠀⠄⠀⠀⠀⣀⣠⣡⠀⠘⣆⠀⠀⠀⠀⠀⠁⠒⠀⢀⡃
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢀⠀⠀⠁⠀⠈⠟⡇⠈⠙⡛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢀⠀⠀⠦⠔⠋⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣎⠘⢻
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠔⠃⠀⠀⠀⠀⠠⣴⣤⡴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⢤⡁⠧⡄⠀⢀⠀⡀⢀⣁⣀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣀⠁⢢⢹⠔⠕⢬⡠⢮⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠰⠂⠀⣆⣄⣨⣐⣾⠸⠛⠁⠈⠉⠉⠁
⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠁⢀⠤⣲⣿⢻⣿⣽⣿⡗⡞⠋⠙⠯⡛⠃⠗⡱⣠⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢠⡙⢋⢁⠽⡏⢺⢠⡷⣠⠀⠀⠀⣀⠀⠈⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠃⠀⡰⠁⠀⠃⡟⣼⠀⠀⢠⡈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠹⡷⠁⠀⠀⠈⢁⡰⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡉⠈⡁⠀⠀⠀⠀⠀⠀⠀⠒⠠⠒⠐⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠰⠟⠀⠄⠒⠂⠄⣄⡀⠀⠀⠀⠠⠌⠀⠂
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠢⢔⢠⠈⠀⠀⠀⠀⠀⡀⠀⣀⣠⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠀⠀⠉⠉⢳⣀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠛⠀⣀⣠⠞⠋⠙⢲⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣤⣤⣤⣤⣤⣤⡼⠃⠀⠀⠀⠀⠀⠀⠀⣰⠋⡽⠟⠁⠀⠀⠀⠀⢸⠇⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢿⡀⠙⠒⡶⠒⠒⠒⠒⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⡉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠉⣛⠉⠐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣚⡋⠙⠓⠿⣄⠈⢧⣀⡤⠴⠒⠒⣒⣦⣤⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⢤⣘⣆⢸⣧⡶⠒⠾⠯⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⣹⠾⢤⣍⠉⠳⢦⠤⢽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡼⠁⠀⠀⠈⠙⠲⣌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠑⡾⠁⠀⡤⠚⠉⣩⣷⡀⠉⠀⣠⠖⠋⣩⣷⡄⠀⠀⢠⠖⠉⢉⡭⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣅⣰⠃⠀⡼⠁⠀⠘⣇⠈⠀⢀⣰⠃⠀⠀⢧⡀⠁⠀⣠⠏⠀⠀⠸⣄⡀⠀⣀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⡿⠐⠋⠁⠀⠀⠀⠈⠉⠛⠉⠁⠀⢀⠀⠀⠉⠛⠛⠁⢀⣀⣀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠓⠒⡇⠀⠠⠞⠋⣉⣳⡄⠀⠀⢠⠞⠉⢉⠭⣦⠀⠀⢀⡞⠉⢀⡼⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⡇⠀⠀⠀⠀⢇⡈⠁⠀⣠⠏⠀⠀⠹⣄⡀⠀⣠⠞⠀⠀⠘⢦⣀⣀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⠤⠴⣇⣀⣀⣀⣀⣀⣉⡛⠋⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠒⠒⠒⠒⠒⠒⠒⠒⣚⣛⣋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢿⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⠶⠶⠶⠦⠤⠴⢶⣟⣉⠉⠉⠉⠉⠉⠉⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠂⢢⠀⢰⠀⣒⠀⣦⠀⠀⠐⠀⠀⢆⠐⠂⢰⡂⡔⠐⢠⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠂⠀⠀⠈⠈⠀⠀⠂⠈⠂⠐⠀⠀⠂⠀⠀⠀⠀⠀⠊⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠑⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠄⢈⠇⣀⣀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⣀⢀⠠⠖⢶⡄⠋⠀⣬⡉⠚⠟⡦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠁⠁⡰⠀⠀⠀⣾⣤⠀⠀⠘⡷⣄⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦⡀⡰⢺⠆
⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠄⣸⢻⣿⣇⠀⢸⠀⠁⠂⡀⠀⠀⠀⠀⠐⠆⢡⡘⠛⢧⡿⣠⣏⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠇⠘⡿⠃⠀⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣭⠆⣹⣷⣍⡳⣤⣁⠀⠸⡖⠀⡠⢒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠗⢺⢃⠒⠁⢻⡌⢣⣿⣌⢵⡶⢿⣿⡚⢶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⠀⠀⠀⢷⠀⠀⢠⠌⡵⣾⣿⠻⣌⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠘⠋⢠⠇⠈⠀⠉
⠀⠀⠀⠀⠀⠒⠒⠀⠀⡃⣀⠀⠈⠁⠐⠒⠀⠐⠂⠀⠀⠀⠀⠈⠉⠙⠛⠃⠠⠤⠀⠀⠀⠀⢷⠀⢰⡄⣾⠠⠆⠒⡒⠐⢤⠠⠖
⠀⠀⠀⢤⡀⠘⠛⠲⠶⠡⢤⣶⣶⡀⠀⠀⠀⠠⠤⣤⡄⠀⠀⠂⠚⠀⠀⠠⠀⣀⠀⠐⠠⠄⢘⣆⠐⢀⡏⠘⠒⠀⠀⠀⠸⠟⠂
⠀⠀⠀⠰⠯⠴⠶⠶⠀⡖⠀⠀⠀⠀⡀⠀⡀⢀⠀⠈⠉⠐⠶⣯⣷⣤⠄⠀⠀⠀⣈⠀⠀⠉⠁⡇⠁⢸⠁⠐⠛⠛⠚⠂
⠀⠀⠀⠰⠿⠶⠀⠀⠀⠃⠀⠀⠛⠛⠓⠟⠓⠞⠛⠊⠐⠂⣀⢈⢀⢀⠀⠀⠚⠛⠛⠿⠗⠶⠂⢂⠐⣴⣤⠄⠰⠆⠐⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠓⠐⠀⠃⠒⠲⠶⠀⠀⢀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡤⣇⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡅⢀⠀⠀⠀⠀⠈⠐⠒⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣧⠀⠀⣼⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠇⢀⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⣸⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢎⣤⣄⡀⠘⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢈⣾⣿⣿⡇⠀⣾⢁⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠤⠀⠀⢀⣴⣿⣿⣿⣿⡗⣞⣷⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⢴⣶⣿⣿⣿⣿⣿⣿⠛⣿⠿⣿⣿⣿⣿⡄⠀⣀⣠⣤⣶⠏
⠀⠀⠀⠀⢸⣿⡀⠀⠀⠐⠀⠠⣤⣤⣤⣤⠄⢀⣠⣤⣶⣭⡝⠉⣻⣿⣿⣿⣿⣿⣄⠻⡷⠈⣻⣿⣿⣿⣧⡿⢷⡿⠿⠿
⠀⠀⠀⠀⢸⣾⣷⣶⣦⣴⣶⣦⣤⣤⣤⣿⣷⣿⠟⠋⠀⠀⠀⢠⣿⣿⣿⣿⣷⣈⣙⣿⣏⠼⠿⠻⣿⣿⣿⣷⣶⣤⣤⣄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⣫⡀⠀⠉⠙⠛⠋⢡⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡀⢠⣤⣄⠈⠉⠹⣿⣿⡿⠿⠟
⠀⠀⠀⠀⠠⠏⣿⣿⣿⠄⠈⠙⠒⢄⣀⣀⣤⣾⢀⣤⡼⢃⣠⠾⣿⣿⣿⡇⠙⣿⣿⣿⣧⡈⠛⠛⢱⣶⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢰⣤⣾⣿⡟⠀⠀⠀⠀⠀⠉⣉⣀⠀⠀⣼⣹⣶⢠⣦⡿⠋⠙⠀⠀⢻⣿⣿⣿⡟⠰⡆⠀⠉⠻⣿⣿⣿⡟
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⣾⣷⣤⣿⣿⣿⣿⣶⣼⡛⢿⣈⣿⠧⠀⠀⠀⠀⣼⣿⣿⠟⠁⠐⠛
⠀⠀⠀⠀⠘⠉⠛⢿⣿⣿⣿⠟⠋⠙⠻⢿⣿⣿⣿⣿⣷⣬⣿⣇⠀⡀⠀⠀⣼⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⢀⡀⣴⠂⣰⠋⢹⠇⢺⣏⣵⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⡴⠃
⠀⠀⣠⣶⡏⢰⡇⣸⠁⠀⣯⠖⢉⡴⠓⠿⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⡼⠁
⠀⠔⠻⠝⣶⣼⢀⡏⠀⢀⡏⠀⡞⠀⠀⠀⡾⠉⠚⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⢀⡜⢰⠁
⠛⣤⡀⣠⢤⡾⣊⣤⢀⡾⠀⢰⠇⠀⣼⢁⣿⠄⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣄⣼⣿⠁⠸⡆⠀⠀⠀⠀⡀
⠀⠀⠰⠿⢊⣾⡿⢟⣾⡁⢴⣯⣤⣾⣛⡏⡁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣴⣿⣿⣿⣷⣗⠀⣷⠀⠀⠀⡞
⠀⠀⠀⠀⠉⠋⠰⠿⠛⠑⠋⠉⠳⢶⠿⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠞⢻⡏⠀⠈⢿⣿⣿⠀⠛⠀⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠀⢸⣷⠀⣀⠘⣿⣿⡶⠃⣼⢃⡀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣿⠁⢠⢠⣴⡗⠀⠋⠀⣿⠘⠂⣾⣿⣯⠀⠈⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⣛⣤⡞⠈⠉⣿⡧⠀⢀⣿⢀⡰⣿⣿⠯⠄⢠⠃
⠀⠀⠀⠀⢰⢏⡽⣗⢶⠶⢾⣆⠣⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣋⠀⠀⢀⣿⠇⢀⣼⠇⣼⢳⠘⣯⠀⢀⡾
⢠⡆⠀⠀⢸⢸⠱⣭⣾⠀⢸⣿⠀⢹⠈⢻⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣦⣘⠋⠀⠾⠟⣼⣧⠨⠀⠘⢇⢸⡇
⢻⡭⠁⢸⣿⣸⠀⢿⡇⠀⢸⡇⠀⢸⡇⢘⡇⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠉⢶⣶⣾⣿⡏⠀⠀⠀⠈⠻⣇
⠀⡵⠀⠀⣹⣹⠀⣾⣧⠀⠸⣧⠀⠀⣷⢰⡆⢺⡮⠅⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠹⣿⣿⡇⠘⡄⠀⠀⠀⠀⠁
⠘⠋⠀⢠⡇⣿⡀⢿⣿⡆⠀⣿⠆⢰⠏⢸⣇⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠁⠁⠀⣧
⠀⠀⠀⠀⠡⣻⣿⣾⣿⢇⣰⣏⣠⢏⢔⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠠⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣴⣾⠿⣻⣥⣤⣄
⠀⠀⠀⠀⠀⠈⢿⡻⠾⣋⠿⢛⡛⠿⠶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢡⣿⣿⢃⣾⠟⠃⠈⠉⠃
⠀⠀⣴⢷⡦⣄⠀⠻⣏⣵⣪⡵⣖⣛⣋⣉⣉⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⣸⣿⡇⣾⡏⣰⣧⠀⠠⣶
⠀⣸⡿⡟⢸⢩⠉⠶⠾⢻⢋⡜⣡⢋⡜⠡⢁⠎⠜⣩⠖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣿⣿⠀⣿⣿⡇⣿⣧⣿⣿⡏⣴⡈
⠀⣿⡇⣇⢠⣨⣠⣦⣦⡇⡼⣰⢃⡞⣰⠣⡎⡈⠰⠃⢆⡆⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⣿⣿⡀⣿⣿⡇⣿⡿⣿⣿⣧⠿⣡
⠀⠙⠿⠿⠛⠋⣡⣤⣬⢷⣿⣇⣾⣠⣏⣳⣠⡒⣀⡰⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠸⣿⡇⢹⣷⡹⢿⠇⠀⢉
⠀⠀⠀⠀⠰⠿⣍⣓⠮⣭⣚⣻⣟⣛⣩⣭⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⢻⠇⢸⣿⣿⣶⣶⣾⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠈⠆
⠀⠀⠀⠀⡔⠊⠈⠉⠀⠁⠒⠤⡀⠀⠀⠸⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⢀⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⡇⠀⠀⠀⠀⣌⡠⠤⠄⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⢣⠀⢀⠔⠉⠀⠀⠉⡆
⠀⠀⠀⠀⠀⠀⠁⠂⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢆⠎⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠈⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠒⠂⠤⢢⡀⠀⠀⠀⠈⠀⠀⠀⢀⡔⠁
⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠒⢄⡀
⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⣀⢴⠃⠀⠀⠀⢰⠜⠒⢄⡀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⢠⠀⠀⠀⠀⠀⢀⠠⠊⠁⡆⠀⠀⠀⠀⠸⣄⠠⠐⠉⠹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢉⠔⡝⠁⠀⠀⡀⠀⠀⠀⠻⠢⢄⣀⠀⠀⢀⠔
⠀⠀⠀⠑⠤⠤⠐⠂⠁⠀⠀⠀⡃⠀⠀⠀⠀⠸⠘⡀⠀⢀⡀⠴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠓⠎⠀⠀⠀⠀⣧⠀⠀⠀⠀⢁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⣠⠃⠀⢰⠈⠁⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠀⠼⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⡦⠤⠐⠂⠉⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠤⣀⠘⢄⠀⠀⢀⠌⠀⠘⢄⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀⣀⠠⠵⠀⠀⠀⠀⠀⠀⠀⢠⣃⠀⠀⠀⠈⡛⠉⠀⠁⠀⠀⠀⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠉⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⠃⠀⠀⠉⠐⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⡠⠄⠒⠀⠉⠙⡀⠀⠀⠀⠀⡘⠉⠀⠒⠂⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠠⠤⠒⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠠⠀⣀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠠⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⡀⠀⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠤⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠃⠀⣈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠤⠤⠀⠒⠒⠠⠤⢀⣀⣀⣀⣁⣀⡀⠀⣀⠤⠒⠐⠀⠀⠒⠠⠄⠀⠤⠐⠂⠉⠀⠀⠀⠉⠐⠀⠁

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠢⢄⡀⠢⠒
⠀⠀⠀⠀⠀⠁⡀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠫⡇⠒⠀⢀⢠⢀⢠⡀
⠀⠀⠀⠀⠀⠀⠁⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡀⠈⡜⢭⢉
⠀⠀⠀⠀⠀⢀⣂⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⢾⢿⣁⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠙⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠓⠈⠙⠘⠚⢉⣁⡉
⣀⣀⡠⢴⣶⣌⢀⡰⣶⠶⣴⡄⠀⠉⠤⠀⠈⠩⠵⠾⣤⠄⠀⠀⣿⠻⠟⠋⠉⠁
⠉⠋⠃⠀⠀⠀⠠⠌⠀⠐⡀⠀⠀⠀⠈⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⡠
⠐⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠐⠀⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⡀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⠈⠙⠛⠣⠤⠌⠈⠁⢤⣶⠲⠀⠀⠀⠀⠙⠻⠿⣿⣛⣿⣿⣿⣿⣿⣿⡿⠿
⣿⣿⣿⡿⡿⠋⠉⠙⠛⠛⠛⠛⠛⠃⠀⠀⠠⣤⣄⣀⠀⠀⠀⠐⠖⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠉⠀⠀⠀⠸⠿⠿⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣿⣿⣿
⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣠⠀⠀⠀⠀⠉⠉⢩⣭⠔⢲⣶⣶⣶⠶⠶⠶⣶⡶⣒⣲⣶⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⣻⣷⣤⣤⣤⠤⠤⠤⠐⠒⠒⣊⣀⠀⠀⣠⡀⣾⣯⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿
⣥⣴⣶⣾⣷⣶⣶⣾⣿⣿⣿⣿⢿⣋⣉⣀⣐⠶⠒⠚⠛⠉⢻⡇⠀⠀⣿⡇⣿⣿⣿⣿⣿⣿⣿⣭⣥⠶⢿⣯⣿
⠿⠿⠿⢛⡛⢛⣛⣟⣽⣷⡾⠝⠛⠛⠉⠉⠀⠀⠀⠀⢀⣀⣿⡇⡆⡍⣿⣇⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣾⣿⣿
⣶⣶⠾⠟⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⣿⣿⣀⣀⣤⣴⣿⡏⣿⡇⠃⣦⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣻⣿⣿⣿
⣿⡿⠗⠒⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⡟⣿⣿⣿⣿⣿⣿⣗⣺⣿⣿⣿⣿⣿⣍⣽⣿⣿⣿⣿⡿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⣯⣿⣟⣹⣻⣤⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣦⣄⠀⠀⠀⢠⣾⡿⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣦⠀⢰⣿⠟⠁⢀⣀⣠⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡾⢻⢟⡿⣛⡶⢦⣭⣿⣧⣿⣭⣴⣞⠯⠝⠪⠙⠉⠋⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠁⢈⣩⣿⣿⣿⣿⣿⣷⣶⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣴⢾⠏⠏⣾⣿⠳⣟⢿⡿⣌⠃⠛⠿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⡀⠀⣼⢿⠘⠈⠀⣼⣏⠇⠰⡄⠀⠹⣼⣆⠀⠀⠈⠘⠳
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠴⠋⡉⢙⡳⡜⠛⠀⢤⣀⢸⡿⠍⢀⡴⠚⠛⠛⢻⣸⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡃⠞⠀⣉⣭⡤⢥⣿⠀⠀⠀⠀⢸⣟⢠⠏⡴⠀⠀⠀⠘⡏⣇
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⡞⡿⡟⠠⠶⠀⠀⠛⠉⠉⠈⠇⢸⡈⠃⠀⠀⠀⠀⣟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⣇⢇⢧⠀⠀⢀⣀⣀⣀⣀⣐⣋⣀⣳⣄⣀⣤⠴⠖⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡹⡌⢮⡳⢾⣉⣑⣒⣂⣀⣩⣭⣭⣥⣤⡤⠤⠶⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡦⣝⠲⠬⠭⣭⡭⠤⠤⠤⠶⠶⠤⣍⣳⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣭⣓⠒⠶⠶⠶⠒⠒⢒⣲⡶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⡀⠄⢠⡀⠀⣀⣰⣦⣦⣤⣤⣀⣰⡀⢀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⠒⢿⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣞⠀⡀⢀⠴⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠛⠿⠛⠛⠛⢿⡏⢻⣿⣿⣿⣿⠿⠿⠟⠿⠓⠚⠃⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠹⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡅⡀⢄⡀⠈⠉⠙⠂⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⣠⣶⣦⣭⡍⢰⣧⣿⠿⠶⠆⠀⢦⠄⣤⡄⣀⡈⣀⡠⣤⣤⡶⣶⡖
⠀⠀⠀⠀⠀⢻⣦⣽⡏⣹⡛⠛⡿⣿⣿⣋⣭⣴⣿⠗⣡⡖⠿⠓⢛⣚⣿⡿⣿⢹⣿⣭⢶⣿⣾⣷⣿⡇
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣾⣿⣧⣿⣿⣿⣷⠾⢫⡴⠟⠀⣴⣿⠿⣿⣫⣾⣿⣸⣿⣿⣿⣿⣿⡿⠟⠇
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⡿⣿⣿⠿⣿⣿⣿⡶⠻⠃⠀⠀⢻⡇⢀⣿⣿⣿⣿⣿⣿⠟⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡆⠀⢤⢴⠯⣁⣠⣿⣿⣿⡟⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠿⢿⣆⠀⡠⠂⠀⣿⣿⠛⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣴⣿⠋⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠲⡄⢠⡔⢈⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠄⠀⠀⢀⠆⠀⠀⠀⠀⢀⣀⡤⠐⢳⡆⡀⢁⣄⡀⡀⠂⠠⠀⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠄⡀⠈⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠁⠃⠘⠀⠀⠀⠀⠂⠀⡆⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⢤⠀⠀⠄⠐⠐⢄⡀⡩⠀⠀⠀⠠⡄⠀⡰⡆⢂⠊⠀⢲⣿⡂⡈⢻⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⢃⠀⠀⠀⠠⢀⡌⢻⡇⠶⠐⠆⠀⠤⠬⢼⢬⣥⠄⠀⠈⠈⠉⠁⠁⠘⣳⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⠋⠶⠀⠀⠁⠀⠀⢹⠢⠄⣀⣦⡖⠀⠀⠈⠉⠀⠘⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠸⠀⠀⠘⢹⠛
⠀⠀⠀⠀⠀⣠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠈⠀⢀
⢠⡄⠀⢀⡾⢛⡁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡄⠀⠀⣀⣼⠀⢀⢀⣧⡀⡀⠀⠠⣀⣶⡀⢀
⠀⠀⠀⠈⠀⠘⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⡇⠰⡿⡇⠀⣌⣙⡟⠓⠛⠛⢋⣩⡁⣰⣀⡯⣟⣻⣿
⠀⠀⠀⠀⠀⢀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣈⠉⠀⠀⠀⠀⢀⠉⠀⠋⠉⠥⠐⠂⠀⢈⣙⠃⠁⠐⠦⠍⠉⣋
⠀⠀⠀⠀⠠⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠁⠀⠀⠉⠙⠂⠒⠲⠌

⠀⠀⠀⠀⡀
⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠄⠀⠀⠀⠐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠄⠠⣠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⢛⠻⣿⡀⢹⡇⣿⢀⠃⣸⣿⠋⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣽⣟⠻⣿⣧⡙⣃⣾⣧⣼⢷⡿⠾⣷⣿⣤⣼⣿⣿⡉⣻⣿⣿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⢿⣿⣧⣤⡾⢿⡋⢿⠀⡇⢰⠇⣸⠃⣰⠋⣨⠟⠻⣿⣿⡟⢡⣾⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣴⣷⣿⣿⣧⣴⣿⠿⡇⠻⠀⠃⢸⠀⡇⡼⢠⠇⣰⠃⡴⠋⣠⠞⠁⣨⠿⣶⡏⢰⡆⢹⣾⣦
⠀⠀⠀⠀⠀⠀⣼⣾⣷⣦⠙⣿⠿⡉⢣⡘⣆⢸⣧⣤⡄⢁⠇⡞⡰⢃⠞⣡⠞⢁⡴⠛⢁⣤⠾⠻⣶⡶⡟⡙⣿⣧
⠀⠀⠀⠀⠀⣼⣿⡧⠉⣙⣾⡟⠢⣌⠢⡑⠌⠘⣿⣿⣿⠘⠰⠰⠡⢋⠜⣡⠞⣉⡴⠞⢉⣀⡤⠶⠻⣧⡴⠟⣛⣿⣧
⠀⠀⠀⠀⢰⣿⡿⠶⢬⣽⡯⣍⡓⠬⡑⠌⠊⠂⠹⣿⡿⠀⠀⢐⠔⠅⡊⠔⣊⡡⠴⠚⢉⣁⣤⡤⠶⢿⣗⣛⢉⣽⣿⡆
⠀⠀⠀⠀⣸⣿⠛⠗⢲⣿⠒⠢⠬⠁⠂⠁⠀⠀⠀⠈⣷⠀⠀⠀⠀⠈⠂⠩⠤⠒⢚⣉⣉⣁⣤⣤⣤⠴⣿⣧⣤⣴⣿⣇
⠀⠀⠀⠀⣿⣿⡶⠾⣾⣯⣉⣉⠉⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⠀⠀⠠⠬⠭⠭⠭⣥⣤⣤⣤⣤⣤⣤⣼⣇⣙⣉⣿⣿
⠀⠀⠀⠀⣿⣿⠰⠷⢸⣷⠴⠒⣒⡀⠤⠀⠀⠀⠀⠻⠿⠙⣳⡄⠀⠀⠠⠅⣑⡒⠒⠶⠤⠤⣤⣄⣀⣀⣸⣿⡿⣿⣿⣿
⠀⠀⠀⠀⢹⣿⣷⣶⡛⣿⣊⣩⠴⢒⠥⡂⢀⠀⠀⠀⠀⠀⠀⢿⣦⣀⠊⢑⠢⢬⣉⠓⠲⠤⣤⣀⡈⠉⣿⣯⣤⣿⣿⡏
⠀⠀⠀⠀⠸⣿⣯⣤⣶⣿⣏⡤⠚⣡⢞⡵⣡⢂⢀⢰⠀⠀⠀⢄⠉⢿⣿⣆⠠⡀⢈⠙⠲⢤⣀⡉⠙⣻⠟⠻⠿⣿⣿⠇
⠀⠀⠀⠀⠀⢻⣿⣿⡟⠛⣿⣶⠊⣠⠊⡴⢡⠇⡎⡄⢰⢸⠸⡘⣆⢠⡙⠿⢁⠀⣈⠙⠦⣄⡈⠙⣿⡿⠶⣿⣶⣿⡟
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⠿⣿⣁⡞⢁⡏⣸⠁⡇⢸⢸⡆⢧⠘⣆⠳⠐⣿⠧⠈⠳⣄⠈⢻⣾⣏⠰⠖⢸⣟⡟
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣟⣡⣶⡼⢻⣧⣞⢀⡏⢸⠇⢸⠀⣇⠘⡆⠹⡄⠐⣆⠀⢰⣄⣨⣿⢿⡁⠛⢳⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⣻⣏⣤⠈⣡⠟⣿⢧⣼⣀⣸⠀⢿⠀⢻⡀⢹⣄⣘⣧⣴⡿⠯⠙⣦⡙⣷⢾⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⣿⣾⣇⣼⠇⢢⡟⢋⡙⣿⠛⠻⣿⣿⠿⣿⣿⡇⢴⣷⡄⣶⣼⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠯⣟⡶⣿⣧⣙⣡⣿⣿⢸⣿⣿⣤⣾⣿⣿⣼⣿⣻⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⣿⣿⣿⡿⠿⠿⠟⠛⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⡀⡀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣾⣥⣤⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⣾⡿⣿⡿⠷⢮⡀⢠⢼⣿⠿⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠁⠸⠇⠀⠀⠋⠀⠞⠁⡄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠃⠠⢶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣲⣾⣿⡛⠂⠀⠀⠀⠀⠀⠇⠀⠀⠀⠘⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠋⠀⢁⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢸⣇⣰⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠑⣦⡤⣤⣴⣦⣬⣷⣶⡿⢫⣿⣿⣽⣿⣷⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⣾⡶⠷⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⣿⢿⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⠉⠙⠉⠓⠀⠠⠤⠄⠀⣠⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠒⠒⠚⠉⠉⢀⣀⣠⡤⠖⠛⠃⠈⠁⠀⠤⠴⠖⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣬⣤⣴⣶⣶⣷⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠛⠛⠉⠁⠀⠀⠋⢄⣤⣀⠈⠀⠙
⠀⠀⠀⠀⠐⠲⠶⠒⠒⠒⠊⠉⠉⠉⠁⠐⠒⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣤⣤⣤⣤⣴⠟⠋⢹⡇⠀⠀⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠶⠞⠛⠛⠛⠋⠉⠙⠛⠛⠛⠋⠙⠓⠒⠋⠉⠀⠉⠈⠀⢀⣀⡤⠞⠀⠀⠀⠀⠁⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠶⠛⢛⣋⣭⡤⡶⡶⠾⠛⠛⠟⢿⠻⠛⠛⠿⠿⢶⣶⠦⠦⠴⠦⠶⣶⠖⠻⠛⠡⣤⣷⣀⠀⠤⠒⠊⠁⠀⠤⡀
⠀⠠⠄⠔⠐⠒⠒⠒⠒⠚⠋⠋⠉⠉⠁⠀⠀⠀⢀⣀⣀⣤⠤⠔⢒⠒⠴⠞⣋⠩⠄⢀⣠⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⣐⣦⣀⣄⡰⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠉⣉⣡⠄⠀⠀⠀⠀⠀⣀⠤⠄⠀⢴⡋⠁⠀⠀⠀⠀⠀⠀⣠⠐⣄⢦⣤⠄⣻⡟⠘⠛⡛⠒
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠴⠤⠤⠤⠤⠤⠴⠖⠛⠁⠀⣀⣤⠴⠒⠋⠉⠀⠀⠈⠀⠀⠂⠀⠂⠀⠀⠀⠔⠊⢨⠛⣛⡿⠉⠙⠿⠆⠨⠿⠛⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁⠀⠀⠀⠀⠀⠂⠀⠁
⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣦⣵⣶⣤⣷⣵⣿⣽⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿