Hippopotamus Emojis & Symbols

⠀⠀⠀⠀⠀⡀⠀⣠⠀⡀
⠀⠀⠀⠀⠡⠀⠀⠀⠀⠈⡑⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠊⠈⠂⠄⠀⠀⠀⠀⢈⠲⠔⠫⠤⢀⠀⠀⢀⠔⠒⠢
⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠂⠿⢗⠀⡈⢧⠁⣤⡃⢀⣠⣄⠤⠔⠂⠉⠉⠉⠉⠉⠉⠐⠒⠤⢄⣀
⠁⠐⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠾⠀⠀⠱⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀
⠀⠀⠀⠈⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠒⠀⠀⠤⠀⢀⠀⠀⠤⠤⠆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⠆⠂⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠤⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢠⢞⣉⠳⡄⢀⣀⣀⣀⠀⠏⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠘⡜⠌⠣⠛⠁⠀⢀⣀⠉⡠⡊
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⣾⣿⣾⣿⣀⣀⣀
⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣢⡀
⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠀⠀⠘⠛⢹
⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠐⠀⠤⠤⠤⢤⠤⠚⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠒⠒⠊
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠈⠙⡒⠲⠤⠤⠤⠤⠸⡄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⣀⢄⡀⣀⠄⡔⠀⢧⡠⢤⢤⢴⡇⠀⣇⠀⠀⠀⢀⣠⢰⠀⣀⡠⣤⢼⡆
⠀⠀⠀⠀⠀⠀⠙⠒⠧⠾⠖⠁⠀⠀⠙⠛⠛⠉⠀⠀⠹⣎⣙⣉⣧⠜⠈⠳⠤⠥⠴⠞⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠛⠉⠉⠁⠀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⢀⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣥⣀⣴⣃⣀⡀⢘⠧⣤⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⠅⢶⣿⣿⣿⣿⣿⣷⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣴⣿⣿⣧⠡⣼⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⣿⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⠿⠀⠙⢿⣿⣿⡏⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠙⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠸⠈⠻⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣷⣶⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠨⡆⠀⠈⠉⠂⡀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣯⠟⠀⠀⠀⠀⠀⠀⢀⢻⡄⠴⠶⠞⠋⠁⠀⠰⠋⠂
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣇⣐⠀⠀⠀⠦⠀⡀⠀⠺⠿⠗⠀⠀⢀⣀⡐⠦⠤⠄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣶⣄⡅⢸⣾⣷⣦⡀⠀⠀⠀⠀⠤⠉⠁⠰⢀⣴⡖⠁
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⠴⠚⠋⠁
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⣿⣿⠿⠿⠿⠟⠛⠁

⢀⠀⠀⡀⠀⠀⢀⠠⠀⠀⠀⠉⠉⠉⠁⠀⠐⠠⠀⠀⢀⠤⠂⠐⠄
⡇⠀⠤⠬⡐⡔⡁⠠⠄⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⠄⢂⠐
⠈⠢⢈⠐⠠⠀⢀⠔⠀⠢⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⡃⠡⠤⡚⠀⠀⠀⠀⠀⠂⠠⠄⢀
⠀⠀⠀⠀⠉⡀⠀⢠⣿⡇⠀⠀⠀⠀⠁⣿⣯⡄⡀⠀⠇⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀
⠀⠀⠀⠀⠀⠃⠂⠬⠭⠥⡄⠀⠀⠀⡄⠙⠝⠠⠃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⡈⠀⠀⠀⠀⡐⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⡀⠀⢀⠄⠠⠎⠀⠀⠀⠀⠀⠀⠈⢢⠀⡀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠐⠀⠀⢀⠀⠑⠈⠀⠀⠀⠀⠀⠀⠈⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠣⡀
⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠐
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠸
⠀⠀⠀⠐⡤⢀⣀⣀⠠⠠⠄⠀⠀⠀⠠⠠⢄⡀⠀⡀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢠⠀⠀⠀⠐⠤⠔⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠘
⠀⠀⠀⠸⠀⠐⢄⡠⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂
⠀⠀⠀⠀⠡⣀⠈⠑⠀⠃⠠⠀⠀⠀⠀⠃⠐⠉⠀⢀⠔⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠠
⠀⠀⠀⠀⠀⠉⠀⡂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⢀⠁
⠀⠀⠀⠀⠀⠀⡀⠈⠂⠄⠀⢀⣀⣀⡀⠀⠄⠊⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⡄⡤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠀⠀⠀⠀⠀⠀⠀⠴⠒⠀⠨⡄⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠇⢠⠄⠄⢀⠀⡀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀⠸⠀⢸⠀⠀⠁⢀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠢⠀⠠⠠⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢡⠁⠀⠀⠀⢀⠄⠀⢸⠁⠀⠀⡄⠀⠀⠀⢀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣟⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⡴⢶⠛⢩⣿⣯⢛⣶⣆⠀⣀⡀
⠀⠀⢀⣴⣿⣿⣿⣿⡿⠋⠉⠋⠁⠓⠋⠓⡅⠉⠉⠉⠛⠛⠛⠛⠻⣷⢼⣧⠟⡗⣸⠟⡉⣭⣹⣾⣿⣿⡅
⠀⢠⣿⣿⣿⣿⣿⠛⠀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡾⠛⢸⣿⢸⠃⠏⢸⡿⡦⠉⡿⢇⠙⡏
⠀⣾⣿⣿⣿⣿⣿⣶⣿⣟⣟⣻⣿⣀⣤⣾⣷⣷⣗⣴⣴⣄⣾⣿⣿⣧⠀⣿⢿⠀⠀⠀⢁⡟⠀⠁⠹⣄⠩⡀
⠀⠘⢿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠸⣶⡟⣿⣆⢱⣤⣾⡀⢤⣿⣽⣿⣿⣿⡀
⠀⠀⠘⣿⣆⠀⢄⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣮⣿⣿⡿⠳⠿⠿⠿⡿⢿⡿
⠀⠀⢀⡼⣉⣙⣲⣿⣾⣿⣿⡿⠛⠛⠉⠙⠛⠛⠛⠛⠛⡿⢛⡿⢿⣿⣿⣿⠏⢻⡏
⠀⠀⢸⣷⡀⢨⣿⣿⣿⣿⡟⠛⠿⢷⣶⣶⣶⣶⣶⡶⠶⠿⢻⣿⣿⣿⣿⣇⡀⠘⡇
⠀⠀⠘⣿⠓⢿⠙⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⡏⠈⢿⡟⢺⡇
⠀⠀⠀⢹⡄⢾⣆⡀⠹⣿⣿⠷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣚⣧⡀⠈⢯⣢⣙⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠋⠉⠉⠉⠉⠉⠉⠛⠓⠲⠦⠤⣤⣤⣤⣤⣤⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠟⠛⠲⠦⢤⣀
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣠⡴⠾⠙⠒⠦⠤⠤⢤⣤⣀⣀
⠀⠀⠀⠀⢀⡼⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⣿⣏⢢⡀⠀⠈⠙⠲⢴⣾⣿
⠀⠀⠀⢀⡞⠁⠀⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠿⠆⠀⠀⠀⠀⡀⢂⡙⡏
⠀⠀⢀⡞⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠂⠀⠀⠀⠀⡄⠀⠀⠀⠀⠁⡀⠀⠆⠀⢀⢤⡈⠀⠀⠁⡼⣄
⠀⠀⣼⠁⠀⠀⣠⣿⣿⡏⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣦⡄⠀⠀⣼⣿⠀⠀⠀⠀⣾⡇⠀⠀⠀⢠⣾⣿⡀⠀⡸⠟⠀⠃⠀⠀⠀⠀⡸
⠀⢀⡏⠀⠀⣾⣿⣿⣿⡇⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢿⣿⡇⠀⢠⣿⣿⠀⠀⠀⢸⣿⡇⢀⠀⠀⢾⣿⣿⣷⣄⡉⠀⠠⣤⢀⠀⠀⠀⡇
⠀⠸⡇⠀⢸⣿⣿⣿⣿⣷⢸⣿⣿⣿⣷⣦⣀⣀⣀⣀⣤⣴⣾⣿⣿⣿⢸⣿⣷⣤⣼⣿⣿⡀⠀⠀⢸⣿⡇⣾⠀⠀⠘⢿⣿⣿⣯⢷⡀⠀⠈⠈⡀⠀⠀⡅
⠀⠀⢷⡀⣿⣿⣿⡿⣹⣿⣧⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡿⣿⣿⣿⣿⣧⡀⠀⠸⣿⣇⢿⣆⠀⣦⡀⢿⣿⣿⣿⠇⣠⢆⡘⠁⠀⠀⠘⣄
⠀⠀⣸⣿⣿⣿⣿⠿⠛⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣇⠻⣿⣿⣿⣿⣟⣶⣶⣿⣿⣾⣿⣦⣘⣿⣿⢿⡟⡜⠰⣿⢋⡆⠀⢄⠀⠄⢸⣇
⠀⢸⣿⣿⣿⣿⠇⡾⠛⠉⠙⠲⠯⣿⣛⡿⠿⢿⣿⣿⣿⣿⣿⡿⠟⠻⠿⠟⠈⢀⢹⣿⣿⣿⣿⣼⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠉⠃⠁⣀⠀⠀⠀⠠⣼
⠀⠘⣿⣿⣿⡟⣸⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣶⠶⣦⣤⣤⡤⠶⠶⣶⣿⣿⣦⡹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠙⠛⠉⠙⠻⠿⣤⣀⣀⣉⣥⣴⣶⣶⣶⠏
⠀⢀⣿⣿⣿⢰⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⢸⣿⠟⠋⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠈⠛⢛⢳⣄⠀⠀⢠⣿⣿⣿⣿⣏⠀⢻⣿⣿⣿⣿
⠀⠘⠿⣶⣦⡤⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠒⠻⠛⠁⠀⠀⠀⠛⠛⠛⠛⠛⠀⠀⢿⣿⣿⡿⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣴⡶⠞⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⢿⠛⡻⠿⡿⠟⣿⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⢀⣀⣤⣤⣼⣿⣿⣿⣿⣿⣷⣿⣾⣾⣷⣿⣿⣾⣿⣿⣯⣿⣿⣷⣶⣦⣤⡤⠄
⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣠⢴⠖⠛⠛⠉⠛⣽⠤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡲⡀
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠈⠀⠀⠀⣧
⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⣤⣈⣉⣒⣶⣶⣦⡴⠏
⠀⠀⠀⢤⣞⣏⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡌⢣⣔⣷⡾⠟⠉
⠀⠀⠀⠀⠀⠘⡟⠀⠀⢳⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠙⣶⡄⠀⢻⣯⣅⣒⡂⠀⠀⠐⠾⠒⣀⡎⠀⠀⣿⠟⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣯⠀⢸⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⢷⠀⢀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⢈⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠈⢺⣇⣤⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠛⠁

⠀⠄
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠁⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣄⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣃⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠠⠂⠁⠀⢠⠖⢺⢲⣶⡔⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⢀⠀⠀⠰⠖⠀⠀⠀⠀⣎⠀⡀⠀⠸⢂⡄
⠀⠀⠀⠀⠀⠀⢀⡠⠐⠒⠂⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠁⠈⠢⠔⠶⡾⠀⠀⠀⠀⠀⢀⠠⠊⠁⠀⢀⠔⠁
⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡄⠰⠮⡀
⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠘⡆
⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⠃⠈⢲⢢
⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠥⠴⠐⠃⠎
⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⢄⠤⠚⠑⠒⠒⠂⠉
⠀⠟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖
⠀⢇⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⡇
⠀⠈⠳⠉⢣⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠀⡇⠀⠉⠹⠉⠁⠒⠒⠒⠈⠉⠀⠈⠑⢤⠀⠀⠀⠨⠀⠀⢡
⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⡀⢇⠀⠀⡀⣡⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢂⠀⣀⣵⣄
⠀⠀⠀⠀⠀⢡⣠⡂⢱⡂⢫⣪⠢⢅⣙⠌⠦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠣⣠⠚⣎⠙⣴⠬⠦⠗⠃

⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡠⠂⠲⠆⣴⣾⡆
⠀⠀⠀⢸⣢⣤⣒⠢⣿⣦⣾⣄⡀
⠀⠀⠀⠀⠉⠑⠛⢷⣬⡛⠿⣿⠟⢶⣦⣀⢤
⠀⠀⠀⠀⠀⡀⠀⠈⣿⣿⣿⢿⣿⣿⣽⠻⣾⣷⡢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⣄⣀⠤⢄⣀
⠀⠀⠀⠀⣀⢱⠀⠐⠋⠋⡉⢨⣏⡿⢟⣧⣿⣿⣿⣿⣗⢭⣓⣒⣀⣀⣀⣤⣤⣀⣀⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣋⡲⡀
⠀⠀⠀⠸⣄⣀⠀⠐⠒⠀⠓⣹⢏⣶⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢳⣼
⠀⠀⠀⠀⠈⠙⠛⠳⠤⠤⠾⢫⣾⣟⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣜⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡙⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡾⢿⣿⣿⡎⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢻⣿⢿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⢻⣿⣿⢣⠁⠀⠀⠉⠙⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⢀⣾⣿⡸⣿⡟⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢞⣼⣿⣏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠾⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣶⢶⠟⢩⣿⣯⢿⣶⣆⠀⣀⡄
⠀⠀⢀⣴⣿⣿⣿⣿⣿⠛⠙⠟⠻⠳⠛⣿⣿⡛⠛⠛⠻⠛⠻⠟⢿⣷⢼⣯⠟⡇⣸⠟⣙⣭⣽⣿⣿⣿⡅
⠀⢠⣿⣿⣿⣿⣿⠟⠃⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢿⢸⣿⣸⠓⡟⢸⡿⡷⠉⣿⣯⠛⡏
⠀⣾⣿⣿⣿⣿⣿⣶⣿⣿⣿⣻⣿⣄⣶⣾⣷⣿⣿⣽⣴⣶⣾⣿⣿⣷⠀⣿⣿⠸⠀⠀⢱⡟⠀⠋⢻⣆⠹⡀
⠀⠙⢿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣷⣿⣿⣆⢱⣤⣾⡁⢶⣿⣿⣿⣿⣿
⠀⠀⠘⣿⣏⠀⣄⠐⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠷⠿⣿⡿⠿⢿⡿
⠀⠀⢀⣿⣉⣙⣺⣿⣿⣿⣿⣿⠿⠟⠻⢟⠿⠛⠛⠛⠛⣿⢿⡿⣿⣿⣿⣿⡟⢻⡏
⠀⠀⢸⣷⡀⢩⣿⣿⣿⣿⡟⠻⠿⣷⣶⣶⣶⣶⣶⣷⡾⠿⢿⣿⣿⣿⣿⣇⡐⢸⡇
⠀⠀⠘⣿⠓⣿⠙⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠈⢿⡿⢾⡇
⠀⠀⠀⢹⡄⢾⣆⠈⠻⣿⣿⡧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣺⣧⡀⠈⢟⢢⡱⢄
⣀⣀⣀⣀⣙⣛⣉⣁⣀⣈⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣈⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄






⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣾⣿⣿⣿⣿⣿⣿⡿⠋⢻⣿⣿⣿⣿⣿⡿⠿⣿⣿⡌⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⠿⢿⣿⣯⣿⣿⠁
⠀⠻⠿⣿⡿⠋⠀⠀⠀⠀⠀⣻⣿⣿⠀⠀⠀⠀⢸⣿⠋⣿⡏⠀⠻⠿⣿⣿⠟⠁⠀⠀⠀⠀⢻⣿⣿⠇⠀⠀⠀⢸⣿⠏⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⡿⡿⠄⠀⠀⠐⠛⠛⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⣿⣿⡆⠀⠀⠐⠚⠛⠃⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠀⠁⢄⡉⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣄⡀⠘⠉⠀⡈⠓⢄⡀
⠀⠀⢀⠈⠀⠀⢀⠞⢩⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⣶⣦⡀⠀⠀⠀⣤⡔⢨⣭⣿⡀⢤⠀⠙⣀⢚⠁⢑⣤⠏
⠀⠀⠂⡤⠂⣰⡏⡀⠈⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⢟⡿⣿⡄⠀⣠⡟⢨⠟⠘⠉⠁⠀⠀⣴⣿⠙⠦⠜⠁
⠀⣸⡐⣧⢈⣾⡇⠀⠀⠀⠄⠀⠀⠀⠈⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠⡀⡄⠄⣿⣿⣶⣄⣤⠈⠁⢹⣿⠀⠫⡇⣽⣤⡆⢀⣼⣿⣸⣿⡇⠀⠘⣶⣶⡾⠆
⠀⣿⠁⣶⣌⣿⡀⠐⠀⠀⡄⡀⡄⣰⠀⢀⠀⢠⠀⡀⠀⡀⢠⡄⣸⣿⣷⣸⣌⣿⣿⣿⣾⡆⠀⢸⡏⠀⠀⣾⣿⢿⣧⣴⡛⠻⠛⠋⢻⠀⠀⠸⣿⣄
⠀⣿⣧⡿⣾⣿⣗⢦⣤⣳⣠⢱⢡⢃⢠⢸⠀⣾⣀⣽⢰⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⡇⠀⠀⢿⡧⡕⣟⡿⣿⠀⠀⡧⠈⠠⠀⠀⢱⡈
⠀⣿⣿⡿⣿⣿⣷⣦⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣷⣿⣼⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣿⡇⠀⠀⠀⣁⣉⣿⣿⠟⡏⠸⡇⠠⠀⠀⢀⠀⣇⠀⢀
⠀⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⢿⣟⣷⡀⣿⣿⣤⣏⣠⣿⣼⣿⡇⡸⠀⠀⠁⠀⠈⠃⠀⢱⣧⠀⠀⠐⢄
⠀⠀⠀⢻⣿⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡣⡌⣡⣿⣼⣧⣻⡿⢿⣿⣿⣿⣿⣿⣦⡇⢀⡶⢀⠀⠀⣄⢦⢹⡿⠒⠣⣾⣿⡆
⠀⠀⠀⠸⣿⣿⣾⣿⣿⣌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⢿⣧⣾⣩⣦⣿⣿⣯⠻⣿⣿⣿⣿⣿⣿⡟⠛⢹⡎⡆⢸⣧⢉⣀⣸⢿⣷⣾⣿⣼⡇⣽⢻⡇
⠀⠀⠀⠀⠈⣿⣿⣿⣿⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⡟⣹⠟⡿⠀⠀⠈⠻⢿⣌⣿⣿⣿⣿⣿⣾⣿⣿⣿⣥⣿⣸⡇
⠀⠀⠀⠀⠀⣞⢿⣿⣿⡃⠀⢸⣿⣿⣿⣿⣿⡿⠿⠿⢿⡿⠿⠿⠛⠋⠉⠉⢻⣿⣿⡙⣿⠃⠹⣿⢿⡇⡴⠇⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠻⢿⣿⣿⡇⠀⠀⠙⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠹⠆⢠⣻⡯⠇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⣠⣼⢾⣿⢿⣦⣄⠀⠀⠀⠹⣿⣿⣿⣿⡶⣦⡄⠀⠀⣆⢠⡄⠀⠀⠀⣿⣟⣂⣀⣤⣽⣿⣯⠑⢄⡀
⠀⠀⠀⠀⠈⠉⠉⠉⠃⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠈⠀⠀⠀⠉⠛⠀⠀⠀⠀⢸⣿⣾⡿⣧⣁⢮⣿⣟⣶⠿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠀⠀⠺⠹⠟⠗⠺⠻⠟⠁⠀⠀⠀⠤⠤⠶⠶⠴⠶⠶⠶⠤⠔⠶⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠟⠛⠛⠷⣦⣀⠀⠀⠀⢀⣀⣤⣶⠶⠾⠛⠛⠛⠛⠛⠳⠶⢶⣤⣄⣀⠀⠀⠀⢀⣤⡶⠟⠛⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⣀⣀⣀⠀⠈⠹⣧⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣴⡿⠉⠀⣀⣀⣀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⣴⠟⠋⠉⠛⢷⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⡾⠋⠉⠙⠻⣦⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡏⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⢹⡇⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡀⢸⣇⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⣸⡇⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠻⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠟⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⢀⣴⠟⠋⠉⠉⠉⠉⠛⢷⣄⠀⠀⠀⢀⣴⠟⠋⠉⠉⠉⠉⠙⠿⣦⡀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⢹⡇⢸⡇⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀
⠀⠀⠀⠀⠀⠀⣴⣿⡇⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⣼⠇⢸⣇⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⠻⣦
⠀⠀⠀⠀⢠⡾⠃⣾⠇⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠉⠋⠁⢀⣼⠟⠀⠀⢻⣦⡀⠈⠉⠉⠀⠀⠀⢀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠙⢷⡄
⠀⠀⠀⢠⡿⠁⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣶⣤⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠙⠻⣶⣤⣤⣤⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⠈⢿⣄
⠀⠀⢰⡿⢡⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠈⢿⡄
⠀⢠⡿⢡⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠈⢿⡄
⠀⣼⠃⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠘⣧
⢰⡟⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢿
⣸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸
⣿⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⣿⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⣿⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟
⢿⡆⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⢰
⢸⣇⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠡⠀⠀⠀⠀⣾
⠀⣿⡀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠶⠟⠋⠁⠀⣿⠀⠀⠀⠀⠀⡀⢀⣠⣾⠟⠃⠀⠀⠀⠀⠀⢰⣿
⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⢀⣿⡄⠀⢀⣀⣤⣾⠿⠋⠁⠈⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣾⣟⣥⣶⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠹⣧⡀⣠⣴⠶⠾⠛⠿⠶⠶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠶⠟⠛⠿⠿⣶⣤⣀⣾⠏
⠀⠀⠀⠀⠀⣸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣇
⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⢸⡇⠀⠀⣠⣤⣤⣤⡀⠀⣀⣀⣀⡀⠀⣠⣤⣶⣶⣤⡀⠀⣿⣇⣀⡀⡀⢀⣀⣀⣸⣇⠀⠀⢀⣤⣤⣤⣄⠀⢀⣀⣀⡀⠀⢀⣤⣴⣦⣤⡀⠀⣸⡇
⠀⠀⠀⠘⣿⣀⣾⠋⠀⠀⠈⣻⡿⠛⠉⠙⠻⣾⠋⠀⠀⠀⠙⣿⣤⣿⠛⠛⠛⠛⠛⠛⠛⠛⣿⡀⣴⠟⠁⠀⠈⢙⣿⠟⠉⠉⠛⢷⡟⠁⠀⠀⠈⣿⣦⣿⠃
⠀⠀⠀⠀⠘⠿⣿⣄⡀⠀⠀⣿⡀⠀⠀⠀⠀⣽⡇⠀⢀⣀⣤⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣷⠀⣀⣀⣤⣿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢀⣀⠀⠀⢀⣀⣶⡌⡁⠌⠠⠀⣠
⠀⠀⠀⠀⠀⠀⠀⣠⢂⣾⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠘⠿⣷⠠⡟⡜⠉⢉⡀⣼⠛⢆⣁⡀
⠀⠀⠀⠀⠀⠀⢰⣯⣿⣿⠀⢀⠀⢀⡄⡀⢠⠄⣠⢄⣸⣶⣼⣿⣿⣷⠀⣽⠀⣱⣿⣧⣾⠿⠛⡄⠘⣿⡁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣳⣾⣶⣿⣾⣽⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠀⣿⠀⠙⢛⣿⣿⡴⡇⡀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧⣿⣾⣴⣿⣿⡑⢀⠀⠈⠀⣼⣄⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣯⣿⣿⣿⣿⣿⣿⠟⢻⡇⣾⣲⣴⣿⣾⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠉⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⢻⣿⣟⡍⠀⠈⠛⢿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡇⠀⠙⢿⣿⣷⣀⡀⠀⠀⠀⠀⠹⣿⡛⠀⣿⡽⠃⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠙⠁⠀⠀⠉⠋⠉⠉⢀⣐⠊⠀⠀⣻⣿⣯⣩⣿⠤⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠉⠉⠁⠀⠀⠘⠉⠉⠉⠃⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠚⠛⠉⠉⠉⠙⠓⠒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⡨⣅⡠⠤⠤⢤⠀⠀⠀⠀⠀⢠⡤⠤⠤⣀⡭⣠⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢏⣟⢟⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⢘⢝⣏⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣺⡔⡅⡆⠀⠀⣠⠀⠀⠀⠀⠀⢠⡀⠀⢀⡆⠕⣽⡊⢷
⠀⠀⠀⠀⠀⠀⠀⢠⠏⡀⡟⠁⠄⠏⠀⡸⠃⠀⠀⠀⠀⠀⠀⠹⡀⠈⠇⠄⠙⡇⡈⢧
⠀⠀⠀⠀⠀⠀⠀⣿⡶⢡⡿⠅⠀⠀⠚⠀⡐⠀⠀⠀⠀⠀⠐⡀⠘⠂⠀⠀⠽⣧⠱⣾⡇
⠀⠀⠀⠀⠀⠀⢘⡿⠁⠹⠃⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠻⠁⠹⣟
⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⡀⡄⠀⠀⢺⠃⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⡄⡄⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠎⣼⣀⠀⠐⠚⠊⠁⠀⠀⠀⠀⠁⠚⠒⠂⢀⣸⡎⢀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⣇⡀⠀⢁⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠁⠀⣀⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣄⣼⡗⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⣿⣄⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢻⣿⠛⡆⠀⠀⠀⢿⡆⠀⠀⠐⢄⠖⠀⠀⠀⣾⠇⠀⠀⠀⡞⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣄⣠⣄⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣠⣀⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⡿⠟⠛⢛⡛⠛⠛⠛⠛⣛⠛⠛⠿⣿⣿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠄⠐⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠃⠀⠁⠀⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⣸⣦⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠀⢀⠀⠀⠀⠘⣦⣀⢀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠛⣷⣤⡀⠀⢸⠀⣠⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⡞⠀⠀⣇⠀⢸⠉⠹⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠠⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⢀

⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⢸⣿⣿⣟⣉⣁⣀⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠉⠀⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠐⠒⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣻⣭⣽⣿⣿⣿⣿⠿⣿⣿⣿⣿⣷⣶⣤⣤⣀⣀⠀⣀⣀⣀⣀⣤⣤
⠀⠀⠀⠀⢠⣤⣴⣿⣿⣿⣿⣿⣷⣶⣾⣿⣶⣶⣶⣾⣯⣭⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣥⣬⣥⣤⣬⣭⣄⣤⣌⣉⡛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⢷⣶⣯⣭⣉⣛⠻⢿⠿⡿⠿⡿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⡳⢦⣍⣛⡻⠿⣷⣷⣶⣶⣦⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠘⠛⠛⣿⣿⣷⣯⣽⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢻⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣇⠀⠉⠉⠉⠉⣿⣿⣿⠻⣿⣿⣿⠀⠀⠀⠀⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠈⠻⣿⣿⣦⡀⠀⠀⠀⢻⣿⣿⡀⢻⣿⣿⡀⠀⠀⠀⠀⠀⢈⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠣⠤⠬⠍⠉⠉⠛⠉⠀⠈⠉⠉⠛⠛⠿⢿⣿⣶⣶⣶⣤⣾⣿⣿⣿⡄
⠀⢠⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⢸
⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠤⣤⣀⠀⠀⣴⣯⣷⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣯⡻⣄⡀⠀⣠⠞⠋⣡⠋⠁⠀⠀⠤⠈⡻⢾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣄⣩⡿⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠿⠋⠀⠀⠀⣠⠖⠂⠀⠀⢄⠀⢰⣿⣿⣿⡿⣿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⢀⠎⠀⠀⡇⠀⣠⣴⣮⣿⣷⡇⠹⣿⣿⣷⢹⣎⢻⡻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣴⠔⠁⠀⠀⠀⢸⣾⣿⢿⡿⠟⠀⠀⠀⠈⣿⠿⡇⢻⡄⢷⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠁⠀⠀⠀⠀⠀⠘⠻⣿⣤⣠⡴⠀⠀⠀⠀⠘⡆⢹⠸⣷⠸⣇⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⠳⣄⠀⠀⠀⠀⠀⢸⡌⣿⣿⡆⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⡔⠉⠋⠀⠎⠀⠀⠀⠁⠀⠀⠀⣀⠀⠈⠲⣅⠀⠀⠀⠀⠀⠀⣸⡇⣿⣿⡇⣿⣿⡿
⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠈⠑⠀⠀⠈⠃⠀⠀⠀⣠⣴⣿⣇⣿⣿⢧⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡏⡿⠀⠀⠀⠀⠀⠸⠟⠋⠀⠀⣴⣶⣦⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣼⣿⣟⣾⣿⡟
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣀⣽⣷⡀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠘⣧⣴⣾⣿⣿⣿⣿⣿⣶⣦⣴⡾⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣶⠿⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣽⡿⣿⣿⣿⢿⣿⣿⣿⡿⡿⣿⢷⡶⣷⣶⡶⢶⢶⣦⣀⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣾⣿⣿⣧⣿⣇⣿⣮⣿⣾⣿⣽⣷⣷⣿⣯⣧⣧⣽⣿⣿⣿⣴⣶⣤⣤⣤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⣷⠞⠟⡶⢚⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠲⠶⠶⠶⣶⠶⠶⣶⠏⠙⠉⠀⠀⠀⠀⠀⠀⠘⠊⠉⠛⠒⠒⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⠍⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠄⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢷⣄⣀⠀⣀⡀⠀⢀⣸⡇
⠀⠀⠀⠀⠀⠀⢰⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢧⠀⠀⠀⠀⠀⢨⣷⣤⣠⣤⠶⠭⠭⣯⠿⠿⠟⠋
⠀⠀⠀⠀⢤⣤⠞⣵⠉⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⠳⣄⠼⣿⣟⣮⠴⠋
⠀⠀⠀⠀⠀⠉⠛⠙⣧⢿⠀⠀⠐⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠘⢿⣦⣰⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡠⠀⠀⢀⣆⣰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⡄⠀⠈⣷⣦⣅⣘⡓⠃⠤⠀⢀⣀⡘⡛⠎⠁⢀⣞⠁⠀⠀⢸⣿⠟⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡃⠀⠀⣏⠀⠀⠉⠉⠙⠛⠓⠒⠒⠒⠚⠛⠋⠉⣿⠀⠀⠀⣸⡿⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠀⠠⡟⣷⡀⠀⠧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⠀⡈⢳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠄⠀⠘⢿⣆⣴⣼⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⠷⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠀⠘⣓⣲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣠⠶⠛⠉⠉⠉⠛⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⢀⡾⠁⢀⠤⣠⢿⠶⢄⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⣞⣁⡴⡟⠋⣻⣶⣧⡩⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⠉⣛⠛⢀⠀⣼⣟⢉⡟⢣⢾⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠴⣶⡷⠙⠀⠉⡷⢎⣾⣿⣯⠿⡣⢟⠜
⠀⠀⠀⠀⠁⣲⠦⣴⠖⠻⣦⡋⢸⡇⠉⠀⠈⠉⠁⠀⢳⢸⣿⣿⣾⡆⣡⡀⠀⠀⢸⢢
⠀⠀⠀⠀⠊⢠⠞⠁⠀⠀⠹⠡⠋⠉⠀⠀⠀⠀⠀⠀⠘⣏⠻⡞⠛⢷⡘⢿⢦⠀⠀⢟⢧
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢻⢰⣿⠘⡖⠁⠀⠲⠑⢄⣼⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⠀⠀⠀⠀⠀⠘⠴⡘⡜⣿⣻⡇⢻⡀⢶⡆⠒⠷⠧⡾⠳⣄
⠀⠀⠀⠀⠀⢠⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠱⡜⢮⡻⠧⢼⡧⠐⠂⠉⠉⠉⠀⣠⡾
⠀⠀⠀⠀⠀⠸⡄⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⢝⢦⣙⠲⠬⣅⣀⣀⣠⢴⡾⠿⠋
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⠀⠀⠀⠀⠀⠀⠐⠺⠤⠀⠀⠠⢙⡛⠛⢳⣶⣶⡿⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠀⠀⠀⠀⢀⣀⡀⠀⣀⣀⣠⣶⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡤⡤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡮⠡⡉⠻⣇⠀⡀⣹⡗⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠈⡈⠁⠀⠀⠀⢨⠀⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣨⠇⠀⢴⣴⣃⣾⣸⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠙⠻⣿⣮⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠁⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢰⡇⠈⠉⠉⠑⠒⠒⠒⠒⠚⢉⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣢⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢿⡋⡠

⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣾⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠾⠻⢿⣿⣿⠀⠀⠀⠀⠀⣀⡴⠊⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⢠⣴⠉⣸⣿⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⡄⠀⠀⠈⠁⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⢴⡶⠀⢀⣤⣤⠄⠐⣈⡁⠜⠿⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠂⠀⠀⢀⣴⣴⠎⡀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⣾⡛⣱⡇⣼⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠼⠿⢿⣷⣆⠀⣰⣿⡟⢁⡘⠻⣆⠀⠀⠀⠀⠀⠿⠉⠈⠉⠁⠈⠀⠙⢇⢿⠀⠀⢀⠐⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⢻⠛⡘⣾⣿⣿⢷⡠⣦⡤⠀⠀⠀⠀⠔⠁⠀⠈⠀⠀⠀⠀⠀⠀⢀⡸⢳⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡟⠁⣿⠀⠈⣿⡯⠭⠞⢧⣉⣴⣄⢀⡴⣤⣴⠊⡀⢀⣀⡤⠤⠀⠀⠀⢈⠡⠊⣷⡍
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣿⡟⠀⢸⣿⡄⠀⠈⠉⠁⠀⠀⠈⣿⣿⣿⡿⣻⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠉⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⢸⣿⢱⣿⣸⣿⣿⡀⡀⠀⠀⠀⠀⠀⣿⢸⡿⣳⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡔
⠀⠀⠀⠀⠀⠀⢰⠃⣿⠀⣼⠏⠸⠏⢹⣿⣿⣿⣿⠛⠶⣦⠀⢀⡿⢠⢑⣿⣿⠏⡀
⠀⠀⠀⠀⠀⢀⡿⢸⡟⢰⣿⡆⠀⠀⠈⠹⢿⣿⣿⣷⣦⠀⠀⢸⠇⢘⣿⡯⠋⠈⠱⠂⠀⠀⠀⠀⠀⠀⠀⣤⡦⠀⠀⠀⠠⠤⠄
⠀⠀⠀⠀⠀⢸⠁⢺⣧⣿⡟⠀⠀⠀⠀⠀⠈⠻⠹⣿⣿⡄⢀⣼⠀⣼⣯⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡤⠀⠀⢀⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢸⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⣿⣿⡟⢰⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠀⠀⠀⢀⣿⣇
⠀⠀⠀⠀⠀⢸⡄⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⣿⣿⣿⣿⠀⠀⢻⣿⣿⣦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠛
⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⠇⠀⠀⠀⠐⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⡿⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⢨⣧⠀⡿⣿⣧⠀⠀⠀⢸⣄⠀⠀⠀⢰⣿⣿⡿⣿⠀⠀⠀⠀⠀⣠⡽⢻⡇
⠀⠀⠀⠀⠀⠀⣿⠀⢻⣸⣿⣽⣆⠀⠀⢹⣦⣰⣿⣿⣿⡿⣷⣿⠆⣤⠀⣠⢞⠋⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠸⣧⠸⣧⣿⢻⣿⠲⢠⣈⣿⣿⣿⣿⡟⣹⢿⣍⢻⣾⣿⣿⠄⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠙⣧⢹⣯⣧⠘⢷⡜⠹⣿⣿⣿⣿⢰⣿⣿⢹⡌⣿⠻⣯⣛⠳⣆⠀⠀⠀⠀⠀⠀⠂⠀⢀⣸⣷⣀⣀⠠⠀⡀⠀⠂⠀⡃⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡻⣿⣷⡄⠹⣦⣈⠿⣿⡇⣿⢽⣿⣦⡝⢺⡙⠺⣌⢷⡌⠧⢤⠰⣄⣄⣄⣙⣬⣋⣿⣿⣿⣯⣭⣤⡤⢀⣤⢂⡁⢊⡴⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣯⣒⡿⢷⣾⣟⡟⢺⣟⣿⣟⣷⡛⠸⣦⣼⣿⣶⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣧⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣾⣿⣷⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣀⣀⢐⣁⣤⣴⣶⣴⣤⣦⣴⣶⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠛⠓⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣏⠛⢛⣯⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠉

⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⠶⣶⠶⢶⣶⠶⠶⡶⠶⣶⠶⠶⠶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⡤⠶⠶⢦⣤⣤⠴⠶⠶⣤⣄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢭⡳⣄⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⣠⢞⡭⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠛⣆⠀⢀⣠⠞⠁⠈⠳⣄⠀⠀⣰⠛⠉⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⣸⠁⢠⢖⡂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢐⡲⡄⠈⣆⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⡇⡆⠸⡘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢃⠇⢸⢸⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠃⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠘⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠈⣇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠱⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢴⣫⣛⠄⠀⠀⠀⠀⠠⣛⣝⣢⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠸⠁⠸⠆⠀⠀⠀⠀⠰⠃⠈⠇⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠶⠶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠉⠉⠁⠀⠀⣀⡀⠀⠀⠈⠉⠉⠉⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠟⠛⠛⠛⠛⠓⠲⠶⠖⠚⠋⠁


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

⠀⠀⠀⠀⠀⠀⢀⢔⣉⠒⢒⣢⡀
⠀⠀⠀⠀⢠⠚⡁⠈⠙⢀⣿⠿⢳⡀
⠀⠀⠀⠀⢺⡩⠭⣭⣝⠲⣿⣷⣿⣦⣄⡄
⠀⠀⠀⠀⠀⠉⠙⠓⠻⣷⣌⠻⠿⣿⡿⠷⢶⣦⡄⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⣶⣶⡿⣶⣯⣻⡿⣷⣿⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢱⣀⠀⣨⠿⡿⠛⠇⢹⠹⣿⣿⢦⢹⢿⣿⣷⣝⢦⣒⠤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠠⢄⣒⣠⣤⣽⣶⣶⣶⣶⣶⣭⣽⡶⢄⡀
⠀⠀⠀⠀⣠⠚⡈⠇⢐⠀⢈⠀⡵⣠⣼⣼⢛⣻⡾⣼⣼⣻⣿⣿⣷⣭⣻⣶⣦⣤⣴⣶⣶⣾⣿⣶⣶⣶⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣦⡱⡄
⠀⠀⠀⠀⠹⣤⣄⣀⡀⠋⠍⠀⠑⣡⡿⣡⣿⣿⣳⡏⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣧⡷
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⠤⠤⠾⢟⣵⣿⢟⣵⣟⢾⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣵⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⡿⡿⣽⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠻⣿⣿⣿⡇⢹⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⢻⣿⡿⣿⣿⣿⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢑⢻⣿⣿⡇⡍⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⢀⣾⣿⢇⣿⣿⡿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣯⠆⣿⣿⡿⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡿⠿⣫⣾⣿⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠛⠡⡾⢿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠛⠛⠛⢿⣦⠀⠀⠀⠀⣰⡾⠟⠛⠛⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⠚⠉⠙⡆⢻⣷⣈⣀⣀⣿⠁⡔⠋⠳⡄⢸⣷⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣬⡳⠤⠒⠁⠀⠛⠛⠛⠛⠛⠀⢧⣀⣠⠟⣸⡇⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠋⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⣿⡀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⢸⡇⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠢⡀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣈⠉⠛⠛⠿⠶⠶⢶⣤⣤⣤⣤⣴⠶⠞⠋⢁⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠦⠤⠤⠤⢤⣤⣤⠤⠴⠶⠞⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣋⣍⡓⠲⠆⠴⠖⠛⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⠤⠤⣄⡀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⣴⠿⡯⠖⠺⢿⣿⣷⣤⣈⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣠⣾⢁⡔⠺⣿⣿⣦⡌⠙⠋⢹⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣦⣤⣀⡀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠔⠁⣴⣿⣿⡇⠀⠰⢄⡿⠟⠁⠴⠶⢾⣇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣹
⠀⠀⠀⠀⠀⠀⣰⠋⢠⠋⠀⢨⣾⣿⣿⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣀⠀⠀⣀⣴⣾⣿⣿⣿⣿⡿⣟⡯⠽⠖⠒⠒⠖⠒⠶⠶⠖⠁
⠀⠀⠀⠀⠀⢰⠃⢠⢂⠄⠀⣾⣿⣿⣿⠀⠈⠂⠀⠀⠀⢀⡀⠤⡴⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⠞⠁
⠀⠀⠀⠀⠀⡏⢠⢃⡎⠀⢰⣿⣿⠉⣿⡀⠈⠂⠀⠀⠀⠀⠨⡭⢿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⠃⢹
⠀⠀⠀⠀⢀⡇⣾⣾⣶⣿⣿⠁⠹⡇⠀⢧⠀⠀⠀⠀⠀⠀⣀⣤⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇⠀⠈⡆
⠀⠀⠀⠀⡼⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢣⡁⠀⠀⠰⠋⡼⢱⡏⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣄
⠀⠀⠀⢸⠷⣿⣿⣿⣿⣿⠿⣷⡀⠀⠀⠀⠀⠑⠄⠀⠀⠘⠀⡾⢇⠀⠀⠀⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠈⠢⡀⠀⢠⠀⢢
⠀⠀⠀⠀⠊⠁⠻⣿⣿⠏⠀⠈⢳⣄⡀⠀⡄⠀⠀⠀⠀⢀⢰⠇⢸⠀⠀⠀⠄⠙⢿⣯⠻⣿⣿⣌⣄⠀⢠⠀⠙⣦⣸⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠙⢻⢠⠖⣉⠉⠙⢻⣿⣷⣰⣆⢀⠀⢸⠈⠀⢸⡆⠀⠀⠀⠀⠀⢸⠀⠹⡀⠉⠉⠳⢤⣑⣄⣠⢏⡇⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣈⡄⠀⠀⠀⢹⣿⣿⣿⣦⣷⣼⣇⠀⠸⡇⠀⠀⠀⠀⠀⡈⡇⠀⠇⠀⠀⠀⠀⠀⠀⠻⣜⣀⡼⡯⡓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣦⡀⢧⢀⠀⠀⠀⢰⡿⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡀⠀⡀⠀⠀⣦⡴⠛⢿⠿⣿⣿⣿⣿⣿⣌⢣⡀⠀⠠⣌⣳⣤⢚⠄⠀⠀⠀⣀⣀⣀⣀⡀⠀⠤⢐⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠰⡟⠲⡧⠤⣷⡌⠉⡟⠉⠁⠂⠀⠀⠉⠛⠻⢿⣿⣧⣍⠓⠦⠤⠬⠭⠥⢖⣒⣋⣉⣭⣤⣴⣶⣶⣿⣿⣿⡿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠎⠈⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠶⠟⠛⠛⠛⠛⠛⠛⠶⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡭⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠩⢽⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⣶⣾⣿⠟⠓⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠐⠫⣿⣿⣶⣶⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⠀⢮⣑⣀⠠⠤⠤⣤⡤⠄⠀⠀⠀⠀⠀⠀⠤⣠⣤⠤⠤⢀⣐⣩⠆⢰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢳⠼⠯⡀⠀⠀⠀⠀⠉⠒⠄⠀⠀⠀⠀⠤⠚⠁⠀⠀⠀⠀⡨⠿⢴⠛⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢠⠃⢈⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣖⣢⠠⡀⢡⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⠁⡰⢠⣖⡇⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⡄⣿⡛⠀⡇⣸⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢸⡀⡇⠘⣫⡇⡄⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⣰⠀⣷⣀⡊⠀⠁⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢦⡀⠀⠁⠈⣀⣴⡇⢰⡀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣷⠃⣰⡿⠷⠀⠀⠀⠀⠁⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠁⠀⠀⠀⠠⠿⣷⡄⢳⣧⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⠞⢿⠉⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠈⢻⠙⠆⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⡰⣰⠃⠀⠀⠀⢺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠂⠀⠀⠀⢳⡰⡀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⢠⠞⣰⡏⢀⠀⠀⠲⠾⠓⠈⠀⠀⠀⠀⠀⠀⠈⠉⠐⠻⠶⠂⠀⢀⠈⣷⡘⢦⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠁⣠⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢧⡀⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣀⡀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⢀⣟⡗⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⣟⣇⢠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⢿⠁⠀⠀⠀⠀⢩⣴⡄⠀⠀⠀⠐⢦⠀⣠⠆⠀⠀⠀⠀⣴⣬⠁⠀⠀⠀⠀⢹⠿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠈⡇⠀⠀⠀⠀⢨⣛⠅⠀⠀⠀⠀⠀⣷⠃⠀⠀⠀⠀⠀⢝⡃⠀⠀⠀⠀⠀⠋⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣦⡀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⡀⢀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⣠⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢻⣿⣿⣉⣡⣄⣀⣤⣤⣄⣀⣀⣀⣀⣠⣤⣄⣀⣤⣉⣹⣿⣿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠀⠘⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠁⣀⣭⣽⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⣠⠞⢁⠀⣠⣀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⣰⢃⣠⡓⢹⣥⣆⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠊⣒⠛⡀⢰⣟⢋⠟⡤⡾⠋⠉
⠀⠀⠀⢀⠀⠀⠀⢀⡒⡲⣿⠊⠁⢈⣗⠢⢿⢿⣾⡞⣥⠁
⠀⠀⠀⡀⠜⡻⠋⠉⢳⠅⠾⠀⠀⠀⠀⠀⠈⣞⣿⣿⣿⡰⣦⠀⠀⢫⣆
⠀⠀⠀⠀⠘⠁⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⢠⢹⠈⣇⢮⠓⠈⢑⢄⢘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠌⣾⢿⠘⡆⢠⡤⠴⠽⣹⠦⡄
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⠪⡛⠣⣿⠐⠊⠁⠀⢁⣠⡞
⠀⠀⠀⠀⠈⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠨⣷⣬⣓⡲⠤⣤⣶⡾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⣩⣭⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠉⡊⢳⡀⠈⢱⠆⠐⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⠈⠀⠀⠀⡀⠈⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠜⠀⠘⠾⣷⣷⣃⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠂⠒⠂⠀⠠⠤⠤⠚⣿⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣢⡾⠀⠀⠀⠀⠀⠀⠀⠠⠼⢿⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠈⡉⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⣶⣆⠈⡄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠰⠂⠘⠛⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠘⣿⠿⠀⠓⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣨⣄⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣡⣤⡁⢠⠀⠀⠀⠀⠠⠀⠠⠄⠀⠀⠐⠒⠀⠂⠺⡿⠟⠀⠂⠐⠆⠀⡀
⠀⠀⠀⠀⠀⣀⠦⠤⠀⠒⠃⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡎
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠁⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠒⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⣶⣶⣶⡤⠀⠀⠀⠀⠒⠒⠒⠶⠿⠿⠏⠉⠉⠁
⠀⠀⠀⠀⠀⠰⠆⠀⣤⡤⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⡤⠊⠢⡈⡀⠄⢄⠈⠛⣁⡀⠙⠋⢀⢀⠐⠶⢗⣀⠀⢶⠖⢀⢄⠀⢶⡶⢀⡄⡘⠇
⠀⠀⠀⠀⢀⡠⢄⠀⠀⠀⣀⡀⠑⠊⠀⠈⠦⠒⠁⠀⠁⠒⠁⠀⠉⠢⠒⠁⠀⠈⠢⠔⠁⠀⠈⠲⠆
⠀⠀⠀⠀⠘⠀⠀⠑⠤⠊⠀⠈⠢⠐⠊⠑⠤⠤⠊⠒⢄⡠⠊⠙⠦⡀⠀⡠⠚⠑⠄⡀⢀⡴⠢⢄⡀
⠀⠀⠀⠀⠃⠴⠿⠀⠀⠀⠿⠆⠀⠀⠰⠷⠄⠀⠘⠃⠀⠀⠴⠷⠀⠙⠊⠀⠴⠿⠆⠀⠉⠠⠶⠀⢁
⣀⣀⣀⣘⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠛⠶⣤⣠⡴⠶⠛⠛⠛⠛⠛⠳⠶⣤⣠⡴⠞⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢀⡵⢟⣡⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣝⡳⣍⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟⠐⢉⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⡉⠙⢷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢠⠞⢉⠤⢭⡳⡀⠀⠀⠀⠀⡰⣫⠥⢌⠙⢦⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣏⠀⣿⣦⢾⡗⡇⠀⠀⠀⠀⡷⣿⢦⣾⡇⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⠦⣈⣙⣫⠜⠁⠀⠀⠀⠀⠙⢬⣛⣉⡠⠞⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣠⠴⠦⢤⣀⣤⣤⡤⠤⢤⣤⣤⣀⣠⠤⠦⢤⡀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣸⢡⠊⠈⢢⠙⠀⠀⠀⠀⠀⠀⠀⠘⢡⠊⠈⢢⢹⡀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠞⠻⠄⠓⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠁⠼⠙⢾⣇⠀⠀⠀⠀⠀⢀⣤⠶⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⢠⡟⠁⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠰⢦⣤⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⠴⠀⠀⠀⢀⣿⠀⣠⡟⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠈⢧⣄⣠⠟⠉⠉⠉⠉⠉⠙⢧⣀⣤⠏⠀⠀⠀⢀⣼⣣⡾⠋⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣀⣽⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠈⠛⠶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⣼⠋⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⣠⡾⠋
⠀⣼⠃⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡴⠟⠉
⢰⡏⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⣾⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⢿⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠘⢷⣤⣀⣤⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠁⠀⠀⢻⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠁
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠉⠙⠓⠲⢶⡶⠶⠶⣶⠶⠖⠛⠉⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣤⡾⠁⠀⠀⠻⣤⣤⣤⠶⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠛⢶⡄⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡆⠀⠸⣦⠹⣦⡀⠀⣠⣶⣿⣯⠍⠀⠀⠀⠀⠀⠀⢩⣽⣿⣶⣄⠀⢀⣴⠟⣼⠇⠀⢰⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠃⠀⣾⡟⣰⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⠛⠛⠻⠿⣆⢻⣷⠀⠈⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣩⡼⠃⠀⠀⠤⠶⢾⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣜⡷⠶⠤⠀⠀⠘⢧⣍⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⣀⠀⠀⠀⠀⠀⠑⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠊⠀⠀⠀⠀⠀⣀⠈⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⣛⣷⣄⠀⠀⠀⠀⢀⡀⢀⠄⠀⠀⠀⠀⠠⣀⢀⡀⠀⠀⠀⠀⣠⣾⣿⠄⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢠⠈⠣⠭⣿⣿⣷⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣾⣿⣿⡭⠜⠁⡄⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢻⣄⠀⢠⡉⢉⣵⡆⠀⠀⣰⡆⠀⠀⢰⣆⠀⠀⢰⣮⡉⢉⡄⠀⣠⡟⠁⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠉⠀⠀⣿⠸⠋⠀⠀⢠⡿⡁⠀⠀⠈⢿⡄⠀⠀⠙⠇⣿⠀⠀⠉⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠰⠯⠞⠁⠀⠀⠈⠳⠝⠆⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣃⣼⠀⠀⠀⠀⢻⣳⣷⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⣾⣾⡟⠀⠀⠀⠀⣧⡐⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠂⠀⠀⣀⣿⣿⣿⡇⣾⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⣷⢸⣿⣿⣿⣀⠀⠀⠐⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⣿⣿⢿⣿⣿⠏⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠹⣿⣿⡿⣿⣿⠀⠀⠀⢹⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠘⠛⣁⣼⠿⠛⠂⠀⠀⠠⣤⣄⠀⠀⠀⠀⣠⣤⠤⠀⠀⠐⠚⠿⣧⡈⠛⠃⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢀⠄⠀⠀⣼⠋⠀⣼⣇⠀⠀⠀⢲⣄⠙⣧⡀⢀⣼⠏⣠⡖⠀⠀⠀⣸⣧⠀⠙⢧⠀⠀⠠⡀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⣤⠀⣸⣇⡄⠀⠘⣿⣦⡀⠙⠾⣿⡄⠹⣷⣾⠏⢠⣿⠷⠋⢀⣴⣿⠃⠀⢠⣸⣇⠀⣤⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⣼⠃⣸⣿⣿⡇⠀⠀⠘⢿⡀⠀⠀⠈⠁⠀⠹⠏⠀⠈⠁⠀⠀⢀⡿⠃⠀⠀⢸⣿⣿⣧⠘⣧⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⡏⠀⣿⣧⡈⠣⢀⢀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⡠⡀⠜⢉⣼⣿⠀⢹⡎⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⠀⠀⣿⣮⡑⠄⠈⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠙⠁⠠⢚⣵⣿⠀⠀⠇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣿⣦⡉⠂⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣿⣿⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠐⢉⣴⣿⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⣆⠘⠻⣿⣝⣒⢶⣶⣾⣿⣿⡿⠟⠋⠭⠤⠤⠭⠙⠻⢿⣿⣿⣷⣶⣶⣒⣻⣿⠟⠃⣰⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⣆⣌⢿⣿⣿⣿⣿⣿⣯⣥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⣬⣽⣿⣿⣿⣿⣿⡿⣡⣰⣧⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡙⢿⣿⣟⡻⠿⣟⣋⠉⠁⠀⠀⠀⠀⠈⠁⢉⣻⡿⢟⣿⣿⡿⢋⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣬⣙⠿⢷⣦⣭⣭⣉⣀⣀⣀⣀⣉⣭⣭⣴⡾⠿⣛⣥⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣶⣮⣭⣝⣛⣛⣛⣛⣛⣛⣩⣭⣵⣶⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠉⠉⠉⠒⠤⢀⠀⠁⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⢀⡠⠔⠒⠒⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⡜⠀⠀⠀⠀⠀⠀⢸⠀⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣺⠤⠀⠴⠀⠀⠀⠀⠘⠃⣤⠀⠀⠙⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠑⢦⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⢀⡀⠀⢀⣠⣄⣀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠁⠉⠉⠀⠁⠀⠀⣄⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢈⠄⢀⠀⢠⠂⢁⠀⡀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢂⡀⣷⠃⢠⡀⠻⢾⡇⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠲⡄⢸⡆⠤⣄
⠀⠀⠀⠀⠁⠘⠀⠁⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⣿⡄⣧⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠾⡀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡰⠁⣼⠋⡆⢹⠀⠀⠀⢳⠄⡀
⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⡼⢃⡼⠃⢸⠀⠀⠀⠈⡆⠐⡄
⠈⠁⠀⠼⠀⠀⠀⠀⠀⠀⠁⠀⢣⡰⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠛⠓⠉⠀⢀⡿⠀⠀⠀⠀⢃⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⡀⠙⢦⣄⡀⠀⠀⠀⠰⢶⣶⣦⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢛⡀⠀⠀⠀⠀⢸⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠈⠢⠀⣈⠙⠻⢶⡶⣤⣤⣤⣤⣤⣤⣤⣤⡶⠶⠾⠛⠉⢀⡟⠀⠀⠀⠀⠀⢸⠀⠀⠀⢡
⠀⠓⠤⣀⢀⣀⠠⠤⡌⠀⠀⠀⠀⡠⠋⠀⠀⣰⠏⠀⡀⣀⣈⣣⡀⠀⣠⠂⠀⠀⠀⡀⠀⠏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈
⠀⠀⠀⠀⠁⠀⠀⠀⠑⢄⠀⠀⡰⠁⠀⢀⡼⠃⠀⠀⠉⠀⠀⠈⠑⡴⠃⠀⠀⠀⠈⠁⠸⡦⣀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⠁⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⡠⠊⠀⠈⠉⠙⠒⠒⠶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠳⣤⡆⠀⡀⠄⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⡄⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⣀⣀⡀⣀⣀⣀⣀⣀⣸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠉⠉⠉⠀⠀⠀⠈⠀⣬⣀⣀⣠⡄⠠⠤⠤⠤⠶⠶⠒⠒⠒⠒⠶⠶⠶⣶⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠈⠉⠛⠶⢦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⠴⠶⠛⠉⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠉⠉⠉⢹⡏⠉⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣈⠘⡤⠂⠄⠀⠄⠐⠄⢱⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠠⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠾⠶⠶⠒⠛⠉⠀⠀⠀⠀⠀⠀⠘⠧⣄⣸⣇⣀⣥⣤⠤⠖⠋
⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⡀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⣅⠀⡡⠀⠒⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⣀⠹⠀⠐⣳⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢘⡧⣦⡤⣬⠇⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⣁⠔⣋⣛⣙⠿⠁⠓⠦⣤⣜⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠀⠉⣩⠛⡇⠀⡿⡛⠆⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢡⠦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣏⠀⠄⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⡀⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⢀⡤⠂⠐⠒⠋⠉⠉⠉⠀⠀⠉⠉⠙⠳⠖⠒⠨⢦⡌⣒⣂⡒⠶⠒⠻⠤⠤⣄⠀⠀⢀⣔⣹⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⣼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠈⢷⣅⡿⡋⠀⡄⠐⢀⣶⡄⠉⠈⣁⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠉⠉⠀⠀⠀⠀⠘⠛⠁⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣡⣀
⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠴⠊⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⣕⡳⣮⡙⠳⣤
⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡔⣿⡻⢋⠅⣷⠁⡀⠈
⠀⠀⠀⠀⠙⠆⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣽⣶⣶⣶⣿⡿⣷⠐⠠⣴⣦⢤⣤⣶⣶⣶⣶⡾⠿⠻⢧⣥⡬⠿⠀⠈⠉⠐⠁⢀
⠀⠀⢀⣠⣤⠂⣼⣥⣿⣿⣿⣿⣿⣿⣿⣿⣶⡦⣤⣤⣤⡄⠀⡠⢤⣴⣾⣽⣿⣿⣿⣯⣽⣟⣛⣻⣬⣡⣽⠥⠤⠿⠿⠿⠿⠋⠐⠚⠋⣀⡭⠤⣒⠭⠐⢊⣠⠖⠉
⠀⠀⠋⠀⠁⠊⠉⠩⠉⠙⠫⠛⢿⡟⠛⠿⣿⣿⡿⢛⣭⠀⠀⣼⡿⠿⠟⠻⠯⢭⣝⣛⣫⣽⡛⠛⢭⣉⣉⠛⠓⠀⠀⠒⠛⠋⠁⢈⣀⣀⣀⣠⠤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⢈⠀⠙⠛⠀⠀⠀⠡⢖⣠⠆⠰⡇⠉⡰⠏⠡⠨⣭⠋⠛⠛⠉⠿⠶⠶⣤⡤⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⠐⠘⠛⠁⠀⠀⠊⠀⠀⠔⠋⠒⠠⣆⠘⠉⠈⠁⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄








⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠃
⠀⣿⣿⣿⣿⣿⡿⠛⠛⠛⠁⠘⢿⣿⣿⡿⠛⠛⠛⠋⠹⣿⣿⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⠟⠿⠛⠁⠈⢿⣿⣿⣿⠟⠛⠛⠛⠻⣿⣿⣿⣿⣿
⠀⠙⠛⠻⠿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢀⣿⡏⢘⣿⡇⠀⠙⠛⠻⠿⠛⠁⠀⠀⠀⠀⠀⢨⣿⣿⣿⠀⠀⠀⠀⢀⣿⡏⢈⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠻⠿⠿⠀⠀⠀⠀⠉⠉⠁⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠿⠆⠀⠀⠀⠉⠉⠁⠘⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠟⠓⠂⠀⣠⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⣤⢿⡇⠀⠀⠀⣴⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⡿⠛⢋⢵⣃⠖⠀⢀⣸⡿⠟⠻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣏⡥⡝⠛⣃⠈⣉⣡⣤⣶⣿⣿⠿⡄⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠁⠀⠈⠰⠆⡉⢁⡹⣽⣿⣿⡳⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⣿⣛⣿⣿⣇⠀⣀⡀⡥⠀⡨⠄⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣻⣿⣿⠃⠀⠰⠟⠂⠠⣀⠉⠁⢹⣿⣿⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣿⣿⣿⣿⢿⣿⡿⠇⠀⢠⡄⠀⠶⠄⠀⠀⠀⢿⣿⣷⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⣷⠾⠋⠉⠁⢤⡌⠻⠽⠀⠀⣾⠙⢀⡀⡀⠀⠠⣀⣘⣿⣿⣷⣌⣢⡀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⢃⡄⠀⣠⣶⣦⣄⣿⠀⠀⠀⠀⠀⠟⠭⢻⡇⠀⠂⠲⠀⠘⡟⡗⠛⠲⣿⣶⡎⡎
⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠃⠀⠀⠀⠉⢿⣧⡙⢿⣧⠀⠀⠀⠀⢀⣐⣿⣄⠀⠀⠳⣴⠀⢱⢡⢿⠀⠉⢙⣚⠁
⠀⠀⠀⣠⣴⣿⡟⠛⠉⣠⡀⢠⠀⠀⠀⡀⠙⢿⣌⢻⣧⣀⠀⠰⢹⣿⣿⣿⣦⣄⠀⠙⣦⠈⠻⣼⠐⠶⠯⢁⡴⠃
⠀⠀⠁⢙⠻⠿⢿⣿⣿⣟⣷⣖⣀⣤⡀⠀⢠⣾⣿⣿⣿⣿⣷⣤⣦⣿⣍⣩⣿⣿⣷⠦⣿⣿⣤⣈⣑⣤⠔⠋
⠀⠀⠀⠀⠈⠁⠒⠀⠈⠉⠉⠉⠛⠛⠛⠛⠋⠉⠉⠙⠛⠩⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠒⠒⠒⠒⠶⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⣩⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣞⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠙⢶⡀⠀⠀⠛⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠙⢀⠄⠂⠀⠀⠀⠀⠀⠀⠈⠢⠀⣧⠀⠀⠀⠀⣀⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠈⠀⠀⡀⠀⠈⠻⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⠉⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠈⠑⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣻⡑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠙⠦⢄⣀⣀⣀⠀⠀⠈⠙⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠐⠃⠀⠀⠀⠀⠀⠀⢀⡀⣠⣀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⣀⡀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠁⠹⣷⠤⣀⣀⣀⣀⠤⢀⡁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠈⠁



⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠉⠉⢉⣉⣽⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⣠⠾⠛⠉⠉⠉⠉⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⢀⡾⠁⠀⣤⡐⣼⡷⠦⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡟⠁⣀⡝⠗⠺⣇⣼⠁⢚⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⢴⢾⠇⠀⢀⣾⡷⠛⣧⡏⢠⣾⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡻⣏⠀⠶⣄⠰⢂⣾⣿⡇⣴⠃⣼⢳⠇
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣼⠉⣍⠳⣿⠁⡁⠀⢠⣯⣉⠾⢻⡟⣟⣿⣽⢡⡇⢣⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡤⠟⣻⠟⠉⠙⣷⣭⢠⣿⡀⠀⠀⠀⠀⠀⠀⠈⣷⢿⣿⢿⣿⣧⢰⣷⡀⠀⠀⠸⣱⡄
⠀⠀⠀⠀⠀⠀⠉⢀⡜⠁⠀⠀⠀⢸⢁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎⠳⡟⢏⠻⣇⠙⠞⢆⠀⠀⢱⠹⡀
⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣇⢱⣿⠈⡗⠈⠀⠐⡦⠑⢆⣸⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠠⠸⡆⢧⠹⣾⢿⡇⢹⡃⠢⣶⠤⠶⠶⠷⣸⠗⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⠣⡛⢿⣷⣨⣿⡀⠯⠑⠒⠓⠈⠁⠀⣠⡗
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢘⢦⡉⠲⣤⡐⠋⠀⠀⠀⠀⣀⣤⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢄⣀⠈⠇⠀⣀⠳⣽⣳⣦⣍⣙⣓⢺⣷⣻⡽⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠑⡒⠤⣭⣭⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠤⠂⠀⠢⠤⠤⠶⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⣤⣀⣤⣀⣀⣠⣄⣀⣠⡤⣀⣀⣀⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⡿⢻⠿⠛⠟⡿⠏⠻⠻⠙⠟⠛⠻⠛⠟⠹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⣄⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⢀⣤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⣮⣻⣿⣷⡀⣠⣾⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣦⡀⣠⡿⣿⡩⡆⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣜⣊⠿⠎⢙⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣟⠉⠾⢏⣘⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣣⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣻⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠡⠐⠲⢶⣤⡐⣄⠀⢀⣀⣾⣧⣀⠀⢀⡔⣠⣴⠶⠒⠂⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⣤⣴⣒⠀⠀⢻⣿⣿⣶⣿⣿⣿⣿⣾⣷⣿⣿⣿⠃⠀⢀⣲⣤⡄⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢿⡆⢯⣾⣿⡄⢸⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⠀⣼⣿⣮⠇⣾⠟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢳⢢⣿⣿⠗⣸⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡐⢿⣿⣧⢲⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠄⠳⣭⣿⣦⠉⠀⢻⣿⡷⣌⢿⣿⣿⢏⣴⣿⣿⠃⠈⢡⣾⣏⡵⠃⡄⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠁⠀⢸⣄⠈⢹⠏⠀⠀⠀⢻⡇⢹⣼⣿⣿⣼⠁⣿⠃⠀⠀⠈⢿⠉⠀⣼⠀⠀⠁⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣄⠻⣦⣿⠀⠀⠀⠀⠈⠀⢸⣿⣿⣿⣿⠀⠉⠀⠀⠀⠀⢸⣧⡾⢃⡄⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠘⣷⣿⣿⠀⠀⠀⠀⢰⢆⣼⣿⣿⣿⣿⣄⢶⠀⠀⠀⠀⢸⣿⣧⡟⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣿⣿⡆⢠⠀⠀⣿⣿⣿⣴⠏⠀⢠⠾⠿⣿⣿⣿⣿⣿⡿⠿⢦⠀⠈⢷⣼⣿⣿⡇⠀⢠⠀⣾⣿⣧
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⢸⣷⣀⣿⠟⢋⡥⣶⣿⠋⠀⠀⠈⢿⣿⣿⠏⠀⠀⠈⢻⣷⡦⣍⠛⢿⣇⣰⣿⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⠏⠀⠀⣼⢡⠏⣡⣄⠀⣀⠀⣸⣿⣿⡀⢀⡀⢀⣤⡉⢧⢹⡆⠀⠈⢿⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀⠀⣼⣿⣌⠧⢳⣿⡄⠈⢻⣿⣿⣿⣿⠏⠀⣼⡿⠣⢏⣼⣿⡄⠀⠘⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⠀⣰⣿⣿⣿⣷⣦⣤⡖⠋⠀⢿⣿⣿⠿⠈⠳⣦⣤⣶⣿⣿⣿⣧⡀⠀⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢀⣿⣿⣿⣿⣿⠛⠷⠖⠀⠀⠀⠀⠀⠀⠀⠐⠶⠟⢛⣿⣿⣿⣿⣇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠈⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⡟⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡘⢿⣿⡿⠿⠿⠿⠛⠛⠛⣉⣉⣉⡙⠛⠛⠻⠿⠿⠿⣿⣿⠟⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣶⣶⣶⡺⣛⢉⠁⠀⠀⢉⢙⡻⣲⣶⣶⣾⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠓⠒⠒⠛⠛⠛⠛⠛⠛⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⡠⠪⣤⠉⣭⣷⡀
⠀⠀⠀⠀⡮⠤⠤⢄⣸⣿⣉⣃
⠀⠀⠀⠀⠳⠭⢽⣷⣍⠻⣿⣿⣿⣶⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣮⣭⣿⣥⣼⢿⣷⣎⣇⡀
⠀⠀⠀⠀⠀⢰⠀⠀⣰⣿⡿⠿⠹⡾⣿⣿⣅⢻⣿⣷⣕⢤⡤⢀⡀⠀⠀⠀⠀⠀⢀⣀⣀⢀⠠⢄⣀⣰⣤⣤⣬⣥⣴⣒⣤⢄
⠀⠀⠀⢀⡔⣆⠇⢀⠁⢈⠀⢄⣸⣧⠟⣻⣼⣾⣿⣿⣿⣷⣝⣷⣮⣭⣭⣭⣴⣶⣶⣶⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢦⡱⡄
⠀⠀⠀⠈⢧⣤⣀⡀⠋⠍⠀⢊⣾⢏⣾⣿⣻⢃⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣷⡷
⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⠶⠛⢵⣿⣿⣽⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢛⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣭⣿⣿⣿⣮⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⠸⣿⣿⣿⠸⠀⠉⠙⠻⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉⠀⠀⣼⣿⢏⣿⣿⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣏⢆⣿⣿⠇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⡿⣢⣿⣿⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠩⡾⣿⡿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠤⠠⠤⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠶⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣰⠏⠙⠀⠀⠀⠀⠀⠀⢀⡤⠴⠶⣄⠀⠀⠈⠳⠄⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠳⠄⢀⡀⠀⠀⠀⠀⠐⠁⠀⠠⡄⠘⣇⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠠⠖⠁⠀⠀⠀⠀⠀⠀⣠⣤⠀⠈⠀⠻⠀⠀⠀⠀⠐⢾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠻⠿⠀⠀⠀⠀⠀⠀⠢⢄⠀⠀⠙⠧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⠲⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠟⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣏⡑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⣀⠀⢀⡀⠀⠀⠙⢦⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠹⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠙⣷⢄⡀⠀⠀⠀⠀⣀⠠⠊⠡⠊⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠶⠶⠶⠖⠒⠚⠉⠁⠀⠀⠀⠈⠑⠪⠭⠭⠭⠭⠑⠊⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠠⣤⡄⠠⠄⠰⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣾⡇⠸⢿⣷⣽⠦⡀⠀⠲⣶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢀⡀⠠⣄⠀⠀⠀⠀⢀⣤⣶⣵⣾⣿⣿⣦⡄⣥⣠⠓⡚⣚⢠⡇⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊⠀⠘⣠⡄⢄⠀⢻⢿⣶⠞⡁⣾⣿⣿⢿⣿⣿⣧⠗⠀⢷⡄⠀⡐⠀⠠⠃⢀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠐⠤⡀⠀⢀⡴⠊⣿⠡⣴⡟⠛⠉⠃⠀⠻⠏⠀⣯⣽⣿⣿⣿⣿⣿⡿⣴⠈⣥⠈⢖⣂⣨⣬⣬⣥⣏⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⣆⠙⡎⠻⠆⡌⢹⣧⠀⠉⠀⡴⠇⠐⠀⠀⣄⡼⣿⣿⣿⣿⣿⣿⡟⠲⠄⣠⣾⣿⣿⣿⣿⣿⠛⠿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣌⣛⠀⠀⠁⠈⣷⠉⠀⠀⠀⠀⠀⠀⠀⠀⢋⣿⣿⣿⣧⣿⣿⣿⣿⡶⠻⡛⡿⠟⠛⠛⠛⠛⢂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠙⣿⡿⠁⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⢹⣿⣿⣿⣿⣿⣿⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡾⠳⠀⠀⠀⠀⠀⠀⡟⢰⠐⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢨⣿⣿⣿⣿⣿⣿⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⠀⠇⠀⠀⠀⠀⠀⠀⠀⢃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⢹⠇⣾⠒⠀⠀⠀⠀⠂⠀⠀⠘⢈⡜⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣟⠃
⠀⠀⠀⠀⠀⠀⠀⢀⢀⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⡖⢂⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⡖⡇
⠀⠀⠀⠀⠠⠀⠀⠈⣸⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⡇⢈⡀⠈⠦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠙⣿⣿⣿⣗⢰⡀
⠀⠀⠀⠀⠀⠆⠠⠀⠏⠀⠘⠀⢠⠀⠡⠀⠀⠀⢰⣅⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣶⡃
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⢄⠺⡶⡆⠐⠀⢀⣿⣿⡆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠈⡤⠐⠁⠈⡛⡉⠉⠛⠛⢦⠀⠀⠀⢀⡄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠈⣷⠳⣿⢿⣤⣌⣿⣿⣏⣶⡆⠑⠀⠀⢶⢌⣓⠀⠀⣌⡓⡀⢤⣻⡆⢀⡀⠑⢬⣄⣀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⠀⠘⣷⣎⢳⢿⠷⣿⣿⣿⣿⣿⣦⣴⠦⣘⣷⣯⣿⣭⣶⣽⢶⣯⣺⣟⢉⡁⠀⠀⠀⠉⠙⠦⢄⡐⠀⢠⠀⡀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡱⠘⢏⢎⢆⣳⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣔⠇⣰⡆⢰⣶⣞⣀⡰⠻⣟⢳⣦⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢁⠘⢿⣧⣥⢶⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣀⣦⣙⠻⠿⣻⣦⣼⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠈⠷⠀⢿⣯⣟⣿⣮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠢⠌⣻⣦⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣿⣾⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠁⠀⠀⠀⠈⠉⠛⠛⠛⠿⠿⠿⠶⠶⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⢙⠨⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣁⣻⣿⣿⣿⣿⣿⣿⣿⣻⣾⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⣻⣿⣿⣿⠿⣻⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢷⣻⣟⠣⠔⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠴⠶⠶⠶⠶⠶⠶⣶⣟⣋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⣀⣀⠤⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠚⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⡀⠀⠀⠀⠀⠀⢀⠹⡆⠠⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢱⢹⣿⡇
⠀⠀⢀⣀⣀⣤⠏⠀⠀⢀⣌⠉⠒⠀⠈⣆⠘⡄⣿⠀⢳⠀⠀⠈⠣⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢘⢸⣿⡇
⠀⠀⠘⢧⣈⠁⠀⠀⣀⠉⠙⠂⠀⠈⢢⢸⡀⠇⢹⡇⢸⡄⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⢠⣏⠳⠀⠀⠾⠁⣤⠀⡀⠀⠀⠀⢻⡇⠀⣿⡇⠘⡇⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠈⣧⠀⢀⡄⠀⠀⣠⠞⠁⠀⠀⠀⢨⡇⣰⣿⣇⡆⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣼⠋
⠀⠀⠀⣼⠀⠘⠃⠀⢀⡏⠀⠀⠀⠀⢀⣼⣷⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣶⣤⣬⣽⣒⣲⣶⣶⣶⣶⣶⣶⣶⣮⣤⣴⣶⣿⡆⠀⠀⣾⡇
⠀⢠⡶⠋⠀⠀⠀⠀⠀⠃⢀⠀⢀⣴⣿⣿⣿⣿⣿⡟⠘⢧⡀⠀⠀⠀⣼⡏⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠛⠛⢻⡿⣿⣿⣿⡇⠀⢀⣿⡇
⠀⢸⠀⢶⠀⠀⠀⡾⠀⠀⠀⣷⡟⢋⡿⠛⢿⣿⣿⠁⠀⠀⠙⡆⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⢈⣿⣿⠇⠀⣼⣿⠁
⠀⢸⡀⠀⠀⠀⠀⠀⠀⢀⣾⢯⠴⠋⠀⠀⣼⡿⠃⠀⢀⣤⠴⠃⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠛⠉⠀⣀⣾⣿⡋⡀⢰⣿⡟
⠀⠈⠻⠶⠞⠛⠛⠿⠿⠟⠋⠘⠻⠾⠶⠞⠛⠀⠀⠀⠘⠾⠶⠷⠶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠙⠛⠋⠉⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⣠⣴⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇
⣶⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿
⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣦⡀⠀⠀⣿
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢸
⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠟
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠟⠛⠉
⣿⣿⠄
⣿⡟
⡿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣝⢦⣀⣠⣤⠴⠶⠶⠶⢤⣄⣀⣀⣠⢯⣮⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢿⣿⣶⣤⡤⠄⠀⠀⠀⠙⢦⡀⠀⠠⣾⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣢⠤⠤⢄⡀⠀⠙⠢⣀⠙⠛⠿⢭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⢻⣿⣿⣿⣶⣶⣀⠀⠱⠀⠂⠀⠘⢷⣦⣀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⣰⡟⣸⠃⣾⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠙⢝⢿⡇
⠀⠀⠀⠀⠀⢀⡞⣹⡇⣿⢸⣿⣧⢿⣿⣥⡴⢛⠿⠿⠆⠀⠀⢑⣄⡀⠈⢣⡻⣄
⠀⠀⠀⠀⠀⣾⢰⣿⢀⣿⢸⣿⣿⣿⣿⠏⣴⠇⣀⠀⠀⠀⢠⡋⢠⡌⠂⠀⠘⠆⢉⡒⣄
⠀⠀⠀⠀⠀⡇⢿⣿⡄⣿⢸⣿⣿⣿⠇⢰⡏⠀⣿⡧⢀⣞⣭⣄⡀⠀⠀⠀⠀⠀⠈⠁⠈⣓⡆
⠀⠀⠀⠀⠀⢳⢸⣿⣇⢿⣇⢿⣿⣿⠇⣾⣿⣄⣾⣀⣼⡞⡟⢿⡿⠀⠀⠀⠀⠀⠀⠀⠸⣿⢻
⠀⠀⠀⠀⠈⡌⠂⢻⣿⡜⣿⣯⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣎⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⢸
⠀⠀⠀⠀⠀⠘⢆⠀⠹⣿⣎⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣤⣤⡶⠶⠿⠿⠿⠷⢶⣤⣄⣿
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠻⢿⣾⣿⣿⣿⣿⣿⣿⣯⣍⣩⣭⣵⣶⣾⣿⣿⣿⣿⣿⣷⣾⡽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⣿⡿⠿⠿⠛⠛⠿⣭⣉⣀⣀⣠⡼⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⣀⡀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢀⠀⠁⠉⢳⡤⠀⠀⠁⠀⡐⠄⠀⠀⠀⡀⠀⠀⠀⠀⠁⠈⠁⠥⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⢈⡄⠀⠙⠢⠀⡀⠀⠈⠢⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣂⠄⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠄⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠘⠇⠠⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠢⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⣠⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⡀⠀⠀⠀⠁⠀⠀⠀⡀⢎⡀⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⢬⣿⠀⠤⣆⣠⣄⣀⠐⡁⠊⡀
⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠈⠉⠉⠀⠚⠒⠁⠀⠷⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣄⡀⠤⠄⠚⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠉⠉⠉⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣶⣤⡀⡀
⠀⠀⠀⠀⠀⠀⠸⣿⣩⡄⠠⠄⠀⠀⠀⠠⠄⢠⣏⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢠⢣⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡼⡄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢠⠃⢈⠀⠀⡀⠁⠀⠀⠀⠈⢀⠐⠈⡃⠸⡄⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣾⠃⠏⠀⠀⢀⡄⠀⠀⠀⢠⡀⠀⠀⠹⠘⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⠇⠀⠀⡀⠀⢘⡃⠀⠀⠀⢈⡇⠀⢀⠀⠀⠸⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⢸⡄⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⢠⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⢻⣶⡏⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⠀⢻⣶⡟⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠁⠀⠀⠉⠀⠀⠈⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⢿⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡿⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⢶⠶⠶⠶⠶⠶⠾⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⢿⣿⠿⠿⠿⢿⣿⠿⠟⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⢙⣋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠱⡤⠖⠋⠉⠉⠉⠉⠓⠦⣄⢀⡶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢄⣀⡀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⣾⣿⡷⠀⠀⠀⢠⣷⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠈⠛⠃⠀⣀⠂⠺⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠲⣆⡃⠀⠋⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⢻⣷⣄⣤⡴⢤⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⠟⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠳⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⢠⠞⠳⣄⠀⠀⠀⠀⢒⡒⠀⠀⠀⠀⣠⠞⠳⡄
⠀⠀⠀⠘⢦⡇⠋⠀⢔⠳⣶⣿⣿⣶⠟⡂⠀⠙⢾⡴⠃
⠀⠀⠀⠀⢀⡜⣗⠀⠀⠁⠈⣿⣿⡁⠈⠀⠀⣹⢣⡀
⠀⠀⠀⢠⠏⢱⠈⠀⠀⢰⡟⠙⠋⢻⡄⠀⠈⠁⡎⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣄⠀⠀⠀⠀⠀⠤⢤⣠⠤⠀⠀⠀⠀⠀⣀⣴⣄
⠀⠀⢀⡟⠰⣿⡄⠐⢒⡋⠀⣀⡀⠀⠙⡒⠀⢠⣷⠄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⢀⡌⣷⠄⢀⣤⣀⣀⣴⣶⣄⣀⣤⣀⠠⢴⡋⡄⢘⡇
⠀⠀⣾⠁⠀⠙⠀⢰⣧⣭⣙⠲⠖⣋⣥⣼⠆⠈⠋⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢏⣅⠀⠀⢮⠙⢿⣿⣿⣿⠟⢩⠂⠀⢀⣘⠟⠛
⠀⣸⣏⠀⣷⠀⠀⢠⡉⠉⢻⣷⣾⡟⠉⢉⡄⠀⠀⣾⠀⠟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⣯⡀⠀⠀⠀⡀⣿⣿⣀⠀⠁⠀⠀⣼⡝⣦
⢀⡇⣿⠀⠈⠸⣦⣤⣭⠔⢀⣿⣿⡀⠠⣭⣤⣴⠇⠁⠀⣴⢸⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣳⠀⠁⠀⠀⣤⡟⠙⠛⠸⣷⠄⠀⠀⠁⢸⠉⢷⡀
⠸⠀⠸⣄⠈⢦⣬⣥⠶⠞⠛⡛⣛⠛⠷⠦⣬⣥⡴⠁⣰⠇⠀⠇⠀⠀⠀⠀⠀⢀⣼⠇⢠⣿⡀⢀⠤⠶⠋⠀⠀⠀⠀⠙⠷⠤⠄⠀⣾⣤⠈⣿⡄
⠀⢀⠀⠈⠓⢦⡀⠠⣤⣤⣤⡶⢶⣤⣤⣤⠤⢀⡴⠚⠁⠀⡀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠘⠿⠃⠀⣴⠛⠖⢤⣭⣭⣥⠖⠊⣶⡀⠈⢻⠇⠀⠸⣿⡀
⠀⠀⠓⢄⡀⠀⢈⡒⠄⠄⠴⠖⠳⠦⠀⠠⢚⠁⠀⢀⡠⠚⠀⠀⠀⠀⠀⠀⣸⣿⠁⢰⡀⠀⠀⠀⠻⠿⣿⣶⣄⢠⣴⣾⠿⠿⠃⠀⠀⠀⡄⠀⢿⣧
⠀⠀⠀⠀⠀⠁⠀⠈⠙⠓⠶⠶⠶⠶⠚⠋⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢸⠀⠘⣿⢀⠀⠐⣦⣀⠀⠹⣿⣿⡟⠀⢀⣰⠇⠀⢀⢸⡇⠀⢸⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢸⡀⠀⠀⠸⣷⣦⣤⠶⠂⢠⣿⣿⣇⠀⠲⢦⣤⣶⡟⠀⠀⠀⣾⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⣧⡀⠘⣦⣤⣤⣴⠶⠟⠛⠋⠙⠛⠻⠷⢶⣤⣤⣤⠎⠀⣰⠇⠀⢸
⠀⠀⠀⠀⢀⠖⢦⡀⠀⠀⠐⢢⡔⠂⠀⠀⢀⡴⢲⡀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠈⠛⢦⣄⠀⢤⣀⣀⣀⣀⣬⣯⣄⣀⣀⣀⣠⠄⣠⡴⠞⠁⠀⠀⢸
⠀⠀⠀⠀⠘⠦⠖⡁⠀⡓⢶⣿⣿⡶⠊⠁⢉⠲⠴⠃⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣄⠀⠀⠈⠳⢤⣈⡉⠉⣉⣥⣬⣉⡉⠉⣁⡤⠞⠁⠀⠀⣀⠄⠀⣼
⠀⠀⠀⠀⠀⢠⡞⢧⠀⠀⠀⣽⣿⡀⠀⠀⡼⢳⡄⠀⠀⠀⠀⠀⠀⠀⠈⣿⡓⠀⣀⠙⢦⣄⡈⠲⢤⣄⣉⣀⣀⣀⣀⣈⣡⡤⠖⠋⣀⣴⠞⢁⠀⢐⣿
⠀⠀⠀⠀⢠⠇⣴⠀⠀⣰⠟⠈⠁⠻⣄⠀⠀⣭⠸⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⡓⠀⠙⠲⢭⣿⣶⠀⠀⠉⠉⠛⠛⠋⠉⠁⠀⢰⣿⣯⠶⠚⠁⢒⣻⣿
⠀⠀⠀⢠⡏⠈⠿⠂⣠⠒⠤⣔⣤⠤⠖⡄⠐⠿⠀⢹⡄⠀⠀⠀⠀⠀⠀⣯⠉⠙⠛⠒⠂⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠐⠒⠛⠋⠉⢹
⠀⠀⠀⡾⠀⣦⠀⠀⡘⠛⢿⣦⣴⡿⠛⢃⠀⠀⣴⠈⣷⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢀⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⢄⠀⠀⠀⠀⠀⡾
⠀⠀⠸⢹⠀⠘⢱⣄⣉⡦⠀⣿⣿⠀⢶⣉⣠⡆⠃⠀⡏⡇⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⣿⠀⠑⠲⠶⠶⠶⠶⠾⠂⠀⢸⡇⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠈⢧⡀⠦⡬⠴⠖⠛⢛⡛⠛⠲⠮⢥⠴⢀⡼⠁⠠⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⣶⣾⣿⠀⠀⣠⡴⠶⠷⢶⣄⠀⠀⢸⣷⣶⠆⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠙⠲⣄⠒⠤⠴⢞⡳⠦⠤⠒⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⢸⣿⠀⡜⠉⠀⠀⠀⠀⠈⠳⡀⣼⣿⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢥⣀⣈⣉⣉⣁⣀⡬⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⠀⠀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡽⣿⣿⢿⣿⡿⣿⡆⠀⠀⠀⠀⠀⣿⡿⣯⣽⣿⣿⠿⣿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⢀⣠⣴⣶⣶⣤⣠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠟⢿⣿⠿⣦⣄⣦⣤⣤⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣿⣿⡿⣫⡙⠇⠈⢁⡀⠈⢿⣿⣟⣿⣿⣦⣑⠢⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⡿⢧⡟⠅⡼⠓⠀⣧⡀⢸⡇⣿⢸⣿⣿⣿⣧⡈⠛⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣫⡞⣡⠞⠋⣈⡤⠃⠀⣿⡇⢸⡇⢸⠀⣿⣿⣧⡙⢏⠀⠀⠳⡄⠀⠀⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⣴⣾⣿⡿⣭⠛⠀⠋⠘⣸⡟⠀⠀⢀⣿⠇⣼⡇⠸⢰⣿⠁⢹⣧⠀⣆⠀⠀⠁⠀⠀⠀⠀⢀⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣭⡞⣦⠀⠀⢸⣷⣔⣤⣾⠏⣴⣿⡇⠀⣾⡇⠀⣸⣿⠀⠸⡄⡄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣦⣤⣠⣾⣿⣿⣿⣧⣾⣿⣿⠁⣸⡿⠀⣰⣿⠏⠀⠀⢧⡇⠀⠀⠀⠀⢸⣿⣿⠟⠉⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠰⣿⣿⣿⣿⣿⣿⣿⣿⠟⣫⣾⡿⣡⠞⣛⣥⣶⣶⣆⢸⡇⠀⠀⠀⢀⣿⣿⡏⢀⣤⣤⢼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣶⠶⠦⠸⣿⣸⢃⡀⠀⢀⣾⣿⣟⣴⣿⠏⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣷⣿⣏⣾⣿⣿⣿⣿⣿⣿⡿⢃⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢉⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡄⠀⣼⣿⣿⠯⢺⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⠿⠷⣶⣶⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣮⣟⣽⣋⣿⣿⣿⣟⡿⢋⡿⠃⣹⣿⣿⣿⣿⣿⣿⣿⣷⣿⣴⣥⣤⣴⣿⠿⠷⠶⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠉⠉⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡂⢄⠀⠀⠀⠀⢀⣠⠴⠶⠶⠤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⣠⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⢻⣿⣎⢢⣀⣀⡴⠋⠀⢀⣀⣀⣨⣽⣿⣿⣥⡀⠀⠉⠛⢦⣄⣼⣿⣿⠛⠉⢙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⢀⣿⣿⣄⡸⢸⠇⠀⠀⠁⠀⠰⠿⠿⠶⠶⠶⠦⢤⣀⠀⢸⡏⢸⣿⣿⣧⡄⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣌⠻⢿⣿⣥⣾⡁⠀⠀⠀⢒⣢⣤⣤⣤⡄⠠⠤⠀⠀⠑⢦⡙⢘⠻⠿⢋⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠿⠋⠁⡄⠀⠀⠀⠀⢀⣀⣭⣥⠤⠄⠀⠴⣚⡉⠀⠀⠙⢾⣻⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⣀⠀⠀⠘⢦⠀⠀⠀⢀⣉⡁⠐⢶⣶⣤⡞⠁⠀⠀⢀⣀⡀⢱⣿⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢧⡀⠀⠀⠀⠘⠩⠒⠀⠀⠀⠀⢿⣿⣧⡀⢀⣾⣩⢯⣷⡼⣿⡄⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣾⢷⡶⢖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⠟⠻⢿⡾⢏⠀⢿⡇⠀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡻⠷⠜⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⡶⠋⠀⣸⡇⣇⢹⡟⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣹⠻⡝⠲⣆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠚⠉⠀⠀⠀⣿⡇⢹⡈⣷⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⡟⠀⠹⣄⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢿⠀⠀⢀⡞⠀⠀⠸⣇⠘⣇⢹⡆⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢸⣇⠀⠀⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣸⣆⠀⡎⠀⠀⠀⠀⢻⠀⣿⢸⡇⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢸⣿⢀⣴⣿⠧⠤⠊⠁⠀⠀⠀⠀⠀⠈⠩⠶⢦⣄⡘⢿⡆⢰⣀⠀⠀⠀⣸⠀⡏⢸⡇⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣿⣿⠈⣿⣿⢋⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡈⠢⣿⣼⣿⣄⢠⣠⡟⢰⠃⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣧⡿⠃⢡⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⣆⠉⠍⠘⢿⣿⣿⣿⣿⢣⡟⣸⣿⡇⣇⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⠁⠀⠈⠛⠛⠻⣿⡆⠀⠀⠀⠀⠀⣿⡿⠛⠛⠁⠀⠂⣸⠈⣿⣿⣿⣿⡟⣴⣿⣿⢰⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣿⣿⡏⠦⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠴⠃⠀⢹⣿⣿⣏⣼⣿⣿⠇⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠳⣄⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠏⣼⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡈⠂⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⣿⣿⣿⣿⡿⢫⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣶⣤⣤⣴⣶⡾⠿⠟⠛⠛⠿⠿⢶⣦⣤⣤⣶⣾⠟⠀⣿⣿⡿⢋⣴⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣤⣄⣼⣿⣵⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⠿⠟⠛⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣷⣄⡀⠀⠀⠀⣀⣀⣠⣶⣿⣿⡿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣽⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁



⣿⣿⡿⠿⣿⠿⢿⠿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣾⣶⣶⣶⣿⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿