Birthday party Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⣤
⠀⠀⠐⠒⡂⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⡀⠀⠀⣾⠢⡀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢀⠤⠷⡀
⠀⠀⠈⠊⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡧⠈⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠗⠒⠀⠀⠀⠀⢆⠊⣀⡠⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠭⠄⠒⢈⡢⠀⠀⠀⠫⡩⠃⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠣⢄⠀⠠⠁
⠀⠐⠆⠀⠀⡀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠁⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡥
⠀⠀⠀⠀⢸⡇⠀⠄⢠⡄⠀⣇⡠⢃⣀⠀⢣⠀⡀⠀⢾⠉⠂⠀⣽⠀⡖⢲⠀⢹⡏⢡⠀⠀⢿⠀⠄⠀⠀⣆⠀⡀⠀⠈
⠀⢀⡀⠀⢸⠁⢈⢀⡟⠰⠀⣷⠀⣿⠀⡁⠈⡗⠀⠀⢸⠉⠑⠀⡇⠀⡟⢅⠀⠸⠇⣸⠀⠄⢸⢀⠄⣰⠇⠘⣦⠀⠀⢠
⠀⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡿⠈⠀⠀⠃⠀⠀⠘⠇⠊⠀⠀⠀⠃⢀⡀⠀⠀⠛⠀⠃⠈⠁⠰⠋⠁⠀⠿⠀⠀⠂
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠈⣎⠀⠀⠀⠀⢀⡀⠀⠀⠀⠠⠄⡄⠀⠀⡇
⠀⢀⠀⠀⠀⠘⢲⠤⣀⠘⠀⠀⠂⠀⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⣄⣄⠤⢤⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠈⠀⠀⠀⢰⠈⠀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠒⢒⡲⠭⠙⡄⠀⠀⠀⡒⠢⠔⠒⡄
⠀⢀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠀⣀⠀⠀⠀⠢⢀⣪⡂⠀⠀⠀⠀⠀⠀⢋⣁⡀⣤⢤⣰⠷⠀⠀⠀⠑⡀⢀⠜⠀⠀⠀⠀⠔
⠊⠀⠈⠂⠐⠊⠀⠀⠉⠁⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠈⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠘⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠤⢀⢀⣀⡀⢀⠀⡀⢀⠀⣀⢀⠀⠤⠄⠀⠀⠀⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⣌⢱⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠈⡬⣱⠖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡷⡅⠄⢉⡴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⡅⠄⣩⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢰⡗⠞⠛⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣸⡏⠏⠙⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⠀⠀⠀⣠⣰⢂⠀⠀⠀⠀⠀⠀⣤⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣐⡳⠟⠀⠀⠙⠖⠧⠉⠈⠀⠀⠠⢁⢀⣱⢆⡨⠅⠀⠀⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⡛⣡⠿⡐⠌⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠠⣤⠄⠀⠀⠀⠀⠀⠧⠈⠝⠋⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⠶⠐⠁⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠦⠀⠀⠸⡀⠈⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠘⠃⠀⠲⠂⠀⠀⠤⠆⠰⠂⠀⠀⠀⠀⠀⠀⣚⣃⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⡵⠆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠑⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠐⠊⠱⡀
⠀⡆⠀⠀⠀⠀⠀⠉⠁⠒⠂⠠⠴⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠐⠒⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠈⢢⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⡠⠐⠺⠁
⠀⠀⠀⢡⠀⢹⠒⠠⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠄⠂⠂⠩⠀⠀⡇
⠀⠀⠀⡿⡰⡀⡇⠀⠀⠀⠀⠀⠉⠐⠀⡄⠀⠀⢢⡀⠀⢠⡀⠀⠀⠀⠀⢀⠊⠱⠀⠀⠁⠀⠀⣦⣆⡇
⠀⠀⠠⠟⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⢣⡀⠀⣀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠘⠎⠙
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠒⠄⠀⢸⠀⣠⠐⠆⠲⠈⠦⡀⠰⠋⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠊⡠⠒⠈⠉⠐⠠⡙⢠⠀⠀⠐⠂⠤⣀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⢀⠇⠌⠀⠀⠀⠀⠀⠀⠈⠾⠁⠀⠀⠀⠀⠈⠆⠀⠁
⠀⠀⠀⠀⠀⢠⠀⠀⠑⠀⠀⠀⠀⡠⢘⠀⢀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠇⠀⠁⡈⠛⠉⠉⠉⠋⡠⠅⠀⠀⠀⠀⡠⠊⠀⠀⣀⡴⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡎⠀⢠⠆⣤⣒⣫⠐⢒⣄⡀⡁⠀⠑⠊⠉⡀
⠂⠈⠁⠈⠑⢤⡀⠃⠀⠀⠘⠗⢀⠀⠀⠀⡀⠈⠁⠀⠀⠈⠑⠢⢄⠧⠘⠎⠒⠋⠀⠙⠇⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢠⠀⡆⠰⠀⠒⠳⠓⣺⠀⠂⣀⠄⠀⠀⠀⠈⠂⠠⠏⣀⣀⠀⡖⠴⢀⢀⢠⠂⠈⣄⣄
⠀⠀⠀⠀⠀⠀⠘⢰⠀⢄⠀⠀⠀⠀⠠⠚⠁⠀⠐⠀⠀⠐⠂⠀⠂⠀⠀⠉⢛⠩⣟⠛⢍⣾⠛⠲⡔⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠻⣆⠘⠀⠀⠀⠀⠠⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢁⠀⠐⣇⡔⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⢀⡀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠉⢄⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢴⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢘⡀⠀⠀⠁⠂⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠀⡈⠢⠈⠑⠢⠄⣀⠀⠀⠀⠀⣀⠠⠀⠀⣀⠔⠀⠈⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠀⠀⠀⠱⠖⠂⠤⠭⠭⠤⠄⠐⠐⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄
⠀⠀⠀⠀⠀⣀⠀⠤⠐⠒⠐⠈⠉⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⢠
⠤⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⣴⠀⠀⠰⠁⠀⠀⠐⢀⠀⠀⠀⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⠉⢦⡀⠀⠀⢡
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠐⠊⠁⠀⠀⠉⠃⠐⠃⠀⠀⠀⠀⠀⠀⠄

⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⣭⠇⠀⠀⠀⠀⠀⠀⠀⠘⢍⡩⠁⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠧
⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠒⠢⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⢠⠾⠤⠬⣭⣉⡆⠀⠀⠀⠀⠚⠲⠆⠀⠀⠀⠀⠑⢤⣀⣧⡇⠀⠀⠀⠀⠀⠀⣠⠖⠒⠒⠢⣄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢯⡉⢉⠐⠒⠒⠂⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢰⠁⠀⠀⣠⠤⠜⢧
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠒⠓⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠔⠉⠁⢀⠤⠼⡄
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢀⡆⠀⠀⠀⠀⠀⢸⡏⠉⠉⢢⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠳⡴⠊⠉⠁⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣸⡇⠀⠀⢸⠀⠀⣰⡷⡀⠀⠸⣷⣀⣠⠜⠁⣀⡀⠀⠀⢹⣆⠀⠀⡜⠀⠀⠀⠀⠈⠲⠤⣀⣠⠏
⠀⠀⠀⢸⠉⠑⠖⠉⠈⡇⠀⠀⠀⣿⠋⠉⠉⡿⠀⢠⡿⠀⣧⠀⠀⣿⠉⠀⠀⣿⠉⠉⠳⡀⠀⢿⣄⡜⠀⠀⠀⠀⠀⠀⠀⠀⠸⣝⠄
⠀⠀⠀⠈⢦⡀⠀⠀⣠⠃⠀⠀⢰⣿⠀⠀⠀⡇⢀⣿⠋⠉⠹⡄⠀⢿⡄⠀⠀⣿⠀⠀⣠⠇⠀⢈⡿⠀⠀⠀⠀⢏⠓⣹⠂⠀⠀⠈⣆
⠀⠀⣀⠀⠀⠙⠢⠔⠁⠀⠀⠀⠀⠉⠀⠀⠀⠁⠸⠇⠀⠀⠀⢧⠀⠈⠁⠀⠀⣿⠛⠋⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠘⠟⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⢴⡏⠉⠳⡄⠀⠀⢸⡇⠀⢰⣾⠉⠳⡄⠈⠉⢹⡏⠀⢀⣀⠀⠀⡀⢸⡇⠀⠑⡄⠀⠀⠀⠀⢶⡄⠀⠀⢠⠀⠀⠸
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⠇⠀⠀⣾⠃⠀⢸⣟⣀⡴⠁⠀⠀⢸⡇⠀⢸⡇⠀⠀⡇⠨⣷⠀⠀⢹⠀⠀⣀⠀⠘⣷⡀⢠⠇⠀⠀⡇
⠀⠀⠤⣀⡄⠀⢸⣟⠉⠉⠲⡀⠀⣿⠀⠀⢸⡏⠳⣄⠀⠀⠀⣼⡇⠀⣼⠷⠦⢴⠃⠀⣿⠀⢀⡞⠀⣼⠟⡄⠀⠘⣧⡜⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠇⠈⠉⠁⠀⢸⡇⠀⠈⠀⠀⠀⠈⠀⠀⣿⠀⠀⢸⠀⠀⠻⠶⠋⠀⣼⡯⠤⣧⠀⠀⢽⡇⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠻⠦⠖⠁⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⡀⠀⠀⠀⠉⠀⠀⠻⠀⣠⠀⠀⠀⣴⠟⠀⠀⠟⠀⠀⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠣⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣖⣦
⠀⠀⠀⠀⠀⣠⡀⠀⣀⡁⠀⠀⠀⠀⢀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠀⠀⠀⠀⠀⠀⡞⠲⠚⡆⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠘⠀⠀⠀⡏⠉⡖⢦⣄⡀⠋⠀⠀⠖⠉⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣘⣄⣧⠤⠖⢲⠀⠀⠘⠦⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⡀⡇⣨⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣉⡥⠤⠔⠒⣚⣉⠭⡆⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠰⡶⠀⠀⠀⠀⢠⠀⢡⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠖⠒⠉⠉⠀⠀⢀⣱⡀
⠀⠀⣀⠀⠀⠀⠀⠀⢸⡤⠊⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⡧⣤⢤⣖⣲⡭⠿⠜⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠴⠊⠀⠙⠦⣀⣀⡠⠋⠀⠀⠀⠀⠀⠀⠀⢟⠏⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠀⠀⠀⣀⡀
⠀⠀⢀⡀⠠⣡⠀⠀⠠⠀⠰⠀⠙⠓⡲⠄⠠⣀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⣀⣄⠠⢴⠞⠉⠙⠀⠠⠀⣠⣒
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠛⠁⠘⠈⠏⠈⠉⠻⠋⠂⠙⠟⠀⠤⠙⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⡀⠈⠁⠀⡨⠳⢤⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⣤⠟⠀⠀⡀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠉⠈⠂⠐⠂⠀⠠⠔⠀⠂⠀⢀⠀⠚⠐⠒⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲
⠀⠀⠀⠀⠀⠁⠀⠈⠁⠰⠂⠀⠀⠛⠀⠀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢤⡆⠀⠀⠀⠀⠐⢂⡄⠀⠀⠀⠀⠒
⠀⠠⠤⠶⠶⠆⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⢐⢂⡀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⢻⡀⠀⠉⡀⠉⠒⢀⡄⠠⠂⢀⡀
⠀⠀⠀⢀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠲⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠓⣀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠥⠁⠂⠁⠀⣆⠀⣆⢸⡇⢆⠀⢢⠀⠀⠀⢀⡶⠃⠀⠃⠀⠀⠀⢉⡀⠀⠀⢰⠆
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠫⡯⣀⠛⡘⣓⣻⠓⢋⠩⠀⠀⠘⠁⠀⠀⠠⠈⠀⠀⠈⠀⠘
⠀⠠⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢧⠁⠀⢠⠁⢠⡀⢈⢰⡀⠀⢠⡄⠀⠘⠀⠀⠀⠒⠈⠠⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⢆⠂⢤⠀⠄⠀⠌⠀⡀⢀⠠⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⡇⠀⠂⠀⡐⠂⠀⠂⠀⠀⠄⠰⠀⠁⠀⠀⠀⠀⡀⠀⠠⣬⠢⢰⡎⠂⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⡀⣘⠁⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠵⠇⠀⠀⠀⠛⠀⡀⠰⠃⠛⠣⣤⠟⠂
⠀⠀⠀⠀⠐⠀⠠⠀⠀⣴⠆⠀⠀⠀⠸⠄⠮⢄⡂⠀⠀⠀⠀⠀⠀⠀⠀⢁⡠⠄⠀⠄⠀⠀⠀⠀⠀⢁⠂
⠀⠀⢀⣄⡄⠄⠀⠀⠀⠀⠀⠀⠀⠶⡐⠒⠈⠢⢉⡉⠓⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠁⠛⠀⠀⠀⠈⠂⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠋⠋⠘⠑⠄⠀⠀⠀⠀⠀⠀⢠⠀⠠⠀⣀⡆⠀⢀⠀⠀⠀⠀⠀⠤⡴⢾⣓⣄⣠⡄⠀⢐⠀⠈⡃⠀⢠⠨⠀⡇
⠀⠀⠆⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠈⠀⠀⠒⠂⠈⠀⠐⢿⣸⣿⠾⢷⢡⡂⢀⢀⡀⡂⠀⠸⠠⠀⠇⠄
⠀⠀⠀⢀⡀⠠⠀⣀⡀⠀⠠⣀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣽⡻⠄⢠⣀⡴⡀⠀⣀⠀⠀⣀⠠
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠐⠎⠀⠈⢀⡀⢠⠄
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⡀⠀⠀⠀⠻⠀⠀⢦⡀⠀⠀⢀⡄⢺⡄⠀⠀⠀⠁⠀⠀⠄⠈⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠰⣤⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠂⠈

⠀⢠⢆⠀⢀⠦⠀⠀⠀⢀⡀⠀⠀⠀⠠⡒⠀⠀⢤⠀⠀⢀⠀⢄⠄⠤⢄⠀⠀⠀⢀⣤⣤⣤⣤⣤⣴⣶⣶⣦⣄⠀⠀⠀⠀⢀⡀⢀⢀⡀⢀⠀⣀
⠀⡠⢯⠀⡠⠛⢄⠀⢀⠡⠄⠀⢠⢲⠰⠃⠀⠤⠏⣤⠐⠅⠛⠀⡎⠁⡰⠃⢄⠀⣿⠉⣹⢋⠻⠉⣽⢹⣝⢹⣿⠀⢀⠄⠀⢄⢀⠀⢈⠁⡉⠀⡈⢠⠄⠀⢄
⠀⠑⠀⠀⠒⠩⢀⠀⢘⣒⡦⢱⢸⠸⠔⠀⠐⠈⢋⠑⠀⣠⡓⣞⡙⣾⣀⡀⢄⠃⢿⣿⣿⣾⣷⣿⣿⣾⣷⡾⠟⠀⠃⢰⣀⠠⠃⢀⡄⠙⠄⣀⠈⠇⢠⣠⡀
⠀⢜⢀⠆⠰⠁⣋⡰⣈⠄⠆⡣⠀⠰⡑⠔⠠⣂⣈⠠⠀⠁⣨⠰⠀⢀⠟⠃⠀⢠⡄⠀⠀⠀⠹⠟⠀⠖⠀⠀⢠⡀⢆⠐⠊⢡⠀⠫⠇⠀⠺⠝⠃⣄⠀⠛⠡
⠀⠀⠀⢈⠆⠀⢐⡣⠈⠀⢨⡄⢀⠜⠂⢄⠀⠀⢀⠄⠀⠐⠋⠁⢠⠏⠀⡀⠔⠃⠊⠁⢠⠀⠀⠀⣈⢶⡀⠀⢇⡰⠀⠀⠓⠁⠑⢤⠔⠉⠂⠤⠊⠀⠐⠊⠁
⠀⢀⢔⡨⠂⠶⢠⠁⡂⢀⠰⠅⣠⡘⠍⡀⡄⠀⡨⠎⡀⠀⠀⠠⠊⠀⣎⠠⠀⠀⠀⠀⡐⢦⣀⠀⡇⠁⡅⢐⠊⢐⠆
⠀⠁⡄⣉⢢⠀⡎⡐⠠⡁⠖⠆⡑⢠⢘⡡⠃⠊⠔⠂⡙⠀⣀⣀⠀⡔⠻⣀⡀⠩⠀⠠⠐⢂⡠⠃⡇⠀⡆⠐⡍⠰⠀⠀⣀⡀⠤⢀⠶⡄⠀⠠⢴⢶⠁
⠀⠑⠠⠤⠊⠀⠔⠀⢀⠰⠒⠆⡑⠀⡤⠤⠀⢆⠢⠐⡡⠀⠡⣠⠀⠁⠒⠀⠂⠐⠲⡌⠉⠀⠀⠀⣇⢀⡇⢀⠒⠘⠇⠈⠈⠕⠀⠀⠉⠀⠀⠀⡊⠈⠧
⠀⠀⠀⠀⠐⠀⢀⠄⠒⢍⠈⢉⣧⣀⣈⠒⡀⢀⠉⠉⠀⢀⠀⡉⢀⣀⡀⠠⠄⠴⠸⡳⠁⠀⠀⠀⡨⠄⠠⠄⠃⠙⠀⠠⠀⠀⠘⠀⠀⠀⠀⡸⠡⠀⠊⢣
⢰⠊⠀⠀⠓⡠⠅⠂⣠⣤⣵⠀⠒⠀⢫⡍⢉⠏⢡⠀⠀⠍⢫⡁⢀⡏⠑⢄⠀⠆⠀⢀⠠⡄⠀⠊⠀⠀⠀⠀⢱⠀⠀⠄⠀⢂⣀⢸⢆⠀⢠⠣⠀⢠⠐⠀⢃
⢨⢴⣶⣶⡆⡇⠣⡸⣿⣿⣿⠀⠀⠀⠀⠙⠊⣄⠀⠑⠌⠀⠀⠙⠚⠀⠀⠀⠉⠀⠀⠍⠀⠁⠀⠀⠀⠀⠀⠀⢸⣀⠀⠰⡌⡀⠈⠀⠀⠃⠸⠢⠤⠤⠀⠒⠘
⠀⢿⣿⣿⡓⠀⠀⠈⠙⠉⠚⣆⠀⠀⠀⠀⢠⢮⠀⠀⠀⠀⠀⠀⡠⠰⠖⠬⠛⠉⠛⠲⠒⡦⣄⠢⡀⠀⠀⠀⠞⠀⠈⠁⡘⡤⠇⢀⢰⠀⠀⠀⠀⣀⣀
⠀⠀⢱⡎⠀⠀⠀⢀⠤⢄⠀⡘⢛⠜⠀⢀⢼⢸⡄⠀⠈⠀⠀⡮⠀⠀⠀⠀⠀⠠⠀⢰⠀⡀⠛⣦⠈⠟⠙⠀⠀⠀⠀⠀⡇⠐⡤⠀⡇⠀⠰⠂⠀⠉⠁
⠀⢀⠼⡧⢄⠀⠀⡚⠀⠀⢱⡈⠀⠀⡁⠀⠀⠀⠀⠀⡁⠀⢰⠃⠀⡖⠉⠐⠜⠐⠃⠚⠀⡇⠈⠘⠀⠀⠠⡀⠀⠀⢀⠜⠀⠀⠘⠒⠀⠀⠢⡀⠳⠀⠀⡠
⠀⠀⠉⠉⢀⢀⢀⡉⠀⠀⢀⣰⠀⡎⠴⡠⠀⠠⢀⠢⠋⡆⠈⡦⠀⡂⠈⢁⢀⡀⠀⠀⠀⠆⠀⣤⠀⠀⠀⠛⠉⠉⢠⠒⠐⢢⠀⠀⠀⠰⠀⠢⡄⠨⣄
⢀⡤⠀⠀⡟⡆⠈⢢⠀⠀⠠⠎⠐⡂⠒⠀⠖⠀⠖⠀⠃⡇⠀⠱⢆⠔⠀⠀⠈⠐⠃⠀⠉⢀⡢⠂⠀⢀⠀⠀⠀⠀⣘⣁⠀⣘⣠⠀⠀⠰⠀⠀⠀⢀⡈⢅
⠀⢀⠁⡜⠀⠘⡄⠈⡄⠀⢰⠀⡜⢇⡐⠀⠐⠀⠀⠀⡡⢛⠀⠀⠈⠁⠒⠒⠒⠒⠒⠒⠒⠈⠀⠀⠰⠿⠀⠿⣿⡟⠁⠀⠀⠀⠈⢻⣿⠗⠀⠀⠈⠁⠔⠀⠁
⠀⠀⡸⠁⠀⠀⠰⡀⠈⠉⠀⠀⢈⠒⠈⡥⠄⠀⠬⠅⠐⠉⠀⣄⡀⠀⠀⠀⢀⠠⢂⠍⠉⢁⠒⠀⠀⡀⠀⠀⠝⠀⠠⠀⠀⠠⠀⢸⠣⡀⢀⠤⠖⠒⠂⠒⢄
⠀⢠⡃⠀⠀⠀⠀⢱⠀⠀⣴⠉⠙⠉⠐⠟⠒⠄⠀⠀⡐⠋⠀⠍⠀⠀⠠⠀⢫⣐⣂⠤⠞⡡⠊⠀⠫⠝⠀⠀⠉⢃⠀⠀⠀⠀⢀⠜⠈⠀⠁⠰⠖⠠⠔⢃⢸
⠀⠈⠁⠚⠒⠋⠈⠉⠀⢠⡏⠀⠀⠄⠄⠄⢐⠀⢀⡜⠁⠈⠠⠀⠒⢺⠍⠁⠀⢃⠈⠉⠋⠀⠀⢇⠀⢀⢨⡄⠀⠘⠉⣲⣒⡆⠉⡂⠀⠀⠙⠀⡀⠀⡁⠠⠊
⠀⠀⠀⠀⣤⡤⠀⠀⠀⣄⡇⠸⠡⢀⡂⠃⠸⠀⡞⠀⢀⣀⠤⠘⠋⠀⠀⠀⠀⠈⠤⣀⣐⣀⠔⠁⣰⡌⠁⠈⠀⠻⠿⠿⣿⠿⠿⠟⠀⠀⠀⠀⠀⠀⢠⣦⡀
⠀⠀⡤⣀⣀⡠⠲⡄⠀⠈⠁⠀⠐⠒⠀⠠⠂⠀⠉⠉⠁⠀⢄⡠⠤⢤⠀⢀⣀⣀⠀⠀⠈⠁⠀⠈⠩⠁⢸⠒⠒⡶⠖⠒⠒⠖⢶⢶⠖⠖⡖⠀⠀⡇⠈⠛
⠀⡚⢄⣈⠯⢷⡠⠑⢦⠀⠂⠢⠀⠀⠀⠀⡠⠢⠀⡀⠀⡴⣉⠀⠀⠀⠻⡏⠀⠀⠀⠀⠀⢐⠁⣄⠀⠀⣜⡤⣄⡇⠀⢀⠀⡇⠀⣨⡂⠀⢀⢀⢀
⠀⠃⢁⠠⡄⠠⠀⠂⠭⠀⠁⠠⠒⠁⠀⠉⡆⣀⣈⠀⠀⡓⠠⢉⡒⠀⢴⠁⡮⢀⠹⠄⠀⠀⠀⠙⠀⠀⠀⠀⠈⠁⠉⠀⠉⠁⠘⠁⠉⠁⠈⠁
⠀⢯⡠⠀⠃⠀⠀⢂⡂⠠⠶⠤⠀⠀⠠⡀⠉⠛⠁⠀⢰⢀⠤⡀⡀⠨⠁⢆⠈⡇⠀⢐⡇⠀⠤⠀⠐⣆⡐⠆⠀⠒⠀⠀⢢⡔⠄⢠⡔⡄⠆⠴⠂⠀⠂
⠀⠀⠉⠺⠄⠐⠊⠁⠀⠀⠀⡀⠀⠀⠀⠇⠀⠀⠀⠀⢠⠈⢢⠐⢁⠂⠀⠈⣌⠉⠉⢭⠁⠀⠠⠀⠀⡀⠀⡥⠈⠈⢀⠀⣰⠒⠁⣰⠒⠀⣈⠀⠀⠀⠄
⠀⠖⠉⠉⠀⠀⠀⠉⡂⠀⠜⠳⡀⠀⠀⡆⠀⢀⠀⠀⠘⠢⠀⠠⠃⠀⢀⡀⢩⠀⠀⡆⠠⢀⡀⠀⠤⠀⢀⠀⠀⠀⠀⣀⢤⠀⢤⠀⠄⡀⠀⢀⠤⠀⢠⢀⡤
⠀⠀⠀⠸⠍⠜⠀⢀⡆⢀⠀⠀⠀⡀⢀⠇⠀⠀⣸⠀⡤⠤⠤⠤⠤⠤⠧⠾⢆⠣⡰⠁⢀⠠⠄⠠⠀⠀⣨⠱⡁⠀⠈⠁⢈⠂⢸⠀⠀⠙⠀⠄⠰⠀⠀⡆
⠀⠛⠀⠐⠂⠀⠂⠐⠁⠀⠉⠒⠐⠉⠀⠀⠀⠀⠒⠀⠙⠒⠛⠚⠓⠓⠒⠐⠁⠀⠀⠀⠈⠉⠉⠀⠉⠀⠋⠈⠁⠈⠃⠀⠈⠀⠈⠈⠉⠉⠀⠁⠀⠉⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⣠⣚⢢⠀⠀⠀⠀⠀⣷⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⢧⠀⠀⠀⠀⢀⠼⣁⣪⠉⠀⠀⠀⠀⠶⠿⣿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠻⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⡛⢄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣵⠃⠀⠀⠀⠀⠀⠀⣠⣜⠣⠙⠋⠀⠀⠠⠒⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡙⡅⠀⠀⠀⠀⠀⠀⠀⠛⠁⠙⠁⠀⠀⠀⠐⠄⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣱⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡧⠄⠀⠀⠀⠀⡠⠢⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⠈⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡂⣣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠠⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠢⣀⡀⠀⠀⠠⢄⠚⠈⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⠈⠒⡤⠂⢄⠀⠀⠀⠀⠀⠀⣶⢑⣈⡄⠛⠁⠀⠀⠀⠀⣥⠐⠺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠉⠢⡀⠀⢄⣀⣴⠀⠀⠀⢴⡙⣄⣨⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⢙⣄⠀⠀⠀⠑⢶⡑⣤⡥⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢠⣾⠉⠨⠿⠁⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⣰⣿⣿⣷⣄⠀⢠⣶⡷⡉⠀⠀⠀⠀⡊⠀⢐⠀⠀⠀⠀⠤⣾⠇⠀⠙⠁
⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⣠⣾⣿⣿⣿⠿⠋⠉⠢⡀⠀⠈⢆⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⣼⡟⠀⢀⣴⣿⣿⡿⠟⠁⠀⠀⣀⣤⣾⣷⣦⣤⠇
⠀⠀⠀⠀⠀⣸⡟⠀⣴⣿⣿⠟⠋⠀⢀⣠⣴⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⢰⠟⣠⣾⡿⠛⢁⣠⣴⣾⡿⠟⠛⠉
⠀⠀⠀⢠⢏⣼⠟⣋⣤⡶⠟⠛⠉
⠀⠀⢀⣿⡿⠷⠛⠉
⠀⠀⠈⠁

⡿⢿⠿⠿⡿⠻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢿⣿⣿⡿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀
⠀⠀⠀⡠⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠑⢤⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⡤⠊⠀⠀⠀⠀⠈⠢⡄⠀⠀⠀⢄
⠀⠀⠈⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⢠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄
⠀⠀⡀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠠
⠀⠀⠈⠀⠀⠀⠀⠀⠈⢢⢄⡀⡀⢤⠊⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠑⠤⣀⠀⠠⡐⠁⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠈⠐⠢⠒⢈⠅⠐⠀⠀⠸⠁⡒⡒⠂⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠁⠂⠖⢂⠩⠀⠂⠀⠀⠏⢐⢒⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢠⡜⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⣤⠀⠀⠀⣀⣱⠈⣁⣇⡀⠀⠀⡈⣤⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢱⣊⠁⠀⠀⠀⠈⠀⣁⡑⠀⡀⠀⡈⢢⠈⣀⠁⡀⠈⡄⢁⡐⠀⠀⠀⠀⠀⣑⡎⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠲⢤⣀⠤⠂⢀⡋⠑⣆⠀⠁⠘⠀⠉⢀⡔⠈⠃⠀⡦⢄⣀⣤⠖⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠒⠂⠐⠀⢿⣿⣷⣶⣶⣿⣿⡇⠐⠒⠂⠐⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡀⠘⢿⠀⠉⠉⢨⠟⠀⢀⠤⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡜⠀⠀⢰⠀⠀⠀⠟⠈⢃⠀⠀⡘⠀⠱⡀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢤⠃⠀⠀⠘⡄⠀⢀⠇⠀⠘⢤⡴⠃⠀⠀⠈⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠒⣶⠒⢲⡖⠒⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣤⣿⠀⢸⣧⣤⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠀⠈⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⢀⡀⠄⠒⡒⠒⢄
⠀⠀⠀⢠⠒⡉⢀⠠⠈⠀⠄⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠄⠀⠂⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣲⣤
⠀⠀⠀⠰⠀⠂⠀⠀⠠⠀⡔⢤⠀⢸⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠀⢇⠀⠉⢀⡄
⠀⠀⠀⠀⢃⠀⠰⠁⠢⠔⠀⠀⠣⠴⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠠⠀⠀⠈⠉⢉⠃⠈⠢
⠀⠀⠀⠀⠀⢄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⢀⡤⡆⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⢔⠞⡟⠁⡧⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢀⠜⢡⠂⡜⠀⠀⢣⡈⠑⠲⣑⣄⡠⡀⢀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⢀⣠⠃⠀⡇⠀⡁⠀⠀⠀⠑⡄⠀⠈⣦⡱⠁⡯⠷⡔⠚⡢⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠐⠂⢫⠀⠸⢆⠀⢇⠀⠱⡀⠀⠀⢀⣇⣀⡠⣗⣌⠉⠵⢄⠘⡖
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠦⠁⡶⠗⡢⡀⡨⠬⡁⡲⢯⢁⠴⢅⡠⢄⢀⢥⡠⠵⢤⢤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢒⠖⢱⠢⠤⠩⡇⠀⢨⠀⠀⡅⠀⠠⠀⢠⢁⠜⡚⠈⠉⠉⠉⠁⠒⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠈⡄⠸⡀⠰⠀⠈⡄⠀⡇⠀⡈⢀⠜⠁⠀⠀⢀⠄⡔⠓⠄⡀⠁⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠰⠀⠀⣀⣰⣀⠗⠤⣇⠀⠇⠀⠁⠀⠃⡎⠀⠀⡀⢫⠛⠉⠀⠈⢑⠇⠂⢀⠀⢰
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠛⠁⠈⠇⠀⠁⠀⠀⢸⠀⠐⠀⠀⠘⠀⢧⢤⡠⢄⠀⠉⠒⡀⠈⠁⠀⣀⠇⠉⠎
⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⣄⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠱⣀⠈⠢⠒⠐⠄⠔⠑⠊⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠂⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⠤⠤⠤⠄⠒⠉

⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹
⠀⠀⠀⠀⡇⠠⠀⠂⠐⠀⠂⠐⠀⠒⠐⠂⠐⠀⠂⠰⠀⠂⠐⠀⠂⠐⠀⠒⠐⠂⠒⠐⠂⠐⠀⠆⠰⠀⠆⠰⠀⠆⠐⠂⠂⠐⠄⢸
⠀⠀⠀⠐⡇⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢸
⠀⠀⠀⠀⡇⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸
⠀⠀⠀⠀⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸
⠀⠀⠀⠀⡇⠐⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⡀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⡃⢸
⠀⠀⠀⠀⡇⢘⠀⠀⠀⠠⠇⠀⡇⢠⢲⠆⡇⢂⣰⢰⣠⠆⠴⠀⠀⠀⠀⣾⠁⡄⠀⠈⢠⠁⠀⢠⢀⢐⠃⡤⡄⢰⠀⠄⠀⠀⡅⢸
⠀⠀⠀⠀⡇⢨⠀⠀⠀⠀⠇⠀⠀⠀⠈⢰⠇⠃⡆⠊⠀⠀⡖⠀⠀⠀⠀⠻⠀⠃⠂⠰⠘⠀⠃⠘⠀⠀⠈⠀⠁⠁⢠⠂⠀⠀⠆⢸
⠀⠀⠀⠀⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠠⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⢸
⠀⢀⡄⠀⡇⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢸⠀⢠⡀
⢠⣾⣧⠀⡇⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠰⠰⠆⠸⠷⠰⠆⠶⠰⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⠆⣼⣷
⢾⣿⣧⣴⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⣦⣼⣿
⡌⠾⠿⢛⣧⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣼⡛⠿⠷
⠏⢀⣶⣿⡟⣈⠀⠠⢾⣇⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⣸⡷⠄⠀⣥⢻⣿⣶⡀
⡠⠈⠉⡩⠿⠿⠂⣤⡀⠈⠉⠻⠀⠀⠀⣀⢀⣾⡀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⢀⣷⡀⣀⠀⠀⠀⠟⠉⠉⢀⣤⠐⠿⠿⢍⠉⠁
⠀⣀⡠⡤⡤⢲⣿⠛⠙⢦⡀⢀⣤⡄⣼⣿⠸⣿⡿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⢿⣿⠇⣿⣧⢠⣤⡀⢀⡴⠋⠛⣿⡖⢤⢤⢄⣀
⣿⣡⡀⠁⣵⢿⣷⣀⡴⣿⡿⡀⠙⡇⢿⣿⠀⢉⣐⣥⣶⣶⡶⠄⠀⠀⠀⠀⠠⢶⣶⣶⣮⣀⡉⠀⣿⡿⢸⠋⢀⢿⣿⠦⣀⣾⡿⣾⠀⢨⣌
⣤⡈⣧⣾⠟⣃⣾⢥⡒⣿⠵⠹⡄⠁⠀⠁⠰⣫⣴⣿⣧⣄⠀⠀⠀⠀⠀⣶⣄⢰⣿⣿⣿⣦⣝⢆⠈⠀⠀⢠⠋⠺⣿⢒⡬⣷⣘⠛⣷⣼⢁
⣯⠀⠉⢳⣶⡽⣏⡢⡈⣿⠀⡀⠘⡆⢠⣿⣙⣿⠉⠉⡟⠉⠑⡄⠀⠀⢶⣜⢿⣿⡿⠟⠉⠛⢉⣈⣷⡄⢰⠣⢄⡀⣿⢑⢔⣹⣮⣷⡞⠉
⢿⣧⡤⢼⡇⠘⢹⠟⠲⠿⣉⢙⣻⣿⠶⣿⠷⣤⣤⡀⢿⣾⣟⣹⢢⢄⠘⢿⣨⣵⡶⢂⣀⣀⡤⡿⣿⠾⣿⣟⡋⣉⠿⠖⠻⡏⡃⢸⡧⢤⣼
⠁⢙⣧⣾⣷⡟⢻⣀⣠⣤⣿⣥⠀⠸⣷⣼⣿⣿⣿⣆⠸⠀⠙⢿⣅⣾⠧⣬⢤⡆⠤⢠⣽⣟⣿⣶⣵⣹⠃⠀⣭⣿⣤⣄⣀⡟⢻⡾⣷⣼⡋
⣠⣟⣵⠋⢮⡗⠛⢛⣿⣿⣿⣿⢿⣿⣿⣿⣊⠟⠃⠀⠈⠛⢻⠟⣛⠁⣀⣴⠖⠻⣗⣣⣴⣿⡿⠄⣍⣻⡀⠀⣿⣿⣿⣟⡛⠛⢺⡤⠝⣮⣻
⢹⡿⢃⣝⣵⡏⠀⠈⣛⣿⣿⠏⠻⣩⣿⣿⣭⣥⠖⢛⣦⣼⣿⠂⢹⣿⡿⣿⣶⠀⡨⣿⣷⡎⠀⠀⠸⣟⠙⠟⠱⣿⣿⡛⠁⠀⢹⣮⣋⡙⢿
⠛⠿⡿⡟⣽⣿⣏⡙⡏⠉⠁⢀⡰⠛⠉⣾⠟⠋⠀⢩⣛⣁⣨⣧⡀⢙⡟⠿⠷⠛⢦⡟⠁⠀⠀⡄⠀⠈⠛⣆⠀⠈⠁⢹⢋⣽⣿⣏⢟⣿⠿
⡿⢿⠿⠿⡿⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠛⠛⠛⠿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠿⣿⣷⠀⠀⠀⣴⡟⠁⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⢀⣿⠏⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⢀⣤⡀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣏⣀⣤⣼⣟⠀⢀⣴⡶⣤⡀⠀⣼⣟⡤⣶⡄⢀⣿⢋⠴⣦⠀⣴⣿⡟⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣻⡟⠉⠉⢹⣿⠁⢰⡿⠋⣰⡟⠀⣰⣿⠋⢠⣿⠃⣾⡿⠁⣸⡿⠀⣾⡏⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣼⡏⠀⢿⣇⠞⣿⣇⣤⣿⢿⣽⡿⠃⣸⡿⣯⣽⠟⠁⠸⣿⡠⢺⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⠀⠀⠀⠀⠈⠻⠄⠀⠀⠘⠷⠄⠀⠁⠀⠈⠀⣾⠇⠀⠀⠀⢠⣿⠁⠀⠀⠀⢀⣀⣈⣠⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠐⡿⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⣿⣡⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠤⣰⣶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⣠⣤⣤⣤⣤⣀⣀⣀⠀⠀⣠⣶⠆⢠⣾⠟⠀⠀⠈⣷⡄⠀⢸⣿⠀⠀⠀⢀⡀⠀⠀⠉⠛⠁
⠀⠀⠀⠀⠀⢀⣶⡿⢛⣿⠏⠉⠉⣧⠀⠀⢀⣤⠀⠀⠈⠉⠉⠛⢻⣿⠷⣶⣿⣧⣤⣤⣤⣴⡿⠃⢠⣿⠃⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⠧⢀⣾⣏⣀⣠⡴⠋⢀⣠⣤⠉⢠⣟⣷⠀⠀⢠⣿⠃⢰⡿⢁⣤⣤⡍⢉⣡⣤⣤⣾⠃⠀⠀⣠⣶⠶⣤⠀⢀⣴⡗⠀⣴⠆
⠀⠀⠀⠀⠀⠀⢀⣾⠏⠉⠉⠉⢱⡄⢩⡿⠁⠀⣠⠟⣻⠇⢀⣾⠃⢀⣿⡵⢋⣿⠏⣰⡿⠋⠀⣾⠃⠀⢀⣼⡟⢁⣼⠇⠀⣼⡟⢀⣾⡟
⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⣀⣤⡟⠁⣿⣧⡴⠞⠁⣾⣋⣴⣿⡏⠀⢸⡟⠁⣼⣏⣠⢿⣤⣤⠾⣿⣤⣴⠿⣿⡠⠊⣿⣤⢼⣿⡠⢺⡿⠁
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠋⠁⠀⠀⠈⠁⠀⠀⠀⠉⠉⢠⣿⠁⠀⠈⠀⠀⠈⠁⠀⠀⠉⠠⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠐⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠶⠶⠶⠶⣶⣦⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣴⣿⠁⣀⣀⣤⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⢛⣿⣿⠟⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠰⣦⣤⣀⣠⣤⣴⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠉⠀⠀⠠⠄


⣿⢿⠿⠿⢿⢛⡿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣛⣻⣛⣿⣿⣿⣻⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠂⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⢰⠁⠀⠀⠈⣲⣤⠲⠀⠀⠘⡄⠀⠀⠀⠀⡰⣦⣡⡶⢀⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠈⠁⠛⠉⠒⠀⠀⠘⠃⢄⣀⠀⠀⠀⠈⡍⠛⠦⣤⣀⣀⣀⣀⣀⣤⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠆⠰⣦⣀⠨⢉⡒⠶⠴⠧⠤⠤⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠘⢹⡖⢤⡀⠁⠀⠀⠀⠉⠑⠦⣿⡠⠆⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢠⡏⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠠⠠⠜⠀⡆⠙⢦⠀⠀⠀⠀⠐⠛⠉⠑⠦⣄⣀⣀⠴⠁
⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡞⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠠⡀⠀⣀
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⡸⠁⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢳⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⡾⠐⠀⠀⠀⠀⡴⠓⠆⠀⠠⡾⠀⢀⠄⢠⡄⠀⣤⠀⢠⡀⢠⡄⠀⣄⠀⡤⠀⣠⠀⠀⠀⠀⠈⢀⠘⡌⢆⠉⠒⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢤⣀⣀⣀⠠⠆⠀⠀⠀⠑⣴⠃⠀⣇⡀⣿⡀⢠⡇⣀⡼⠁⣼⢁⣠⠏⢰⡇⠀⡯⠀⠀⠀⠀⢀⠎⢠⢧⠀⠑⠤⢤⣀⣀⣀⣤⠚⠀⠁
⠀⠀⠀⢰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⠄⠃⠀⡖⢸⡆⠶⠖⠀⠦⠈
⠀⠀⠀⣾⠀⢀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠛⠀⠀⠀⠀⠐⠄⠃⠀⠀⠀⢀⠔⠀⢰⠇⠸⠇
⠀⠀⠀⣿⢠⡯⠐⠁⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⢀⡏⠈⠀⢂
⠀⠀⠀⢁⡾⠁⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⢸⠁⢠⡄⣜⡀
⠀⠀⡀⢰⠃⢠⣄⠈⠀⠀⠤⠀⠀⠀⠀⢰⠇⠀⡾⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢹⠯⣍
⠀⡐⢠⠏⡄⠄⠈⠻⠀⢠⠄⢀⡄⢤⠀⡟⠁⢸⣇⢤⠀⠀⡠⠀⣼⠁⢀⠤⢀⡄⠀⡤⠀⣠⠀⠀⠀⠀⠄⠀⠀⢸
⠀⡤⢋⣀⣉⣀⡠⠎⠀⣟⠀⢸⠃⠀⢸⡃⠀⡾⠁⣼⠀⢸⡁⠰⡇⠀⣏⡀⣾⠁⢠⡇⠀⡏⠀⠀⠀⠀⠇⠀⠀⠘⢆⡀⣀⠇
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠘⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⣦⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢬⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊
⣄⣀⣄⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣍⣙⣶⣶⣦⣤⣤⣴⣶⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣀⠠⠤⠄⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡉⠉⠀⢀⣀⣀⣤⡤⠽⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠛⠋⠡⣤⢶⣛⢉⣡⣴⣻⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠉⠉⡟⠋⠑⠨⠴⡀
⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⢣⣀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡏⠙⠒⠲⠤⣤⣀
⠀⠀⠀⡠⠖⠋⠁⠠⢔⣮⡅⠻⢼⣽⣿⣿⡶⠦⣤⣠⣇⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⣇⣭⣵⠦⣄⠀⠈⠙⠲⢄
⠀⠀⠈⠀⠀⢠⣴⣿⣛⣻⣥⡴⠶⠛⠛⢛⣻⣿⣷⡿⣯⣿⣓⣲⡦⢤⣼⣀⣀⠀⠀⡷⠟⠛⠉⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠦⣀⠈⠉⠉⠙⠳⠀⠀⢠⣶⣿⣯⠭⠶⠶⢒⣻⠿⣋⣉⣽⠿⠛⠷⠿⠿⠽⠇⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠈⠙⠒⠦⢤⣄⣀⣀⠀⠉⠁⠀⠀⠀⠀⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠓⠒⠒⠲⠶⠶⠶⠤⠤⠶⠶⠶⠒⠒⠒⠛⠉⠉⠁

⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠂⠀⢀⣀⠡⠠⠂⡀⠀⠀⠀⠀⠀⠂
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⣈⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠀⠀⢀⠄⠀⠐⡈⡀
⠀⠀⠀⠀⠀⢄⠀⠀⠀⠤⠀⠄⠁⡠⠀⠄⠀⠈⠑⠠⡄⠈⠂⠤⠐⠉⠀⠈⠀⠀⠀⠐⠁⠹⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡀⡀⠂⠀⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⢀⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⢀⢀⠀⠀⠀⠦
⠀⠀⠀⠀⠐⠂⠈⠂⠀⠀⠀⠀⢀⠀⠀⠀⠂⠰⠊⠀⠀⢸⠁⠀⠈⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠐
⠈⠀⠀⠀⠀⠀⠠⠼⠁⠀⡀⠀⠄⠀⠰⠀⠀⠀⢀⠀⠀⢸⡀⠀⠀⡀⠀⠀⠀⠀⠀⠤⠀⢀⠀⠈⠧⠄
⠀⠀⢄⠰⢀⢀⠀⠀⠀⡀⠀⠀⣀⠀⡀⠀⠀⠀⠠⢀⠀⢨⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠐
⠀⠐⢂⠀⠀⠒⠀⠀⠈⠃⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠑⢈⡀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠂
⠀⠈⠀⠁⠈⢀⠀⠠⠀⠀⠀⡀⠐⠂⠐⡀⠀⠀⠀⡒⠒⠚⠓⢒⠂⢀⡐⠀⠐⠂⠐⠂⢢⠀⠄⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⡄⠰⠀⡆⠂⢈⠐⠂⠆⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣂⠀⠀⠒⢉⠀⠂⠁⢈⡈⠀⠀⢄⡀⠀⠀⠀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠛⠀⠀⠀⠘⠂⠀⠀⠘⠃⠀⠀⠐⠃⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠔
⠀⠀⠀⠀⠄⠀⠀⡠⢠⠐⡄⢄⡀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⢬⠀⠀⢨⠄
⠀⠀⠀⠀⠀⠠⠐⡀⠐⣀⡖⢀⠐⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠢⠠
⠀⠀⠀⠀⠀⠠⡁⣀⠅⠀⠨⢀⢈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠈⠁⠈⡠⠠⠈⠀⠉
⠀⠀⠀⠀⠀⠈⢒⣀⠴⠀⠣⢀⡐⠁⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠴⠀⠀⠰⠄
⠀⠘⠀⠀⠀⠀⠀⠀⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠊⠀⠀⠐⠆
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠂⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⢀
⠀⠀⠁⠂⠉⠐⠉⡀⠀⠀⠀⠀⠀⡀⠴⠐⠀⠠⣀⠀⣰⠄⠠⠰⠀⠀⢀⠄⢠⠀⠀⠠⠀⠀⠀⠀⠘⡌⣰⠢⠌⡀
⠀⠈⠀⠄⠀⠠⠁⠁⠀⠄⠀⠀⠀⠥⠐⠀⠐⢀⠀⠀⠀⢈⢁⠀⠀⠀⠈⠐⠀⢆⠁⠀⠀⠀⠀⠀⠘⠠⠈⡈⠠
⠀⠀⠁⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠘⠈⠀⠃⠀⠐⠀⠐⠘⠀⠈⠀⠀⠐⠘⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠁⠀⠒

⠀⠀⠀⠀⠂⠀⠀⠉⠉⠀⢠⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠉⠉⠀⢠⡄⠀⠀⠉⠉
⠐⠄⠄⠀⠀⠀⠀⠀⠀⡤⠔⢇⠀⠀⠘⠀⠀⠀⠀⠀⠐⠄⠄⠀⠀⠀⠀⠀⠀⡤⠔⣇⠀⠀⠘
⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠎⠀⢀
⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠄⠈⠉⠁⠀⠀⠀⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠄⠈⠉⠁
⠀⠀⠀⠘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠋⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠘⠄⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠈⠄⠀⣀⠆
⠂⠀⢐⠘⠙⢢⠄⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙⢢⠆⠀⢘⠘⠉⢢⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙
⠀⠀⠈⠓⠒⠉⠀⢠⡄⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠒⠉⠀⢠⡄⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠
⠀⠀⠀⠀⠢⠀⠀⠉⠉⠀⢠⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠉⠉⠀⢠⡀⠀⠀⠉⠉
⠐⠄⢄⠀⠀⠀⠀⠀⠀⡬⠔⣃⠀⠀⠘⠀⠀⠀⠀⠀⠐⠄⠄⠀⠀⠀⠀⠀⠈⡭⠔⣂⠀⠀⠘
⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠆⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠊⠀⢀⠀⠄
⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠀⠈⠉⠁⠀⠀⠀⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠊⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠋⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠈⠄⠀⢀⠆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⡀⠀⠀⠈⠄⠀⢀⠆
⠀⠀⢈⠘⠙⢢⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙⢀⠄⠀⢐⠘⠉⢢⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙
⠀⠀⠈⠑⠒⠉⠀⢠⡄⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠒⠉⠀⢠⡄⠀⠀⣿⡄
⠀⠀⠀⠀⠀⡀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠁⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣄⠢⣴⢶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣌⠛⠻⢿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢐⠊⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠘⣿⣿
⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⣴⠒⠙⠇⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⠀⢀⢀⣠⡴⠻⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠐⢀⡄⣴⡂⠖⡌⠁⠈⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠙⠋⠉⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠈
⠀⠀⠈⣇⠀⠁⠈⠃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣠⠠⢤⣤⢶⡾⠋⣄⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠈⢢⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠡⣌⣩⣅⠞⢣⡜⢱⡇⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠀⠀⠀⠘⠀⠂⢨⢇⣼⡤⢛⡁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠐⢇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⣹⡆⠀⠀⠘⠆⠀⢛⡏⠰⠏⠎⡰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡔
⠀⠀⠀⠀⠀⠀⠱⡘⠿⠓⠀⣀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣠⢹⡅⠀⣎⠵⠆⠊⠀⠈⠀⠀⣰⣼⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⢤⠶⠚⠋⠉⠦⢀⠀⠀⣴⠶⣦⠤⠒⠺⣧⠖⢫⣿⠯⢄⣈⡄⠄⠀⠅⢘⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠐⠂⢽⡀⢫⣵⣄⠀⢟⣂⡤⠕⢾⠉⠙⣇⣘⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠉⠐⠚⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⡆⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣗⡐⠀⣷⠀⡴⣄⣄⣷⡘⢂
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠳⡆⢀⣄⠹⡆⢻⣴⣄⡿⡄⠻⠙⠯⠁⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣷⣸⣟⢲⣻⡄⢿⠈⠁⠈⠁⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠸⡆⠿⠈⠀⠁⠹⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠐⡆⠀⠀⡀⠀⢀⡀⣤⢶⡸⡼⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠊⢻⡀⢺⡹⣼⣇⢱⣹⡶⠟⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡇⠀⠳⠜⠁⠙⠹⡎⠀⢻⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠒⠒⠀⠀⠐⠒⠒⠲⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⢀⠀⠰⡀⢠⣂⠄⣰⢠⠀⡀⠀⠈⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⢗⠙⠀⠋⠉⠈⠀⠀⠉⠀⠀⠏⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⣀⣀⣀⡀⠀⠀⣾⠋⣶⣄⠀⠀⠀⢀⡀⠀⠀⣀⣀⣀⡀⠀⢰⣦⠀⠙⡄
⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠰⠁⠀⠀⢸⣿⠏⠁⣨⡑⠂⠤⣀⣿⡿⠀⣄⠀⠀⣿⡆⢸⣿⠁⠀⣿⡆⢸⡿⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⢰⣿⠋⠀⣿⡆⢠⠎⣹⡧⠀⢩⡁⢠⣿⡇⠀⠀⣸⣿⠇⢰⣿⡧⠴⠟⠁⠀⠉⠓⣾⣿⡟⠋⠁⠸⣿⠁⠀⣹⣦
⠀⠀⠀⠀⠀⠀⠙⠁⣸⣿⣇⢃⡼⠛⠁⢀⣛⠋⠈⢿⣄⠀⢰⣿⡟⢀⣿⡿⢁⣀⠀⠀⣀⣤⣴⣿⡟⠀⢀⣤⡤⣭⡁⢠⣿⡿⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠈⣿⣦⠀⣾⣿⠀⠌⣼⣿⠃⣾⣿⠁⣸⣿⡧⢡⣿⠇⣴⣿⠏⣼⣿⠃⣴⣿⢋⣼⣿⠇⣿⣿⢁⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⣿⣿⠀⣿⣇⠎⠀⢿⣏⠔⢿⣧⠔⠹⣿⠁⣼⡿⠀⢿⡿⠎⠻⡧⠜⣿⡿⠎⢻⣿⠘⢿⡧⢊⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢉⢀⣠⣾⠟⠁⣠⣬⣁⠀⠀⠀⠀⣀⣤⢄⠀⠀⠀⠀⢹⣧⣀⠄⢤⣤⠀⠀⠀⢀⣤⠴⢤⡀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠢⣄⢉⣸⣿⠀⠀⠀⣾⡏⢀⣸⡇⠀⠀⢀⡴⠻⣄⣀⣼⡿⠁⠀⠀⣾⡏⢠⣼⡗⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠉⠉⠁⠀⠀⠀⠹⣧⣈⠛⣁⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⣉⡠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⠎⢠⠔⠄⠀⢀⢀⠀⡤⢄⠠⡀⢂⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⠀⠀⠘⠠⠂⠀⠀⠇⠀⠦⠔⠀⠉⠁⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠤⠤⢀⣀⣀⣀⡠⠤⠤⠖⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣣⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢽⡓⣆
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⡖⠒⢲⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠉⢻
⠀⠀⠀⠀⠀⠀⡠⠟⢤⡀⢹⠀⡜⠀⡸⠙⢆⠀⠀⠀⠀⢠⣄⠤⠖⠢⡀⠀⠀⠀⠀⠀⠀⣧⠈⠓⢾
⠀⠀⠀⠀⠀⢠⠃⢀⣀⠱⣜⣴⣁⠔⠁⣠⠎⢧⠀⠀⠀⠈⢦⢀⠀⢠⠇⠀⠀⠀⠀⠀⠀⡟⠓⢦⣸
⠀⠀⠀⠀⠀⠸⡎⠁⢀⡽⠋⣿⠯⣐⣉⡠⠤⢺⠀⠀⠀⠀⠀⣳⣾⣎⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀⠙
⠀⠀⠀⠀⠀⠀⠳⣀⠎⠀⠀⡇⢆⠀⠀⠀⣠⠃⠀⠀⠀⢠⡋⠙⠀⢨⢷⠀⠀⠀⠀⠀⠀⢠⠀⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣄⣧⣀⣱⠶⠚⠁⠀⠀⠀⠀⡟⠋⠠⡦⠀⣀⡇⠀⠀⠀⠀⠀⢸⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢹⠀⠀⠀⠀⠀⠀⠀⠀⡷⠆⢀⣄⠀⠉⡇⠀⠀⠀⠀⠀⢸⣤⡀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⣀⠐⠶⡇⠀⠀⠀⠀⠀⠸⠀⠙⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⢀⣀⡀⠀⠀⠀⠀⢻⣁⠀⡉⢀⣼⠁⠀⠀⠀⠀⠀⠸⠶⣄⡀⠱
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⢾⣶⣖⣉⣠⡼⠀⠀⠀⠀⠈⠫⢤⣫⡴⠃⠀⠀⠀⠀⠀⠀⠀⣆⡀⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⣹⠛⡷⢄⡀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠷⡄⠀⠀⠀⠀⠀⠀⠀⡇⠙⠢⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢹⠀⡄⠀⠙⠂⠀⠀⠀⠀⠀⢀⡇⣀⠤⠼⠀⠀⠀⠀⠀⠀⠀⢸⠦⣄⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⣤⠤⠼⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡥⠵⡆⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⢘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⣀⢄⠀⠀⠀⠀⠀⠀⠀⠙⠗⡴⠷⠀⠀⠀⠀⠀⠀⠀⢠⢧⡄⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠘⠀⡁⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠁⣈⠔⠁⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⡠⢂⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠒⠡⣦⠀⠀⠀⠀⠣⡈⠄⡠⠀⠀⠀⣰⢦⠄⠀⠀⠀⠀⠀⠀⢀⠤⠟⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠓⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢷⠼⠧⠀⠀⠀⠀⠀⠀⠉⠒⣶⠮⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⢾⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⢸⠀⢀⡈⠀⣠⠄⠤⡀⠀⣆⡆⠒⠒⢄⡖⡦⠐⠒⢄⢠⠀⠀⢰⡆⠀⠀⠀⢀⠄⠠⣤⠒⢢⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⡔⢉⠠⣴⢆⢃⠀⠀⢸⠀⠀⢱⠀⠁⠀⠀⠁⠀⠀⣃⡀⠀⠈⠀⠈⣀⡀⠀⢸⠀⠀⢸⠁⠀⠀⠀⠈⠢⡀⠉⢀⠌⠀⠀⠀⠀⠁⡆
⠀⠀⠀⠀⢣⠸⠙⠀⠀⠏⠀⠀⠀⠀⠀⢸⣀⢢⡀⣀⠧⡈⠀⠧⡐⣁⠜⠀⡸⢄⣊⠔⠀⠄⠠⢻⠀⠀⣠⡀⠀⠀⠈⠲⠁⠀⠀⠀⠀⣄⠚⠛⠓⣠
⠀⠀⠀⠀⠀⠉⠣⡀⠀⠆⠀⠀⠀⠀⠀⠀⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⢸⠀⠀⢇⠈⡢⠀⠀⠀⠀⠀⠀⠀⣠⣅⣀⠉⡁⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⡎⠙⢠⠀⠀⡏⠐⠀⡄⠀⠀⠠⡠⠔⠀⢸⠀⠀⠀⠁⢛⢀⠖⢹⠀⠀⠀⠀⡧⠤⠤⠤⠤⠄⠚
⠀⠀⠀⠀⠀⡄⢒⡀⠌⠀⢀⠔⡂⠐⠀⡠⢄⣀⠤⢄⠑⠒⠊⠀⠀⠑⠒⠊⠀⠀⠀⡀⠉⠐⠐⠁⠀⠀⡆⢐⠀⡼⠖⠊⢀⠀⠀⠀⠧⢀⣀⢀⣀⡠⠄
⠀⠀⠀⠀⠀⠈⠈⠙⠀⢠⠡⡠⠃⠀⠸⣀⠀⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡇⠀⠀⠈⠈⡱⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣶⣭⠈⠋⠀⠀⠀⠀⠀⠀⠶⠖⠊⠢⡀⠂⠀⠀⠤⣠⠀⠀⠶⣴⣀⡀⠀⠀⡧⠀⢄⠀⠀⠀⡠⠤⠤⣸⠀⠠⠊⠉⢢⠀⠀⡆⠀⠀⢸
⠀⠀⠀⠀⠀⡠⣄⣢⠀⢸⣴⣆⠦⠀⠀⠀⢴⠃⢦⠀⠀⠇⡄⡠⢌⠀⡆⢠⠢⡀⠘⠀⡠⠠⠠⠀⠀⢘⠀⠀⠎⠀⢀⡀⡈⢢⠀⠀⠀⢸⠀⣀⠇⠀⠀⣾
⠀⠀⠀⠀⠀⠑⠊⠀⠡⣈⠀⠀⠀⠀⠀⠘⣄⡋⢊⡠⠊⠀⢅⣙⠜⠀⠆⢈⠕⠀⠠⣀⣑⠔⠀⠀⠀⠠⣘⠟⠢⡀⠃⡈⢇⡸⠐⢄⢀⠜⠠⠔⠑⠄⠜⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠔⠢⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠒⡄⢀⣀⠀⠠⠤⠤⠤⠤⠤⠤⠀⠀⢐⡈⠲⠋⢀⠅⠀⠤⠤⠀⠤⠀⠀⠀⠄⠀⢎⡛⡝⠀⠀⠘⡀⠤⠁⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠈⠑⠲⠁⠀⠀⠀⠁⠀⠀⠀⠉⠉⠀⠀⠀⠈⠀⠀⠀⠀⠈⠒⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢘⢉⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⢻⢅⠀⠀⠀⠀⠀⠀⣠⠕⣶⠂⠀⠀⠀⠀⠀⠀⠀⢨⠀⡔⠂⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠟⠉⠀⠀⠀⠀⠀⠈⠗⡰⢏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠠⠒⣉⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠚⠳⠀⠀⠀⠀⠀⠀⡔⢁⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠴⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠣⠔⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠒⠤⢀⠀⠀⠀⠀⠀⣀⣴⣎⣩⣶⣦⡀⠀⠀⠀⠀⠀⣀⢆⠁⠀⡌⢆⠀⠀⠀⠀⠀⡠⣶⣬⣿⣷⣴⣿⡐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡎⠀⠀⠀⠀⠂⠁⠀⠀⠉⠛⣿⣿⡄⠀⠀⠀⢰⠌⡁⣈⢁⠡⠄⠇⠀⠀⠀⢠⣴⣿⣿⡁⠀⢀⣹⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡘⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣸⣿⣟⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠈⠉⠉⠙⠓⠍⣁⠀⠠⠁⠀⠀⠀⠀⠐⠤⣄⡀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠭⠹⠿⠋⠍⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠔⠒⠒⠤
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⡀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⢴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⣀⡔⠀⠀⠀⠀⠀⠀⠈⠢⠊⡀⠤⠈⡄⠀⠀⠀⠠⠆⠀⠉⠿⠛⠁⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⢸⠷⣽⣿⣛⣛⣛⣫⠭⠇⠀⠀⠀⠀⠀⢄⠀⠠⢄⢁⠄⠀⠁⠀⠀⠀⢸⠓⠲⠶⠤⣤⣀⣀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠦⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠠⢀⡈⠃⠀⢃⡦⠂⠀⠀⠀⠀⠘⠉⠙⠛⠒⠶⠶⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠤⠐⠀⠈⠀⠀⠈⠐⠄⠀⠀⠀⠀⡼⢿⡟⠁⢹⡟⠻⣷⠀⠀⠀⠀⠀⣰⣾⣿⣛⣻⣷⣶⡀⠀⠀⠀⠀⠀⠀⢸⠃⢠⠞⠙⢢⠈⣷
⠀⠀⠀⠀⠘⠠⠶⠀⠀⡤⠀⠀⠰⠊⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⢀⠈⠙⠛⠛⠛⠛⠉⢃⠀⠀⠀⠀⠀⠀⠘⣄⠸⣦⣐⣁⣼⠇
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⡤⡠⢤⠀⠁⠀⠀⡠⠂⡍⠀⠀⠀⠀⠀⠀⠀⠘⡅⠠⠀⠀⠀⠀⠀⠈⡷⠆⠉⠉
⠀⠀⠀⠀⠀⠢⡀⠈⠀⠀⠀⠈⠕⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠈⠞⠀⠀⠀⠣⡀⠐⠢⠤⢤⣀⣤⠤⠴⠎⠁⡠⠀⠀⠀⠀⠀⡐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡌
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠆⠙⣿⣿⣿⣿⡿⠃⡓⠀⠀⠀⠀⠀⠀⢀⣀⣠⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠆⠀⠀⠀⠀⠀⣀⠐⠁⠑⠉⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢈⠻⣿⣋⠌⠀⠀⠀⠀⠀⢠⣾⣻⢻⣟⣞⣻⣿⢽⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⡶⡶⠀⠀⠀⢀⡴⠋⠉⠉⠉⠳⣄⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠸⣷⣷⣿⣿⣷⣯⣿⣿⣿⢿⠏⠀⠀⠀⠀⠀⠀⠀⣰⢶⠇⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠉⠉⠁⠉⠈⠁⠀⠀⠀⠀⠀⢣⡾⢅⡠⠷⡶⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢸⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠃⠸⠷⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠛

⠀⣀⢀⡀
⠀⡁⠀⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⠒⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣼⠏⠀⣠⣤⡀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣿⣧⣴⣦⠀⠀⢀⣀⣀⣰⣶⣶⣼⣷⣿⡇⠀⠀⢸⡏⠀⠀⠈⢻⣿⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⣿⣯⣤⠹⣿⣿⣾⣯⣿⢿⣿⢿⣁⣛⣿⡟⢻⡆⠸⣷⣄⣀⣀⡼⠋⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢿⡴⠿⠛⢻⣿⠁⢸⡿⠈⢛⠋⢹⣷⣸⠃⠀⠈⠉⠉⠁⠀⡿⣴⣄⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣌⠁⠀⠀⠀⠀⠈⢉⣾⡆⠀⢰⣿⠀⠀⠉⠀⠀⠀⡀⢀⣤⣤⣶⡀⢹⠻⣿⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⣿⢀⡀⠀⠀⢠⣄⢸⣿⡇⠀⢸⣿⡄⣤⣤⣶⣴⣿⢹⠟⣿⡿⣿⡇⠌⣜⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⢀⣴⠃⢹⣿⠀⠀⢈⣩⢸⣿⠁⣰⡿⣿⡇⣿⡏⠉⠙⠿⠥⠔⠛⠁⠙⠋
⠀⠀⠀⠀⣷⣶⣦⣤⣾⣿⡿⠛⠁⠀⢸⣿⣾⣷⢸⣿⠈⢿⣆⠿⣿⠟⢷⣛⡁⠀⠀⠀⠀⠀⠀⠠⣤⡀⢰⣿
⠀⠀⠀⠀⠉⠛⠛⠉⢿⣿⣧⠀⠀⠀⠘⣿⠙⠿⠜⠛⠃⠀⠁⣠⠶⣛⣋⠙⢿⣿⣦⠀⣠⢤⣦⡀⢹⣷⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⡀⣀⡜⠁⢀⣤⣄⡀⠀⢀⣾⠃⠐⣿⣿⠀⠀⣿⣿⡇⢻⣿⣿⣷⢸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⣋⠉⠀⠀⣾⠁⢹⣷⠀⢸⣿⣶⣦⢻⣿⡆⠀⣿⣿⠇⢿⣿⠛⠿⠊⣙⣽⣿⡟⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠛⠻⣶⣤⣿⠀⢀⣿⡇⠀⠙⠛⠋⢸⣿⡇⣠⡿⠏⠀⠀⠀⣠⡴⠚⠁⠘⣿⡇⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠙⠟⠀⣸⣿⠁⠀⠀⣠⡖⢺⣿⠋⠉⠀⢀⣠⡴⠟⠁⠀⠀⠀⠀⠿⡷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⣀⣀⣴⡿⠃⠀⠀⠈⠻⠟⠛⠁⢀⣠⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣬⣉⡉⠀⠀⠀⠀⣀⣀⣤⣶⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣀⠤⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⢩⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⢈⠀⠀⠀⠀⣀⠤⠒⠒⠂⡧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠸⡀⠀⢀⡜⠀⠀⠀⠀⡇⠀⠀⠀⣠⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉⠉⠉⠒⠒⠀⠀⠀⠀⢠⡇⠀⠀⡠⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠉⣒⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢰⠇⣤⠀⠀⡇⠀⡿⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠒⠀⣸⠁⠀⢸⡇⢀⢀⠀⡼⠉⣦⠀⢸⡁⢠⡟⠠⡇⢀⡼⠁⣸⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠈⢧⡀⣀⠇⠳⠀⢿⠀⣾⠶⠋⠀⢸⡇⢈⠄⠀⠘⠂⢠⡏
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⡠⠤⠶⠶⢬⣄⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡴⢢⡇⠀⡀⠀⠸⢣⠏⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠎⠀⠀⢠⠆⠀⠈⢷⠀⠠⠄⠀⠀⠀⢀⠄⠀⣼⠁⠸⠇⣠⠆⠀⢠⡏⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢠⡏⠀⠀⠀⣸⠀⡤⢀⠀⠀⠀⣽⠁⢰⡟⠒⠂⠉⠀⡀⢀⡿⠀⠀⢀⠀⣀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣾⠔⠢⠴⠚⠥⣼⠁⡟⢠⡇⢠⡇⠀⣼⠀⢸⡆⢠⠏⠀⣸⡇⠀⡴⠁⢰⠇⠀⠀⠀⡄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠤⠤⢄⡀⠀⢯⠹⡇⢸⠃⢸⡇⡠⡏⠀⢸⠀⣿⡠⠊⢸⠁⢰⡇⡠⣿⠀⢸⠀⢰⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢼⡇⠀⡀⠀⢹⠀⠀⠀⣿⣾⢀⡄⠉⠀⠀⠀⠈⠃⠀⠀⠀⠘⠡⠈⠉⠀⢷⣀⠜⠓⢙⡇⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠉⠀⠀⠀⣰⠟⡈⢉⢀⠀⠀⡀⡀⠠⠀⠒⠐⠒⠐⠒⠀⢀⡀⠊⠁⠀⠀⢸⠇⠀⠀⠉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠶⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠁⠀⠂⠀⠁⠀⠀⠀⠀⡼⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡏⠘⣯⡁⠂⠀⠄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠣⡀⠈⠙⠲⢤⣀⠐⡸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⠀⠀⢱⣤⠀⢀⠀⠹⣿⣾⠇⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⢀⠤⠐⠀⣠⠃⢈⠤⠀⣀⣈⡀⠐⢿⡇⠀⠀⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠒⠒⠛⠂⠙⠱⢂⠋⠁⣡⠶⠋⠀⠈⢢⠀⠀⣩⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢸⠃⠀⠀⠀⠀⢨⣷⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠲⠤⠴⠤⠞⠃⠀⣼⠀⠀⠀⠀⠀⣸⠁⢸⣄⠈⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠚⣁⣀⣠⡤⠖⠋⠁⠀⢠⡧⢀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⢦⣶⠖⠒⠶⠒⠒⠉⠓⠀⠀⢀⡴⠞⠋⠉⠉⠁⠀⢀⣀⣤⣴⣿⣿⣛⡳⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠉⠢⢤⡀⠀⠀⠀⣠⣶⡛⠁⠀⠀⣀⣀⣤⣴⣾⠿⢟⠭⠋⡙⡉⡍⢐⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢀⠀⠀⠀⠀⠉⠋⠛⠛⠛⠛⠟⡛⠚⡛⠟⠻⡏⢍⠁⠀⠈⠀⣾⣶⣾⣷⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠹⡶⣤⣄⣠⡄⠀⣀⠀⣀⢀⣄⣀⢡⣈⣠⣇⣴⣥⣼⣿⢷⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢧⢸⡆⠸⡏⠉⣻⠉⢿⠉⢻⡋⢻⠛⢻⠍⢉⡇⢠⣯⢸⣿⣭⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⡄⣷⠀⣷⠀⢹⡀⢿⠀⣼⠀⢸⠁⣸⠀⣸⡇⣸⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠰⣸⡆⢻⠂⠸⣇⢼⠣⣸⡅⢸⠆⣿⢈⣿⣹⣿⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⣿⣟⣹⣧⠀⣏⣾⡇⣿⣧⣿⢐⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡿⣿⣻⣲⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡼⣿⣿⣷⣿⡟⣿⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣧⣤⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣷⣿⣿⣷⣿⣿⣷⣿⣏⣿⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡷⠿⡏⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣏⠿⠿⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠻⠟⠻⠿⠻⠛⠛⠛⠛⠛⠋⠛⠉⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠾⠿⠷⠶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣴⣶⣶⣶⣶⣶⣶⣤⣉⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⠉⠙⠋⠉⠛⠋⠛⠛⠛⣿⡇⠀⠀⠀⠀⠀⢻⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠻⡿⣛⡀
⠀⠀⠀⠀⠀⠀⠀⠠⢛⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠀⠀⠰⠀⠀⠀⠀⠀⡇⠙
⠀⠀⠀⠀⠀⡀⠀⢈⠉⠇⠀⠀⠀⠀⠐⠂⠀⠀⣀⠀⠀⠀⠀⠠⣴⡾⠦⠆⠀⢘⠀⠀⠀⠐⣲⢶⠆⠀⠀⠀⠀⠀⢀⣿⡀⠰⠘⢻⡵
⠀⠀⠀⢤⡷⠓⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠑⠠⣔⠳⢞⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠃⠁⠀⠈⠁
⠀⠀⠀⠈⠁⠐⠪⡀⠄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⢀⠤⠑⠠⡀⠚⢷⣶⣶⡄⢠⣶⣾⠿⠟⠋⣠⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠁⠨⢀⠀⠀⠄⠀⠀⠠⠤⠀⠐⠄⠂⠀⠐⠁⠀⠀⠀⠀⠐⣆⠀⠉⠁⠈⠘⠁⣀⣴⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡄⠀⠐⠆⠂⠀⠑⠂⠉⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠁⠀⠀⠀⠈⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠂⠀⠀⠀⠀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡻⠷⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢀⡀⠄⠐⡀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⣡⣀⢡
⠀⠀⠀⠀⠀⠀⠠⢂⠒⠦⠀⡘⠂⠀⠀⠀⣀⣀⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠆⠂⠀⠀⠑⠒
⠀⠀⠀⠀⠀⠀⡃⠲⠒⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠈⠈⠁⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⢀⠡⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠛⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢠⠀⠐⠂⠀⠔⠈⠀⠀⠀⢈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠄⠘⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠢⢄⡄⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠼⠐⠄⠈⠶⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠐⠀⣀
⠀⠀⠀⠀⠀⠀⠰⡡⢔⡰⠐⣀⣉⢨⢁⠀⠀⠐⠸⠀⠀⠀⠀⠀⠀⠀⠃⡆⠀⢰⠁⠐⠀⢐⢀
⠀⠀⠀⠀⠀⠀⣠⠀⡈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⣀⠀⠀⠂⣂⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⢁⠈⢖⢤⠀⠘
⠀⠀⠀⠀⠀⢁⠹⠈⠉⠁⠠⣹⠀⠀⠉⠀⠈⡀⣄⡀⠀⠀⠀⡨⢉⠃⡈⠛⠛⠀⠀⠁⠐⠂⡀⠠⡀⠆
⠀⠀⠈⡀⠀⢒⠀⣄⠀⠀⠠⠚⠀⠀⠀⡠⢚⠧⠀⠣⠤⠦⠴⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠒⠇⠀⠃
⠀⠀⠀⠈⠀⠀⠡⠌⡄⠂⠁⠀⠀⠀⠔⠃⢠⡤⡟⠒⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⣰⠒⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠠⡟⠛⣦⣿⠀⢹⡴⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠐⠦⣄⡀⠀⠀⠀⠀⠀⢀⣀⣹⣄⠈⢿⠀⡾⠁⣠⠇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣤⠞⠃
⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⢾⡀⠈⠙⢷⣼⣾⣧⠾⣻⠟⢻⠟⠿⣷⡺⢧⣀⢀⡤⠀⠀⠀⠀⠞⠋
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠉⣻⠿⢿⡿⠉⠀⠀⠁⠀⠘⠀⠀⠀⠙⠦⠙⢿
⠀⠀⠀⠀⠀⠸⡤⠞⠓⢦⣤⠀⢾⣁⣴⡟⢀⣤⠶⠖⠒⠒⠒⠒⠀⠀⠀⠀⠀⠈⣧⡤⠀⠀⢹⡴⢦⣤⠆
⠀⠀⠀⠀⣤⡾⠁⠀⠀⠀⢹⡄⠀⢁⣼⠐⢫⡇⢸⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⡆⢸⡀⢀⣰⠏⢀⠀⢿⣀
⠀⠀⠀⠀⢸⡇⠀⠀⠗⠀⠀⣧⠀⠀⡏⠀⢸⡇⢸⣧⡄⢠⡾⡆⣷⠶⡄⣷⡼⠁⢸⡇⠀⣿⠀⠘⠃⢸⠁
⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⢹⠀⢹⡇⠀⢸⡇⢸⡇⣿⢾⣠⣧⢻⠀⡟⣿⢳⡀⢸⡇⢠⡇⢀⠀⠀⣾⠒
⠀⠀⠀⠠⢾⡄⠘⠁⠀⠸⠀⢸⡆⢸⡇⠀⠀⠁⠀⠀⠈⠀⠁⠈⠁⠀⠁⠀⠸⠃⢸⢁⡾⠀⠘⠀⢰⠇
⠀⠀⠀⠀⠀⢧⠀⠀⢀⠀⠀⠀⢧⠈⣧⠀⠀⢸⠀⢸⢰⡟⠹⡆⡿⠀⣶⠀⠀⠀⣾⣋⠀⠀⣀⣠⠏
⠀⠀⠀⠀⠀⠈⢷⣀⠈⠀⠀⠀⠈⠳⣿⠀⠀⢸⡄⢸⠘⢧⡴⠃⣧⣠⣇⠀⠀⠀⡏⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⠤⠤⠶⢾⡄⠀⠀⠙⢻⠀⠀⠴⡴⢾⣅⡈⢁⠀⢸⠇⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠈⣧⠀⢀⣀⡼⠀⠀⢰⡇⢘⣉⡽⠘⠀⣼
⠀⠀⠀⠖⠋⠉⠀⠀⣰⠆⠀⠀⠀⠀⠀⢻⡀⠈⠉⠀⠀⠀⠈⠟⠋⠁⠀⠀⢠⡇⠀⠀⠀⠀⣀⠀⠀⠉⠙⠂
⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⣴⠀⠀⠀⢹⡏⠉⠉⠉⢉⣙⣛⣛⣛⣛⡛⠛⠛⠛⠙⡏⠀⠀⠀⠈⠳⢤⡀
⠀⠀⠀⠀⠀⣰⠏⠀⠀⢰⠃⠀⠐⠒⢺⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢿⠛⠓⠂⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣉⣀⠂⠀⠒⠲⢭⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⣛⣫⣭⣭⣭⣙⣂⣀⣀⣀⡐⣿⣾⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣫⢵⡿⢿⠿⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣗⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡸⠁⠈⠀⠀⠀⠀⠘⠛⠓⠀⠀⠀⠀⠀⠀⠀⣿⡄⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠊⢹⡆⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠁⠀⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡞⠁⠀⠀⠰⡲⡀⠠⢂⠈⠠⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠖⠆⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢀⡗⠃⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⠉⠁⠀⠀⢀⡤⡆⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠈⢆⠀⠀⠀⠐⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣁⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠉⠀⡇⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠘⠀⠊⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡄⠀⠀⠀⠀⠀⢧⣀⣀⠤⠖⣡⡇⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢀⠔⡱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠳⢤⣐⣪⠟⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠒⡡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⣀⡠⠴⠋⢷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠤⠤⣤⢤⠖⠛⢉⡏⡉⣀⠤⠔⠒⠁
⠀⠀⠀⠀⠀⠀⠂⣀⣀⠀⠀⠐⠁⠀⠀⠀⠀⠀⢀⡀⣀⡠⠴⠊⢁⠀⠓⠤⠚⠀⡇
⠀⠀⠀⠀⠀⠃⠀⠤⠇⠀⠀⠀⣀⣀⣀⣒⣒⣒⣸⡀⣀⣠⠴⠚⡹⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠈⠂⡀⠠⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠖⠒⠦⣌⡉⠑⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⠄⣤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⣄⣀⡀⠀⠈⠱⠒⠤⢄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⣚⣳⡄⠀⠀⠀⠀⠈⠓⠦⢤⣄⣀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢹⠀⡟⠘⠉⠉⠐⠒⠒⠊
⠀⠠⠤⠀⠀⠀⠀⠀⠀⣤⡁⡴⠊⠁⠈⠳⠒⠚⠉⠉⠉⠙⠂⢄⣀⠈⠉⠉⠛⠛⠛⠥⣤⠀⠀⠀⢀⠞⣰⠃
⠐⡀⢄⠀⠐⠢⢄⣀⠎⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣇⠀⠀⠀⢠⡏⡀⠤⠔⣨⠖⠁
⠀⠈⠢⡙⢄⠀⠀⠈⠓⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⣀⡼⠓⠒⠒⠉⠁
⠀⠀⠀⠈⠢⡑⠦⡀⢠⠃
⣤⣤⣤⣤⣤⣬⣤⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣬⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣀
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣣⡼⠀⠀⠀⠀⠀⠀⠀⠘⢌⠝⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗
⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠭⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠭⠭⢘⡆⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⢠⢦⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⡠⠴⣉⣁⣒⠒⢺⠀⠀⠀⠀⠁⠉⠃⠀⠀⠀⠀⠑⠂⠜⠫⠄⠤⠀⠀⠀⢀⠞⠉⠀⠉⠓⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⣤⢤⣈⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡠⠤⠋⠉⠘⡄
⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢠⠀⠀⠀⠀⠀⢠⡤⠶⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣉⣀⠤⠤⠋⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡸⠀⠀⣤⡀⠀⠘⣧⠀⢀⡹⠀⠀⠀⠀⠸⣆⠀⠀⢠⠀⠀⠀⠈⠢⣀⠀⠀⡰⠁
⠀⠀⠀⡴⠒⢤⠔⠊⢢⠀⠀⠀⣿⠗⠒⠲⡇⠀⣸⠇⢧⠀⠀⣿⠒⠉⢠⣶⠒⠢⡄⠀⢻⡄⣠⠃⠀⠀⠀⠀⠀⠀⠉⡟⣄
⠀⠀⠀⠱⡀⠀⠀⢀⡎⠀⠀⢠⣿⠀⠀⢸⠃⢰⡟⠒⠚⡆⠀⢻⡀⠀⢰⡟⠀⠀⡹⠀⠈⣿⠁⠀⠀⠠⡖⠔⡲⠀⠀⠈⢇
⠀⠀⡀⠀⠈⠢⠤⠊⠀⠀⠀⠀⠉⠀⠀⠘⠀⣿⠁⠀⠀⢱⠀⠘⠃⠀⢸⡟⠒⠋⠁⠀⠀⣿⠀⠀⠀⠀⠈⠚⠁⠀⠀⠀⢸
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠸⠇⠀⣀⣀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⣾⠉⠑⢆⠀⠀⢸⡇⠀⢰⡏⠙⢢⠀⠉⢹⡏⠀⢀⡄⠀⢀⡀⣿⠀⠉⢦⠀⠀⠀⠀⢶⡀⠀⠀⡄⠀⢠⠃
⠀⠀⠀⠀⠀⠀⣿⣀⣠⠇⠀⠀⣿⠁⠀⢸⣇⠤⠋⠀⠀⢸⡇⠀⢸⡇⠀⢸⠀⢹⡆⠀⢘⠄⠀⣤⠀⠘⣷⠀⡸⠀⠀⢸
⠀⠀⠲⠴⡄⠀⢿⡉⠀⠙⡆⢀⣿⠀⠀⢸⡏⠲⡄⠀⠀⢸⡇⠀⣾⠓⠒⢾⠀⢸⡇⢀⡜⠀⣼⠏⡆⠀⠸⣷⠁⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⠃⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⡏⠀⠈⠛⠁⠀⣼⠟⠒⡇⠀⠀⣿⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠁⢠⢢⠀⠀⠘⠋⠀⠀⠃⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠈⠑⠆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⡀⠀⠀⠀⠀⠀⣠⣀⣤⠀⠀⠀⠀⠀⠘⠝
⠀⠀⠀⠀⠔⠃⠀⢰⠢⣤⡀⠀⠀⠜⠁⢀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢃⠀⣀⣀⠀⠀⠣⡀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠈⡗⢒⡤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠔⣒⣛⣈⡩⠄⢐⡇⠀⠀⠈⠁⠀⠀⠀⣀
⠀⠀⢠⡄⠀⠀⠀⢸⠀⢲⢀⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⠤⠤⠒⠒⠉⠁⢡⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⣀⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠈⣆⡀⣤⠤⣔⣲⡼⠯⠗
⠤⠊⠉⠢⣄⡀⣀⠼⠁⠀⠀⠀⠀⠀⠨⣳⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠎⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡖⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⢰⢲⠀⠀⡠⠀⠈⠀⠀⠀⠸⣉⡝⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⢿⠁⠀⠀⠀⠆⠀⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠠⠞⠀⠀⠰⠤⠜⠓⠒⠊⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠋⠈⠀⠀⣠⠾⠭⣙⡆⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠥⢍⣑⡲⡇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡠⠖⠒⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣍⡉⠑⠒⠤⠭⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⢀⡞⠂⢦⣀⡀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢸⠀⢦⡀⠉⠙⠆⡼
⠀⠸⡀⠀⠈⠉⢓⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠗
⠀⠀⠱⣤⠤⠒⠁
⠀⠀⢺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⡎⠀⡀
⠀⠀⡅⠘⡝⢋⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠴
⠀⠀⢱⠀⠈⠁
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⠑⠊⠈⡇
⠀⢀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⡠⣄
⠀⠀⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠂
⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢀⢭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⠀⠠⠦⡀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢑⡠⢴⠎⢹⠁⢸
⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣉⣐⠚⣚⠓⣒⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠈⠲⣼⠀⢸⠀⡘⠀⢴⡄
⠀⠀⠈⠉⠃⠀⡀⢀⡀⠀⠀⡖⠒⠤⠭⠤⠭⠤⢩⡇⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣎⠀⡟
⠀⠀⠀⠀⠀⢺⠈⢁⡇⠀⢀⢇⡠⢤⠄⣀⣀⣀⣀⣅⠀⠀⠀⠁⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⡠⢶⢶⠉⠁⠀⠀⠀⠈⠑⢧⠀⠀⠀⢀
⠀⠀⠁⠀⠀⠀⠑⠋⠀⠀⠈⠉⠉⠉⠐⠋⠚⠓⠛⠊⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣸⣿⣿⣜⣇⣿⣧⣻⣿⣿⢿⣦⣄⠀⠀⠀⠀⢠⣶⣿⠿⢿⣿⡿⠿⣾⣶⣿⣷⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡟⣿⣿⡿⣿⣿⣿⡟⣿⣿⠿⡿⣿⡿⣿⣷⡀⠀⢺⡿⠿⣿⣶⡾⢻⠛⢶⢿⠿⡷⣶⠿⠷⠶⠦
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣛⣟⣻⣟⣛⣿⣿⢿⡿⠿⢿⠿⣷⡿⣿⠾⢿⢷⣶⣾⣷⣶⣿⣿⣷⣾⣶⣶⣾⣿⣷⣿⣷⣴⢶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⣘⣛⣻⡟⣛⣛⣛⣷⣿⣮⣿⣵⣾⣦⣿⣿⣷⣽⣦⣾⡿⢿⡿⢿⣿⣿⣿⣿⠛⠟⣿⠛⢻⣿⣿⣿⣷⣾⣿⣦
⠀⠀⠀⠀⠀⠀⢀⣋⣉⣿⣏⣋⣋⣿⣸⣿⣌⣩⣭⣍⣽⣯⣩⣉⣍⣹⣿⣧⣴⣧⣼⡟⣿⠻⠯⣻⢻⡏⣿⡟⣿⠹⡻⢻⣿⣾⣿⠄
⠀⠀⠀⠀⠀⠀⢸⡿⣟⣿⣿⣿⣧⣭⣭⣯⣿⣯⣯⣭⣽⣿⣻⣛⣻⣿⣻⣛⣿⣿⣿⣛⣟⣟⣻⡏⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣾⠆
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣯⣹⣿⣫⣽⣿⣏⣉⣹⣏⣉⣿⣿⣏⣏⣻⣹⣍⣋⣹⣏⣹⣹⣉⣿⣿⣿⣿⣻⣿⣿⣿⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡟⡶⢿⠿⣿⠿⠿⡿⢿⣿⣿⣯⣉⣿⣿⣹⣍⣻⣿⣹⣏⣋⣉⣹⣿⣙⣉⣹⣿⣿⣻⣟⣿⣿⣻⣿⣽⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⡾⢷⢿⡷⠷⢷⣾⣿⠿⢿⡿⢿⣏⣿⣉⣫⣿⣿⢉⣙⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣯⣽⣽⣯⣽⣿⣿⣿⣿⣿⣽⣽⣿⣯⣿⣿⣸⣿⣸⣐⣉⣹⣻⣿⣉⣀⣺⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⢿⡿⠿⠿⠿⢿⡟⠗⠿⢻⣾⢻⣿⡟⣿⢿⣿⣻⣿⢻⣿⣽⢿⡿⣿⡿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣍⣹⣾⢷⣶⣶⡶⢾⣧⣴⣾⣾⣿⣼⣿⣧⣿⣬⣿⣧⣿⣼⣿⣿⣧⣧⣽⣷⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣽⣭⣯⣿⣭⣭⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⡿⢿⣿⣿⢻⣿⣿⢟⣷⣾⣿⣶⡾⠿⢿⠿⢿⣿⢭⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⡟⢻⣿⣿⡿⣿⡿⢷⣿⣧⣷⠵⠶⡧⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠾⣿⣿⣧⣿⣴⣤⣤⣤⣿⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣦⣤⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠐⠀⠀⠀⠀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⠀⠀⣀⠀⠀⢸⡇⠀⠀⣾⠁⣄⢀⡤⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⣿⢸⡇⣸⠇⣾⠁⣾⠃⣸⢶⣿⢀⡿⠸⣇⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢸⡇⠹⠄⢻⡀⣿⠀⠟⢸⡇⠈⠀⠀⠀⠈⣷⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⠀⠈⢧⠀⢠⡀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠈⠀⠀⠀⠀⠀⠇⠀⠙⠀⠀⣼⠁⠀⠀⠀⠀⢰⠇⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠐⠁⠀⠀⠹⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢠⡞⠀⠂⠀⠀⣤⠀⠀⣴⠋⠀⠀⠀⠀⠀⣷⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⢸⡇⠀⠀⢀⠀⢼⠅⠀⠄⠀⢸⡇⠀⣸⠇⠀⠀⠀⠀⠀⠀⣿⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⢸⡇⠀⠀⠂⠀⠘⣇⠀⣀⠀⣸⠃⠀⣿⠀⢠⡀⠀⠀⡀⢰⡟⠀⢀⡀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠅⠀⠈⣷⠀⢀⠀⢠⡆⠀⢁⡟⠀⣿⠀⠀⣿⠀⢸⡇⠀⡾⠁⣸⠇⢰⠏⢰⡏⢰⡏⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢻⡄⠈⣧⢸⡇⠀⢸⡇⠀⢻⡀⠐⣿⠀⢸⡇⢸⡇⠀⣿⠀⢿⡀⢺⡅⠻⠅⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠘⠃⢰⡟⠈⠓⠀⠈⠧⠀⠈⠧⠀⠙⠀⢸⡇⠈⠓⢀⠹⣎⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠙⣶⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠓⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁




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

⠀⠀⡸⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠒⠌⠻⡄
⠀⢠⠁⠀⠀⠀⠀⠛⠀⠶⠒⠢⠤⠄⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⣀⡤⠤⣀⡠⠶⠶⠄⠘⠒⠂⠈⠁⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠺⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠤⠄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡕
⠀⠀⠈⢷⡢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠉⠀⠀⠈⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢊⠹
⠀⠀⠀⠈⣡⠀⠈⠻⠒⠤⠄⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⠀⣀⠤⠒⠊⢻⠀⠀⠸⠇
⠀⠀⠀⠀⣿⠀⡀⠀⡇⠀⠀⠀⠀⠉⠁⠐⠒⠠⠤⠂⡈⠀⠀⠂⣀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠞⠢⠈⠀⠠⠀⠀⠀⢈⡀⣀⢀⡇
⠀⠀⠀⠀⢟⣤⠛⡄⡃⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠋⠀⠀⠀⠈⠶⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⣠⠂⠀⠘⠀⠀⠀⠀⠀⠀⠈⢿⡛⣼⡇
⠀⠀⠀⠸⠏⠁⠀⠵⠁⠀⠀⠀⠀⠀⠔⠂⠀⠉⠂⢰⠂⠀⠀⠀⠀⠄⠑⣄⠐⠈⢧⡀⠀⠀⣠⠞⠁⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠃⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠒⠲⢄⠀⠀⢸⠆⠀⣀⠠⣄⠤⣆⠈⣧⡀⠀⣩⠂⠉⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠱⡀⢸⡤⠞⢁⣠⡤⠄⠤⡄⣉⠚⣆⠀⠀⠀⢀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢁⡜⢁⠔⠉⠀⠀⠀⠀⠀⠈⠳⡄⢶⡠⠚⠀⠁⠀⠉⠙⢦⡀⠀⠀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⢸⠇⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠰
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠓⠄⡀⠀⠀⠀⠀⡆⡸⠀⠀⠄⠀⠀⠉⠁⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢠⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢼⠁⠑⢆⠀⢳⣶⡶⠶⠶⠶⣿⠃⢠⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⢸⠀⣤⣀⠚⠉⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠃⠀⠀⠑⢄⡁⠀⠀⠀⠀⠀⡠⠛⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⡴⠟⢫⠿⢣⠴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⡂⠀⠀⠀⣏⠀⠀⠰⠆⠴⣐⢪⣍⠊⠁⢐⣦⣀⠀⠀⠀⠁⠘⠂⠀⠉
⠀⠐⠂⠈⠉⠐⠢⣀⠀⠰⠀⠀⠀⠀⢪⡗⢄⠀⠀⠀⠀⢀⡀⠜⠑⠀⠀⠀⠂⠓⠶⠤⡀⢰⡦⠴⡦⢣⠴⠋⠁⠈⢳⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⠀⣠⢤⡤⢤⣨⣆⠣⣄⣤⠄⢋⠀⠀⠀⠰⢀⠀⠀⡀⠆⡀⠈⢣⡴⠀⠀⠀⡠⣀⢀⡤⠚⠀⡅⢀⠠⠤⡀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠃⠀⠀⠀⠀⠈⠁⠁⡾⢂⣠⠀⠐⢋⠂⠈⠉⠀⡉⠀⠉⠉⠎⢰⠴⣤⣆⣸⢅⣈⣥⣚⣤⠐⣋⣀⠀⠾⠐⣦⠰
⠀⠀⠀⠄⠀⠀⠀⠀⠀⡇⡲⠀⠰⣀⠀⡀⠆⠀⠀⠰⠙⠃⠀⠀⠈⠁⠀⠀⠈⠛⠀⠀⠃⠀⠀⠀⠀⠹⠁⠠⢷⣉⡩⢆⣭⡍⠙⠻⣶⠁⢀⠤⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣛⠤⠩⠀⠀⠀⠈⠁⠀⢂⠀⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⡀⠁⠉⠈⢱⠀⠰⢷⡀⠰⠯⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⣄⡀⠈⠀⠤⠀⠘⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡭⠑⠢⠤⢺⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠠⠖⢂⣝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠈⢢⡀⠈⠲⠇⢀⡀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢁⠀⠀⡇⠈⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⢠⣅⡀⠠⠀⠀⠁⠂⠢⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠸⠀⡇⠑⢄⠈⠑⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠀⢀⡴⠃⠈⠉⠒⠤⣀⠀⠂⠄⠐⢀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⠀⠀⠈⠐⠠⢄⣀⣉⠁⠒⠒⠒⠒⠒⠉⢉⣀⡠⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣧⣼⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠋⠉⠉⠉⠀⠨⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠦⠐⠚⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣀⡀⠤⠔⠒⠈⢉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠇⠀⠀⠀⠀⠁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⣀⡀⢀⡀⠀⠀⠀⡰⠀⠀⠈⠢⡀⠀⠀⢀⡀⠀⠀⠀⠰⣀⡠⠎
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⣸⡇⠈⠈⠈⠁⢄⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡰⠁⠙⢆⡀⠀⠀⠀⢱⠀⠀⠀⠀⠈
⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠀⠘⠣⠦⠄⠊⠀⠀⠀⠀⠙⠲⠴⠄⠋⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶
⣿⣭⣭⣽⣭⣭⣭⣬⣍⣿⣩⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣥⣮⣧⣼⣿⣿⣧⣽⣿⣭⣭⣿

⠀⠀⠀⠀⠀⢀⠠⠄⠀⢠⢄⡀⡚⠑⠀⠂⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠠⣀⡀
⠀⣂⠳⣠⡴⢯⡁⠀⣈⠆⠀⢙⡤⠞⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⠃⠴⠙⡌⠄⢉⠁⠉⢳⠆⠀⡆
⡠⠊⠀⠀⢀⠝⠻⠀⠀⠠⣀⠇⣷⢴⠈⡡⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠊⢀⡈⣣⠀⢸⠀⢸⡄⣈⡿⢗⡔⠊
⠣⠀⠖⠣⡈⢑⣔⡌⡈⢂⢐⡶⠙⠢⠤⠃⠀⠀⣠⠄⠰⠒⣒⡲⠂⠤⢄⠀⠉⣟⡴⠈⠁⠁⠋⠁⠉⠉⠉
⠀⠀⠀⠀⠈⠁⠀⠉⠒⠊⠁⠀⠀⠀⠀⠀⠀⠘⠂⠬⠄⣋⣉⣉⣑⡍⠴⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀
⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠉⠢⡀⠀⠀⠀⠀⠘⠀⣐⠀⠀⣀⠀⢀⣇⠜⠁⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⢠⠒⡋⢂
⠀⠀⠀⢀⡀⠣⡀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠔⠀⠀⠆⠈⠀⢎⡀
⠀⠀⠀⠀⡓⢄⡈⠢⠄⣀⢀⣀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠂⠠⠄⣀⠀⠀⠀⠀⠀⢆⠠⠀⠀⠀⠤⠜⡀⠁
⠀⠀⠀⠀⠘⢄⡈⠀⠂⠠⠀⡴⠊⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⡀⠀⠠⠖⠉⠀⠀⠉⠰⠆⠀⠀⠙⠠⠠⣠⠶⠊⣑⡢
⠀⠀⠀⠀⠀⡸⠈⠗⠒⠒⠉⠀⠀⠀⠀⠀⣀⣈⠓⢆⠀⠀⠀⠀⠁⠀⠲⠄⠀⠂⠀⠀⡸⠀⠀⠀⠀⠐⠂⠑⠂⠐⡄
⠀⠀⠀⠀⢠⠃⡌⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⡀⠛⠶⠄⣀⣀⠤⣄⠀⢸⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⢠⠃⡘⠀⠀⠀⠀⠀⠀⠣⢄⡂⣄⣀⣀⠬⠄⣀⡀⣀⠐⠉⠂⢈⡄⠈⠁⠀⠀⢀⡠⠴⠲⠶⢤⡀⠀⠀⠀⠂
⠀⠀⠀⠁⠴⠁⠀⠀⠀⠀⠀⠀⠑⠤⣈⡀⢀⡅⠀⠀⣇⡀⢀⡁⢀⠜⠚⠀⠀⠀⢀⠞⠁⠀⢀⣀⡀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⡀⠉⠀⠀⠀⠀⠀⠀⡟⢀⣀⠔⢁⣄⢹⠃⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣦⠀⠢⡀⠀⠀⠀⠀⠀⢧⡀⢸⡀⡨⠶⠚⠠⣀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠐⠂⠛⢍⢂⠀⢱⡄⠀⡃⠀⠀⠀⠀⠀⠀⠑⠯⣙⣦⡤⠴⠞⢁
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣒⠈⠁⠀⠀⠑⡀⠀⢀⣦⠴⠋⠉⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠱⡀
⠀⠀⠀⠀⠑⡒⠠⠤⠀⠑⠄⠑⠠⣀⡠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠘⢆
⠀⠀⠀⡏⠀⣈⣒⡖⠊⠤⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡚⠛⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣄⠀⠀⠆⠠⣄⣰⠂⢀⡄⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠃⠀⠀⠀⠀⠀⠀⠄⠡⠀⠃⠀⠀⠀⢸⣿⣿⢹⣿⣿⠀⠀⠢⣰⢮⠵⡐⠮⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⠒⠀⠀⠀⠸⣿⣷⢈⣿⡟⠀⠀⠙⠴⠂⠚⠑⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢠⡶⣦⢶⢀⡶⣶⡒⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⣀⣀⠀⠀⠀⢀⣶⣿⠿⠿⢿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡜⢧⠞⠘⠿⠁⢿⡥⠀⠀⠘⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⠟⠀⠀⠀⠘⣿⣿⣦⣠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣄⠀⠀⢀⣤⡶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣴⣿⣿⠀⢸⡇⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⢠⡿⠁⠀⠀⠀⠙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠻⠟⠀⠰⣶⠆⠈⠛⠁
⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢶⡶⠀⢠⣤⡄⠀⠰⣶⠆
⠀⠀⠀⠀⠀⠷⠤⠤⠤⠤⠞⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠤⠤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠀⠀⠀⠀⠀⠉⠈⠛⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣾⣿⡆
⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⠀⠀⠀⠈⠹⣿⣿⡇⠀⠀⢷⣾⠂⠀⠈⣿⡿⠏⠁⠀⠀⠀⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠉⣾⣧⡉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡎⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠸⠇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠻⣿⠗⠺⣿⡟⠀⠀⠀⢲⡶⠀⠰⣶⠖⠀⠀⠀⠀⠀⠀⣀⠀⡐⠠⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠄⢔
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠈⠁⠀⠀⠀⣄⡀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢰⣶⣶⣶⣶⡆⠀⢀⣴⣶⣶⣶⣆
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠋⠀⠀⣶⣶⣶⣦⠀⠀⠀⠀⠀⢘⠃⠀⠀⠀⠈⡟⠉⠉⢻⠃⠀⠘⠋⢉⣉⡉⠙⠁
⠀⠀⠀⠸⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣉⡉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣷⣄⣠⣾⠀⠀⠀⠀⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢀
⠀⠀⠀⠁⠀⠀⠀⠈⠢⠀⠀⡀⠀⠀⠐⠂⠀⠈⠀⠀⠀⠀⠀⠡⠄⠀⠁⠐⠀⠄⠀⠘⠀⠀⠀⠉⠀⠄⠀⠈⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠠⠨⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡴⠀⡈⠉⠀⢱⠀⠀⠀⠰⠀⡈⠀⠈⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠐⠀⠃⠂⠀⠀⠁⠐⠂⠀⠀⠀⠀⠂⠀⠀⠠⠤⠄
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠖⠂⡀⠀⠀⠀⠐⢈⠀⠢
⠀⠀⠀⠀⠐⠖⠆⠀⠀⠀⠠⠀⡀⠀⠀⡠⠄⢁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⢴⢱⠂⠱⠀⠀⠀⠀⠄⠐⠀⠁
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢅⠁⠀⠁⡖⠁⠄⢀⠀⠀⠀⠠⠉⡐⠀⠀⠁⠀⠄⠈⠁
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⢡⠄⠰⠀⠀⠀⡂⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠠⠤⠀⠂⠈⢁⡈⠀⠉⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠀⠀⠀⠁⠀⠄
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠉⠐⠀⠀⢀⠉⠀⠑⣄⠠⠀⠀⠀⠀⡄⡨⠄⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠈⡅⢋⠠⢀⠰⠠⠈⡀⠀⠀⠀⡠⡀⠀⢂⣁⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠡⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌⠀⠧⠜⠀⠀⠀⣁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠐⠀⠀⠀⠀⡇⠀⠀⠈⠃⠀⠁⠀⠈⠡⠄⠀⠀⡼⠈⠀⠈⠈⠀⠀⡀⠀⣀⠂⠈⢂⠈⢀⠀⠀⠂⠀⠀⠈⠀⠀⠐⠂
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⠁⡠⠀⠀⠀⠀⠀⠁⠁⠀⠀⣀⠘⠀⡀⠠⠡⠈⢆⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠡⠄⠆⢠⠀⡦⡀⠁⠀⡀⠄⠀⠀⠀⢀⢀⠀⠀⠤⠄⠀⠀⠀⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐
⠀⠀⠀⠀⠈⠁⠢⡀⢀⠀⠂⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⠤⢇⡑⠠⠄⡀⠀⠀⠀⠠⡂⠆⠰⢀⢀
⠀⠐⠀⠀⠐⠀⠐⠃⠀⠓⠀⠘⠀⠀⠠⠀⠀⠠⠀⢂⠀⢀⠓⡰⢤⠃⠒⡀⠀⠠⠍⣤⠘⠃⠚⢀⡐⢃⠀⠀⠀⠀⠀⠘⠁
⠀⠠⡄⠀⠀⠀⠠⠄⠀⡤⠀⠀⠀⠀⠜⠀⠀⠀⠁⠀⠀⠀⠀⠅⠒⠈⠀⠀⠀⡕⠠⡆⢀⡀⣀⠀⡄⠠⡀
⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢔⠂⢀⠠⠆⢀⠑⠁⠀⠠⢄⣉⠀⠄
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠁⠴⠀⠆⠔⠈⠀⠀⠈⠤⠈⠒⠁⡄
⠀⠀⠁⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠶⠄⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⣠⣀⣴⠇⠀⠀⠀⢀⠀⣤
⠋⠐⠀⠀⠀⠀⠀⣸⣏⠀⠠⡐⠀⣴⢠⡆⠀⠀⠀⠀⠀⠀⡰⠶⠶⣿⡉⠀⠂⣀⠀⣠⡀⠟⠈⠀⠀⠀⠀⣼⠿⠛⣃
⣀⡄⠀⠀⠀⠀⠐⠉⣉⣀⡀⠀⠀⡆⠘⠀⠀⠀⠃⠀⠀⢸⡇⠀⠀⠸⡇⠀⠀⠀⠁⡙⠀⠀⠀⠀⠀⠀⢰⣧⣴⠿⠛
⢸⡇⠀⠀⠀⠀⠀⣰⣿⣿⡿⠿⣤⣿⠿⢦⣤⣤⣀⠀⠀⠀⠀⠐⠆⣴⡇⠀⠀⠀⢠⣅⣴⠞⠃⠀⠀⠀⢿⣭⡏
⠀⠀⠀⠀⠀⠀⣾⣻⠋⠁⠀⠀⢾⠾⣾⡿⠟⠛⠛⢦⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⣿⡉⠀⠀⠀⠀⠀⠈⠁⡁
⠀⠀⠀⠀⢰⣶⣍⣍⠀⠀⠀⠀⢠⣤⣿⡇⠀⠀⠀⢸⠀⠀⢠⣀⣌⡁⠀⠀⠀⠀⠀⢨⠱⣶⣿⣿⣿⣿⣷⣦⣿⡀
⠐⠃⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠘⠛⠋⠃⠀⠀⠀⠘⠒⠚⠛⠛⠛⠛⠃⠀⠀⠀⠀⠘⠊⠀⠈⠙⠛⠛⠛⠛⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠪⢈⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⡿⠗⠀⠀⠀⠴⣭⠪⡵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢶⡴⠓⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠀⠀⠀⠀⠀⢘⢸⡰⠭⣵⢉⠄
⠀⠀⠀⢀⣀⣤⣤⣴⣶⣤⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣰⣡⣤⣬⣄⠀⠀⠀⠀⠀⢰⣿⠁⣉⣿⠏⠀⠀⠀⠀⠀⠈⠦⣙⣙⡥⠜
⠀⠀⣴⣿⣿⣿⠿⡿⣛⣹⡄⠀⠀⠀⢸⠀⠀⠀⠀⢀⢼⠿⠿⠿⡿⠻⠤⠀⠀⠀⠀⣺⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⣶⣷⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⢂⠂⢠⠀⠁⢇⠁⠀⢀⣴⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠢⠤⠼⠼⠌⠀⠀⠀⠛⠿⣿⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣦⢀⣀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢠⣴⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠫⠬⠯⠥⡞⠉⢃⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢈⠖⠀⠒⠄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⡈
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢢⠀⠀⠀⡼⠉⡇⠀⠀⠘⠢⠤⠤⠤⠤⠗⠋
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠑⠚
⠀⠀⠀⠀⠀⢹⡢⣞⣢⢯⠇⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⡚⢳⣤⡀
⠀⠀⠀⠀⠀⠀⣷⢾⣉⡾⠀⠀⠀⠀⢠⠞⠡⢀⠀⠈⠀⡀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡞⠙⣦⡴⠛⢏⣠⠟⢦⡀
⠀⠀⠀⠀⠀⠀⠸⣞⣭⠇⠀⠀⠀⠀⠇⠨⢠⢰⣿⠿⣦⠀⠠⠀⠃⠀⠀⠀⠀⠀⠀⣠⣴⠚⢣⣠⠽⢏⢉⡷⣖⢋⣱⣶⠋⣱
⠀⠀⠀⠀⠀⠀⠀⢫⡟⠀⠀⠀⠀⠀⡇⢁⠀⢘⠦⠤⠊⠈⠀⠀⡇⠀⠀⠀⠀⠀⣾⢀⡸⢶⠋⣹⣴⠚⢻⣤⠞⢻⣀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢳⣆⣀⠂⠄⠂⠐⢀⣀⣾⠃⠀⠀⠀⠀⠀⠙⣯⣠⠼⢻⣁⡼⢿⡉⣹⣶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⠷⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⣴⠚⢹⣤⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠞⠛⠉⣉⠉⠀⠀⠀⠉⠉⠙⠛⠷⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⡣⠔⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⢀⡤⢾⣵⢟⣥⠶⢚⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠙⢶⡄
⠀⠀⠀⠀⢀⣴⠟⠀⢸⡵⣫⠖⢋⣩⣤⣤⡤⠤⠤⣀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣭⣭⣍⢙⠓⢦⣻⣆
⠀⠀⠀⢀⣾⢏⡔⠀⠘⡎⣀⣭⣴⣶⣬⠁⠒⠒⠢⠤⣉⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣀⣀⣀⣹⡿⠷⠲⠂
⠀⠀⠀⣼⡟⡞⢀⢀⠀⠈⠛⠛⠓⢦⣍⠳⣄⠒⠦⠤⢬⠙⠒⠤⠤⠤⠀⠀⠀⠉⠁⠀⣀⣀⣀⣉⢻⣦
⠀⠀⠀⣿⣿⠁⣆⡎⠀⠀⠀⠀⠀⠀⠙⢷⣜⠳⣶⠦⠤⠤⠤⠤⠤⠤⠀⠀⣀⣤⠶⠋⠉⠀⢠⡈⡌⣇
⠀⠀⠀⣿⣿⢸⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣶⣦⣤⣤⣶⣶⡶⠾⠟⠋⠁⠀⠀⠀⠀⠀⢷⣻⣿
⠀⠀⠀⢸⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠈⣿⣿⠇⠀⠀⠀⠀⣠⣤⡾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣀⠀⠀⠀⠀⠀⢼⣿⠁
⠀⠀⠀⣠⢽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠃⠀⠀⠀⠀⣼⣇
⠀⠀⢸⠁⠛⣿⡆⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⣴⠟⠊⡇
⠀⠀⠘⢷⡀⠘⣷⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⢰⡟⠀⣼⠃
⠀⠀⠀⠈⠻⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡾⠃
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠤⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆
⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢶⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠙⠿⣍⡛⠓⠒⠒⠒⠒⢒⣻⠟⠋⠁⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⡀⠀⠀⠀⠀⠈⠛⢷⣤⣀⣤⠾⠋⠁⠀⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠷⠶⠚⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⢠⣾⣿⣦⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀⠀⠀⠘⢿⣿⣿⠟⠋⢀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠁⠀⢠⣶⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣷⣦⣄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣠⣴⣾⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⠃⠀⠀⠘⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢻⣿⣿⡏⠀⠀⠀⠀⢹⣿⣿⡟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⡾⠿⠿⣿⣿⣿⣿⣿⣶⣶⣿⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⣶⣶⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⠋⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⣴⣆⠀⠀⠙⣿⣿⣿⣿⣿⠿⠛⠋
⠀⠀⠀⠀⠛⠻⠗⠀⠀⠘⠻⠟⠀⠀⠀⠀⠈⠉⣋⣿⣷⠀⠀⢿⣿⠃⠀⠀⠀⠀⠘⣿⡿⠈⠀⣾⣿⡙⠉⠁⠀⠀⠀⠀⠻⠟⠃⠀⠀⠺⠟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟
⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠒⡘⠉⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡔⠁⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣠⠁⠀⠈⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣰⠁⡠⠔⠂⠩⠉⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⠇⠎⠀⠀⣀⠀⡉⠉⠁⡀⠀⡀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠀⢠⠂⠀⠀⠀⠀⠌⠀⠀⢸⢸⢀⠀⢠⠃⡸⠁⡸⢡⠃⢠⢃⡎⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠦⡀⡏⠀⠀⠀⠀⠈⠀⠀⠀⢸⠸⠘⠂⠘⢠⠛⠀⢀⠎⠂⠀⠘⠀⡜⠀⠀⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⣹⠙⠆⠀⠀⠀⠀⠀⠀⢄⡈⠢⠑⠒⠒⠁⢀⡤⠋⠀⡠⠂⠀⡰⠁⠀⠀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠔⠃⢀⡜⠁⠀⣀⣠⠖⠁⠀⠀⠀⠀⠀⡖⠉⠐⠀⠘⡆⠀⠀⢀⡨⠭⡀⢀⡜⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠈⠁⠀⠉⠓⣄⠀⠀⠐⠀⡀⠀⠔⠀⢠⠇⢀⡔⠑⠐⠀⠁⣼⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠆⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⡤⠖⠒⠉⢁⡟⢂⡞⠤⣑⡀⠂⠀⠙⠊⠀⠀⠀⠀⢀⠀⠀⠀⣰⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⣀⣀⣀⣀⠀⠀⣼⠁⠀⠃⣀⠀⠀⢀⡞⢀⡞⠀⠀⠀⠀⠈⢩⠏⠀⠀⠀⠀⠀⠀⠑⠒⠊⠁⠀⡸
⠀⡰⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⣠⠔⠋⠉⠀⠀⠉⠳⣴⠃⢀⠞⠀⠀⡤⠀⡜⠀⡼⠂⢸⠃⠀⠀⢀⡏⠀⡀⠀⢸⠃⢠⠇⢀⡞⠀⠀⡴⠁
⢰⠁⠀⠀⠀⠀⠀⠀⢠⠊⠀⡐⠁⠀⠀⠀⠀⠀⢀⠜⢻⠀⣼⡀⠀⢰⠃⢸⡃⠸⠁⢀⡏⢰⡃⠀⣾⠀⢼⠀⠀⡇⢠⡏⠀⡼⠀⠀⠈
⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡁⠀⠀⠀⠀⠀⢐⣁⠄⣼⢀⡈⠀⠀⠈⠀⠈⠀⠀⠀⠀⠁⠀⠉⠀⠈⠀⠈⠁⠀⠁⠀⠁⢰⠃
⠈⠳⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⣠⠃⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⣀⠔⠢⡀⠀⠀⠀⠀⠀⡤⠊⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠔⠁⠀⠀⠀⢠⠊⠹⣆⠀⠀⠀⡼⠁⠀⠀⢸⠀⠀⠀⢠⠎⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⣆⠀⢸⣇⠀⠀⣠⠟⠀⠀⢠⠏⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⣻⠀⠀⠉⠉⠉⠀⠀⠀⠀⢾⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠴⠋
⣿⣿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠲⠂⠈⠉⠉⠉⠉⠉⠉⠒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⢂
⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡁⠀⠁⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠸⠇⢀⠀⢀⡠⠄⢲⡾⠉⠉⠉⠉⠉⠉⠉⠀⠒⠒⠂⠠⠤⢈⣳⠀⠀⠀⠀⢄⠀⠀⠃
⠀⠀⠀⠀⠆⠀⣾⠞⠁⠀⠀⢈⡴⢂⣈⠁⠢⡀⠀⠀⠀⠀⡠⢊⣡⡌⠑⢤⡈⠑⠤⣀⠀⠀⠀⢸
⠀⢀⡤⠞⠂⢴⡇⠀⠀⠀⠰⠋⣰⣿⣯⣴⣦⣸⡆⠀⠀⢠⣧⠼⠿⠷⠷⠤⣵⠀⠀⠘⡷⠀⠀⢸
⠀⢸⡇⠀⠀⢾⠀⠀⠀⠀⠙⠋⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸
⠀⠀⠙⡗⠒⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣀⠸
⠀⠀⠀⢇⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠀⠀⠀⠀⠀⢀⡏⠀⠉⢿
⠀⠀⠀⠘⢧⡀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠘⣏⠃⠠⠴⠦⠖⠘⢋⡼⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠈⠳⢤⣀⠙⢦⡀⠀⠀⠀⠀⠀⠈⠑⠦⣤⣤⣤⠴⠋⠁⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⣐⠂⠲⡄⠀⢀⠔⠁⣠⠞⣠⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠳⢦⣀⡀⠀⠀⠀⠀⠀⠴⠄⠀⠀⠀⢀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⢈⣤⡁⠀⠘⠣⠚⠁⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⡶⠶⠶⣶⠶⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠓⠀⠀⠰⣉⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⠇⠀⠀⢷⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡷⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠁⠈⠯⣀⠀⠀⠀⢀⣨⠋⠈⠁⠀⠙⠛⠒⢶⡆⠠⠤⠴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢤⣤⡤⣤⠞⠓⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⠤⠤⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣸⡧⣤⣤⠤⠤⠴⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⢀⠘⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡐⠁⠀⠀⠘⢄⢸⣧⣤⣤⣤⣤⣤⡤⠶⠶⠶⠶⠶⠶⠶⠶⢶⡿
⠀⠀⠀⠀⣌⠁⠀⠀⠀⠀⠈⠻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠀⢃⠀⠀⠀⠀⠀⢀⡴⣦⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⢤⣀⡘⠀⣴⠀⠘⣧⣈⡄⠀⠀⠀⢀⡏⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠉⠛⠦⠻⡤⠚⠀⠈⠀⠀⠀⠀⣘⠁⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠶⠒⠀⠀⠀⡟⠀⠀⠀⢸⡄⠀⠀⠠⠴⠶⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣀⣀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣰⠇⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣇
⠀⢀⠴⠚⠓⠠⣄⠀⠀⠀⠀⠀⠀⠀⡌⠉⢻⡄⠀⠀⠀⠀⠀⢸⠇⠀⣠⣤⠤⠴⠦⠄⢈⣦
⡰⠃⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠙⢒⠦⣷⠀⠀⠀⠀⠀⢸⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⣧⣀⣀⣀⣀⣀⣀⣀⣘⣁⢀⠀⠀⠀⢘⠋⠀⣼⠀⠀⠀⠀⠀⠸⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣽⣿⣷⣶⣶⣶⣶⣶⣾⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠛⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⡀⠑⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠸⠀⠘⠀⠐⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⢈⢩⡙⠘⠒⠁⠀⠀⠆⠈⠀⠀⠁⠁⠢⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠘⣄⠢⡑⠀⠀⢠⠀⠀⠀⠂⠈⠀⠀⡆⠀⠀⠈⢆⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠈⠑⠀⠩⡥⠀⠀⠀⠀⠁⢈⠀⠀⠸⡀⠀⠀⠀⢣⠀⠡⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣁⣨⠀⠀⢄⢡⠀⠀⢕⢄⣇⠀⣁⠀⠄⠑⣇⠠⠀⠀⠀⢀⠂⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡠⢀⠔⠼⠢⠠⠀⠊⠀⢣⠀⠀⠦⢻⢀⢀⠠⠌⠦⠧⢀⠀⠀⠀⠀⠀⡠⠜⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠈⢲⠒⣦⣀⠀⠒⠐⣬⠡⡆⢤⡾⢠⣌⣒⣐⣒⠶⡊⠭⠩⠉⣁⣠⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠑⠒⠒⠳⠤⠤⠜⠋⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⠠⠀⢀⡀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⢂⠀⠁⠀⠀⠐⠀⡰⠂⠀⢀⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠤⢀⡀⡑⢄⠀⠀⠈⠹⠀⠀⠀⠀⡏⠁⠀⠀⢀
⠀⡎⠀⢴⡁⠉⠉⠉⢇⣀⣀⠀⠀⡁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⠁⠈⠀⠈⠀⠀⡀⠉⡀⠀⢀⡀⠁⢠⠀⠀⣠
⠀⠈⠒⠤⠤⣀⡴⠀⠀⠀⠀⠉⠉⠉⠒⠀⠀⠰⠤⠄⠀⠀⠠⡚⠀⠀⠠⢀⠁⡀⠉⠁⢠⠀⠀⠈⠐⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠧⢄⣀⠴⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣿
⠀⣀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⡀⠀⢠⡏
⠀⠐⠈⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠃⣠⠟⠀⠀⠀⠀⠀⠀⠀⢠⠞⡆⢀⢤⡀⠀⢄⠢
⠀⠀⡤⣘⢎⠣⣀⠞⣹⠂⠀⠀⠀⠀⣴⢞⡋⠙⠀⠀⠛⠛⠲⣄⠀⠀⠀⠀⡤⠤⢼⡀⠓⢡⢞⣀⠀⠘⡄
⠀⠀⠑⠬⡙⢁⠝⠒⡅⠀⠀⠀⠀⢸⠃⣿⡀⠀⠀⠀⠀⠀⢳⡌⢧⠀⠀⠀⠃⠉⡆⠙⢆⠈⡥⠜⠁⢀⡇
⠀⠐⠣⢠⠅⠈⠀⠠⡇⠀⠀⠀⠀⣿⠀⡇⠙⠦⢤⣤⡤⠴⠋⡇⠸⡆⠀⠀⠀⢀⡧⢀⣀⠴⠦⠗⠀⠘
⠀⠀⠀⠓⠊⠓⠚⠳⣌⠢⡀⠀⢰⣉⠀⢿⣄⡀⠀⠀⠀⠀⢀⡇⠈⢉⡷⠀⣠⠊⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠢⡀⣿⠀⢸⣿⣿⣷⣶⣶⣿⣿⡇⠀⣿⢀⠜⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡈⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⢋⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠘⣌⠉⠙⠛⡻⠋⠀⠀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠈⢦⡈⠓⠒⠋⣀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⠢⣄⣉⡓⠒⠛⣁⣀⡤⠔⣿
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠘⣠⠊⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠲⢄
⠀⠀⠀⠀⠀⠀⠃⠀⡖⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡉⠢⡈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣠⠋⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠑⣄⠀⠘⢳⣤⣀⣀⡀⠀⠀⣀⣀⣀⣤⣼⠃⢀⡠⠖⠉⠁⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⠓⢤⠎⡼⠀⠉⠉⠉⠉⠉⠉⠁⠈⢦⡓⠋⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣠⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢳⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠈⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠚⠛⠛⠛⠛⠛⠶⣾⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠀⠀⠀⠀⠁⠀⠀⠀⢀⡠⡀⠑⠀⠀⠀⠀⠀⠰⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠔⢈⡐⠄⠅⠀⠀⠀⢀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠐⠀⠀⠀⠀⠀⢀⠰⡉⠙⠂⠈⠗⠁⡠⠄⠀⠀⢲⠶⣤⣑⠀⢂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢨⠀⠀⠀⣀⠤⣰⠁⢄⠄⠑⠄⠗⠚⠉⠀⠀⠀⠀⣸⠀⠀⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠠⠃⠀⠀⡜⠁⢀⢜⠧⢠⢸⠐⢊⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢆⠀⠈⠁⣠⠎⠁⠀⢀⡀⠀⠈⠀⠀⣠⡟
⠀⢠⡴⢒⠒⠶⠶⠴⠋⠁⠀⢢⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋
⠠⡏⠈⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠹⣦⡀⠁⠉⠙⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣠⡴⠞⠋
⠀⠀⢨⡇⠀⠀⠈⠂⡑⠁⠀⠀⠀⣿⠙⠓⠲⠶⠶⠶⠚⠋⠉
⠀⠀⠈⢷⡀⠀⠀⠀⡄⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠉⠛⢶⡄⢇⡘⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠶⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣀⣀⣉⣀⡀⠀⠐⠒⠯⣑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⢟⣛⣭⣭⣭⣝⣓⣀⣀⣀⣐⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣛⡵⡾⢟⠿⠛⠉⠉⠉⠉⠉⠉⠈⠉⠉⠙⣟⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢰⠋⠀⠀⠀⠀⠀⠘⠛⠓⠆⠀⠀⠀⠀⠀⠀⢹⡇⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠐⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠁⠀⠀⠀⠀⠀⢀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⣞⠁⠀⠀⠀⡖⢆⠀⠔⠄⡁⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⡔⠢⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡸⠈⠀⠀⠠⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠰⠋⠉⠀⠀⢀⡠⢦⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢣⡀⠀⢀⡀⠒⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢁⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠉⠀⣸⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢀⢃⠒⠉⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣄⠀⠀⠀⠀⠀⢳⣀⣀⠤⠖⢋⡞⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢀⡠⢢⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠑⠦⣐⣪⠝⠁⠀⠀⠀⠀⣰⠏⠀⠀⡀⠔⣉⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢞⣁⣀⠤⠚⢹⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⠤⢤⡴⡖⠚⠉⡏⣈⣁⠤⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠒⠁⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡄⠀⠠⠤⠒⢁⡀⠑⠦⠞⠁⢡
⠀⠀⠀⠀⠀⠃⠀⠀⠺⠀⠀⠀⣤⣀⣀⣐⣒⣚⣻⣇⣀⣠⠴⠖⢻⠃⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠈⠀⠀⡠⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠠⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⡔⠓⠲⠤⣈⠉⠒⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⠤⢤⡒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢧⣀⣀⠀⠀⠉⠗⠲⠤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⣊⣻⡄⠀⠀⠀⠀⠀⠑⠲⠤⣤⣀⣀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡇⢸⠋⠉⠉⠁⠒⠒⠊
⠀⡀⠤⠀⠀⠀⠀⠀⠀⣤⣉⡤⠊⠁⠀⠙⠒⠛⠉⠉⠉⠉⠐⠤⣀⡀⠈⠉⠙⠛⠛⠩⢤⡄⠀⠀⠀⡸⢁⡏
⠐⡌⢆⠀⠐⠲⢤⣀⠞⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢳⠀⠀⠀⠀⡾⠀⠠⠔⣊⡵⠊
⠀⠈⠢⡙⢄⠀⠀⠈⠑⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣸⠓⠒⠒⠉⠁
⠀⠀⠀⠈⠢⣝⠢⣀⢠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠁⠀⠀⠀⠈⠢⣄⠈⠉⠓⠲⢄⡀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠙⢦⡴⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⣀⣀⠀⠀⠀⠀⠀⡟⠓⠢⠤⣄⣀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⣠⠖⠒⠛⠉⠉⠉⠉⠉⠉⢹⠀⠀⠈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢚⠇⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠉⠒⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠹⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠁⠀⠈⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠞⠢⣉⠒⠲⠤⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⡀⠀⠀⠀⠀⢀⡞⠀⠀⠈⠙⠲⠤⣤⣀⣀⣀⣀⣤⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⡤⠞⠁




⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⢂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠱⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠐⠁⠉⢡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⢀⠁⠀⠄⠐⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢲⠀⠐⠢⠅⢀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡰⢇⠈⠈⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠱⠀⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⡤⠔⠂⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡣⢠⠠⠔⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⢠⠃⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⡠⢁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠒⠒⠢⢤⣀⡰⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠠⡀⠘⣀⣠⠤⠤⠴⠤⠤⠤⣄⡀⠡⠀⠀⠀⠈⠳⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢱⠖⡉⠀⠀⠠⠤⢄⠀⠀⠀⠈⠑⠧⡀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠃⠀⠀⢀⠤⡄⠀⠀⠀⠀⠀⢀⡀⠀⠈⢦⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠓⠄⠀⠱⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⠀⠀⠠⡤⠄⠀⠀⠠⠤⠀⢀⣥⣾⠇⠀⠀⠀⢀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⢻⣶⣶⣶⣶⣶⠿⠿⣿⠟⠀⠀⠀⠀⡌⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠙⢿⣟⠁⠁⣠⡴⠋⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠈⠈⠤⠁⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠜⠉⠑⠒⠒⠒⢲⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⠎
⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⢁⠀⠀⡀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡞
⢳⡀⠀⠀⠐⢄⠀⠀⠈⠰⠁⠈⠲⠀⠑⢄⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠙⣄⠎⠀⠈⠑⢄⣀⢀⠀⠀⠀⡀⠀⠀⠁⠰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠈⠳⣄⠠⡀⠀⠘⠁⠱⠀⠀⠑⠤⢀⡀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀
⠀⠀⠀⠀⠈⠑⠦⣝⠀⠀⢀⡄⠀⠀⠀⠀⠈⠑⠲⠤⢀⡙⠦⣄⡀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠸⡀⢀⠔⠃⠀⠈⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠉⠓⠲⠤⢇⠀⠀⠀⠀⠀⠀⠀⠀⠑⠗⠠⠄⡀⠀⠀⠈⠂⠌⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⢆⠀⠀⠀⠈⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⢀⡗⠀⠀⠄⠤⠐⢀⠜⠀⠀⠀⠳⡀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⡌⠀⠉⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠛⠒⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠄
⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠒⠒⠶⠦⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠀⠀⣴⠖⠰⢠⡆⠀⡆⣠⡾⠃⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⣿⠀⠀⣼⡏⡠⠀⢸⠇⠀⠠⣿⠀⡠⠀⠀⠀⠀⠀⣠⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠈⠁⠀⠀⠹⠃⠀⠀⠉⠁⠀⠀⠀⢀⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠂⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢯⢣⠈⢻⣄⠀⣀⡠⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢁⡀⠀⠣⡑⣄⠹⡏⠀⠀⠀⠀⠀⠀⡴⣺⣛⠻⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠁⠀⠈⠁⠀⠀⠈⠪⡵⠁⠀⠀⠀⠀⠀⠈⠘⢐⡠⡁⠀⢠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣧⡀⠋⠀⠀⡤⠀⠀⠙⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠽⢑⣫⣷⠶⠮⡙⢦
⠀⠀⠀⠀⠀⠀⣀⣀⠨⣧⠈⢗⡄⠀⡀⠀⠀⡶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⡠⡤⡀⡀⡼⡄
⠀⠀⠀⠀⠰⢍⠀⠀⠀⠈⢷⣀⠪⣒⣏⠔⠊⠀⠀⠀⠀⠀⠀⡀⠠⠠⢀⠀⠀⣄⣀⣀⠀⠓⣬⡥⠞⠋⡠
⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⢀⠟⠓⠉⠀⠀⢀⠔⠈⠀⠀⠀⠈⠀⠘⠛⠖⠀⠄⠠⠄⣀⣀⣀⣀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⢈⢀⠔⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢀⣀⡥⣐⣂⠄⠶⢦⡀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢁⠀⠀⠀⠀⠀⣀⠄⠂
⠀⠀⠀⠀⠰⠚⠉⠃⠀⠀⠀⡀⢀⠀⢷⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⡠⠂⠀⠀⢠⠖⠭⣀
⠀⠀⠀⠀⠀⣀⠠⠼⠖⠒⠈⢁⠀⠀⢸⡆⠀⠀⠀⠑⢄⠀⠀⠀⡠⠊⠀⠀⠀⡠⠁⠀⠀⠀⠉⠒⢤
⠀⠀⠀⠀⠀⢁⠀⢀⣡⠠⠤⠘⣆⠀⠩⣦⠀⠀⠀⠀⠀⠁⠲⠊⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⢀⠛
⠀⠀⠀⠀⠀⠈⠯⠀⠠⠖⠉⠓⠁⢀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠂⠌
⠀⠀⠀⠀⠀⢀⣀⠀⠄⠐⠀⠈⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠠⠁⡌
⠀⠀⠀⠀⠀⠀⠈⡀⢀⡀⠄⠄⠄⠂⠈⠂⢻⠀⠀⠀⠀⠀⠀⠀⠀⢠⣅⠀⠀⠀⠀⠀⠠⠁⠌
⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⣀⡰⢁⠊
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡔⢛⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⣀⣀⠠⠄⠒⠁⠀⠀⠀⠀⠆⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⢠⠤⡀⢠⠙⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⡀⣼⡀⠀⣬⠀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢩⠀⣠⠚⣣
⡇⠘⡁⠀⢷⠄⠘⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣈⠷⠁⡰⠉
⠃⡀⠀⠀⠠⠠⣤⣄⣡⠄⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣴⡇⠀⠛⠀⠼⠁⠀⢀
⠀⢡⠀⠀⠀⠀⠀⠈⠁⢠⠄⠼⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠈⠡⠀⢀⣀⣠⡀⣠⡀⠀⠀⠀⠀⠀⠙⠶⣀⠈⠃⠀⠀⠀⠀⠐⠂⡀
⠀⠀⠳⣀⠀⠀⠀⣀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠈⠛⠀⠀⠋⠀⠀⠠⠟⠀⢹⠀⠀⠀⠀⠀⠀⠀⣹⠀⠘⠳⠄⠀⢀⡔⠦⢀
⠀⠀⠀⠈⠛⡦⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠤⣄⡀⠀⠀⠘⢦⡀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⢰⡄⠸⣧⠀⠀⠀⠀⠀⠀⠀⢴⣆⢀⣀⠠⡤⣤⢤⡄⣀⡀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⢀⠌⠁⠀⠖⠋
⠀⠀⠀⠀⠀⠘⡇⠀⢹⡆⠀⠀⠀⠀⠀⣠⡴⠛⠉⠁⠀⠀⠀⠀⠀⠉⠙⠲⣄⠀⠀⠀⠀⠻⣄⠀⠀⠀⣰⠋⠀⢀⡿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⣷⠀⠀⢀⡤⠊⠁⠀⢀⣄⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠙⠀⠀⣴⠁⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠈⣦⠀⣀⣧⣠⠛⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠱⡆⠀⠀⣄⢠⡜⠁⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⢸⠛⠉⠉⢨⡏⠀⠀⠀⠀⠀⠀⠐⠀⠈⠃⠀⠀⣀⡤⠞⣋⠀⠀⠀⢰⠀⠀⣿⡏⠁⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⡘⠁⠀⠀⠀⣤⣄⠤⡤⢤⣤⡤⠚⠛⠉⢀⣴⡿⠀⠀⠀⠘⠓⣤⣿⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⡇⠀⠀⠀⠀⣿⣿⡀⠀⠀⢀⣀⣤⡴⠾⢿⣿⠃⠀⠀⢠⣄⢀⡼⠋⠙⢶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢠⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⢋⣀⣀⣀⣼⠃⠀⠀⠀⢠⡟⠁⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠈⢣⠀⠀⠀⠀⠙⢿⣟⠉⠀⠀⣀⡤⠏⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠷⣀⠀⠀⠀⠀⠀⠈⠛⠁⠁⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠙⠳⢤⣄⣀⣀⣀⣀⣀⣀⣠⣤⡶⠛⠉⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠻⡏⠉⠉⠉⠉⠉⠀⠲⠶⠒⠦⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠈⠉⠉⠉⠓⠒⠶⡶⠶⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠈⠉⠠⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢣⡀⠀⠀⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⢀⣀⣀⣀⣀⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠉⠉⠉⢛⠉⠉⠀⠘⠒⠒⣶⠶⠤⣤⣤⣤⡤⠔⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣿⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠸⠃⠀⠀⠀⠀⠀⠘⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⡆⠀⠀⠀⠀⠀⠀⢀⡦⠀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠉⠉⡷⠀⠀⠀⠀⣀⡤⠋⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⣀⣠⠔⠊⠁⠀⠀⠀⠀⢿⡀⢠⡄⠒⠉⠀⠀⠀⢀⢼⡇
⠀⠐⠋⣀⠀⠁⠙⣀⠀⠀⠀⠀⢀⡼⠶⠊⠙⠂⡀⠀⠀⠀⠀⡰⠃⢠⠃
⠀⠈⠲⠄⣀⣉⣉⣉⣉⣉⠉⣰⠛⠤⢀⡀⠀⠀⢡⡄⢀⣀⠐⠷⢀⡙⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣠⣤⣤⣤⣬⣥⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⡿⠻⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⣀⣀⣀⣀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⣴⣶⣦⡀⠀⠀⠀⠀⢀⣿⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣸⡇⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠟⠀⠀⠀⠀⡀⠀⣿⡕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢈⠀⠀⢀⡀⠀⠀⠀⢰⠁⠀⣿⡆⠀⠀⢠⡴⠦⠀⣠⡴⢦⢸⡟⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠁⠀⠀⢸⡇⠀⠀⣶⠸⡀⠀⣸⡇⠀⠀⣿⠠⠊⢠⣿⠠⠊⢸⡇⠀⠀⠀⡀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⡠⠼⣇⠀⢸⣿⡄⠑⢄⣿⣃⡠⠴⣿⡀⠀⡸⣿⡀⠀⣸⡇⠀⠀⡰⠁⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⣿⡅⠀⠀⠙⠦⠃⢻⣇⠀⣸⠏⠀⠀⠀⠈⠉⠉⠀⠈⠉⠉⠀⠻⡤⠖⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠱⢄⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠴⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


⣶⣶⡶⠶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⣏⣇⣤⠜⠛⠓⢶⡦⡄⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⡧⠖⠿⠽⠗⠒⠉⠘⠲⠇⠀⠀⠀⠉⠛⠂⠿⣾⣁⣀⡴⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⢠⣎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡽⠈⠙⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⠛⠓⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢔⡶⠁⠀⠀⠀⠀⢀⡀⢠⡀⠀⣀⣀⠀⢀⡀⠀⢀⡀⠀⣀⣀⠀⠀⠀⠀⠈⢢⣴⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡶⣤⠟⠉⠀⠀⠀⠀⠀⠀⢸⡇⢸⠁⢰⡏⣿⠀⢸⣧⠀⣼⡇⠀⡏⠀⠀⠀⠀⠀⠀⢠⢿⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠻⢀⡀⠀⠀⠀⠀⠀⠀⢸⡟⢹⠀⢸⡇⣿⠀⢸⡟⣾⢹⡇⠀⡟⠃⠀⠀⠀⠀⠀⠘⠛⠀⢻⡭⠆
⠀⠀⠀⠀⠀⠀⠀⢠⡤⣸⠷⠛⠀⠀⠀⠀⠀⠀⠸⠇⠸⠀⠘⠷⠟⠀⢸⠄⠀⠸⠇⠐⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⠀⠀⠀⠀⠀⠀⠀⠀⡶⣴⡆⠀⡀⢀⠀⠀⣀⢀⢀⡞⠀⡶⣴⡖⠀⠀⠀⠀⠀⠀⠀⠐⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⠄⠀⠀⠀⠀⠀⠀⠀⠘⠞⠀⠠⠟⠃⠏⠘⠁⠋⣾⠀⠀⠘⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢸⠆⢀⡶⣦⠀⢰⡆⠀⢰⡆⠀⡶⠒⠀⠀⠀⠀⠀⠀⣤⢲⡏⠚⠃
⠀⠀⠀⠀⠀⠀⠀⢰⣚⣧⠀⣤⡄⠀⠀⠀⠀⠀⢸⣧⣼⠀⢸⡇⣿⠀⢸⣿⣠⢿⡇⠀⣧⡄⠀⠀⠀⠀⠀⠀⠈⠁⣦⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣙⣷⠃⠀⠀⠀⠀⠀⢸⡇⢸⠀⢸⣇⣿⠀⢸⠇⠛⢸⡇⢀⣇⠀⠀⠀⠀⠀⠀⠀⣀⣴⠛⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠟⠣⡀⠀⠀⠀⠀⠈⠁⠘⠀⠀⠉⠁⠀⠘⠃⠀⠈⠃⠀⠉⠁⠀⠀⠀⠀⢀⠾⠕⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⣤⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣄⡀⣞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⠃⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠞⠉⢉⡿⣶⠠⣤⣀⠀⠀⠀⢰⠦⡄⣀⠠⢴⣖⣶⠴⢺⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠘⠺⠷⢤⣤⡔⠛⢹⣹⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠃⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠓⠠⠤⠚⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⢠⣀⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⣁⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠑⠂⠀⠤⠋
⠀⠀⠀⠀⠀⠀⠐⠤⡔⠓⠁⡮⠐⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢒⠒⠒⠂⡁
⠀⠀⠀⠀⠀⠀⠐⠀⢙⣄⣰⡁⢉⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠡⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢡⠠⠀⠀⠀⠀⠀⣀⢠⡤⢐⡒⠒⡲⣶⠈⠱⠎⢉⡡⡋⢐⡶⡒⠒⣠⡤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢸⠀⠡⠀⠀⡰⡫⡀⢯⡾⡕⠼⡨⣋⢡⢲⠘⡧⡈⠉⢰⢢⠑⡫⡼⠕⡩⣦⠗⣩⡳
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⢡⠀⡷⣱⠃⡨⡄⠠⢲⠈⠪⢟⣉⠰⡟⢻⡪⢂⣁⠯⠚⢱⠲⡙⢺⢄⠱⡸
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠁⠀⠀⠆⢠⣧⠤⡘⠚⡥⡓⠃⡰⡒⠳⡪⡈⡗⢆⡴⡌⣪⠗⡖⡄⣓⠃⣈⡑⡡⢤
⠀⠀⠀⠀⠀⠀⡰⠀⠀⠄⠀⠀⠈⠀⠀⢧⡉⢱⢹⠙⣚⢠⢻⢁⢴⣄⠋⢋⡁⣍⠕⢅⢣⢺⠹⠵⡧⡈⣥⡩⣅
⠀⠀⠀⠀⠀⢠⠁⠀⠌⠀⠀⡰⠁⠀⠀⠂⠩⢹⠘⣼⢽⡇⢸⡼⡍⢸⠀⠀⠑⠋⠀⠸⣪⢗⣶⠳⣑⣋⠀⣞⡾
⠀⠀⠀⠀⠀⠂⠀⠌⠀⠀⡐⠁⠀⠀⠌⠀⠀⢸⡀⠈⠉⠀⢸⠒⢽⣹⠀⠀⠀⠀⠀⠀⠙⠓⠃⠀⡓⠚⣶
⠀⠀⠀⠀⠐⡠⠂⠀⡠⠀⠀⠀⠀⡔⠀⠀⠀⠀⠣⡀⠀⠀⢸⠰⣳⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡿⡏
⠀⠀⠀⢀⠋⢀⠄⠊⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠑⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠘⠁⠀⠀⠀⠀⡠⠔⠁⠀⠀⢀⠠⠊⠀⠀⠘⠦⠤⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠤⡌
⠀⠀⠀⠂⠀⣀⠀⠔⠈⠀⡀⠄⠐⠈⠀⠀⠀⠀⠀⣀⠜⠦⠤⠤⠤⠤⠤⢤⣤⣤⠤⠤⠤⠤⠤⠤⢴⠃
⠀⠀⣸⠁⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⣀⠠⠄⠂⠈⠀⠀⠜⠁⠐⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠉⠁
⡔⠀⠀⠑⠢⠅⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠤⠐⠀⠁⢀⠄⠀⠜
⠈⠐⠒⠢⡀⠀⣀⠀⠀⠀⡀⠀⠀⠀⡄⣀⣀⠔⠂⠐⠁
⣤⣤⣤⣤⣬⣥⣬⣴⣦⣬⣬⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⢠⠣⠀⠀⠴⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠈⠀⠀⠀⠀⠻⠡⠁⠀⠀⠀⠀⠀⠑⠀⣀⠀⠀⢐⠦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠇⠀⠀⠀⠀⣤⢀⠀⠀⠀⠀⠈⠀⠻⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠈⡰⠲⢶⠦⠂⠀⠄⠀⣀⠐⠀⠒⠄⡁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠄⢂⠀⠊⠔⢡⠀⠔⠄⠀⢀⡀⠂⠀⢀⠀⠀⡠⠊⠀⡳⠀⠀⠀⠀⠀⣰⠄⠀⣐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⡀⠀⠀⡀⠀⢀⠉⠃⠠⠄⢀⠄⣴⢤⠀⡐⠠⠵⠀⠐⠀⠀⠂⠁
⠀⠀⠀⠀⠉⠀⠀⠀⢠⠎⠟⠀⠀⠀⢀⠄⡋⠀⠀⠀⠁⠀⠀⡠⠆⠀⠠⠤⠔⠀⠈⠄⠀⠀⠀⠀⠔⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠜⠀⠐⠀⠀⠀⠀⠃⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠐⢀⠀⠓⠀⠀⠀⠀⢀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠌⠀⠀⠀⠃⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⠀⢀⠁⠀⠀⠋⠀⠂⠄⠠⠲⡔⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⠉⡄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠁⠀⠀⠀⢃⠀⠠⠀⠈⢆⠀⠈⠂⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⢀⠢⠀⠰⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠃⠀⢰⠀⠀⢈⠀⢀⠀⠀⠐⠋⠁⠀⠐⡒⡎⠀⠀⠄⠀⢀⣀⡀⠀⠂⠠⠀⠖⠎⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣬⣤⣤⣥⣤⣤⣤⣬⣤⣤⣤⣤⣤⣥⣤⣧⣧⣤⣤⣤⣬⣭⣥⣤⣥⣤⣤⣥⣬⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⠛⣝⢟⣉⡛⣻⢟⣽⡟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿