Onion Emojis & Symbols

⠀⠀⢀⠠⠒⠒⠢⢄⠀⠖⡙
⠀⠀⠙⠖⠢⣄⠀⠀⢻⠸⡠⠀⢀⣤⣀
⠀⠀⠀⢨⠀⠈⠳⡀⠀⣯⣁⠻⣄⣀⠀⠀⢀⣀⣠⣤⣤⡶⠶⠶⠶⠶⠶⠶⠶⠶⣤⣤⣀
⠀⠇⠀⠈⠉⠐⠲⠽⠦⡏⠙⡿⣛⠭⣛⡛⠋⠉⠀⠀⠤⠄⣀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⡀
⠀⢘⢀⣀⡠⠒⠒⠢⠔⢻⠹⡈⠢⡉⠙⠛⠫⠍⡑⠒⠢⢄⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠈⠁⠀⠑⠉⢉⡇⠀⠈⡄⠁⠀⠈⠒⢄⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⣠⡞⠀⢰⠀⡇⢀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠘⣷⡀
⠀⠀⠀⢠⡞⠁⠀⠀⠃⠀⡅⠈⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠈⢷⡀
⠀⠀⣠⠏⠀⠀⠀⡀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠘⣧
⠀⢰⠏⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠰⡀⢻
⢀⡟⠀⠀⠀⠀⠠⠈⠀⠀⡇⠀⠀⠐⡀⠀⠀⠀⡀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡆⠀⢇⢸
⢸⠃⠠⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠱⡀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⢰⠀⢸⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢧⠀⠀⠀⠱⡀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠸⡄⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠘⣆⠀⠀⠀⠱⡀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⡇⠀⡿
⣿⠀⢀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠘⣆⠀⠀⠀⠱⡀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣇⠀⡇⣸⠇
⢻⡀⠀⡀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠘⣆⠀⠀⠀⠈⢆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢸⠀⣷⡟
⠘⣇⠀⠱⠀⠀⠄⠀⠀⠀⠀⠘⢄⠀⠈⢦⠀⠀⠀⠀⠁⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⣷⡟
⠀⢹⡄⠀⠡⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠈⣇⣼⠏
⠀⠀⢻⣄⠀⠱⡀⠀⠀⡀⠀⠑⡀⠀⠀⠀⠀⠀⠙⠢⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠘⣄⡴⢿⣟⡢⠄
⠀⠀⠀⠙⢦⡀⠙⣄⠀⠈⠢⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⣆⣠⠾⠋⠅⠂⠑⠀⢄⢀
⠀⠀⠀⠀⠀⠙⢦⣌⠳⢄⠀⠙⢤⡀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢳⣠⡴⠟⠁⡄⡄⠲⢤⠀⠘⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣭⣒⣀⡉⠢⢄⡈⠑⠲⠤⣄⣉⣐⣒⣤⣤⡴⠾⠛⠉⠉⠃⠠⠘⢀⡆⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⢃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢁⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣼⠁⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⠀⠀⠀⠀⠀⠀⠀⣸⠃⠠⡏⠀⠀⠀⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣧⠀⠀⠀⠀⠀⢰⡏⠀⢸⡇⠀⠀⢰⡟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⡄⠀⠀⠀⠀⢸⠇⠀⢸⡇⠀⢰⡟⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⢇⠀⠀⠀⠀⣾⠀⠀⢸⡇⠀⣾⠁⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠰⣦⣀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⡟⠀⠀⢸⡇⣰⠏⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⣤⠀⠈⣧⠀⠀⠀⡇⠀⠀⢸⣇⡿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⠀⢹⠀⠀⠻⡄⠀⠀⡇⠀⠀⢸⣿⡇⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⢳⣄⡦⠀⠀⣿⠀⠀⡇⠀⠀⢸⣿⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠹⣿⡀⠀⠸⣇⠀⣷⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠘⢷⡄⠀⢸⣆⣿⠀⠀⣸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠈⢷⡀⠀⢿⣿⠀⠀⣿⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢿⡀⠈⣿⠀⠀⣿⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠘⢧⡀⢹⡄⠀⣿⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠘⣧⠈⢃⠀⠇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠘⣄⠘⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢻⡄⠸⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⢃⠀⢺⡅⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣱⡄⠀⢸⡇⠸⣇⣀⡼⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣧⣤⡜⠳⣤⠟⠉⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠉⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠶⠋⠁⣠⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⠛⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠶⠛⠋⠁⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⣠⠤⠚⠋⠁⠀⠀⠀⢠⠀⠀⠀⠘⡀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠙⢳⣄
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢠⠖⠈⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠈⢷⣄
⠀⠀⠀⢀⡾⠃⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠃⠀⠘⠃⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠙⢦
⠀⠀⣠⠟⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠃⠀⠀⠈⢧
⠀⢰⡏⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠈⣵⠀⠀⠀⠀⠀⠈⣷
⢠⡏⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⢸⡇
⡜⠁⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⠀⢹
⣷⠀⠀⠀⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠘
⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡇
⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀
⠈⢷⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⣸
⠀⠘⢷⡀⠀⠀⠀⠀⠈⢄⡀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠑⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠓⠶⠶⠶⠶⢾⣦⡴⢶⣤⡶⣤⡾⠛⠛⠛⠛⠛⠛⠛⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠉⠁⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡠⠖⠒⠒⠤⡀⢠⢊⠝
⠀⠀⠚⢲⠤⣄⠀⠀⠘⡇⣆⠤⠀⢀⣀⡀
⠀⠀⠀⢸⠀⠈⠳⡄⠀⢱⣞⠒⢮⡁⠀⠁⠀⠀⢀⣀⣀⣤⣤⡴⠶⠶⠶⠶⠶⠶⢦⣤⣤⣀⡀
⠀⡎⠉⠉⠑⠒⠤⠬⢦⣸⠙⠛⣿⠭⣛⠛⠛⠛⠉⠉⠁⠌⣀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣦⣄
⠀⢰⠂⠀⢀⠤⠠⠤⡀⠼⡖⢎⠢⣍⠒⠛⠶⠖⡒⠒⠠⢄⡀⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⠳⣄⡀
⠀⠀⠂⠉⠻⠔⠒⢲⠀⠀⢡⠘⡀⠀⠑⢄⠀⠀⠀⠈⠂⠄⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⣠⠏⠀⡆⢸⠀⠁⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠙⣧⡀
⠀⠀⠀⠀⣠⠞⠉⠀⢀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠘⢷⡀
⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠘⣷
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢸
⠀⣸⠁⠀⠀⠀⠀⡀⡄⠀⢸⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠈⡀⠀⢣
⢠⡇⠀⠀⠀⠀⠀⠁⡇⠀⠈⡄⠀⠀⠈⡄⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⢰⠀⠸⡄
⣸⠀⢠⠀⠀⠀⠀⠀⢀⠀⠀⢣⠀⠀⠀⠘⡄⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⡆⠀⣧
⣿⠀⠈⠀⠀⠀⠀⠀⠘⡀⠀⠈⢧⠀⠀⠀⠘⡄⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⢇⠀⠀⡇⠀⣿
⣿⠀⢀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠘⣆⠀⠀⠀⠘⡄⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⡆⠀⣿⠀⣿
⣿⠀⠘⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠘⣆⠀⠀⠀⠈⢆⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⢹⠀⢹⢰⡏
⢹⡄⠀⠄⠀⠀⠀⠀⠁⠀⠀⠑⡀⠀⠘⢆⠀⠀⠀⠀⠡⡀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⡇⣼⡿
⠈⣷⠀⠈⠄⠀⠐⡀⠀⠁⠀⠀⠘⢄⠀⠈⢧⡀⠀⠀⠀⠈⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⡆⠀⣷⡿⠁
⠀⠸⣇⠀⠘⡄⠀⠐⠀⠀⠀⢄⠀⠀⠁⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⣇⣴⠏
⠀⠀⠹⣦⠀⠘⢆⠀⠈⠂⠀⠀⠠⡀⠀⠀⠀⠀⠀⠈⠒⠄⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⢀⠀⠀⠘⣦⡼⠻⡧⣑⠤
⠀⠀⠀⠘⢷⣄⠈⢣⡀⠀⠑⢄⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⣆⣤⠞⠋⠨⠂⠙⠂⠡⣀
⠀⠀⠀⠀⠀⠙⠳⣤⡙⠦⡀⠀⠑⢄⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠈⣧⣤⡶⠛⠡⡀⡀⠒⢦⡀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢮⣕⣂⠠⠑⠦⣄⠈⠓⠦⢤⣄⣈⠐⠲⢦⣤⣤⠶⠿⠛⠋⠉⠆⠀⡖⢂⢆⠀⠀⢀⠀⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣙⣛⣛⣚⣿⣿⣶⣶⣾⣛⣛⣛⣋⣉⣀⣀⣀⣀⣊⣈⣂⣙⣋⣕⣀⣁⣀⣁⣀⣀⣀⣀
⣿⣿⠋⢛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠻⠲⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠖⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢰⠊⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠚⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠈⡆⠀⢄⠠⡀⠀⠀⠀⠀⠀⠀⣠⠖⡩⠐⢀⠠⠐⠂⡉⠄⢂⠀⠀⠀⠀⠀⠰⠘⡄
⠀⠀⠀⠀⠀⢠⠇⡀⠠⡑⠨⢑⡒⠤⢤⣀⡔⠁⠀⠔⠈⣀⠄⠂⠁⡀⠔⠁⠀⠀⠀⠀⠘⡄⠀⠘⡄
⠀⠀⠀⠀⢀⠎⠃⠃⠀⠈⠒⠠⢀⣉⠐⠂⠨⢙⠲⢤⡈⠀⢀⠔⠈⠀⠀⠀⠀⠀⠁⠀⠀⠰⡀⠀⠸⡄
⠀⠀⠀⢀⠎⠌⡘⠠⠀⠀⠀⠀⠐⠠⢈⠁⠒⠄⡉⠢⡙⢎⢀⠔⠀⡠⠀⠀⠀⠀⠀⡀⠀⠀⢃⠀⠀⢣
⠀⠀⠀⡎⡜⠠⠁⠂⠀⡄⠀⠀⠀⠐⢄⠉⠂⠀⠘⡄⠱⡈⣇⠀⠊⢀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠀⠇⢸
⠀⠀⡸⠰⢀⠃⡈⢀⠀⠁⠀⠀⠀⠑⠄⠑⠀⠀⠀⠰⠀⠃⢹⡀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⡸
⠀⠀⡇⠇⡄⠀⠁⢸⠀⡀⢀⠘⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⡗⠊⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⢲⠃
⠀⠀⡇⠀⠃⠀⠀⠀⠆⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⢃⠟⡇⠀⠒⠀⠀⠀⠊⠀⢀⠔⢁⠀⡰⠃
⠀⠀⢇⢇⠘⠄⠀⠀⠈⠢⡑⠀⠀⠀⠀⠀⠀⠂⡶⡡⢃⠞⣰⠃⠀⠤⠀⠀⠀⠀⠀⠀⢐⡡⠚
⠀⠀⠘⢎⠢⡈⠐⠤⣀⠀⠠⠄⠀⠀⠀⠀⠀⢀⠔⡡⠋⣰⣏⠀⠀⠀⠀⠀⣀⣀⠤⠒⠉
⠀⠀⠀⠈⠳⢌⡐⠢⠄⢉⣀⠐⠂⠀⠀⠀⣀⡤⢺⣿⡴⠋⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠉⠛⠶⢶⣖⣒⣲⣒⣚⣻⣿⡿⢿⣏⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡔⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⡏⡆⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⢀⠎⡜⠀⠀⢀⣶
⠀⠀⠀⠀⠀⠀⢶⡶⣄⡀⠀⠀⠀⠹⣦⠀⠀⠀⡇⠸⡆⠀⠀⠀⠀⢠⡞⢸⠀⣰⠃⡜⠀⠀⣴⢋⠇
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⠲⢄⡀⠀⠹⣷⡀⠀⢠⠀⢻⡀⠀⠀⢠⡏⠀⡇⢰⠃⡾⠁⢀⡞⠁⣺
⣀⣀⣀⣀⠀⠀⠀⠀⠀⠘⢦⡀⠙⢦⣄⠹⣷⡄⢸⠀⠀⢳⡀⢀⡞⠀⢸⢠⠃⣼⠃⢠⠎⠀⠀⡇
⠉⠉⠉⠉⠛⠛⠷⢦⣤⣀⠀⠙⠢⡀⠈⠳⣭⣿⡄⡆⠀⠀⠱⡜⠀⠀⣸⠆⢰⡏⢠⠏⠀⠀⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣤⣈⠠⠀⠈⢻⣟⣷⡄⠀⢀⠃⠀⢠⡿⠀⡏⢠⠏⠀⠀⢠⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⣓⢷⣄⠀⠙⡌⢳⡀⠘⠀⠀⢸⡇⢸⢠⡟⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡝⢷⡄⠘⠀⠹⡆⠀⠀⠈⠑⣼⡏⠀⠀⠀⡸⠀⠀⠀⣀⠤⠴⠒⠉⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠙⢦⠹⠄⠁⠀⠀⡀⠀⠸⠁⠀⠀⡰⠁⣠⠶⠋⠁⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⢷⡘⡄⠀⠀⠉⢠⡄⠀⠀⣸⡵⠋⢀⣀⡤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠹⡡⠀⠀⠀⢨⠀⢀⡾⠋⣠⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢱⢃⠀⣠⡌⢀⡟⢁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣧⡏⠻⠃⠹⠇⢹⡀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠁⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠑⢄⠀⠈⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠳⡀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣴⢇⣤⣼⣶⣄⢶⣀⡴⠖⠚⠛⠋⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣛⣉⣉⣀⣿⣁⣽⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢻⣷⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠘⣿⡄⠀⠀⠀⢀⣴⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⣦⡀⠀⠀⠸⣿⡄⣿⡇⠀⠀⢠⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣄⠀⣿⡇⢸⣿⠀⣰⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡝⢿⣦⣿⡇⢸⣿⣴⣿⣻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⢻⣿⡇⢸⣿⡿⣱⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡈⣿⡇⣾⡟⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢸⣷⡿⢡⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⢻⡇⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⢸⣿⣤⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⢸⣿⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣏⢠⣶⣸⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡏⢹⣿⣿⣿⣿⣟⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⣩⠋⣠⣾⣿⣿⢹⣏⣟⣿⣿⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢋⡵⠊⢁⡜⡱⢻⡏⢻⠈⡟⡜⣿⢯⠳⡈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢉⡴⠊⣴⣠⢏⡜⢁⠇⡿⢸⡆⡇⢹⡘⣇⢳⠙⢦⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⣠⠞⠁⣠⠞⢡⠞⠀⡎⢰⡇⠀⡇⢹⠈⣧⢹⡎⢳⡾⢻⡄⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⣰⠋⢀⡞⠁⢠⠏⠀⡸⠀⢸⠇⠀⡟⠋⡆⢹⡍⠘⡄⢧⠀⠹⡄⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢠⠃⢠⡞⠀⢀⡏⠀⢠⠇⠀⣼⠀⠘⡇⠀⡇⠸⡇⠀⢱⠘⣇⠀⢹⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠀⢸⠀⢸⠁⠀⢸⠀⠀⣾⠀⠀⣧⠀⠀⡇⠀⢷⠀⡇⠀⢸⠀⢸⡄⢸⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⢸⠀⢹⠀⠀⢸⠀⠀⢿⠀⠀⣿⠀⠀⣧⠀⣸⠀⡇⠀⢸⠀⢸⡇⢸⠀⢀⣿⡇
⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡉⠚⣆⠘⣇⠀⠸⡄⠀⢻⡀⠀⢹⠀⠀⡟⠀⡇⠀⡟⠀⢸⠀⣼⢡⡞⣂⣼⡿
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠘⣧⠙⢶⠲⠻⡄⢀⣣⠀⢸⡇⠀⡇⢀⡇⢸⣇⢀⠷⣴⢃⡾⢀⣾⡟⠁
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣈⠳⣌⠓⢤⡙⢦⠉⣆⠈⣇⢰⡇⡸⢡⡟⢀⡟⡰⣣⠞⣡⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣮⣷⣤⣙⢮⣳⣌⣆⡟⣼⢠⢃⠎⣠⣿⣾⣟⣥⣾⠟⠁
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣿⣿⣿⡟⠋⠁
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠡⠾⠋⠟⠋⠉⠙⠛⠉⠛⠷⠶⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠐⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠊⣠⠊⠀⠀⠀⠆⠀⠀⠀⠐⡄⢄
⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⡰⠁⠀⠀⠀⡘⠀⡆⠀⠀⠁⢰⠈⢆
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠰⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠃⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠴⡷⠆
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡠⠥⠐⠒⠒⠒⠒⢂⠐⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣀⣠⠤⠴⠒⣈⢔⠴⠀⡈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢀⠔⠉⢀⣀⣠⠴⢊⡴⡱⡡⢡⠁⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠦⠤⠄⠀⠀⠒⢸⢠⠃⡔⠊⢉⣀⠠⠤⠊⡜⢱⠁⠘⠀⡄⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢼⡘⠀⠚⠉⢀⣀⠀⢠⠃⡟⠀⡆⠀⡇⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⢋⠏⠀⡼⢀⠇⢀⠇⢀⠃⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠢⡄⠀⠂⠀⠚⠠⠊⡀⠎⣠⠎⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠆⠠⣤⣀⡐⠀⠨⠔⢚⣡⣾⠿⠃
⠀⠀⠀⠀⠀⠀⢠⡶⠐⣆⣀⣀⡀⡆⢀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠘⢧⣠⠏⢸⢸⠇⡇⢻⡸⠇⡇⡿


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣨⣿⣇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⢉⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡌⠣⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⣦⣽⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢿⣿⣿⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣿⣧⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢨⣿⣿⡶⠹⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢿⣿⡇⢹⣿⣷⣤⠀⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣷⣶⠜⠃⠸⣿⣿⣿⣦⠀⠈⠁⠖⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠿⢋⣵⠟⠉⠉⠀⣠⣼⣿⣿⣿⣿⣷⣦⣀⠈⢀⠀⢉⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⠟⠋⠁⣠⠟⣁⣀⡈⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠛⢦⡛⠱⣤⡀
⠀⠀⠀⠀⠀⣰⡾⣽⠋⢀⣴⣿⢋⡤⢁⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⢻⠻⠻⢿⡎⠻⣿⣿⣶⡄⠀⠙⢢⠈⠽⣦
⠀⠀⠀⠀⣾⣿⣿⣷⣴⡿⣫⣿⣟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣯⡟⢿⠘⠃⠁⠀⠑⠀⠹⠉⠻⣧⠀⠀⠀⠠⠀⢎⣷⡀
⠀⠀⠀⣼⣿⣿⣿⣷⣿⣶⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣽⡇⣗⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠈⡿⣷
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⢹⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣆⢰⣆⣄⣰⣤⣼⡏⠀⠀⠀⠠⠀⠸⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠄⠘⠀⣿⣿⡇
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢁⣤⣿⣿⣿⣾⣿⣿
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⠻⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢠⠑⣀⣿⣿⣿⣿⣿⣻⡟⠻⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠀⠟⣿⣹⡿⣿⡙⠉⠀⠀⢀⡀⠠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠉⠉⡤⠄⠈⢇⣘⣿⠅⠂⢛⠀⠀⡙⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠁⠀⢰⡘⢃⠉⠀⠀⠍⠀⡰⣀⠂⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⢀⠆⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠐⠀⠈⠉⠉⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠓⠠⠄⠀⠤⠦⠖⠀⠠⠀⠠⠄⠂⠄⠀⠿⠀⠆⠀⠄⠰⠀⠂⠀⠀⠀⠰⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡲⡴⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⠾⣽⠛⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠋⠉⠉⠀⠀⠀⠀⠀⠚⠹⣇⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠒⣚⣋⣉⣉⡭⠭⠵⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⡤⠖⠋⢉⣠⠤⠖⠛⠉⠉
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡴⠚⠉⠀⣀⣀⣤⠤⠤⠶⠖⠒⠒⠛⣛⣛⣶⠶
⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠔⣛⣉⣁⣀⣀⡠⠤⠶⠶⣿⣉⠉⠉⠁
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠛⠉⠉⠉⠀⠀⠀⠉⢻⣏⠉⠉⠉
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢹⡀
⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⣠⠔⠁⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠈⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠐⠂⠀⠀⢀⣀⣤⠴⠒⠉⠀⠀⠀⠀⢠⡇
⠀⠀⠀⣠⡤⠖⣋⠅⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⢿⠒⠒⠲⠖⠒⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠘⠷⠖⠚⢥⡤⠤⠶⠛⢳⣤⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠚⠛⠉⠙⠛⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠶⠶⠶⠶⠚⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣖⠁⠀⠀⠀⠀⠀⠀⠀⠐⠦⡀⠀⠀⠀⠀⠀⠀⠀⠰⢶⡀⠈
⠀⠀⠀⠀⠀⠀⡀⢤⠙⠧⠀⠢⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⣀⣾⣄⡀⢠⠇⢈⣴⠿⣦⠀⡀⠀⠀⠀⠈⣾⣿⣿⣿⣿⣇⢄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠈⠁
⢀⠶⢴⡧⢻⣿⣿⣿⣀⡘⠻⢷⣿⠃⠀⠀⠀⠀⠁⠙⠛⠻⠿⡿⠙⣻⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁
⠀⠀⣾⣷⢸⡘⡉⠋⠻⣟⢷⣶⣷⠀⠠⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠
⠀⠀⠈⣿⣽⣿⣿⡄⠂⠈⠀⠙⠻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⣨⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⢻⡏⣹⠀⠀⠁⠀⠀⠀⡐⡁⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣀⢔⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣄⢀
⠀⠀⠀⡼⠁⠙⡀⠀⠀⣀⣄⣀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣬⡧⠀⠀⠀⠀⠀⠀⠀⣸⠛⠋⠁⠁
⠀⠀⠀⠀⠀⠀⢁⣴⣾⣿⣿⣷⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⡄⣼⣿⢁⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⢻⢶⣦⠀⠀⠀⠀⠀⠀⣨
⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⡀⠀⠀⠀⠤⡆⢿⣿⣥⠀⠀⠀⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⠀⠀⠀⢀⣿⣇⡀
⠀⠀⠀⠀⠘⠊⠟⢿⢿⣿⣿⣿⡙⢿⣿⣿⣟⣒⣋⡀⢀⣘⣧⢸⣿⣿⡄⠀⠀⠀⣿⢿⡍⠀⠀⠀⠀⠀⠀⢸⣝⣿⣿⣿⣶⠂⢀⣾⣿⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⣿⣿⣿⣶⣾⣯⣽⣿⣶⣿⣿⣿⣿⣇⠻⣿⣿⡤⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣶⣾⡿⣟⡅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⡻⣿⣷⢆⣀⡄⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡍⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠹⠟⠻⠿⢿⣿⣿⣿⣿⣷⣦⣤⣬⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⢿⡋⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠉⠙⠀⠀⠛⠉⠙⠋⠛⠉⠙⠋⠋⠉
⠀⠀⠀⠀⢰⠂⠆⠀⠀⠀⠐⠐⠀⠀⠀⢰⠄⢠⢰⣄⣄⢠⠀⠀⠂⠄⣀⡄⠀⡄⣄⠀⢀⢦⠀⡀⠀⡀⢠⢀⡄⠠⠀⠀⠀⠀⠀⢠⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⠿⠿⠟⠛⠛⢿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢦⣴⠟⢷⣄
⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠛⠉⢀⣀⣤⠴⠖⠛⠋⣉⣁⣀⣀⣉⣙⠻⣶⣄⡀⠀⠀⣼⠟⠀⣰⠏⢀⣼⣏
⠀⠀⠀⠀⣠⣾⠿⠋⠀⢀⣴⠞⠋⠁⣀⣤⠶⠞⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⢿⣦⡼⠋⢀⡾⢃⣴⠋⠀⢙
⠀⠀⢀⣼⡿⠋⠀⢀⡴⠋⠀⠀⣠⠞⠉⠀⠀⠀⢀⣠⡴⠶⠛⠛⠋⠉⠁⢀⣀⣼⣿⣶⢋⣴⠟⢁⣤⠖⠻
⠀⢀⣾⣿⠁⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⣠⡴⠞⠋⠉⠀⠀⢻⣿⡥⠖⠋⣁⣴⠶
⠀⣼⣿⠇⠀⣰⠏⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⢻⣧⠴⠛⠁
⢠⣿⡿⠀⣰⠏⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⢸⣿⡇⢀⡏⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⢿⡇
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠉⠀⠀⠀⢸⣧
⠈⣿⡇⠀⡴⣲⣴⡄⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢿⣷⠀⡇⡅⢹⡇⣸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟
⠀⢸⣿⣼⢃⢧⣟⣿⢣⠋⣰⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢻⣿⠃
⠀⡾⣿⣿⣸⣸⣾⡼⣇⣴⣿⢗⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠟⠋⢠⣿⠏
⢸⡃⡟⢿⣧⣹⣭⣶⣗⣛⡥⠊⣀⠀⢀⣤⣀⣀⣀⣤⣤⣤⣴⠶⠾⠛⠛⠉⠀⠀⠀⣠⣿⠏
⠈⠧⣑⣊⣥⣾⣿⣲⣏⡉⠿⠭⠝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣾⡿⠃
⣴⡖⢚⡳⣳⣿⣿⣕⢪⣽⣟⣛⣶⠦⣄⡀⠀⠀⠈⠉⠉⠙⠛⠛⠛⢛⣻⣿⣿⡿⠋
⠀⠉⠉⠿⠵⢋⣿⡆⢯⣛⢛⣛⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣴⣶⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠿⠊⠀⠀⠉⠉⠉⠀⠉⠛⠛⠻⠿⠿⠿⠿⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⠇
⠀⢀⣴⣶⣶⣦⣀⠀⠀⠀⠀⢻⣿⣿⣿⡀⠀⠀⠀⢿⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⢽⣿⣿⣿⣧⡀
⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣄⠀⠀⠸⣿⣿⣿⣅⠀⠀⠈⣿⣿⣿⣿⣧⠀⠀⠀⠸⣿⣿⣿⣿⣷
⠀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⡗
⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣿⠇⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⡀
⠀⠘⠛⠛⠙⠛⠛⠛⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⢸⣶⣶⣾⣿⣿⣷⣶⣾⣿⠀⠀⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⣿⣄⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⠃
⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠯⠀⢠⣿⣿⣿⣿⡆⠀⠀⣸⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⠏
⠀⢀⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⢸⣿⣽⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⠃⠀⣼⣿⣿⣿⣷⠀⠀⠀⢀⣿⣿⣿⣿⣆
⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠀⠀⢠⣿⣿⣿⠟⠁⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⢨⣿⣿⣿⣿⣷
⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⣰⣿⣿⣿⠋⠀⠀⠀⣼⣿⣿⣿⣦⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⢼⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⣾⣿⣿⣿⣧⠀⠀⠀⠀⣿⣿⣿⣿⡁
⣶⣶⣶⣶⢶⣶⣶⢶⣶⢶⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢒⣁⡤⣠⣦⣤⡐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠞⠛⠛⢻⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⣤⠀⡏
⠀⠀⠀⠀⠀⠀⢠⡲⣿⣿⡆⠀⠀⠀⣠⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠙⣀⢰⣿⡄⠀⠀⠀⠀⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠟⠁⢀⣀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠀⠀⠀⠈⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⠀⠀⠀⡀⠒⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣇⠂⠀⠀⠀⠁⡴
⠀⠀⠀⠀⠀⠀⠀⢀⡤⣞⡻⣿⣿⣷⣄⡀⠶⣾⡁
⠀⠀⠀⠀⠀⢀⠖⠛⢢⡀⠙⢮⡛⠿⠿⢿⣿⣿⡻⡢⡀
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠹⡄⠀⠱⡄⠀⢰⣿⣿⣿⣇⢡⠀⠀⠀⠀⠀⣀
⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢹⡀⠀⠙⣄⠀⢹⣿⡿⣿⣿⣇⠀⠀⠀⠀⢾
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⢧⠀⠀⠈⠉⠈⢿⣷⠘⠿⠸⡄⠀⠀⡰⠛
⠀⠀⠀⡳⠀⠀⠀⠀⠀⠀⣾⢸⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢱⠀⡸⠁⠀⠘⢿⡆
⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣰⠁⠀⣤⠀⢺⡏⠁
⠀⠀⠀⡇⠀⠀⠀⢀⠀⢾⣣⡟⠀⠀⠀⢀⣀⣠⠀⠁⠀⠈⢁⡠⠂⠀⠙⠛⠛⠀⢀
⠀⠀⠀⢡⠀⠀⠀⡡⢖⢛⡷⠒⠘⠉⠉⠁⠀⢰⠀⠀⠀⠀⢸⣽⣇⠤
⠀⠀⠀⠘⠀⠀⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠖⠒⠉⢸⠐⠄⣾⣛⠛⠛⠛⣛⠛⠃⡄
⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠏⠀⢀⠀⠀⢸⡄⡆⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠈⠲⠆⠶⢶⠒⢚⠋⠍⠅⠤⢨⡧⠷⠶⠶⠾⠶⠶⠞⠣⠶⠀⠀⠀⠀⠀⠠⠀⠼⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡆
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⣿⣿⠟⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⡶⠒⠒⠒⠒⠒⢲⡄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⢸⡇⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⡇⠠⠴⠆⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠒⠒⢒⣒⡒⠒⠒⠒⠒⠒⠚⠃⣠⠗⠒⠒⠒⠒⠒⠚⢧⡀⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣠⡽⣛⡛⢦⡀⠀⠀⣞⢓⣒⣒⣒⠒⣒⣒⡒⣒⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠐⠿⠞⠹⡟⠁⠉⢻⠇⠀⠀⠉⠉⠉⠉⠉⣩⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⡶⢶⣏⣀⠀⠀⠀⠀⠀⢯⠀⢸⠆⢸⡄⠀⠀⠒⠒⠲⡖⠒⢲⡖⠒⢶⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠉⠉⠀⠈⣷⠀⠀⠀⠀⢘⣀⣤⣄⣘⠁⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡼⠁⢀⡴⠀⠀⡶⢳⢄⣿⡀⠀⣀⣰⠯⠥⠤⠤⠭⢷⣀⡀⠀⠀⠀⡇⠀⣸⣇⠀⢸
⠀⠀⠀⠀⠀⠀⢸⣅⠀⠘⠳⢦⣠⣟⡏⢠⠈⠓⠶⠯⣿⠀⠀⠀⠀⠀⢸⠉⠁⠀⠀⡞⢹⣆⡏⢹⢰⠋⢳
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⡶⠴⣇⣹⠇⢺⠶⠶⠶⠶⢾⣀⣀⣀⣀⣀⣸⠀⠀⠀⠀⠙⠚⠙⠓⠚⠈⠓⠋
⠀⠀⠀⠀⠀⠀⢰⠶⠶⠶⠳⠶⠶⠶⠶⠞⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶
⠀⠀⠀⠀⠀⠀⢸⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⠶⣶⠶⠶⣶⣶⡶⠶⢶⡶⢶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠀⣿⠸⠭⠇⠸⠭⠭⠿⠀⠯⠟⢸⠀⠘⠚⠂⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢛⣛⣛⣛⣛⣛⣛⣛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣈⣉⣉⣉⣉⣉⣉⣉⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠁⠀⠀⠐⢀⠠⣄⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⠀⠀⠀⠀⠈⠁⠈⠃⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘


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

⠀⠀⠀⢰⠶⢶⣶⠶⣆⠀⠀⠀⠀⣖⣶⣲⣖⣶⣲⣖⣶⣒⠀⠀⠀⣶⣶⠆⠀⠀⠀⢀⣒⣢⣒⣢⣖⣲⣔⣒⣔⣒⣔⣒⡂
⠀⠀⠀⢀⠕⢇⣨⠶⡅⠀⠀⠀⠀⣽⣿⣯⡿⠛⢿⣭⣿⣯⠀⠀⠀⢧⡎⡆⠀⠀⠀⢈⠻⣟⠟⣛⢟⡻⢟⡻⢛⡻⣛⠻⡃
⠀⠀⠀⠘⣟⣿⣽⣟⡇⠀⠀⠀⠀⢿⣾⣾⣄⢀⣠⣷⣷⡿⠀⠀⠀⣯⣚⠁⠀⠀⠀⢈⠒⣭⠒⣭⢪⡕⢪⡕⢨⠕⣩⠲⡅
⠀⠀⠀⠈⣿⣿⣿⣿⠃⠀⠀⠀⠀⠘⠾⢷⣿⣿⣿⡿⠿⠃⠀⠀⠀⣻⣵⡅⠀⠀⠀⢨⣶⣭⣦⣭⣮⣵⣮⣵⣮⣵⣭⣶⡅
⠀⠀⠀⠀⠀⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠁⠀⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⠈⠭⠝⠭⠝⠯⠽⠯⠭⠫⠭⠫⠭⠅
⠀⠀⠀⠀⣀⡀⣀⡀⣀⣀⢀⣀⢀⢀⣀⢀⢀⣀⡀⡀⣀⡀⣀⣀⢀⣀⢀⣀⢀⢀⣀⢀⡀⡀⣀⡀⡀⡀⣀⣀⢀⢀⣀⢀
⠀⠀⠀⠘⢝⠛⠝⠫⡝⠫⠝⠫⠛⠫⠛⠭⠛⠭⠛⡝⠛⠝⢫⠝⠫⡝⠫⠛⢫⠛⠭⠛⠭⠛⢝⠛⠝⠫⠝⢫⠝⠫⠛⡩⠃
⠀⠀⠀⢸⣾⣽⣾⣓⣾⣷⣚⣷⣿⣷⣿⣳⣿⣶⣟⣾⣿⣞⣷⣾⣷⣾⣳⣿⣷⣿⣶⣿⣖⣟⣾⣿⣾⣳⣾⣷⣺⣷⣿⣷⡇
⠀⠀⠀⠀⠻⡿⠃⠘⢿⡿⠃⠘⢿⠟⠀⠻⣿⠟⠀⠻⡿⠃⠘⢿⡿⠃⠘⢿⠟⠀⠻⣿⠟⠀⠻⡿⠃⠘⢿⡿⠃⠘⢿⠟

⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⢸⣿⣈⣿⠿⣿⣉⣿⡿⣿⣅⣽⡿⣿⣅⣹⡿⣿⣇⣹⣿⣿⣏⣸⣿⢿⣏⣸⣿⢿⣯⣨⣿⢿⣿⣈⣿⠿⣿⣁⣿⡇
⠀⠀⠀⠀⠙⠛⠉⠀⠉⠛⠋⠀⠈⠻⠋⠀⠈⠛⠋⠀⠈⠛⠋⠁⠈⠛⠛⠁⠀⠙⠟⠁⠀⠙⠟⠁⠀⠙⠛⠉⠀⠉⠛⠋

⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇
⠀⠀⠀⢸⣕⣽⣔⣯⣞⣯⣞⣯⣨⣯⣺⣥⣻⣕⣣⣕⣿⣕⣽⣔⣯⣚⣯⣪⣭⣳⣵⣪⣅⣿⣕⣯⣔⣿⣜⣬⣺⣯⣪⣯⡂
⠀⠀⠀⢸⣾⢿⣶⢻⡾⢿⡞⣶⡞⣷⡿⣷⠿⣶⢻⣷⢻⣾⢿⡾⢷⡾⣷⡞⣾⡞⣶⠿⣷⢿⣶⢳⣶⢻⡾⢿⡞⣷⡿⣷⡇
⠀⠀⠀⠀⠁⠀⠁⠀⠁⠈⠀⠈⠀⠈⠀⠈⠀⠉⠀⠁⠀⠁⠈⠁⠈⠁⠈⠀⠈⠀⠉⠀⠁⠀⠁⠀⠁⠀⠁⠈⠀⠈⠀⠈
⠀⠀⠀⢠⣠⣠⣄⣤⣠⣄⣤⣤⣠⣄⣤⣤⣠⣄⣤⣠⣤⣄⣤⣠⣄⣤⣤⣤⣄⣤⣠⣤⣄⣤⣠⣄⣤⣤⣠⣄⣤⣠⣤⣤⡄
⠀⠀⠀⠀⢑⢑⢕⡇⡋⡪⡛⢙⢸⢘⡃⡋⡫⣛⢕⢝⠍⡊⡇⡃⢘⢸⢐⠉⡫⡊⣖⢝⢙⢑⡃⡇⡋⣺⢙⢕⢽⡪⡋⡃⠁
⠀⠀⠀⠰⢶⠶⠷⠷⠶⠷⡷⠿⠾⠾⠶⢿⠾⡾⠶⠿⠷⠷⠷⠷⠾⡾⢾⠶⡾⠾⢶⠿⡿⠶⠶⠷⡷⢾⠷⠷⢾⠾⠶⡷⠆

⣖⣦⣄⡀⠀⠀⠀⢀⣠⣴⣲⣖⣦⣄⡀⠀⠀⠀⢀⣠⣴⣲⣖⣦⢄⡀⠀⠀⠀⢀⣠⣴⣲⣖⣦⣄⡀⠀⠀⠀⢀⣠⣴
⣀⣌⣙⠻⣦⣀⣴⠿⣋⣡⣀⢀⣌⣙⢻⣦⣀⣴⠟⣋⣡⡀⣀⣌⣙⠻⣦⣀⣴⡿⣋⣡⡀⣀⣌⣙⠻⣦⣀⣴⡿⣋⣡
⣿⣯⣞⣦⠈⠒⠁⣴⣳⣽⡟⢻⣯⣞⣦⠈⠒⠁⣴⣳⣽⡟⣻⣯⣟⣦⠈⠒⠁⣴⣳⣽⡟⢻⣯⣞⣦⠈⠒⠁⣴⣳⣽
⡞⢺⣟⠿⢦⣦⡔⠿⣻⡗⣳⡞⢺⡟⠿⢢⣤⡔⠿⣻⡗⣳⡞⢺⡟⠿⢢⣤⡔⠿⢻⡗⢳⣞⢺⣟⠿⢦⣤⡴⠿⣻⡗
⣧⢼⣯⣶⠞⠛⠳⣶⣽⡧⡽⢧⢼⣧⣶⠜⠛⢣⣶⣼⡧⡼⢯⢼⣧⣶⠜⠛⠣⣶⣼⡧⡼⢯⢼⣯⣶⠞⠻⠳⣶⣽⡧
⣾⣟⢯⠟⢀⠤⡀⠻⡽⣻⣷⢼⣟⢯⠟⢀⠤⡀⠻⡽⣻⣷⣽⣟⢯⠟⣀⠤⡀⠻⡝⣻⡧⣼⣟⢯⠟⢀⠤⡀⠻⡽⣻
⠉⢋⣩⣴⠟⠉⠻⣦⣍⡙⠉⠈⢋⣩⣾⠟⠉⠻⣦⣍⡙⠁⠉⢋⣩⣼⠟⠉⠻⣷⣍⡙⠁⠈⢋⣩⣴⠟⠉⠻⣶⣍⡙
⠯⠟⠋⠁⠀⠀⠀⠈⠙⠻⠽⠯⠟⠊⠁⠀⠀⠀⠈⠙⠻⠽⠯⠟⠋⠁⠀⠀⠀⠈⠑⠻⠽⠯⠟⠋⠁⠀⠀⠀⠈⠙⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠠⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⣀⢤⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⠇⠄⢨⡆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠐⡉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠖⠀⠀⠀⠤⠄⠆
⢀⣀⣀⣀⠀⠀⠀⠀⢀⣀⡀⠘⠄⠇⡸⠀⠀⠀⠀⠀⠀⢀⡀⢠⠄⠀⠀⠀⠀⠠⢘⠀⠀⠀⡛⠠⠀⠀⠀⠀⠀⠀⠄
⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠁⠈⡆⠀⡇⠀⠀⠀⠀⠀⡔⠙⠁⠞⠸⠳⣆⠀⠀⠐⠨⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡇⠀⠀⠀⡠⠈⠀⡀⠀⠀⠀⠀⢂⡄⠀⢨⣧⣄⢀⢀⡀
⠀⠀⢀⠀⠀⠀⡀⣀⢀⠀⠀⠀⣿⠀⢀⠀⠀⠀⠀⡰⠊⠉⠂⠈⠫⠤⡈⠃⡄⠘⠦⣅⡀⢦⠗
⠀⠀⠀⠀⠀⠜⠁⠀⠀⠑⡀⠀⢸⠀⢸⠀⠀⢀⠲⡀⠀⠀⠀⠀⠀⠀⠷⡄⢌⢲⠀⢈⢃⡟⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⢀⠀⠀⢘⠀⠀⠀⠀⠀⠡⠀⢸⡀⢸⠀⠀⠀⠙⠀⣆⡀⠈⢀⣰⠂⠇⠀⠈⢢⡹⣏⠎⠀⠈⠀⠀⠀⠀⠀⠀⢀⠃⠀⡅
⠀⠀⠀⣤⣽⡀⠀⠀⠀⢀⠗⠀⠸⠇⢸⠀⠀⠀⠀⠑⠮⠁⠀⠀⡠⠈⠀⠀⠀⣠⢉⢈⡢⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⢀⡀⡁⢀⣀⡠⠆⠀⠀⢀⠻⣿⠤⠀⠀⢀⣀⡐⠁⠀⠈⠢⣀⡀⠀⢸⣁⣽⠓⢶⠋⠀⠈⠉⠛⠒⠤⡴⢉⡁⠀⠠
⠀⠀⠀⠂⠀⠀⣸⢀⡀⠤⢀⣀⠈⣧⡠⣃⢾⣶⣁⠀⠁⠸⠈⠀⠀⠀⠀⢦⡴⠁⢐⠖⠚⠑⠂⠄⡤⢀⠀⠀⡀⢀⣀⡈
⠒⠒⠐⠒⠀⣋⣀⡬⠡⠤⠤⠬⠑⢆⠀⠙⠳⡌⠛⡃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠈⣰⡬⠃⠹⡦⠐
⠈⠉⠉⡽⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⠀⠉⢇⠀⠀⠀⠀⠀⠀⡗⣄⢠⡜⠀⠀⠀⠠⠄⠀⠀⠀⢰⠀⠁⠀⠀⢛⡶
⠤⠤⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⠒⠒⠒⢺⠀⠀⠀⠀⠀⢸⠘⠆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢢⢄⠀⠀⠐⠈
⠀⠐⣀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢗⢀⡀⠠⢼⡀⠀⠈⠀⠀⠸⠀⠐⠢⢄⣀⠀⠀⠀⠀⠀⠀⢰⠤⠀⢀⡠⠃⢀⡀
⠀⢀⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢈⠀⠀⠀⠸⠀⠈⠁⠂⠀⢣⠀⠀⠀⠀⠈⠙⠒⠦⢀⡀⠀⠀⠀⠘⠉
⣀⠀⢦⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠈⠉⠁⠑⠁⠀⣀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣁⣂⠆
⠀⠀⠈⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⠀⠀⢠⠀⠀⠀⣾⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠀⠒⠲⡐⠀⠀⢉⡝⢻⠀⠀⠈⠀⢸⠀⠀⠀⡹⠄⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢅⠀⠉⡀⢈⣀⣘⠀⢀⣀⠤⡴⠀⠀⠀⡇⠆⠀⠀⠸⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣈⣴⠉⠃⠈⡀⢹⡉⠀⠁⢀⡇⠀⠀⠀⠇⢰⠀⠀⠀⡆
⠶⠒⠒⠚⠛⠉⠁⡠⠒⡄⠀⠀⠧⠎⠀⠈⡆⠀⡀⠀⠀⢰⠂⠘⡇⠀⠀⢱⠀⠀⠀⠀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⠀⠀⠀⢀⡠⠔⣀⠌⠁⠉⠉⢻⠀⢀⡴⠒⠒⠛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠙⠚⠛⠛⠑⠋⠀⠸⠧⠠⠄⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣶⣶⣶⣶⣶⡿⢷⣶⣷⣷⣷⣿⣾⣷⣾⣷⣿⣾⣷⣶⣶⣶⣿⣿⣶⣿⣾⣿⣷⣾⣶⣾⣷⣾⢷⡶⢾⠷⢷⣿⡾⢷⣾⠾⢶

⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷
⠀⠀⣴⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿
⢠⣾⣿⣿⣿⡿⠋⠀⠀⠀⢀⣠⣾⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠙⣿⣿
⣿⣿⣿⣿⠟⠁⠀⠀⠀⣴⣿⣿⣿⡿⠋⠁⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠈⠙⢿⣿⣿⣿⣶⡄⠀⠀⠀⠈⠻
⣿⣿⣿⠏⠀⠀⠀⣠⣾⣿⣿⡿⠋⠀⠀⢀⣴⣾⣿⣿⠿⠛⠋⠉⠉⠀⠀⠀⠉⠉⠉⠛⠻⢿⣿⣿⣷⣤⡀⠀⠀⠉⠻⣿⣿⣿⣦⡀
⣿⣿⠃⠀⠀⠀⣰⣿⣿⣿⠋⠀⠀⣠⣾⣿⡿⠟⠉⠀⢀⣠⣤⣶⣶⣶⣶⣶⣶⣶⣤⣄⣀⠀⠈⠙⠿⣿⣿⣦⡀⠀⠀⠙⢿⣿⣿⣿⣄
⣿⠏⠀⠀⠀⣼⣿⣿⡿⠁⠀⢀⣴⣿⡿⠋⠀⢀⣤⣾⡿⠟⠛⠉⠉⠁⠀⠈⠉⠉⠛⠻⢿⣷⣦⣀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠻⣿⣿⣿⣆
⡟⠀⠀⠀⣰⣿⣿⡿⠁⠀⢀⣾⣿⡟⠁⢀⣴⣿⠟⠉⢀⣤⣶⡾⠿⠟⠛⠿⠿⢷⣶⣤⡀⠉⠻⣿⣷⡄⠀⠘⢿⣿⣷⡄⠀⠀⠹⣿⣿⣿⡆
⠁⠀⠀⢀⣿⣿⣿⠃⠀⢀⣾⣿⡟⠀⢠⣾⡿⠁⢀⣶⠟⠋⣠⣤⡶⠶⠶⠶⣦⣤⡈⠙⢿⣦⡀⠈⢻⣿⣦⠀⠈⢻⣿⣿⡄⠀⠀⢹⣿⣿⣿
⠀⠀⠀⢸⣿⣿⡏⠀⠀⣸⣿⡿⠀⢀⣿⡿⠁⣰⡿⠃⣠⡾⢋⣤⠶⠒⠒⠶⢦⣌⠛⢷⣄⠙⣿⣆⠀⠹⣿⣧⠀⠀⢿⣿⣷⠀⠀⠀⣿⣿⣿
⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⡇⠀⣸⣿⠃⢠⣿⠃⣼⠏⣰⢋⡴⣫⠭⠭⢝⡲⣌⢳⡄⢻⣆⠈⣿⣆⠀⢻⣿⡆⠀⠸⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⢸⡟⠀⣿⢰⡇⡞⡜⡠⠈⠁⠑⠙⡜⡆⢿⠀⣿⡀⢸⣿⠀⠸⣿⣇⠀⠀⣿⣿⣧⠀⠀⠘⣿⣿
⠀⠀⠀⣿⣿⣿⡄⠀⠀⣿⣿⡄⠀⢿⣿⠀⢸⣷⠀⣿⠸⡇⢧⢣⠁⢀⠀⢀⢫⢇⡇⣼⠀⣿⠇⢸⣿⠀⢀⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿
⠀⠀⠀⢹⣿⣿⡇⠀⠀⢿⣿⣇⠀⠸⣿⡆⠈⣿⡄⠹⣧⠙⣮⡳⠭⣴⣬⠵⣫⠞⣰⠏⢰⡿⠀⣼⡿⠀⢸⣿⡇⠀⠀⣿⣿⡏⠀⠀⢠⣿⣿
⡀⠀⠀⠘⣿⣿⣿⠀⠀⠘⣿⣿⡄⠀⢻⣿⣄⠈⢿⣦⡈⠳⣦⣉⡓⠒⠒⣋⣡⡾⠋⣰⡿⠁⣰⣿⠃⢀⣿⣿⠁⠀⢸⣿⣿⡇⠀⠀⢸⣿⣿
⣧⠀⠀⠀⢹⣿⣿⣧⠀⠀⠹⣿⣿⡄⠀⠹⣿⣦⡀⠙⠿⣦⣄⣉⣉⠛⢋⣉⣡⣴⡿⠋⢀⣼⡿⠃⢀⣾⣿⠏⠀⢀⣿⣿⡿⠀⠀⠀⣿⣿⣿
⣿⣆⠀⠀⠀⢻⣿⣿⣧⠀⠀⠘⢿⣿⣦⡀⠈⠻⢿⣶⣤⣀⠉⠙⠛⠛⠛⠛⠉⣁⣠⣶⡿⠋⠀⣠⣾⣿⠋⠀⢀⣾⣿⣿⠁⠀⠀⣸⣿⣿⣿
⣿⣿⣆⠀⠀⠀⠻⣿⣿⣷⡄⠀⠈⠻⣿⣿⣦⣀⠀⠉⠛⠿⢿⣷⣶⣶⣶⣾⠿⠿⠛⠉⢀⣠⣾⣿⠟⠁⠀⢠⣾⣿⡿⠃⠀⠀⢰⣿⣿⣿⡟
⣿⣿⣿⣆⠀⠀⠀⠙⢿⣿⣿⣦⡀⠀⠀⠙⠿⣿⣿⣶⣤⣄⣀⣀⠀⠀⠀⣀⣀⣠⣤⣶⣿⡿⠟⠁⠀⢀⣴⣿⣿⡟⠁⠀⠀⣰⣿⣿⣿⡟
⢿⣿⣿⣿⣷⡀⠀⠀⠀⠙⢿⣿⣿⣶⣄⡀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⣠⣴⣿⣿⡿⠋⠀⠀⢀⣴⣿⣿⣿⡟
⠀⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠙⠿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⠟⠋⠀⠀⠀⣠⣾⣿⣿⣿⠏
⠀⠀⠈⠻⣿⣿⣿⣿⣦⣀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⢀⣠⣾⣿⣿⣿⠟⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣠⣾
⣦⡀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⣠⣾⣿⣿
⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣼⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣿⢿⡿⠿⢿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠂⠀⢀⠰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⣶⠳⡖⢋⠕⢊⣾⠟⠓⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⢀⣿⠃⠀⠉⠉⢠⣿⠇⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⢧⠀⠀⠀⣾⣿⣀⣀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⣧⣀⣼⡇⢀⣿⣿⣿⣿⣿⣿⠀⠀⠸⣄⠀⣀⣠⣤⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣟⢶⡀⠀⠀⠀⡼⠁⠀⣰⠋⠉⠁⢸⡇⢐⣿⣿⣿⣿⣿⣿⠀⠀⠀⣽⢫⠁⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢠⠿⠀⢹⡆⠀⡰⠁⢀⡜⠁⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣇⢀⣠⠗⠉⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣦⡿⣄⢀⣀⡼⢀⠔⠁⠀⡎⠀⠀⠀⠀⠀⠈⡇⢸⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣾⢷⡿⡆⣤⠀⢁⠀⡀⢰⠃⠀⠀⠀⠀⠀⣰⠃⣬⣿⡿⠟⠋⠉⠀⠀⣀⣤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢹⡿⣔⣿⡻⠛⢡⡀⠀⠀⠀⠀⡴⢁⣾⣿⣿⡄⠀⠀⢀⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣷⠀⠈⠁⠙⠉⠳⠤⠏⢹⣄⣀⢀⣜⡡⢟⣫⣥⣾⣤⣤⣴⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠉⠀⢀⣺⣷⣤⣦⡀⠀⢀⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠸⣿⣏⠀⠉⣷⢀⣼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠓⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣙⣿⣿⣿⠿⠿⠛⠉

⠰⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣦⣄⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣻⣟⣷⣦⣀⣄⣄⠀⣠
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⡉⠙⣿⣿⣿⠋⠀⢻⣿⡿⠋⣽⣿⣿⠘⠀⠙⠻⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣷⣄⠈⠛⠁⠀⠀⠈⣿⠁⣼⣿⣿⣿⢸⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⡋⠉⠉⠉⠳⣄⠐⢾⡴⣼⢣⣾⠋⢛⣿⡟⢸⣷⣦⣀⠀⠀⠈⠛⠿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠃⢨⣄⣵⣿⣿⠰⣿⣿⡇⢸⣻⣿⣿⣷⣦⣄⡀⠀⠀⠉⠻⠿⠃
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠰⢾⣷⣾⡟⣛⣿⠀⠋⠉⡇⢸⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢠⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⣤⣛⣿⣿⢡⣀⣧⣰⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⢾⣯⣿⣿⣿⣿⡿⣾⣿⣿⡇⢸⣿⣿⣿⣿⣿⠟⠙⠻⣿⣿⣿⣿⣶
⢤⢠⣔⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠇⠀⣾⠀⠀⠀⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⠟⢉⣾⣷⠀⣼⣿⣽⣿⣿⣿
⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢠⣿⡇⠀⠀⣿⣿⣿⣷⣼⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣡⣴⣿⡿⠥⠴⠿⠿⠿⠿⠿⠿
⠻⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠒⠚⠛⠓⠒⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⢨⣥⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠶⠖⠒⠛⠛⠋⢙⡃⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⡤⠤⠤⠶⢶⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀⠀⠀⠀⠀⣀⡤⠴⠚⠋⣉⣡⠤⠤⠶⠒⠒⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⠒⠉⢀⣤⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡞⠉⢀⣀⣤⠤⠶⠖⠒⠚⠛⠉⢉⣉⣉⣩⡭⠿⠛
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣚⣉⣡⣤⣤⣤⣤⡖⠒⢛⣛⣯⣥
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠉⠉⠁⠀⠀⠀⠀⠢⠉⣿⡍⠉
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡠⠃⢷
⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣀⣤⠴⠚⠉⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⣀⣤⠶⢛⠽⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹⠦⠤⠤⡦⠤⠦⠥⠴⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⣿⣁⡤⣞⣁⣀⣀⣩⡷⣤⡀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠘⠻⣦⣤⣴⣶⠶⠦⠬⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠓⠶⢤⣤⣤⣀⣀⣀⣀⣠⣤⠶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁



⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡏⢽⣟⠻⢟⣟⡻⣻⣟⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢀⣸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣉⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⡿⢿⠙⠶⠖⠀⠀⠈⢛⡄⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣌⣀⠠⠀⠀⠀⠀⠈⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⣄⠤⠀⠠⠀⠀⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⣠⠆⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣾⢷⣶⠾⠛⣉⡤⠞⣡⣿⡿⠛⠷⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⢡⣾⡟⠁⠀⠿⢤⡼⠥⢤⣴⣿⡿⠁⠀⠀⠀⠀⠈⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠀⠀⠀⠀⣾⣿⠁⠄⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣯⡀⠀⠀⠀⠀⢀⣼⣿⡏⠀⠀⠀⠀⠀⠈⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠈⢷⡀⠀⠀⠀⣸⡿⠛⢿⣶⣤⣤⣤⣤⣤⣼⣿⣿⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠈⣷⡀⠀⣠⣿⡇⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠘⣷⡀⠀⠀⢀⣀⣀⣀⣀⣿
⢀⠀⠀⠀⠀⠀⠀⣾⣆⢠⡀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣰⠞⠿⠷⠛⠉⣿⠃⠀⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣷⣴⠞⠋⠉⠉⠉⠙⣿
⣼⡄⠀⠀⠀⠀⠀⢻⡜⠛⣧⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⣻⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢰⡿⠹⡆⠀⠀⠀⠀⠀⢿
⣿⣧⠀⠀⠀⠀⢠⡜⡇⠀⠸⣷⡇⠀⠀⠀⡼⠁⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣾⡧⠚⠁⠀⠀⠀⠀⠀⣸
⣿⣿⣆⠀⢰⡄⠸⠀⠀⠀⠀⣸⠇⠀⢀⡼⠃⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⡿
⢹⡟⢿⣆⣺⢷⡜⢦⣀⢀⣠⠟⢀⡴⠋⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁
⠈⣧⣈⣿⣯⣠⣿⡆⠈⢉⠁⠀⢸⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠈⠛⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⢀⣠⡴⠖⠋⠁
⠀⠘⣿⣇⠙⢿⠙⢿⣀⣿⡀⢀⠘⡴⢀⣴⢆⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⢀⣶⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⡏
⠀⠀⠈⣿⡄⠀⠀⠘⣿⡿⣇⢸⣷⡙⡟⠼⠋⢁⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⢠⣾⣿⣿⣿⣡⡄⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡀
⠀⣧⠀⢹⣷⡀⠀⠀⢻⡇⠹⣾⡏⢿⡆⠀⠀⣼⠿⣆⠀⠀⠀⠀⠀⢀⡾⠁⣤⣿⡿⠿⠛⢉⡝⠀⡔⣠⢀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⢳⣾⣿⡇⠀⠀⠀⠀⡀⠈⠀⠀⠙⠳⠛⠋⠀⢹⣧⣀⣀⡀⢠⣞⣡⠶⠋⣁⣤⣶⣿⣿⣤⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢿⡀⠈⠋⠋⠀⠀⠀⢦⣿⣦⡀⢠⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠘⣧⠀⠀⠀⠀⠀⣷⣾⣿⡯⠻⢿⣿⣦⠀⠀⠀⢸⣿⣿⡿⢟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠘⣧⡀⠀⠀⠀⢻⣿⣿⡁⠀⠀⠈⣿⣿⣀⣤⢿⣛⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢿⣿⢷⣤⣤⣀⠹⠿⠿⠶⣖⣒⣭⣭⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠈⢻⡉⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠙⠷⣤⡀⠛⢿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣭⣷⣶⣾⣿⣿⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡑⠤⡰⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠳⡑⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⠒⢄⠀⠿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⠀⠀⠀⠀⡥⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⢄⢀⡆⠠⠀⢠⡌⠀⠁⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠀⠀⠀⠀⠐⠂⠤⠄⣀⣀⣡⣀⢀⡎⠉⠁⡀⢀⡆⠀⢠⣠⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣀⣠⠃⣸⡟⠁⠉⠙⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⢟⡩⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢖⠢⡄⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠄⠀⠁⠄⠀⠀⠐⠊⢹⠁⠀⠀⠀⠀⠀⠈⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⡀⢀⠠⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠙⠁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢙⣅⠒⠠⠀⡀⡀⠀⠀⠀⠀⠑⡀⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⡁⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⢈⠎⠙⠒⠤⣀⠈⠙⠒⠤⢄⠀⡈⢄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠻⣦⡈⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠙⠒⠶⢤⣌⣉⣎⠁⠐⠤⡀⠀⠀⠀⠜⠠⠄⡈⢻⠈⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⡅⢹⡍⠲⡤⡝⠲⠆⢑⡃⣀⠇⠛⢠⢴⠀⠀⠀⠀⠀⢸⠰⣂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠈⠂⢝⡲⠧⣌⠛⠂⠀⢅⠼⡄⠀⠣⣌⣀⢠⡤⠀⠀⢁⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠁⠀⠀⠀⠀⢝⡖⠁⡀⠀⠀⠣⣄⣠⡔⠁⢫⠀⠀⠿⢤⠔⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢁⡀⠀⣀⠤⡈⢱⠈⢀⡀⠀⢀⡀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⢘⠑⠂⢀⠌⠈⠒⠁⢀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣀⠀⠀⠀⠀⠀⣱⠀⠀⠀⢸⠁⠒⠉⣑⠠⠤⠔⠁⠀⠀⠀⠀⢀⣨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢉⠆⠀⠀⠀⡀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠄⠄⠀⠀⢀⠀⠀⠒⣤⡤⠀⣀⡀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠉⠐⠂⠤⣘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠐⠣⠀⠀⠀⠀⠀⠀⠹⡿⠿⣷⣶⡂⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡀⣠⠀⣀⢀⣁⡍⠈⢧⡚⢣⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⢄⠄⠀⠀⠤⠀⠀⢀⠀⢀⠆⠀⢹⠊⠁⠀⢰⠁⠆⠀⠈⠣⡙⢄⢰⠆⠈⠁⠊⡡⠜⢓⠖⢒⡦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠈⠀⠉⠀⣀⣀⣋⠀⢨⠦⡄⢠⡎⠀⠀⠃⠰⠁⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠠⠤⠌⠀⠁⠀⠀⠀⠁⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣠⣭⣳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣰⣿⣿⢿⣟⡻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⣴⣿⣿⣟⡷⣮⣛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣼⣻⣿⣿⣯⣛⠶⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⣾⣿⣿⣽⡻⢶⣝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⣾⣿⣿⡿⣯⣝⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠻⣄⠀⠀⠀⠀⠀⠀⢠⠏⢠⣿⣿⣿⣯⣛⠷⣭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠙⣦⠀⠀⠀⠀⣠⠋⣠⣿⣿⣿⣟⢶⣍⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⢷⡀⠀⣰⠃⣰⣿⣿⣿⢾⣝⡳⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⣠⠤⡳⡴⠁⢰⣿⣿⣿⣟⠷⣮⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠽⠃⠙⣆⠀⠻⣿⡷⣭⡛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠈⢷⡒⠒⠿⣶⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢹⡦⠤⣄⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣠⠋⢹⡀⢸⠙⠲⣌⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⡰⠃⠀⠀⢣⢸⡄⠀⠈⠳⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⡜⠁⠀⠀⠀⠈⣇⢧⠀⠀⠀⠈⢦⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⠞⠀⠀⠀⠀⠀⠀⢹⡈⣆⠀⠀⠀⠀⢳⡀⠈⣩⣭⣭⣲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣡⠋⠀⠀⠀⠀⠀⠀⠀⠈⡇⠘⣆⠀⠀⠀⠀⡇⡾⠁⠀⠀⠙⢿⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣈⣓⢤⡀⠀⡇⢧⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣱⠋⠉⠉⠻⣮⣶⣛⣞⢧⡀⠀⠀⢀⡿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣇⠀⠀⠀⠀⠈⣿⣇⠈⠳⢭⣛⣚⣫⣞⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣣⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡘⣄⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠈⢣⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣓⠦⠤⢾⡻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠱⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠘⡤⠔⠀⠉⠉⠉⠉⠉⠁⠐⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⣀⢀⣀⢀⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠏⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⣠⡟⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⢸⠀⠀⠀⠀⠠⣄⡀⠀⠀⠤⠄⠒⣩⠏⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢻⠀⠀⠀⠀⠀⢀⠶⢆⡀⣀⠰⠚⠁⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⡇⠀⠀⠉⠀⠀⠀⠀⠀⠀⣷⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠖⠓⠀⠤⠤⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡛⢌⡦⣀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠻⣦⠈⠡⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠶⢶⠶⠶⠶⠆⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠘⣧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠠⠔⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢋⡆⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡺⠏⠦⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠰⠀⠳⣄⠀⠀⠀⣀⢠⠔⠒⡝⠁⠈⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆⠀⠀⠈⠷⠐⠊⠁⠀⢀⡠⠟⠲⠦⣤⣀⡀⠀⡌⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠈⠱⣤⡜⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠈⠉⠈
⠀⠀⠀⠀⠀⠀⡠⠛⠻⠉⠉⠉⠁⠀⠀⠈⠒⢄⡀⠀⢀⠞⠀⠈⠙⠃⠤⠤⠌⠿⠿⣧⡀
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠙⠓⠤⣀⣀⣀⣀⣀⣀⣀⡀⠀⡨⠛⢷⣄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢈⣳⣤⡚⢠⡄⠀⠀⠀⠀⠀⣤⣤⣤⡀⣀
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠛⠋
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⠒⣒⣖⡚⠛⣻⣿⡛⢻⣿⣖⠒⠒⠖⠲⠚⠷⠲⣶⣶⡶⠶⣶⣶⡿⢵⣶⣤⢶⣤
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠘⠋⠉⠃⠈⢉⠉⠃⢹⣏⣹⠃⠀⠀⠀⠀⠀⠰⣿⣽⣿⢺⣿⣹⡿⢺⣯⣽⣿⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡦⠤⠴⣦⠤⠤⠤⣤⡤⣥⣤⣤⣤⠤⠤⣤⣤⣤⣬⢭⣥⣤⣭⣭⣥⣬⣭⣉⣠⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡀⠀⢠⣀⣀⣠⣘⣀⣀⣀⣀⣀⣀⣀⣀⣛⣛⣛⣛⣛⣛⣻⣛⣛⣛⣻⣻⣯⢸⡇
⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠐⠒⠚⢦⠔⡄⠤⠀⠀⠀⠤⠄⠤⠤⠤⠤⠤⠤⠤⢤⣤⣄⠀⠀⠈⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⣁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠰⣆⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡇⠀⠀⢸⠀⠀⠀⠀⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠍⢹⠀⠀⠀⠉⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⡇⠀⢰⠀⠀⠀⠀⠀⠀⢘⣄⠀⡀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠭⠥⠤⠬⠤⠤⠤⠤⠤⠤⠤⢴
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠓⢤⣤⣇⠀⠱⢦⣄⠀⠠⣄⡀⢀⣀⣀⡀⢀⣀⣀⣀⣀⣀⢀⣀⠀⠀⢀⣀⣀⣀⣀⡀⣀⣀⣀⢀⡀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠛⠓⠒⠚⠛⠛⠛⠒⠛⠓⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠈⣇⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⠀⠀⠀⡟⠀⢿⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⢷⡄⢸⡇⠀⠸⡇⠀⠀⠀⣶⢹⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠙⢦⣥⠀⠀⠸⣄⠀⢠⡏⢸⠀⠀⠀⠀⠀⡶⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠻⡀⠀⠀⢹⡆⢸⠁⢸⠀⠀⠀⠀⢰⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠘⣄⠀⠀⠹⡯⠀⢸⡄⠀⠀⣠⠏⠀⢠⠇⠀⠀⠀⢀⣀⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠈⢇⠀⠀⢱⠀⠀⣷⣀⡴⠋⠀⠀⢸⠀⢀⣤⠖⢋⡥⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠈⡆⠀⠀⠤⠀⣸⠋⠀⠀⠀⢠⣧⠞⠋⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠐⠆⠀⠀⡴⠁⠀⠀⠀⡰⠟⠁⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢰⠀⠀⠇⠀⠀⢠⡞⠁⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⡆⠀⡄⠀⢀⠛⢇⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢡⠀⡄⠀⢸⠀⠈⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣧⠀⣸⡆⡄⠀⢈⡀⠀⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠀⠻⠉⣴⠓⠂⣹⣃⡠⠿⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡉⠠⡄⠐⠀⠀⢀⠟⠁⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠠⠀⠀⡰⠃⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠁⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠰⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⣰⠋⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢹⡆
⠀⣠⠃⠀⢠⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢱
⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢸
⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰
⡇⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡼
⡇⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣌⠁⠀⠀⠀⠰⡇
⢠⡀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⣶
⠈⣧⠀⠀⠃⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣰⠃
⠀⠘⣆⠀⠈⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠐⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠘⢷⡀⠀⠀⠀⠀⠈⠲⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠙⠲⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣦⣤⡀⠀⠀⠀⠀⣠⣤⣤⣤⣤⡤⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢱⡷⢻⡾⢿⡟⠛
⣶⣶⣶⣦⣶⣶⣶⣴⣴⣶⣶⣶⣶⣦⣴⣾⣷⣴⣧⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣶⣶
⣿⣿⣿⡏⠉⠛⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⣿⣿⢰⣾⡿⣿⡷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠈⠁⠀⠘⠃⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⣠⠄⡠⢔⣶⣶⣤⡀⠀⠀⠘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠁⠋⡴⣫⣿⡿⣿⣿⣦⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⣤⡼⢋⣴⣾⣿⢿⣿⡆⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢈⡴⢉⡜⣿⣵⠏⡴⠚⣿⡇⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠰⣫⠞⠁⠀⠀⠀⠾⢿⡷⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣡⣴⡶⠾⢿⣶⢶⣄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣾⣯⢤⡄⠀⠀⠠⠛⣿⣧⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⣠⡾⣿⡟⠠⡤⠀⠀⠰⠄⢿⣿⡀⣀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⠛⠋⠉⢧⡀⠀⠀⠀⠀⢰⠞⠳⠿⠿⢋⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢠⡒⢤⡀⠀⠈⣵⠀⠘⠛⢠⡜⠀⠀⣠⠖⠉⠹⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢶⠀⠰⠟⠳⣄⠻⡀⠈⠛⠛⠅⢠⡞⠁⠛⠀⠰⢶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣛⣛⠛⠻⣷⣶⠟⣲⠛⠲⠶⠋⣠⡞⠁⠚⡛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⣠⡶⠋⠙⠃⠈⣉⠉⠙⠃⣜⠉⢷⣟⡂⢻⡍⢠⣾⠠⣦⠉⠑⢶⡄
⠀⠀⠀⠀⠀⠸⣿⣆⠘⠃⠀⠀⠉⠀⢠⡄⢹⣆⠂⣙⠛⣂⣤⡿⠋⡀⠀⢠⣤⠀⠻⠄⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢈⣿⠇⠀⠀⡶⠀⠀⠈⠀⠀⢻⣄⠛⠉⢉⡄⠀⠈⠁⠀⣀⣀⠀⠀⣤⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣠⠞⠁⠘⠃⠀⠀⠀⠛⠁⠀⠈⠠⠿⣶⣤⡀⣁⣤⠶⠞⠛⠋⠉⢹⠀⣀⠀⢰⡄⢻⡄
⠀⠀⠀⠀⣸⣧⠀⠋⠀⠀⠀⠛⠀⠰⠀⡀⣤⢀⠀⠀⠈⡄⢡⠀⠀⠀⢀⠀⠀⢸⠈⠋⠀⠀⣠⡼⢧⡀
⠀⠀⠀⢸⣿⠃⠰⠄⠀⠛⠀⢴⡄⠂⠲⣍⡄⠠⠀⠀⠀⡇⠸⠀⠀⠀⣨⣥⠂⠘⠷⣄⠓⠐⡏⠀⠀⠙⠷⣄
⠀⠀⢀⠄⠁⠙⢦⠀⠀⣠⡄⠁⠀⠀⣈⣿⠞⠁⠀⠀⠀⠉⠀⠀⠀⠀⠁⠟⢀⣀⣀⠈⠛⠶⢜⣧⣄⣀⡀⠈⠳⣄⠀⠀⠀⠀⠗
⢀⡴⠃⠀⠀⠀⠀⠈⠉⠁⣠⡴⠾⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢦⣄⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠗
⣼⠁⠀⠀⠀⢀⣠⡴⠶⠿⣿⣶⡆⠀⣆⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⠀⠀⠀⣠⠔⠛⠃⠀⢠⡍⠻⢶⣤⣀⡀⠀⢀⣿⠂⠀⠀⠦
⠻⣶⣶⡾⠟⣟⠁⠌⠙⠶⠈⣿⡀⠤⠈⠉⠀⠒⠢⢤⣄⣀⣀⣁⡀⠐⠶⣭⣄⡀⠀⠀⠀⠀⠀⠠⠤⠄⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠙⠷⠞⠻⡆⠀⣿⡿⠀⠀⠦⠀⠀⢂⣤⣾⣿⣿⡿⠛⠳⣄⠀⠉⠛⠧⠐⣴⠀⢀⣴⢾⣶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⢀⣿⠁⣠⡄⠀⣠⣾⣿⣿⣿⣿⠏⠀⠀⠀⠘⣆⠺⠆⠀⠀⣿⡀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠈⢋⣿⡏⠀⣿⣿⣿⣿⡿⠋⠻⣄⠀⠀⠀⠀⢹⣆⠀⠀⠰⢿⣧⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⡿⢀⣇⢰⣾⣿⡀⢰⣿⣿⣿⣿⠁⠀⠀⠘⡆⠀⠀⠀⠀⢿⣆⢀⡄⠀⠉⠣⡈⢣
⠀⠀⠀⠀⠀⠀⣼⣧⣾⣹⣿⣿⡏⠁⣿⣿⣿⣿⡏⢠⡄⠀⠀⡿⠀⠀⠀⠀⠸⣿⡌⠛⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⢠⡟⠇⣼⡇⢹⣿⡇⠀⢸⣿⣿⣿⡇⠀⠁⠀⠀⢷⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠘⠶⠀⠘⣷⡄⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠈⣇⢠⡿⢀⣿⣿⡷⠶⠈⣿⣿⣿⡇⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢹⣿⠃⠀⢹⣿⣧⠀⠀⠹⣿⣿⡇⠀⠀⠀⠀⣾⣿⡄⠀⠀⠀⣿⣿⡇⠘⠃⠀⠀⠘⠃⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⣾⣯⠀⠀⠘⣿⣿⣶⠄⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⣷⡄⠀⠀⢹⣿⡇⠀⠀⣀⠀⠀⠀⢀⡀⠈⢻⣧⠀⠀⠀⠉
⠀⠀⠀⠀⠀⣼⡿⠁⠀⢾⠆⠘⠛⠃⠀⠀⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣷⠀⠀⢸⣿⡇⠀⠀⠉⠀⠀⠀⠘⠋⠀⠈⣿⡇⠀⠀⣤
⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⢴⡄⠀⣰⣿⣿⣧⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⢸⣿⣷⠀⠶⠀⠀⢸⠆⠀⠀⠀⠘⢿⣿⠀⠀⠁
⠀⠀⠀⠀⣿⣿⠀⠀⠛⠂⠀⠀⠀⢀⡴⠉⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⣿⣿⣄⣀⣀⣀⡀⠀⠀⢰⡦⠀⢸⣿
⠀⠀⠀⠀⠸⣿⡀⣠⡄⠀⠰⢀⠴⡏⠀⠀⠈⠛⢻⠀⠀⡟⢻⣿⣿⣿⣿⣿⣷⠀⢡⡈⠙⣇⠀⢈⡇⠈⠳⣄⠀⠀⢸⡿⠀⠂
⠀⠀⠀⠀⠀⠙⢷⣄⠀⢀⣶⡇⠀⠁⠀⠀⠀⠀⢸⡇⢰⠀⠀⠙⠿⠿⠿⠋⠸⣆⠀⢁⢀⡇⠀⣠⠁⠀⠀⢸⣷⠀⣾⠃⠀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠘⣷⠀⡆⠀⠀⠀⠀⢸⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⢿⡇⢰⠇⠀⠀⠀⠀⠻⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡇⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣈⣵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠃⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡟⠀⠀⠀⠀⠀⢸⣦⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣳⡀

⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⢤⡀
⠀⠀⠀⠀⠊⠁⠯⠽⠭⠇⠤⠀⠿⠿⠼⠵⠸⠥⠁⠸⠿⠫⠼⠯⠼⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠔⠁⠀⠀⠀⠀⠈⠶⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠛⠂⠀⠀⠀⠢⣤⣀⣠⣴⠶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠙⠢⢄⣀⡀⠀⠀⢀⣀⣠⠟⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⠅⠠⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢁⡄⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡒⠒⠂⠀⣀⠄⠀⠀⣀⡄⣀⡤⠞⣹⠁⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠣⠀⠈⠉⠁⠒⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⣉⠙⠛⠛⠉⠁⠉⠁⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⢅⣀⠤⣤⢤⣤⢤⡤⠼⢑⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠘⡄⠀⠜⣀⡀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠼⡇⠂⠀⠒⠒⠒⠒⠂⠀⠐⡁⠀⠠⠀⠀⠀⠀⠀⠀⡆⠀⠃⠀⠀⠀⠀⠀⠰⠀⠀⠀⠣⠜⠉⡤⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡖⠂⠉⠉⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠢⣀⡠⠆⠀⠀⠀⠀⠀⠀⡠⢶⠁
⠀⠀⡀⠀⠠⠀⠀⠀⠀⠇⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠢⠀⠀⢀⣀⠀⠀⠀⠀⠑⠢⢄⣀⣀⣀⣀⣀⣤⣤⡲⠯⠖⠋
⡀⢀⡍⠀⠐⠒⠒⠂⠀⢸⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⠀⢀⠀⣤⢯⡑⢢⣀⠀⢀⡔⠙⣏⡙⠉⢹⠏⠀⠀⠙⣄⠀⠀⡀
⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡦⢀⢀⡀⠀⠀⡀⠀⣀⠠⠤⠌⠀⠠⠀⠘⢯⣻⠄⠈⠒⠚⠳⠆⠀⠀⠉⢹⠀⠀⠀⠀⡇
⡇⠠⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠓⠠⠀⢀⠀⢀⡀⠀⢀⠤⢄⠀⠀⢀⡤⠴⠖⠊⠷⠀⠚⠀⠘⠒⠲⠤⢄⣸⠒⠤⣀⡴⠁
⡇⠀⠈⠦⠤⢤⠤⠤⠴⠏⣄⠀⠀⢩⠀⠀⠀⠁⠀⡯⠉⠐⠅⢤⣀⠀⠀⠘⡄⠀⠈⠁⠠⠠⠠⠄⠀⠀⣀⡤⠞⠋⠀⢠⣧⡴⢲
⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣟⠀⠀⠀⠐⡬⠤⣈⡤⠼⡆⠁⡀⠀⠀⠀⣺⠌⠉⠀⠀⢀⣠⠔⠉⢹⣤⠶⠥⠤⠤⠤⠤⠤
⡇⠁⠈⠁⠀⠉⠁⠉⠉⠉⠉⠁⠈⠈⠉⠁⠁⠁⠁⠉⠐⡀⠀⡌⠁⠉⠉⠁⠉⠁⠐⠠⠄⢀⣀⠳⣊⣤⠤⠚⠉⠀⠀⠀⠸⡎⡅⠉⠁⠉⠉⠈⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠦⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡖
⡇⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠉⢹⠃⠀⠒⠂⠒⠁⢧
⡇⠀⠀⠀⠀⠀⠈⠉⠒⠂⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⡄
⠧⠤⠤⠤⠤⡌⠀⠀⠀⠀⢨⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡔⠉⠑⠲⠤⢤⡼⠀⠀⠀⠀⠀⠀⠀⢣⠠⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⢣⡀⠀⠀⠀⢀⠷⠤⣄⣀⠀⠀⠀⠀⢸
⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠆⠀⠐⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠙⣄⠀⠀⠀⠉⠉⠐⣒⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠂⠉⠁
⡿⢿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⢸⢣⡄⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⢀⠜⡼⠃⠀⠀⣴⠆
⠀⠀⠀⠀⠀⠀⢤⡤⣄⠀⠀⠀⠀⠘⢷⡀⠀⠀⢸⠀⢷⠀⠀⠀⠀⠀⢠⡞⢹⠀⢠⠏⡼⠁⠀⣠⠞⡯
⠀⠀⠀⠀⠀⠀⠀⠙⢤⡙⠶⣄⠀⠀⠈⣿⣄⠀⠀⡄⠀⢇⠀⠀⠀⢀⠏⢰⡇⢠⠋⣼⠁⠀⣴⠃⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⢦⣀⠘⣻⣆⠀⡏⠀⠈⣆⠀⢀⡎⠀⣼⢀⠇⣸⠇⢀⡜⠁⠀⡌
⠛⠛⠛⠛⠷⠶⣦⣤⣀⠀⠀⠙⢦⡀⠈⠳⣌⢫⣆⠀⡀⠀⠘⣦⡻⠀⠀⢳⡌⢠⡟⢀⡞⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢶⣦⣄⡙⢆⠀⠈⠻⣿⣷⣥⠀⠀⠘⠃⠀⢰⡿⠀⡞⢀⡞⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢟⡢⢵⣄⠀⠘⢧⠻⡆⠀⠆⠀⠀⢸⡇⢰⠁⡾⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢷⡄⠈⢡⠘⣦⡀⠀⠀⡙⢀⣸⡼⠁⠀⠀⢠⠋⠀⠀⠀⠀⣀⣤⡴⠆⣉⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠙⣦⡀⢆⠸⠁⠀⠀⠀⠀⢹⠃⠀⠀⢀⠆⠀⣀⠤⠒⠉⠉⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡈⢳⡈⢴⠀⠀⠰⠆⠀⠈⠀⠀⢠⢎⡴⠊⠁⠀⣀⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠹⡼⠀⠀⢸⠀⠸⠃⠀⣠⡿⠋⣀⡴⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠰⢃⡀⠀⠀⠚⠀⣴⠏⢀⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢠⣯⣴⠔⣿⡀⣼⠃⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⠻⠀⠉⠀⠉⠁⠰⠞⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡀⠈⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠢⡀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⣄⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢣
⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢳⠀⣰⡀⠄⢤⣀⠰⣄⠀⣠⣤⡴⠶⠶⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠩⠾⠻⠟⠙⣷⠉⢾⡇
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣀⣀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢛⣷⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⣿⣿⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢲⡟⠛⠏⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⡖⠶⣹⣗⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣾⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣻⡟⢹⢿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⢹⡇⡸⠈⣿⣃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⡇⢇⠀⣸⡟⢃⡀⠛⠷⢦⠐⢠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠉⡎⣴⣿⣓⡿⣾⣷⠲⠻⠟⠫⠁⠁⠈⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠿⠀⠀⣽⣿⣿⡟⣹⠨⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⢶⡿⠿⠛⠀⠀⣰⣿⣿⣇⣤⠾⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⡯⠟⠀⠂⠀⢀⠀⠀⢠⣿⣿⣿⣿⣿⡀⠀⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⢋⠰⠿⠃⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢀⣾⣿⣿⣿⣿⡃⠆⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⣼⣿⣿⣿⣿⣿⣧⣶⡆⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⢸⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⣾⣿⣏⣿⣿⣿⣿⣿⣿⣿⣷⣆⣠⣀⢀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣦⡁⠀⢠⣄⣤⡿⠃
⠀⠸⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡠⣺⣿⡟⠁
⠀⠀⢻⣿⣿⣿⣿⣿⣏⣀⣤⡶⠚⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡟
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⠟⠀⠈⠋⠙⠛⠿⣿⡿⢿⣿⣿⣿⣯⣿⣤⠄
⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠇⠀⠀⠨⠻⠿⡿⠀⡁
⠀⠀⠀⠀⠘⣿⣿⣽⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⣦⣿⡿
⠀⠀⠀⠀⠀⣼⣏⠁⠂⠈⠹⠯⢭⣤⣦⣶⣶⣿⣷⣧⡄⠀⠀⠀⠀⢀⠀⢀⣿⠟⠁
⠀⠀⠀⢀⠵⢿⣿⡟⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣻⣵⠞⠋
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⡗⠀⢀⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣁⣄⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡟⢻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠀⠀⠉⠁⠀⠀⠈⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⠊⠀⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⡀⡠⠔⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠩⠿⠛⠂⠠⡤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⠛⠣⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠰⠉⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⢤⣄⡀⢀⣀⠼⠖⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠒⠛⣻⠟⠉⠉⠉⢅⣀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠾⠛⠛⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠸⡁⠈⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢬⣽⣷⣦⣤⠤⠴⠦⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⣀⣀⡀⠀⠀⠀⣸⡤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡦⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠿⠟⠛⠛⠄⢤⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠕

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⣀⡀⠀⢀⣠⢤⡀
⠀⠀⣿⠀⠀⢠⡎⠁⠀⠀⠈⠙⡆⠀⣼⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣀⠀⠀⢸⠀⠀⢸⠀⠀⢹⣿⠀⠀⠀⢸⣿⠀⣼⠁⠀⢳
⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⢠⠃⠀⠘⠿⢿⣿⣿⠿⠿⠛⠛⠛⠛⠙⠉⠀⠀⠀⢸⠀⠀⢸⠀⠀⠸⣿⠀⠀⠀⢸⣿⠀⣏⠀⠀⢸
⠀⠀⣿⠀⠀⠀⢣⠀⠀⠀⠀⣸⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢾⠀⠀⠀⣿⠀⠀⠀⢸⣿⠀⢹⡀⢀⡟
⠀⠀⣿⠀⠀⠀⠀⠉⢲⡶⠋⠁⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⠀⠀⠑⣿⠀⠀⠐⢾⣿⠀⠀⢹⡟
⠀⠀⣿⣦⡀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠘⠀⠀⠀⣸⠀⠀⠀⢸⣿⠀⠀⢸⣇
⠀⢰⣿⡆⢹⡄⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⠀⠚⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣞⡿⠀⠀⢸⡿
⠀⠸⣿⡇⠀⠁⠀⠀⠘⠃⠀⠀⠀⢀⠀⠀⢆⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁
⠀⠀⣿⡄⠀⠀⠀⢀⡠⠤⠤⢄⡀⠀⠑⢄⠸⣆⠀⠀⠐⠋⠁⠀⣠⣀⣤⡄⠀⠀⠀⠀⠀⠀⠰⣶⣶⣦⣶⣶⡶⠀⠀⣰⡾⠿⢿⣦
⠀⢠⣿⡇⠀⠀⡴⠁⠀⠀⠀⠀⠉⢦⠀⠈⠳⣿⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⢈⣿⡏⠀⠀⠀⠀⣿⣅⠀⢠⣿⠂
⠀⠘⣿⡇⠀⣴⠃⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠈⢷⣦⡀⠀⠀⠀⠈⠉⢿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⠛⠿⠛⠁
⠀⠀⣽⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⢰⠏⠑⢦⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡳⢦⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⣤⡀
⠀⠀⠛⠀⠀⠀⠫⢗⠤⠤⠤⠴⡺⠏⠀⠀⠀⢀⠼⡀⠀⠀⣍⠈⣢⠀⠀⠀⢻⣻⣿⣿⣿⣿⣷⡄⠀⠀⠀⡇⠀⠀⢸⡀⠀⠀⣿⡇
⠀⠀⢀⡀⠀⠀⠀⠀⣬⣽⣮⣥⠀⠀⠀⠀⠀⢆⢀⡼⠀⠀⠀⠈⠉⠲⠀⠀⠀⠁⠙⠛⢿⡿⣿⣿⠆⠀⢸⣿⣿⣿⣿⡇⠀⠀⣿⡇
⠀⠀⣸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡄⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⣤⣄⣀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⣿⡇
⠀⠀⣿⣿⣧⠀⢠⣤⣤⣤⡄⠀⠀⢰⣷⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠀⠀⣹⣿⣿⣿⣶⢤⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⠀⠉
⠀⠀⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⣴⣾⣿⣶⡄⠀⠀⣿⣿⠃⠀⠀⡆⠀⣠⠟⠋⠉⣿⣿⠁⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣇⠀⠀⡇
⠀⠀⣿⣿⣿⠀⠸⣿⣿⣿⠃⠀⣿⣿⣿⣿⡇⠀⠓⣿⡇⠀⠀⢀⡇⠈⠁⠀⠀⢸⣿⣿⡁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇
⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⢀⣴⣿⣿⣿⣿⣦⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇
⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⠀⣿⠀⠀⠀⣼⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⡷
⠀⠀⣿⣿⡿⠀⠀⢽⣛⣿⠀⠀⣿⣿⣿⣿⡇⠀⠀⡟⠀⠀⠀⣿⣿⡁⠀⠈⢿⣿⣿⣿⣿⠟⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣦⣤⣀⡤⠤⢤⡀⠀⠀⠀⠙⠆⣰⠿⠃⠀⠀⠀⢀⣶⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢱⠀⠀⢀⡀⠀⠀⢠⡞⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠞⠀⠀⢸⣧⠀⢰⡿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢀⣴⣦
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⢧⡉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⡴⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⣇⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢸⠃⠀⠀⠀⠚⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠈⠲⠤⠞⠋⠛⠿⠿⣿⡿⠿⠟⠋⠀⠀⠀⠀⠀⠈⢧⣄⣀⣠⡞⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣴⣶⣦⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⢀⣤⠀⠀⠀⢸⡏⠉⠉⠉⠉⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⡂⠀⠀⢸⣧⣤⣤⣤⣄⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣴⣿⣿⣿⣄⡀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⠇⠀⠀⢸⣿⣿⣟⣿⣿⣿
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⡿⣿⣿⣿⣷⡀⠀⠀⠛⠻⠛⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿⣇⣽⣿⣿⣿⡇⠀⣀⣀⣀⢀⣀⣀⠀⠨⣿⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⡿⠁⠀⢨⡟⣱⣿⡇⠀⢿⣿⣿⣿⣿⣿⠁⠈⣿⠀⠀⠀⣼⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣷⠀⠀⠀⠁⠙⢿⡇⠀⠀⠛⠻⠿⠛⠁⠀⠀⣿⠀⠀⠀⣿⣿⣿⣿⣿⣯⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢠⣾⡇⠀⢀⠀⠀⠤⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣷⣾⣿⣿⡇⠀⢈⠀⢁⠀⠆⠀⣠⣴⣿⣤⡀
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⡆⠀⢠⣄⣀⣀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠇⠀⢿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠙⠻⠟⠛⠁⠀⠀⠀⠙⠛⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣛⣿⠿⣶⣽⣿⡸⢷⣎⣷⣣⣸⣟⠵⠀⠐⡀⠠⣣⡚⠟⢿⣷⠗⢿⡏⣛⣿⠿⣶⣿⣿⡘⢷⣎⣷⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢛⢹⣗⢿⣭⣼⢿⣬⣤⣿⠏⢁⣷⣶⣖⣴⣶⡰⡳⣀⢎⢎⣿⣇⠛⣷⡟⣹⡗⣻⣥⣼⢿⣤⣥⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣧⣶⣿⡉⢿⣿⣿⣿⣶⣟⣓⣯⢿⣫⣙⣳⣔⣾⠟⢟⣻⡛⣶⡉⡻⣿⣧⣶⣿⡭⢿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣿⣽⣿⠛⠟⠋⢼⣯⢡⣷⢶⣯⣭⣿⣿⢏⢺⣏⣈⡷⣾⣏⢇⢈⢾⣏⣿⣽⣿⠛⡟⠋⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢸⣟⣻⣧⡿⣀⡖⠐⡀⢻⣿⣾⣀⣿⡾⢯⣿⣿⡏⡭⠽⣳⡬⡧⢤⡿⢸⣟⣻⣧⡿⣒⡖⠒⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡦⣠⣞⡰⡶⢿⢿⢶⢾⡟⢣⣶⣶⣶⡏⣉⣉⣁⣐⣂⣈⢻⡷⣞⣲⣾⠦⣷⣞⡰⠶⢿⢿⢶⣾⡟⣣⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⢟⣵⣭⣿⡿⠉⣨⣶⣾⣿⣿⣿⣷⠿⠽⣍⢿⢯⡝⣿⣧⣏⢿⣷⣤⣿⣟⣵⣭⣿⡿⠉⣨⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⢫⡿⢁⣬⣤⢻⣿⣿⡋⠩⣿⣾⡶⢶⢾⣿⣯⡗⢻⣿⣿⣿⣻⣯⣹⣾⢋⡿⣁⣬⣥⢻⣿⣿⡏⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⢸⣯⣿⣿⣧⣄⣅⢹⣼⣿⣧⢶⢲⢺⣿⠝⠣⣮⣴⡽⢿⣷⣤⠗⠽⣾⢸⣯⣿⣿⣇⣌⣅⢻⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠙⣻⣥⣌⢁⣉⣿⣿⣶⣮⢐⠡⡠⣻⣵⣿⣧⡽⠷⢾⡶⢻⡷⡎⠹⣆⠛⣻⣥⣌⢁⣉⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠦⣿⣛⣽⡷⢻⣿⣽⣓⣿⠷⢾⣯⠐⠰⠱⢯⣷⡽⡧⣶⢾⡿⢧⣿⣷⢶⡿⣛⣹⡿⢻⣿⣿⣓⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⠟⢋⡁⣂⠺⣿⣾⠋⢹⣿⡾⠿⣡⡤⠴⠬⣿⣶⣷⡿⣶⣿⡛⡏⣹⣿⠟⠋⠁⣒⢺⣯⣾⠫⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣿⣶⠶⣆⡄⠠⣬⣟⠛⡿⠟⢛⣶⣿⣆⣴⣿⣬⣭⠻⡖⡶⡩⡟⣠⡶⣿⣶⡶⣆⡄⢐⣬⣟⠛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣛⣷⠺⣮⣽⢿⡜⢷⣎⣷⣡⣨⣟⠥⡂⡞⡀⠲⡱⡉⢟⣻⣷⠗⢻⡏⣛⣿⠺⢦⣿⢿⡜⢳⣎⣿⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡋⢽⡗⠻⣴⣼⢯⣤⣤⣿⠏⢡⣵⣷⣵⣴⣶⡴⡱⠄⢎⣎⣿⣇⠙⣷⡋⢽⣟⠻⣔⣾⢿⣤⣤⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣷⣶⢿⣍⢿⣿⣿⣿⣾⣟⣱⣽⠿⣩⣟⣻⣄⣷⢏⢋⣙⡙⢶⡉⡹⢿⣷⣶⢿⣍⢿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣏⣿⣽⣿⠛⠟⢋⢾⣯⢣⣷⢶⣏⣯⣿⣾⢧⢻⣯⣀⡟⢾⣯⢧⢀⢾⣏⣿⣽⣟⡛⠛⢋⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢸⣏⣻⣷⠟⢰⡖⠐⠂⠹⣿⣧⣀⣿⠾⠿⣿⣿⣏⡭⠼⣷⡤⠇⢤⡿⢸⣏⣻⣷⠟⣰⡖⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⣠⣞⡴⠶⣟⣿⢶⣾⠏⢣⣶⣾⣷⡏⣩⣩⣡⡈⣀⣈⢻⡷⣎⣐⣾⠶⣷⢟⡴⠶⣟⣿⢶⢾⠏⢣⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢷⣭⡿⠾⠉⣨⣷⣿⣿⣿⣿⣿⠿⠵⣭⢿⢯⡝⣿⣧⣯⢿⣳⣬⣿⣿⣵⣭⡿⠿⠉⣨⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢩⡟⣁⣤⣭⢻⣿⡿⡫⠨⣿⡼⠿⠿⢿⣿⣯⡟⢻⣿⣽⣿⣿⣿⡹⣿⢩⡟⣁⣤⣭⢻⣿⡿⡍⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⢸⣯⢿⣿⣗⣀⣀⣹⣼⣿⣧⣟⣺⢺⣿⠘⢧⣦⣼⡽⣿⣷⣤⠓⢼⣾⢸⣯⢿⣿⣗⣀⣠⣹⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣚⣻⡥⣄⣀⣂⣽⠿⣦⣬⠔⠁⡠⣻⣵⣿⣧⡾⠟⢶⠟⠻⡷⡎⠹⣆⣛⣻⡧⣬⣀⣀⣽⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢦⡿⣫⣽⠾⢹⣿⢽⣛⣿⠗⢺⣯⠸⠔⡱⢿⣾⡼⣷⣶⢺⢿⢷⣿⣿⠶⡿⣫⣵⠿⢹⣿⢽⣛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠟⠉⠁⢂⠸⢿⣿⢛⢻⣿⡿⠿⣡⠴⠶⠼⣿⣶⣿⡿⢶⣟⣛⡏⢹⣿⠟⠉⠁⡂⠸⢯⣿⢑⢹
⢀⠀⡀⠀⢀⠀⠀⠀⡀⠀⢀⠀⠀⣠⣶⣟⣷⣶⣦⣬⣨⣤⣝⣻⣿⣟⣛⣧⣻⣦⣴⣿⣤⣭⢻⣖⣶⣩⣟⣤⣶⣟⣷⣶⣦⣬⣈⣤⣽⣛⣿
⣿⣏⢩⣟⡛⣛⣛⡛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠀⠛⠙⠋⠠⠈⠻⣿⢿⣿⣿⣿⡿⢿⡿⢿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣷⣿⠹⠛
⠟⠛⠛⠛⠛⠛⠛⢻⢻⡿⣿⣿⡿⠿⠛⠛⠛⠛⠛⠛⠛⠻⠛⠛⠛⣛⣻⠟⠿⠿⠿⠛⢿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿
⣀⡀⠘⠋⠀⠀⠀⠉⠈⢉⣿⣿⣿⡿⠆⠀⠀⠠⢄⣀⠀⣠⣈⣻⣤⣌⣉⣩⣥⣤⣤⣴⣼⣿⣿⣿⣿⣬⣽⣿⣿⣿⣿
⣿⣷⣶⣷⡒⠒⠒⠒⠓⢾⣿⠟⠛⠓⠒⠒⠒⠚⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⠟⠛⠛⠛⢻⣿⣿⣿⣿
⣺⣋⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣟⠻⠿⠻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠐⠒⠒⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠦⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠂⢰⣶⡖⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠙⠳⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠘⣃⠈⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿
⣿⣿⣿⣷⡷⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢸⣿⣿⣶⣶
⣿⣿⣿⣿⣷⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣟⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠡⢈⡀⠰⠀⠄⠀⠙⡵⡀⡀⠀⠀⠀⠀⠠⣄⣶⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣤⣺⠆⠀⠀⠀⠀⠉⠐⢤⠧⡄⢳⣹⢧⠀⠀⣰⣬⣟⠟⠉⠀⡸⠀⠀⠀⢸⣿⣿⡿⢿
⠿⠿⠿⠿⠗⢀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠐⠂⠀⠀⠀⣳⣷⡘⣭⣿⡆⣴⣿⡟⠃⠀⠀⢊⣀⠀⠀⠀⢸⣿⣿⣷⣿
⣀⡀⠘⠗⠀⠷⠿⢿⣦⡄⣜⣁⠀⠠⠀⠀⡀⢰⡾⠛⢈⡁⠉⠃⣿⣿⣿⣿⣿⣁⣴⣶⢟⣻⣬⣷⣤⠀⢸⣿⣿⣿⣿
⣿⣷⣶⣶⠆⠀⠤⣀⣈⠓⠾⠦⠤⠄⠊⢀⢡⠋⠀⠀⠀⣿⣧⠀⣿⣿⣿⣿⡿⡿⠚⠊⠉⠀⠈⢿⣿⣧⣼⣿⣿⣿⣿
⢳⣞⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢧⡯⠁⠀⣀⢺⡿⠋⣠⣿⣛⣉⣡⣴⣬⣽⣲⣆⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠇⣀⣄⣀⡀⠀⠀⠀⠀⠐⡠⠋⠀⠀⠀⠟⠀⠀⠜⣻⣾⣿⡟⠁⠀⢰⣿⣿⢿⣿⡆⠀⠈⠻⢿⣿⣿⣿⣿
⠬⠤⠦⠄⠉⠉⠉⠉⠙⠓⠢⠀⠂⠁⠀⠀⠰⠒⠀⠀⠀⠀⢠⣿⡵⢿⠀⠀⠀⠘⣯⢼⡌⢿⣿⠀⠀⠀⢸⣿⣿⣿⣿
⠀⢠⣶⡶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣿⡝⠐⠂⠀⠀⠀⠀⣿⣼⡃⢸⣿⡄⠀⠀⢸⣿⣿⣿⠿
⠀⠋⠙⠉⡙⢦⡀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠈⡸⣿⠛⠀⠀⠀⠀⠀⠀⠙⣟⢳⣿⣿⠃⠀⠀⢸⣿⣿⡿⠿
⣶⣿⣶⣷⣧⠈⣿⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢠⡰⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡧⣤⣀⠀⢸⣿⣿⣦⣤
⣿⣿⣿⣿⣿⠀⡟⠀⠀⠀⠀⠀⠀⠘⠻⠠⡄⠄⢲⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⠁⠑⠚⠿⠿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠱⢖⣯⣿⠵⠛⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿
⣿⡿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣿
⠀⠀⠰⠶⠀⠲⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣤⣤⠤⠤⠤⣬⣽⣿⣯⣿⣿⣭⣭⣤⣭⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⡿⠿⢿⠷⠄⠲⡜⠛⡟⢿⣿⠿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠖⠻⢏⠉⠉⠉⠉⠝⢦⠁⠈⠉⠉⠛⣶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣛⡛⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡼⠀⠀⠀⠀⢀⢘⡇⠈⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠙⡆⠀⠀⠀⡾⠀⠀⠀⠀⡾⠁⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⣿⢦⣄
⠀⠀⠀⠀⠀⣠⡿⠭⣄⠀⠀⠀⢸⡁⠀⠀⠀⠘⣆⠀⠀⠀⢹⠀⠀⡀⠀⡞⠀⠀⠀⠀⡀⠄⣀⡟⠐⠉⠳⣄
⠀⠀⠀⠀⣴⠋⠈⠁⠈⣧⠂⠀⠀⠑⢦⠂⠀⠀⢸⡎⠀⠀⢸⠀⠀⠀⢀⡇⡀⠀⠀⣰⠞⠉⠑⠀⠀⠀⠀⢨⠷⣄
⠀⠀⠀⣼⢃⠠⠀⠀⠀⠘⢦⡂⠀⠀⠈⢳⠀⠀⡸⣇⠀⣠⢿⡀⠀⣠⠞⠁⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⣌⡼⡀⠙⢧⡀
⠀⠀⣸⡏⠙⠉⢦⡆⠀⠀⠀⠘⢦⡀⠀⣸⣷⠶⠛⡟⠉⢹⡝⠛⢻⡾⣦⣀⢤⠞⠁⠀⠀⢀⡴⢊⠉⠉⠁⠀⠀⠀⠈⢷⡀
⠀⢀⡟⠀⠀⠀⠈⠟⠒⠾⢤⣄⠀⣯⡿⠛⢹⠀⢰⡃⢀⡏⠀⣴⠖⠁⠀⢽⢾⡀⠀⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠠⢹⢷
⠀⢸⣇⣤⣤⠀⠀⢀⠀⠀⠀⠈⢻⡟⠍⢧⡊⢳⣄⣷⣤⣏⣠⠇⢀⡞⠋⠉⠀⢻⣿⠉⠀⠀⠀⠀⢀⡤⠤⠤⣤⡤⠶⠋⠺⣇
⠀⢸⠃⠁⠈⠙⠒⠒⠒⠒⠦⣴⣿⠙⠢⠤⣽⣿⣟⣏⣏⡟⣻⣶⣏⣀⡴⠛⠛⠏⢻⡦⡤⠤⠴⠚⠉⠀⠀⠈⠀⠀⠀⠀⠀⢻⡀
⠀⢸⡄⠀⠀⠀⡀⠀⠀⣀⣀⣠⣿⠓⠦⠲⢾⡏⣼⣯⡟⢷⣵⣻⣿⣉⡤⠖⠲⢦⠞⣿⡋⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣸⡇
⠀⠸⣷⠚⠛⡲⠾⠒⠯⠁⠀⢠⣿⣶⠲⠚⣹⣷⣬⣯⣷⣿⠷⢮⣿⣌⣀⡤⢤⡈⠀⣹⣽⢶⠦⠴⠶⠚⠩⠩⠉⢓⢲⠒⠚⠝⡇
⠀⠀⢻⡀⠀⠀⠀⠀⢔⡤⢞⠉⢁⣿⣶⠉⣡⠏⢹⢹⡏⢫⢉⣾⡷⣄⣀⡀⠁⠉⢋⣿⢇⣀⠀⠈⠀⠀⠈⠀⠀⠀⠈⠐⠀⠀⡇
⠀⠀⠈⢷⣠⠶⠒⠛⠉⠀⠀⢠⠞⠁⢈⣿⣧⣴⣯⣼⡵⣾⡟⠳⡄⠀⠉⢉⢷⣀⣰⡟⠋⠙⠒⠳⠶⠶⠖⠶⢤⡄⠀⠀⠀⣸⡇
⠀⠀⠀⠈⢿⡁⠀⠀⠠⢀⣠⠏⠐⢢⡟⠀⢤⡏⠀⢹⠐⠸⣆⠀⠌⠙⢦⠀⠀⣼⠿⠶⠤⣤⣀⡀⠀⢀⠀⠀⠀⠉⠙⡒⢋⣸⠃
⠀⠀⠀⠀⠀⠻⣦⣰⠚⠉⠀⠀⢀⡼⠁⠀⢸⡇⠀⠸⡄⠀⠈⢳⠀⠀⠘⢲⡾⠃⠀⠀⠀⠀⠉⠛⠲⢬⣀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⡀⣰⠋⠀⠀⠀⡼⡁⠀⢀⡇⠀⠀⠸⣄⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣴⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣄⣈⣸⡁⠀⠀⠘⣆⣠⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⢸⣏⣿⣿⣿⡛⠛⣿⠛⣛⣿⣟⣛⣿⠿⣿⠛⠛⠃⠀⠀⠀⠀⠈⠛⠛⣿⠿⣿⣛⣻⣿⣛⠛⣿⠛⢛⣿⣿⣿⣻⡇
⠀⠀⠀⠀⢸⣿⡇⠈⢻⣷⢦⣽⡿⠋⢩⣭⣿⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⣿⣯⡍⠙⢿⣯⡶⣮⣟⠁⢸⣿⡇
⠀⠀⠀⠀⢸⣯⣿⡟⠋⣀⣠⣿⡅⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⣠⣾⣷⣄⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⢨⣿⣄⣈⠙⢻⣿⣽⡇
⠀⠀⠀⠀⢸⣿⣆⢠⡾⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⣿⣿⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠛⢷⡄⣰⣿⡇
⠀⠀⠀⠀⢸⣇⣿⣿⢠⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢿⣦⣰⣿⣿⣆⣴⡿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡌⣿⣿⣸⡇
⠀⠀⠀⠀⢸⠏⠁⠙⠿⠟⠁⠀⠀⠀⠀⠀⠀⣠⣾⣫⣴⣾⡿⢃⣿⣿⡘⢿⣷⣤⣝⣷⣄⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠈⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⠿⠷⣾⡏⠀⠀⢽⡯⠀⠀⢹⣶⠿⠿⣿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠻⣿⠀⢲⣿⣆⠀⠀⠘⠃⠀⠀⣸⣿⡖⠀⣿⠟⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⠛⠛⠷⢿⣿⣿⣥⣿⠇⠀⠀⠀⠀⠸⣿⣬⣿⣿⡷⠾⠛⠛⣿⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠚⠛⠳⣶⣦⣤⣤⣴⠞⠋⠀⠀⠀⠀⠀⠀⠙⠳⣦⣤⣤⣴⣶⠞⠛⠓⢿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣟⣁⣿⣠⡶⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⢶⣄⣿⣈⣷⣄
⠀⠀⠀⠀⢀⣴⣟⣿⠋⣉⠹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠏⣉⠙⣿⣻⣦⡀
⠀⠀⠀⠴⠟⠋⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣧⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠙⠻⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⡉⠙⠁⠈⠋⢙⠿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡟⠳⠀⠀⠀⠀⠀⠀⠀⠀⠞⢻⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⠶⠖⠀⠀⠀⠀⠲⠶⣶⣶⣿⣿⣿⣾⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⡞⠳⣿⣿⠟⠋⠉⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠉⠙⠻⣿⣏⠞⢻⣿⣦⡀
⠀⠀⠀⠀⠀⣠⡾⠟⠉⠛⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠋⠉⠻⢷⣄
⠀⠀⢀⣴⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣦⡀
⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⣀⣷⣾⣀⡙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠛⠉⠉⠉⠉⠛⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢋⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣷⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⢀⣤⡮⠜⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⠀⠀⢀⠴
⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠠⢿⠏
⠀⠀⠀⠀⠀⠸⠿⢿⣿⡟⠋⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣠⣤⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠚⠙⠓⠶⣤⣄⡀⠀⠀⠀⠀⠀⣇
⢀⣼⣿⠋⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠀⠀⠀⠀⢿
⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠉⢰⠣⠀⠀⠀⠀⠀⠀⡾⠃
⠀⠀⠀⠀⠀⠀⠈⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⢀
⣄⠀⠀⠀⠀⠀⠀⠀⡜⢄⢁⣄⠀⠀⠀⠀⠐⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠻
⠈⠳⢦⡀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢸⣦
⠀⠀⠀⠉⠳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⢀⢴⠏⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣿⣷⠄⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠿⠇⠀⠀⠀⠀⠀⢓⠊⠀⠀⠀⠀⢠⣤⣤⣾⣿⣿⡿⠟⠉⠀⠀⠀⠈⠻⣧
⠀⠀⠀⠀⠀⠐⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢻⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⣆
⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠈⠙⠛⠛⠓⠶⠒⠃⠐⠂⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⡠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠈⢀⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢤⢧⣀⣿⠀⠀⠀⠀⠀⠀⠀⢠⠐⢦⣷⣀⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⡼⠀⠈⠉⠂⠀⠀⠀⠀⠀⠀⠘⢦⡼⠇⠈⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣦⣄⠀⠀⠀⠀⢠⣿⣷⣶⣠⡀⠀⠀⠀⠀⠀⣰⣿⣷⡶⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠃⠀⠀⠀⣰⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠁⠀⠀⠀⢴⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠁⠀⠀⠀⠀⠈⠉⠛⢿⡿⠁⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⡀⠀⠙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠻⠿⠃⠀⠀⠀⠀⠀⠀⣴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠏
⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢟⠐⠡⠆
⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠃⠀⠀⢀⡔⠱⠀⠀⠀⠀⠀⠀⣠⢘⠂⡀⠀⠨⠗
⠀⠀⠀⠒⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡘⠀⠀⢀⠎⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣰⡄
⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⠃⠀⡠⠃⠊⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠛⠛⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡚⠀⡔⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢈⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠈
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠾⠃
⣀⣀⣄⣀⣄⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡛⣛⢛⣉⡛⣻⡛⣻⠟⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠒⠲⡶⡦⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⢤⠤⠤⠤⡄⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣢⣠⡀⠸⣄⣇⣀⣀⣀⣀⣀⣀⠀⠀⠀⠈⣆⣃⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠒⠒⠒⢒⡀⠠⡀⠀⠉⣯⠉⠀⠀⠀⠈⠁⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠃⠀⠀⢸⠀⠀⠀⠀⠀⢀⣰⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠈⡍⠋⠉⠙⠒⠒⠲⠂⠀⠀⣾⡇⠀⠠⠧⠄⠀⠛⠒⠀⢀⠈⠭⠉⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠠⠀⡠⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣡⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⡀⠂⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠍⣁⡐⢂⡀⠀⠀⠀⣿⠁⠂⠀⢣⢀⣀⣤⠤⠒⠒⢩⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣼⠃⠀⠀⢰⠈⠉⠀⠈⠀⠀⠀⢸⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠠⠤⣀⠀⠀⠀⠀⢨⠀⠀⠀⠀⡀⠀⠀⠀⢸⠀⠀⠀⢠⠀⠀⠀⠘⠀⠀⣠⡟⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠿⠶⠤⡀⡘⠀⠀⣀⣀⣇⣀⣠⣤⣬⣤⣤⣤⠶⠶⠶⠾⢿⢟⣽⠏⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠃⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠁⠐⠒⠒⠒⠒⠒⠒⠂⠐⠶⠦⠤⠤⠤⠤⠤⠤⣀⣀⣀⣀⡀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⢀⠤⠔⠢⢤⣀⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡤⣤⢤⠀⡠⢠⣄⢀⣄⢀⣀⠀⢠⣤⡀⣠⠄⡤
⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⠀⠁⠉⠉⠉⠉⠈⠁⠁⠈⠉⠀⠉⠉⠁
⠀⠀⢀⡴⠊⠁⠀⠀⢀⡤⣄⠀⠀⠀⠀⡼
⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠙⠒⠒⠊⢳
⠀⠀⠈⠓⠒⢷⠒⠂⠸⠤⠖⠉⠛⣄⢀⡮⣀⡀
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢀⡨⠋⠀⠀⠉⠓⢤⡀
⠀⠀⠀⢀⠎⠈⠙⠒⠒⠒⠒⠋⠁⢀⠀⠀⠀⠀⠀⠀⠘⢉⡆
⠀⠀⠀⡜⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠑⠄⠀⠐⠠⠀⣀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠃⠀⠀⠀⠀⠀⢳⠤⣀⣈⡠⢄⣀⠈⣀⣤⣀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠈⡄⢀⠀⠀⠀⠀⠀⢧⠀⠤⠀⠀⠈⠉⠁⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢐⠀⠀⠀⠀⡀⠠⠤⣌⠢⡀
⠀⠀⠀⡇⠠⠀⠀⠀⠀⠀⢸⠀⣀⠀⠀⠀⠀⠀⠠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠉⠉⠉⢨⠀⡠⡖⠁⠀⠀⠀⠀⠀⠈⡖⢄
⠀⠀⠀⡇⢠⠀⠀⡆⠀⠀⡇⠀⠀⢀⡀⢀⡠⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠳⡌⠉⠭⠭⠭⠭⠍⠋⠥⠎
⠀⠀⢴⠃⠠⠀⠀⠀⠀⢀⣇⣀⣀⠀⠈⣉⣠⣴⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⡀⠀⠀⠉⠳⣄⣠⣄⡀⢸⠉⠙⢏⠙⠛⢡⡟⢦⡀⠀⣀⠄⢢⢧⠄⠀⠀⠀⡀⠀⠇⠀⠀⠀⠀⣤⠁⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢘⡀
⡇⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠘⡏⠉⠀⠰⠚⠂⠀⠀⢴⠋⠂⠄⡀⠀⠀⠐⠂⠤⠔⠒⣁⠀⣇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇
⡇⠀⠀⠀⠀⠀⠀⠶⣼⣄⣀⠤⢞⡥⠒⡂⠉⠁⠙⠁⠀⠊⠓⠲⠦⣅⠀⠀⠁⠀⠀⠀⠈⠀⠈⠗⠀⣤⠀⠀⣸⡀⠀⠀⠀⠀⠀⢸⠗
⠇⠀⠀⠀⠀⠀⠈⠂⡤⠏⠡⡀⠈⠑⠨⠑⣒⠀⠀⠀⠀⠒⠒⠂⢁⠅⠀⠀⢠⣀⣀⣀⣠⠀⠰⡀⠀⠇⠀⡀⠩⣷⣦⣤⣤⣤⣶⡧
⡆⠀⠀⠀⠀⠀⠀⡔⢸⠁⠀⠘⠢⠄⡀⠀⠀⠰⢁⠀⠀⠀⢀⡠⠂
⠁⠀⠀⠀⠀⠀⠀⣗⠃⣀⠀⠀⠀⠀⠈⠐⠒⠚⡳⣶⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⡬⠤⠭⢭⡭⠄⡾⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠙⢄⠀⢀⡾⠄⡀⢥
⠁⠀⠀⠀⠀⢀⠞⠁⠉⢦⠤⠉⣽⠂⠠⠐⠚⡦⡀
⠁⠀⠀⠀⠀⠘⡀⠀⠀⠘⢄⣀⠼⡄⠀⠉⠈⠀⠈⠆
⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⡳⠄⣀⢀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠤⠚⠁
⣶⡶⢶⢶⡶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⢶⣶⣶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⣲⣲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣞⣻⠁⢈⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⣀⡀⠀⣀⣀⣀⡀⠀⠀⠠⠅⠈⣇⠀⠉⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣰⣷⣤⣤⣤⣤⣤⣤⣤⡀⠀⣺⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠸⠏⠹⣿⡧⠀⠀⠀⠀⢀⠀⠀⠀⠚⠀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢴⣄⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⢨⣪⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣲⢟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⠀⠀⠀⠈⠀⢀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⢀⠞⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢈⡖⣀⠘⠀⢩⠁⠘⢛⢭⣞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠄⠠⠤⠄⠀⠀⠀⠀⠞⠊⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠪⢦⠀⣩⠇⢼⣁⠑⣍⣇
⠀⠀⠀⠀⠀⠀⠀⠐⠲⠀⠒⠒⢔⢰⠔⢤⠀⠀⢀⠞⠀⡤⠀⠀⠂⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠓⠛⠉⠉⠉⠀⠀⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⡆⠀⡌⢺⢀⠀⣀⣴⡁⠀⡰⠁⠀⠀⣀⣄⣀⣀⣀⣀⣀⣀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠁⠀⣀⣜⠁⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⢠⡀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠨⠈⠉⠙⠉⡉⠑⢁⡀⠀⠁⠀⠀⠘⠀⠀⠀⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⣀⡄⣤⣀⡀
⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⢀⣠⡔⢥⣈⡉⢙⢦⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣜⡓⢶⣿⡏⠈⠘⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⡍⠋⠉⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⢄⠐⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠒⠒⠒⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⢀⡀⠀⠀⠀⠀⠀⠀⠘⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⣰⠋⠉⠉⠉⣗⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣧⣄⠀⢀⣀⡈⠲⣀⣤⡀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢘⡷⡆⠀⢠⣄⠁⠀⠋⠀⣹⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⢸⠀⣄⠀⠀⠀⠀⠀⢀⠔⠃⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⢰⡬⢤⡤⠀⠀⠀⣿⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠼⣆⠓⠊⠀⠀⣠⠔⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⠒⠉⠀⠀⠹⣷⣄⣀⣠⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⢧⡀⠀⠀⢀⡏⠉⠉⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠉⠓⠢⠞⠀⠀⠀⠀⠀⠘⢆
⣠⠶⠿⣽⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠁⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⣀⣧⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠦⣤⣀⣤⠖⣫⡥⢭⣑⣶⠚⠛⢳⡀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⣤⠖⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠔⠋⠀⠀⠀⢯⠙⢷⡄⠀⢧⡀⠀⠀⠀⠀⠀⠀⣸⠀⣞⢇⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠻⣦⡀⠱⣄⠀⠀⠀⠀⠀⡇⠀⠘⢾⣷⢄⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠈⠻⡓⠾⢦⣄⣀⣀⠀⣷⣄⠀⠀⠻⣮⠳⡄⠀⢀⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠳⣄⠈⠓⠒⢶⡙⠲⣝⢷⠈⠓⠦⣄⣹⡷⡈⠢⣼⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠑⢄⡀⠀⠹⢤⣈⣻⡆⠀⢀⣀⣩⢃⣷⣄⣈⣳⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⠛⠛⠛⢻⠿⠆⠀⠀⠉⡿⠯⢭⣉⣽⣟⣋⣉⣉⣉⣉⣉⣉⣉⣩⠭⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠘⠒⢾⠀⠀⠈⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠤⠤⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⠤⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡏⠙⠲⢤⣄⡀⠀⠀⠉⠳⣶⣦⣤⣤⣤⡤⢤⣤⣤⡶⢶⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠙⠒⠤⢄⣉⠉⠉⠁⠀⠀⢀⣤⣤⣭⣭⣥⣤⡴⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣤⡤⠶⠴⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⢤⣀⣼⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⡇⠉⠓⠲⢤⣉⡙⠲⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⢸⠅⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⡇⣰⡄⣄⢠⡀⣼⡇⢸⡇⢢⣰⢠⢠⣠⠋⡿⡶⣤⣬⣙⡶⡦⣶⣀⣠⠂⣼⣦⣾⣾⢦⠀⠀⡀⠀⠀⢉⠧⡎⡦⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠉⠁⠈⠀⠁⢹⠉⢹⡏⠉⠈⠈⠈⠈⠀⠁⠁⠋⠉⠉⠛⠧⢬⣉⠉⠛⠻⠇⢿⢹⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣓⣦⣄⣸⣼⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠹⡄⢸⠇⡇⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⣇⢳⣸⢠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣹⡄⣿⢰⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣻⡇⠈⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠸⡆⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣧⠀⠸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⢻⠀⢀⠙⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⢏⡀⢸⠀⢧⠳⣄⠙⠻⢷⣶⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⡵⢋⡞⠀⡍⠀⠈⢧⡈⠑⠦⣄⡀⠀⠉⠉⠉⠙⠛⠛⠷⠶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⣛⠝⣠⢞⣵⠋⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠉⠛⠲⢤⣄⡀⠀⠀⠀⠀⠲⢬⡉⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⢋⣩⠖⠋⣡⠞⣡⠟⠁⠀⢰⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⣄⠈⠉⠓⠦⣄⡀⠀⠀⠙⢦⡀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⣠⡶⠛⠁⣠⠴⠋⢀⣴⠞⢡⡾⠁⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠈⢳⡀⠀⠀⠈⠙⢦⣄⠀⠀⢻⣄⠀⠈⢿⡄
⠀⠀⠀⣠⡾⠋⠀⣠⠞⠁⢀⣴⠟⠁⣴⠏⠀⠀⢀⠂⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠹⣆⠀⠀⠀⠀⠙⢧⡀⠀⢻⡆⠀⠀⢻⡄
⠀⠀⣰⡿⠁⢀⡾⡡⠀⣰⠟⠁⠀⣼⠏⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠘⣆⠀⠀⠀⠀⠀⢳⡀⠈⣿⠀⡀⠈⣷
⠀⢰⣿⠁⢠⡟⣰⠃⣼⠃⠀⠀⢰⡟⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⢹⡆⠀⠀⠀⠀⠈⡇⠀⢸⡇⢳⠀⢹
⠀⢸⡿⢀⡟⢀⡇⣸⠃⠀⠀⠀⣾⠃⠀⠀⠀⠀⢸⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⣿⠀⠀⠀⡀⠀⠀⠀⢸⡇⣸⠀⢸
⠀⢸⣧⢸⠁⢸⡇⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⢸⡇⠀⠀⡇⠀⠀⠀⣼⢃⡟⠀⡿
⠀⠀⣿⡄⠀⢸⡇⣷⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⢀⣿⡾⠁⣸⠃
⠀⠀⠘⣷⡀⠀⠃⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡾⠁⠀⠀⣼⡿⢁⣼⠃
⠀⠀⠀⠈⢷⡀⠀⠈⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠁⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⣀⣠⣴⣚⣡⣤⠴⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠶⣤⣤⣴⣷⣶⠞⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⠦⣤⣭⣴⣶⠶⠶⠾⣿⢟⣿⢹⡏⠻⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠘⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⢀⡬⠍⠝⠢⢱⠀⡄⠀⠀⠀⠀⠀⣠⠖⠉⡠⠀⠀⠀⡢⡀
⠀⢠⠖⠚⠒⢁⠔⢠⠀⠀⠀⠀⠀⠀⠀⠀⣰⢳⠎⠉⠁⠀⠈⣞⡁⠀⠀⠀⠀⡼⠁⣠⠊⣠⠴⠊⠀⢱⡘⡄
⠀⢸⠗⠀⡤⢌⡆⠀⡆⠀⡄⠀⠋⡇⠀⠀⡇⠂⠄⠰⠀⠀⠀⡠⡄⠀⠀⠀⢰⡇⢰⠃⡀⠀⠀⠘⠀⠂⡇⢹
⠀⠀⠁⠁⠹⠚⠁⠀⠀⠀⠀⠰⡯⠀⠀⠀⠘⢄⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⡇⢻⠀⠀⠀⠀⠀⠐⠀⡗⢸
⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⡑⠂⠀⠀⠀⠀⢀⠇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢠⢖⣺⡶⠰⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⣉⠭⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠂⡚⠑
⠀⠀⢸⠙⠊⠐⢶⡞⠋⠀⠀⠀⠀⠀⢀⡠⠴⠒⠋⠁⢠⠞⡱⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃
⠀⠀⠈⠑⠈⢝⠉⠀⠀⠆⠠⠀⠀⠐⠁⠀⣀⣠⠤⠖⠃⣼⠁⠆⠀⠆⠀⢄⠀⠀⠀⠀⠀⣀⠀⠀⠊⠆
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠊⠁⠀⠀⣀⡴⠃⠀⠀⠀⠀⠀⣸⠂⠀⠀⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠐⠀⠆⠀⠅⣀
⠀⠀⠀⠀⠀⠄⡀⢀⠀⠘⠀⠁⢀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⡀⠀⢀⡱⠀⠀⢀
⠀⠀⠀⠀⠈⢀⠃⡌⠀⠄⠀⠤⣾⠀⠀⠀⠀⠀⠈⢠⠰⢀⠀⠘⡘⠄⠀⠀⠀⠀⠀⠁⠀⢯⠄⠀⠴⠘⢢⠐⠀⡁
⠀⠀⠀⠀⠃⢸⠀⡇⠀⠀⡄⢀⡇⠀⠀⠀⠀⠀⠀⠈⠀⠐⠃⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⣞⠀⠄⠀⠀⢺⠀⠀⠐
⠀⠀⠀⠀⠀⠸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠗⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣤⣤⠄⢀⣠⣤⣤⣀⠀⠀⠤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⠀⠀⠠⣤⣤
⣫⠁⠀⠉⢰⣿⣿⡟⠀⠀⣰⣿⣿⠏⠀⢀⣼⣿⡿⠓⠶⠶⣶⣦⣤⣤⣤⣀⣀⣀⣀⢢⠘⢿⣷⣄⠀⠀⠙
⣿⠀⠀⠀⢸⣿⣿⠃⠀⢠⣿⡿⠃⠀⣴⣿⠿⠋⠀⣠⣼⣶⣦⣌⡉⠛⠛⠿⢿⣿⣿⣿⣧⠈⠻⣿⣷⣄
⣿⠀⠀⠀⣿⣿⡏⠀⢠⣿⡟⠁⣠⣾⠟⢁⣠⣶⠿⠛⠋⢉⣀⣨⡛⢷⣦⣄⣀⠀⠉⠉⠘⣧⡀⠙⣿⣿⣧
⣿⠀⠀⢠⣿⣿⠀⢠⣿⠏⣠⠾⣋⣴⠞⣫⡥⠴⣶⡚⠛⠛⠛⠛⠛⢦⣈⠛⢿⣿⣶⣤⣄⢹⣷⡀⠈⢻⣿
⣿⠀⠀⢸⣿⠇⢠⡿⢡⣾⡇⠀⣿⡏⢠⡿⢁⡾⢋⣨⠯⢍⣛⠛⠿⢧⡙⣷⣄⠈⠙⠿⢿⠀⢿⣷⡀⠀⠙
⣿⠀⠀⣾⡟⢠⣟⡀⠀⢿⣇⠀⣿⢁⡟⡴⡫⢾⢹⢖⣚⣛⡮⡙⠶⣦⢳⡈⠻⣷⣄⡀⢸⡆⠘⣿⣷⡀
⣿⡆⠀⣿⠁⠿⣿⣷⠀⢸⣿⢀⡏⣞⢸⡆⡇⣇⢫⡫⣤⢔⡚⣌⢷⢼⡌⢿⡄⠘⠿⡇⢸⣧⠀⢹⣿⣷⡀
⣿⡇⢸⣏⡀⠀⠙⣿⣇⠈⣿⢸⡁⠹⣆⢧⣝⢏⡺⣿⣿⢏⠺⡜⢷⡆⣧⠘⣿⣦⢰⡇⢸⣿⡀⠀⢿⣿⣷
⣿⡇⣼⣿⣿⣆⠀⠘⣿⡆⢹⠈⠻⣦⡙⡜⠮⣕⣲⠍⣢⢇⢗⡞⣸⠁⣿⡄⣸⠃⣾⠁⢸⣿⡇⠀⠘⣿⣿
⣿⠇⠁⠈⠻⣿⣷⡄⠘⢿⡈⣿⣦⣌⠙⢮⡛⠒⢒⣊⣰⣋⠾⣁⠿⣠⠞⣴⠇⢸⣿⠀⢸⣿⣷⠀⠀⢹⡿
⢿⢣⣄⠀⠀⠈⠻⣿⣦⠈⢷⢀⡈⠙⠛⠶⣝⡛⢉⣩⣥⠶⢋⣥⠞⢁⣾⠏⠀⣿⡟⠀⢸⣿⣿⣄⡠⢠⣾
⢸⣿⣿⣿⣦⣄⠀⠈⠻⣷⡌⢿⠿⠿⣶⣶⣤⣭⣙⣋⢀⣴⡿⠋⢠⣾⡟⠀⣸⣿⡇⠀⠘⣟⡿⠋⣰⣿⠃
⠸⠏⠛⠿⣿⣿⣿⣦⣀⠈⠻⣦⢀⣀⣀⣀⣀⣀⣈⣭⣭⣭⣥⡤⠿⠟⢀⣀⡿⠟⢋⣥⡾⠋⢀⣾⣿⠃
⡄⠀⠀⠀⠀⠉⠛⠿⣿⣷⣦⣈⠻⣿⠿⠿⠛⠛⠋⠉⠉⣁⣠⣴⣶⠿⠛⠉⣠⣶⡿⠋⠀⣠⣿⣿⠃
⣷⢸⣶⣤⣤⣀⡀⠀⠀⠉⠛⠿⣷⣬⡀⢀⣠⣤⣶⣾⣿⡿⠟⠉⠀⣀⣴⣿⡿⠋⠀⢀⣼⣿⣿⠃⠀⠀⣸

⠀⠰⢿⣿⣾⠃⠀⠀⠹⠻⠳⠀⠀⠢⠄⡉⠓⠟⠁⡀⢀⣌⠻⣿⠾⣷⡆⠀⠈⠛⠛⠰⠿⠀⠀⠀⠹⡷⡿⠅
⠀⢰⡿⣿⣿⠃⠀⠈⢛⣠⡛⠀⠀⠒⠂⢛⣄⣄⠘⠃⠘⢻⡟⣿⣷⡄⠀⠀⣾⠏⣴⣶⡄⠀⠀⠒⠋⣄⡀⠑⠂
⠀⢈⣻⣿⣟⠃⠀⠐⡿⣿⡷⠂⠀⣀⠀⠚⢧⡿⠆⠀⠀⢼⢟⣿⣋⡦⠀⠀⠈⠛⠈⢉⡀⠀⠀⠀⢑⡤⡜⠂
⠀⢈⣿⣿⣹⡇⠀⠰⠖⡁⠶⠆⠀⣨⠁⢶⡀⠀⠰⠇⠀⠰⣿⣿⣹⣏⡀⠀⠰⣿⡿⢈⣿⠀⠀⠀⠒⣀⡁⠂⠁
⠀⢈⣽⣿⣿⡄⠀⠀⣶⣻⡧⠄⠀⠀⠀⢼⣟⣿⠀⠀⢰⣶⣬⣿⣍⠛⠇⠀⣠⡤⢀⣈⠉⠀⠀⠀⣾⣟⣿⣖
⠀⠨⣯⣿⣿⡄⠀⢀⣈⠙⣉⠀⠀⠙⠒⣄⠙⠁⢠⡇⠀⢸⣧⣿⡿⡃⠀⠀⠿⣧⠻⠿⠃⠀⠀⠀⣈⠟⠏⡂
⠀⠰⣾⣿⢷⡄⠀⠀⣰⣴⡤⠀⠀⠉⠀⣸⡶⣖⠀⠀⠀⢘⣵⣿⢶⡯⠀⠀⢀⣤⣤⠰⣦⠀⠀⠀⣀⠆⢖⠈⠃
⠀⠰⢿⣿⣾⠃⠀⠈⡛⡿⣋⠀⠀⠦⠠⡙⠲⠏⢀⡂⢀⣌⠻⣿⠾⣷⡆⠀⠀⠛⠋⠰⠟⠀⠀⢀⠨⠒⠎⢁⡄
⠀⢰⡟⣿⣿⠃⠀⠈⣃⣄⡛⠁⠀⠒⠈⢻⣤⡤⠘⠁⠘⢻⡟⣿⣷⡄⠁⠀⣾⡏⣴⣶⡄⠀⠀⠀⢩⣦⣆⠅
⠀⢈⣻⣿⣿⠃⠀⠐⢺⣽⠯⠂⠀⣀⢐⢺⢭⡿⠀⠀⠀⢼⢟⣿⣫⡦⠀⠀⠉⠛⠈⢉⡀⠀⠀⠀⢿⣯⣿⠯
⠀⢈⣿⣿⣹⡇⠀⠀⠶⢈⠦⠀⠀⡬⠈⢆⠀⠀⠸⠂⠀⠰⣿⣿⣹⣏⡀⠀⠀⣿⡿⢈⣿⠀⠀⠀⠤⡉⠁⠄⡀
⠀⢈⣽⣿⣷⡄⠀⠠⣼⣿⣶⠀⠀⠀⠠⢼⣛⣧⠀⠀⢰⣷⣬⣿⣍⠛⠇⠀⣠⡤⢀⣈⠁⠀⠀⠀⠢⠋⡱
⠀⠸⣷⣿⣿⡄⠀⢠⡍⠋⣥⡄⠀⠑⢐⣌⠙⠁⢰⠅⠀⢸⣧⣿⡿⡃⠀⠀⠿⣧⠻⠿⠃⠀⠀⠠⠌⠉⠃⡤⠆
⠀⠰⢺⣿⢧⡄⠀⠀⢥⢧⣆⠀⠈⠉⠀⣸⢶⣖⠀⠀⠀⢙⣵⣿⢶⡯⠀⠀⢀⣤⣤⠰⣦⠀⠀⠀⣰⡷⣷⡂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠿⠗⠶⢦⡙⢇⣠⣤⣤⠄⡀⢀⣴⢞⣫⣭⣬⣥⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠁⠀⠀⠐⢠⣶⡿⣽⠋⣴⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣦⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠋⣠⣾⣿⣿⣷⠹⣿⣇⣯⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⣼⣿⣿⣿⣿⣿⣷⣌⠻⣾⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⢰⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⣽⣿⣷⣾⣿⣿⣿⣿⣿⣿⡿⠟⣫⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣏⡄⢸⣿⣿⡿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠉⠙⠛⠶⠾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢸⡇⠘⣿⣿⣿⣮⣻⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢸⣷⡀⠹⣿⣿⠋⠀⠹⠟⠀⠀⠀⠒⠚⠛⠻⢶⣄⡀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡀⣿⣧⠀⢻⣿⣇⠀⠀⠀⠀⢲⣿⣶⣶⣶⣤⡄⠉⠁⠀⠠⠖⢒⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⢻⣿⡄⢠⢻⣿⣄⡀⠀⠀⠀⠙⠳⡮⣭⠟⠃⠀⢀⣶⣶⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⣿⢿⣿⣿⡇⣼⡞⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣻⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣟⣿⣿⣣⣿⣇⣿⣿⣿⠙⢦⡀⠀⠀⠀⢤⣀⡀⠀⠁⢠⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⣠⢞⣛⣲⠹⡿⢋⣥⡉⢻⣿⡿⣿⣿⠀⠀⠙⣦⡀⠀⠀⠍⠉⣠⣶⣯⣿⣿⣿⡏
⠀⠀⠀⠀⠀⣼⣏⢺⣿⡿⢠⠃⣿⣿⣿⢸⣿⣧⣿⣿⡄⠀⠀⠈⢻⣶⣤⣴⣿⣿⣿⣿⢟⣥⣶⣶⣄
⠀⠀⠀⠀⠀⣿⣿⣦⣭⡤⣋⣾⣿⣿⠏⣼⣿⣿⣿⠋⢧⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡸⠿⣿⡿⣹⠃
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡿⠟⠁⠀⠈⠃⠀⠀⠀⠙⠻⠿⣿⣿⣿⡿⠿⠿⣋⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢠⣤⣀⣤⣀⣤⢠⣤⣤⣤⣤⣄⡄⠀⣤⡀⣄⣄⣤⣄⠀⣤⣤⢀⣄⢠⣠⣤⡀⢀⣤⡀⣤⢠⡄⢀⣤⣀⣄⡄
⠀⠀⠸⠿⠿⠿⠼⠿⠾⢿⠇⠿⠁⠿⠁⠰⠿⠧⠿⠧⠿⠿⠀⠿⠿⠼⠿⠼⠼⠿⠇⠸⠿⠾⠿⠿⠷⠾⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡅⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠈⣻⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⠀⠊⠑⠀⢙⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢄⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⣀⠄⡀⠀⠀⠀⠀⠀⠘⣰⣤⠔⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠋⠐⠲⠟⡩⢆⠈⠀⠀⠀⠀⠀⠀⢇⣀⠀⢠⡴⠂⠸⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⣢⣬⣤⡀⠀⡄⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠈⠑⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⡇⠀⠙⣄⠀⠀⢨⡛⢷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠈⢣⡀⠀⠁⠀⠀⠀⠀⠀⡴⠀⠀⠀⠈⠁⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠱⣤⠁⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠳⣄⣀⣴⠃⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⣀⣤⣤⣄⣀⠀⣀⣀⡄⡀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠈⠙⡆⠀⠀⠀⠀⠀⠀⣴⣻⠃
⠀⠀⠀⠀⢀⣠⣴⣶⣆⠈⣿⡟⢳⡄⠈⢹⣿⠿⠟⠋⢉⣭⣅⣀⡀⠀⠀⢰⢻⣆⡀⠀⠀⠀⡠⠀⠁⠀⠀⠀⢀⣴⡾⢡⡏
⠀⠀⠀⠀⠈⢛⠻⣿⣿⣶⣿⣭⣬⠍⢠⡀⢲⣿⠻⠇⠈⠳⣮⣛⣄⡈⠀⣿⠘⠿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠁⣼
⠀⠀⠀⠀⠀⠈⢦⡹⣿⣿⣿⣿⣿⠦⣈⠁⣼⠿⠀⠀⠀⠀⠈⣿⣾⢁⣀⡏⠀⠀⣿⣿⣦⣄⠀⢀⣤⣶⣿⡿⠁⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠿⠛⠛⠛⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⢇⣾⣿⠇⠀⠀⠈⠙⢿⣿⣿⣿⡿⠛⠉⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣜⡻⢿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠡⠀⠀⠀⢀⡀⡀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣖⣨⣴⠚⡤⣀⢄⣸⣦⣤⣤⣾⣷⣚⠉⡀⣰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢳⠻⣿⣜⣿⣽⡿⢽⣿⣷⣿⣿⣯⣿⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡘⢿⣧⣿⣿⣿⣧⣼⣿⣿⣿⣿⣧⣼⣿⣏⡧⢤⠀⣀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣏⡸⣽⡄⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⡖⢉⠴
⠀⠀⠀⠀⠀⠠⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⡭⢔⣠
⠀⠀⠀⠀⠀⠀⢸⡍⣷⢬⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣕⢷⠁
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣜⣧⠊
⠀⠀⠀⠀⠀⠀⠈⠉⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⢀⠀⣼⣧⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⡇
⠀⠀⠀⠀⠀⠈⢿⣿⣯⡿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠨⠜⠰⠻⠷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⢣⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⣫⣟⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡧⢴⡯⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⡉⠽⣿⣻⡾⠿⠛⠣⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂

⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣰⣄⡀⠀⠀⣀⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠝⠉⠀⢰⠿⡛⠃⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠰⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢄⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⡴⠠⡄⠀⠀⠐⠃⠀⠀⠀⠀⠅⠀⠀⠀⠋⠀⡀⠂
⠀⠀⠀⠠⠀⠀⠀⠀⠀⡖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠈⠀⢀⠀⠀⢀⠑⠋⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⡄⡀⢀⠀⣠⡀⢀⢤⡀⡀⡀⢀⣄⡀⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣧⡇⣿⡀⢻⡀⠘⢦⢠⣇⠀⢸⢸⢻⡇⠀⠀⠀⠈⢢⠄⠀⢀⣴⡿
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⠓⠋⠁⠘⠖⠋⠘⠐⠂⠂⠀⠁⠐⡃⠀⠀⠀⠀⡀⠸⠟⠀⠀⠀⣀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⡀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠈⠈⠀⠀⠁⠀⠀⡀⠀⢄⠀⠉⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠖⠋⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠞⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⡰⠋⡦⠀⢠⡀⡇⠀⠀⠀⢀⣰⠏
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢅⢤⠞⠀⣀⠂⠀⠀⠳⣷⡀⠀⠄⠉⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣆⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠉⠁⣿⡄⠀⠀⠀⡰⡇⠉⠓⢆⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠆⠁⠀⡠⠔⠂
⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⠀⠀⠀⠑⠀⠄⡀⣀⣀⠀⠀⠀⠀⠓⠃⠀⠈⠁⢠⡄⠀⠀⠀⠀⠀⠾⠄⢸⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠑⠀⠀⠀⠀⣀⠀⠀⢀⣤⣦⡄⠀⢠⠀⠀⣶⠀⠈⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠈⢩⡥⠀⠸⠀⢀⢛⡀⠀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠐⠃⠈⠉⠀⠀⠓⠂⠧⠀⠊

⠠⣶⠄⠀⢔⡦⢐⣤⡀⠀⡠⣆⠠⣦⠄⠀⢔⡦⢐⣤⡀⠀⣠⡂⠠⣢⠄⠠⢔⡄⢰⢄⠀⢀⣤⡂⠰⡢⠀⠠⣴⠄⣰⢄⠀⢀⣤⡂⢴⡢⠀⠠⣶⠄⣰⣄⠀⢀⣴
⠀⠁⠀⠀⠀⠁⠀⠉⠀⠀⠈⠁⠈⠀⠀⠀⠀⠁⠀⠁⠀⠀⠈⠁⠈⠀⠀⠀⠀⠁⠀⠁⠀⠀⠈⠀⠈⠀⠀⠀⠀⠁⠈⠁⠀⠀⠈⠀⠈⠀⠀⠀⠀⠁⠈⠁⠀⠀⠉

⢀⠄⠰⠆⣄⡠⠠⠀⠀⠭⠠⠠⠠⠐⠐⠄⠰⢀⠰⠃⢀⠀⡆⢀⠀⡀⠄⡀⡐⢂⢀⠀⡠⠤⢀⠀⠄⠀⣒⢠⠰⠠⠀⠀⠀⣒⢀⠀⡀⠀⢀⢀⠂⡀⡀⡀⠄⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠈⠛⠟⠛⠛⠛⠻⠛⠛⠟⠛⠻⠛⠛⠟⠛⠻⠛⠛⠟⠛⠻⠛⠛⠛⠛⠟⠛⠻⠛⠛⠟⠛⠻⠛⠛⠟⠛⠻⠛⠻⠛⠛⠟⠛⠻⠛⠛⠟⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠘⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⡿⠿⠿⠿⠿⡿⠛⠛⠿⠟⠻⢿⣿⠿⣿⡿⢿⣿⠿⣿⡿⢿⣿⢿⣿⡿⣿⣿



⠠⠈⠁⠄⠃⠄⠉⠠⠈⠀⠀⠁⠄⠁⠠⠈⠠⠈⠁⠄⠃⠄⠉⠠⠈⠀⠀⠁⠄⠁⠠⠈⠠⠈⠀⠄⠁⠄⠉⠠⠈⠠⠈⠁⠄⠁⠄⠈⠠⠈⠀⠀⠁⠄⠉⠠⠘⠠⠈


⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄⠀⠀⡀⠀⠀⡄
⠀⠀⠚⠀⡀⠚⠁⡀⠚⠃⡀⠘⠃⡀⠘⠃⢀⠐⠃⢀⠐⠃⢀⠐⠛⢀⠀⠛⢀⠀⠚⠀⡀⠚⠀⡀⠚⠁⡀⠚⠃

⠀⠡⠎⡈⠡⠶⡈⠩⠾⡉⠨⠴⠉⠩⠴⢈⠌⠴⢂⠄⠵⢎⠉⠥⢎⠀⠥⢆⡁⠥⠖⡉⠡⠖⡨⠠⠖⡉⠨⠴⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢠⠰⠂⢠⠐⠂⢀⠰⠂⢀⠐⠂⢀⡐⠂⠀⡄⠒⠀⡄⠖⠀⡀⠖⠀⣀⠰⠀⢠⠐⠀⢀⠐⠂⢠⠰⠂⢠⠐
⠀⠄⠁⠀⠢⠈⠀⠢⠈⠀⠢⠈⠀⠲⠈⠀⠲⠈⠁⠐⠄⠁⠐⠅⠁⠐⠄⠁⠐⠆⠁⠀⠆⠈⠀⠢⠉⠀⠢⠈
⠀⠀⠔⠂⡀⠔⠂⡀⠀⠂⡀⠠⠂⡀⠠⠂⣀⠠⠒⢀⠀⠒⢀⠀⠐⢀⠀⠔⢀⠀⠔⢀⡀⠔⠂⡀⠐⠂⡀⠀⠂
⠀⠀⠆⠀⠀⠆⠀⠀⠆⠀⠃⠖⠁⠀⠲⠁⠀⠰⠁⠈⠰⠀⠀⠰⠂⠀⠰⠂⠀⠀⠆⠀⠀⠎⠀⠁⠆⠀⠃⠆
⠀⢰⠀⣄⢴⡄⣄⢤⡆⣄⠤⡆⢤⠠⡆⢠⠤⡆⢠⡠⡦⢰⡠⣴⢠⡠⢴⠠⡄⢴⠀⣄⢴⠀⣄⢴⡄⣄⠠⡆⢤
⠀⠘⠉⠧⠘⠉⠷⠘⠏⠿⠘⠏⠵⠘⠃⠱⠄⠋⠹⠆⠋⠱⠇⠻⠹⠆⠛⠩⠇⠛⠉⠇⠙⠉⠷⠘⠊⠿⠘⠏⠵
⠀⠀⠀⢠⠀⠀⢠⠀⠀⢠⠀⠀⢠⠀⠀⢠⠀⠀⢠⠀⠀⣤⠀⠀⢤⠀⠀⣤⠀⠀⣤⠀⠀⣤⠀⠀⣤⠀⠀⡤
⠀⠚⡔⠂⠛⡔⠃⠛⡔⠂⠛⡔⠀⠛⡔⠀⠛⡔⠀⠛⡔⠀⠛⡔⠈⠛⡔⠐⠻⡔⠘⠛⡜⠘⠻⡔⠘⠻⡜⠘⠃
⠀⠀⡁⢀⠀⡁⠀⠀⡁⠀⠀⡁⠀⠀⣁⠀⡀⢁⠀⡀⢁⠀⠀⢁⠀⠀⢁⠀⢀⢁⡀⢀⠁⡀⢀⠁⡀⠀⠁⡀
⠀⠉⢳⡤⡉⠱⡤⡉⠹⡤⣍⠹⡤⢍⠙⣤⢍⠙⣦⢌⠉⢦⢬⠉⢧⢬⡉⢣⠬⡉⢳⡬⡉⢳⡤⡉⠹⡤⣍⠹⡤
⠀⢀⡀⠀⠀⡀⠠⠀⡀⠠⠀⡀⠠⠀⣀⠀⠀⣀⠀⠀⢀⠀⠄⢀⠀⠄⢀⠀⠄⢀⡀⠀⢀⡀⠠⠀⡀⠠⠀⡀⠠
⠀⠠⠑⠆⠠⠁⠃⠠⠁⠆⠠⠁⠂⠠⠁⠒⠠⠄⠰⠀⠌⠸⠀⠌⠐⠀⠌⠐⠀⠤⠐⠆⠠⠁⠆⠠⠁⠂⠠⠁⠃
⠀⠀⠀⠀⠀⢀⢀⠀⢀⠀⠀⢀⠀⠀⢀⠀⠀⢀⠀⠀⣀⠀⠀⢀⠀⠀⣀⠀⠀⡀⠀⠀⡀⠀⠀⡀⠀⠀⡀
⠀⠀⠘⠘⠃⠙⠘⠃⠙⠘⠃⠙⠘⠃⠙⠘⠀⠉⠘⠀⠁⠘⠁⠉⠙⠀⠉⠙⠈⠁⠙⠈⠃⠛⠈⠁⠛⠈⠃⠑

⣿⡫⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣠⢄
⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠻⣦⣀⡀⠀⠀⣈⣿⣿⣽⣿⣿⣯⣿⣏⡀⠀⠀⣀⣠⡾⠃⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠏⠀⠉⢳⣦⡀⠀⠀⠀⠈⠙⠛⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠛⠉⠀⠀⠀⢀⣠⡾⠋⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣶⣤⣤⣤⣤⣶⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣦⣤⣤⣤⣶⡿⠋
⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠉⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠉⠉⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⣾⠟⠛⠻⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⢻⣿⠟⠁⠙⣿⣿⢻⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠛⠛⢿
⠻⢤⡄⠀⠈⠛⢿⣿⣷⣶⣦⣤⣤⣶⣶⣿⣿⣿⠿⠟⠉⢸⣿⠁⠀⠀⢹⣿⠈⠙⠿⢿⣿⣿⣷⣶⣦⣤⣤⣶⣶⣿⣿⠟⠋⠀⠀⣤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠻⠿⠿⠛⠛⠛⠁⠀⠀⠀⢸⣿⠀⠀⠀⠸⣿⠀⠀⠀⠀⠙⠛⠛⠻⠿⠿⠛⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⢀⠆

⠀⢄
⠀⠀⠑⠦⣀
⣀⠀⠀⠀⠈⠉⠒⠀⢀
⣿⣷⣦⣄⣀⣤⡀⠀⠀⢱⣄
⠉⠛⠛⠛⢿⣯⠔⠀⠀⠀⠙⠛⢦⡀
⠀⠀⠀⠀⠀⢷⣾⠀⠀⢠⠀⠢⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢻⣿⢁⡀⠀⣱⠀⠙⣦⢄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⣿⣿⡄⢠⡏⠀⣶⡏⠀⣿⠈⣇
⠀⠀⠀⠀⠀⢸⣿⡿⢀⣿⡁⢠⣿⣇⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⠛⠿⠾⠿⣧⣾⣿⣿⡀⠙⣷⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠻⣍⠓⢆⣻⡀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣹⡇⠈⡇⠀⠀⠀⠀⠀⠠⠂⠀⠄⠀⠸⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠀⠀⠚⠛⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠅⠀⠀⠀⠙⠲⢌⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠙⢴⡠⠀⢰⠁⠈⠔⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣔⠠⠀⣀⣀⠛⠁⠀⠀⠦⠀⠸⡀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣼⣆⠀⢰⣶⣄⣀⢤⣤⣤⣦⣴⣥⣀⣀⣀⣤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣷⣾⣿⣿⣮⡻⠛⠻⣷⡹⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠓⠒⠛⠛⠛⣛⣿⣿⣿⣿⣿⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠦⠤⣤⠤⠤⠤⠴⠾⠿⠛⠛⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⣦⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⡿⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣧⣛⣸⣸⣸⣸⣘⣸⣰⣸⣆⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠘⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉
⠀⠀⠀⠀⠀⠀⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⢸⡀⡀⡆
⠀⠀⠀⠀⠀⠀⡀⡇⠹
⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⢹⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠘⣧⣼⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢃⢹⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⠉⠍⠻⡖⠀⢀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠛⠛⠛⢴⣦⣀⠀⠀⠀⢀⣤⡤
⠀⠀⠀⠀⠀⠀⢠⠊⠀⠈⠈⣥⠐⡀⠀⠀⠂⠀⠀⠄⠀⠀⣠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡷⣾⣿⣴⡶⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠃⠐⠀⠀⠀⠀⠀⠀⠄⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣠⠔⠀⣼⠞⠋⠁
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⢀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠍⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⢈⠀⠀⡈⣿⡀⠀⠀⠀⠈⠀⠀⠄⠂⠀⠀⠠⠀⠀⡿
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢁⢸⠀⡀⠀⠸⣷⡴⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣠⣎⣾⡞⠁⠀⠀⠘⠿⣦⡀⠀⠀⠀⠀⠀⠀⢈⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢤⣤⣼⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠲⠶⠶⠛⠛⠈⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿

⠀⠀⣠⠤⠤⠤⠤⠤⣄⠀⡴⠶⠶⠶⠶⢶⡄⠀⠠⣀⢀⡠⠀⠀⢠⣤⣤⣤⣤⡄⢀⡤⢦⣄⡴⢦⣄⡤⢦⣄⣤⢦⣄⡤⢦⣄⣤⢦⣄
⠀⢻⣯⡟⠐⢯⠃⢻⣯⡟⣽⠃⠛⡝⠘⣿⠀⢠⠿⣋⣏⡿⣧⠀⢠⡾⣿⣿⠷⡄⢘⡷⣷⡿⣻⡳⣿⡳⣳⡛⣻⡳⣻⡿⣷⡿⣿⡷⣟
⠀⠀⢞⡌⢶⣟⡶⢁⣷⠀⣦⠱⣾⣳⠎⢰⠀⡟⢒⣿⡿⣟⠘⡇⠀⣼⢻⡟⣧⠀⢨⣥⣽⣥⣽⣥⣽⣥⣽⣥⣽⣥⣿⣥⣽⣥⣽⣥⣭
⠀⠀⠀⠈⠛⠛⠛⠉⠀⠀⠈⠑⠛⠝⠋⠁⠀⠷⠶⠶⠷⠶⠶⠇⠀⠀⠘⠃⠀⠀⠈⠓⠖⠋⠓⠖⠋⠳⠖⠋⠓⠖⠋⠓⠖⠋⠓⠖⠋

⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⢹⢣⣇⢻⢡⣇⣻⣡⣇⣻⢡⣇⢻⢩⣇⢻⣩⣇⢻⣡⣇⢻⢡⣇⣻⢡⣇⢻⢡⣇⣻⣩⣏⢻⣩⣇⣻⢨⣇⣻⢡⣇⣻⢩⡏⠻
⠀⠀⠀⠈⠉⠀⠈⠉⠀⠈⠁⠀⠈⠉⠀⠈⠁⠀⠈⠉⠀⠈⠉⠀⠈⠁⠀⠈⠁⠀⠈⠉⠀⠈⠁⠀⠈⠉⠀⠈⠁⠀⠈⠁⠀⠈⠁

⠀⠀⢀⡆⡒⣶⡔⡖⣶⡄⡄⣶⡖⠂⣶⡖⡂⣶⡴⡖⣶⠖⡖⣶⡖⠄⣶⠶⡆⣶⠄⠶⣶⠔⡆⣶⠔⠖⣶⠔⡆⣶⠦⠆⣶⠄⠲⡆
⠀⠀⠀⢲⡷⠩⢲⠷⠹⢰⠷⠼⢰⡷⠽⢰⡷⠩⠰⡷⠹⢼⡷⠭⢰⡷⠽⢸⡷⠹⢲⠷⠫⢺⡗⠭⢺⡷⠹⢼⡷⠽⢺⡷⠯⢺⡗⠁


⠀⠀⢀⠶⣿⢦⡴⣿⢦⡴⣿⡶⡴⢾⡷⣤⢾⡷⣦⠖⣻⢦⡶⣿⢦⡴⣿⡶⣴⢾⡷⣤⢾⡗⢦⢞⣿⢦⡴⣟⢢⡴⣿⡷⣴⢾⡷⡄
⠀⠀⠀⠈⠋⠘⠂⠛⠐⠃⠛⠁⠓⠙⠃⠛⠘⠋⠘⠈⠛⠘⠂⠛⠐⠃⠙⠁⠓⠘⠃⠛⠘⠃⠘⠀⠋⠘⠂⠛⠘⠃⠙⠁⠃⠘⠃⠂

⠀⠀⠀⣶⣶⣶⢶⣶⣶⡶⣶⣶⣶⢶⣶⣶⠶⣶⣶⡶⣶⣶⣶⢶⣶⣶⡶⣶⣶⣶⢶⣶⣶⡶⣶⣶⣶⢶⣶⣶⡶⣶⣶⣶⢶⣶⣶⡆
⠀⠀⠈⡽⣿⡏⢩⢿⢿⠉⡿⡿⡏⢹⢿⢿⠉⡿⡿⡏⢹⢿⢿⢋⡿⡿⡝⣽⣿⣯⢩⣿⡿⡝⡽⣿⣯⢫⢿⢿⠉⡽⡿⡏⢹⢿⢿⠁
⠀⠀⠀⠀⠋⠀⠀⠘⠀⠀⠀⠃⠀⠀⠘⠀⠀⠀⠃⠀⠀⠘⠀⠀⠀⠃⠀⠀⠉⠀⠀⠘⠁⠀⠀⠛⠀⠀⠈⠁⠀⠀⠃⠀⠀⠘

⠀⠀⠠⣶⣴⣦⣶⣴⣦⣶⣴⣦⣶⣴⣦⣶⣴⣦⣶⣴⣦⣶⣴⣦⣶⣶⣦⣦⣴⣦⣶⣴⣦⣶⣴⣦⣶⣶⣦⣶⣶⣦⣦⣴⣶⣶⣴⡄
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⢿⠿⡿⢿⠿⠿⠿⠿⠿⢿⠿⡿⠿⠿⠿⢿⠿⡿⢿⠿⡿⢿⠿⡿⢿⠿⡿⠿⠿⡿⢿⠇


⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⢹⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣨⡏⣼⠀⣿⣧⡀⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⡧⣽⢀⣿⣏⣿⣤⣟⣿⣿⣿⣶⣦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠁⣯⣿⣿⣾⣿⣿⡏⠋⠹⠙⠛⠈⠀⠀⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣏⠁⢀⣿⣿⡿⣻⣿⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣭⠟⠟⢹⠋⠀⣾⣿⣿⣿⡿⡍⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣟⣿⣾⠟⠀⠀⠉⠀⢰⣿⣿⣿⣿⣷⡇⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⢠⣾⣿⣿⣿⣿⡵⠋⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢀⣾⣿⣿⣿⣿⣿⣾⣆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⢸⣿⣿⣿⣿⣿⡟⠛⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣦⣠⠀⢀⣠⠀⠀⠀⣀⣤⣿⠃
⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⡂⠐⣼⣿⣿⠋
⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⡿⠁
⠀⠀⢿⣿⣿⣿⣿⣿⣶⣾⠟⠉⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⠀⠸⠀⠉⣽⣿⡟⠛⠻⢿⣿⣿⣟⠧
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⠇⠀⠀⠰⠈⠹⠃⠑
⠀⠀⠀⠀⠘⣿⠟⢝⡻⢿⣿⣟⣒⣀⣠⣤⣶⣿⡅⠀⠀⠀⠀⢨⢃⣿⣿⠏
⠀⠀⠀⢀⣾⣿⣷⠟⠈⠉⠉⠙⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣠⣯⣷⡿⠁
⠀⠀⠀⠀⠰⠋⠋⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⠀⠀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠡⣠⡾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⡀⠙⣦⡠⠄⠒⠒⠒⠒⠒⠒⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⢰⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠋⠀⠀⡴⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠉⠁⣀⠰⡟⠃⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢠⣼⠀⠀⠀⠀⠀⠙⠋⣀⠀⠉⠉⣀⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠋⠉⠲⠄⠒⠉⠀⠀⠀⠀⡄⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠘⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⣀⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⡰⠋⠁⠐⠒⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠤⡱⢄⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠹⣦⡈⠋⠴⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣤⣤⣤⣤⠤⠤⠐⡄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠘⢷⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣀⠠⠄⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠸⢡⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣾⠢⠄⠀⠀⠀⠀⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠂⠘⢆⠀⠀⠀⠀⠀⢀⡀⡤⢸⠇⠀⠂⠀⠀⠀⠀⠀⡸⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠓⣤⠠⠔⠒⠈⠁⠀⣸⢤⣄⡀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠦⡀⠀⡴⠁⠀⠀⢀⡠⠔⠋⠀⠀⠈⠉⠛⠲⠦⠴⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⢟⡤⠤⠤⠤⠴⠀⠉⠳⢄⠀⠀⠀⠀⢀⡜⠛⠦⢤⡄⠉⠀⠀⢦⣤⣄
⠀⠀⠀⠀⠀⢀⡴⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⡄⣠⠊⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠛⢷⣄⡀
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⠉⠑⠒⠒⠒⠀⠐⠒⠒⠢⣤⠔⠁⠈⠻⣦⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠵⠾⠅⠴⠂⠀⠀⠀⠐⠀⠒⢾⣶⣦⣠⡄
⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁
⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢐⠋⢉⣉⣉⡙⢛⣛⣛⡛⢛⣛⣋⡉⠉⠉⠉⠀⠉⠛⠛⣛⣛⣛⠛⣛⣛⣛⠁⣀⣦⣀⢰⡄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂⠿⠉⠉⠁⠘⢋⣉⡟⠸⣏⡉⠟⠀⠀⠀⠀⠀⠀⠸⣿⣩⣿⠺⣿⣭⣿⠺⣿⣭⣿⢿⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣷⠦⠤⠴⠦⠤⠬⣭⠤⢤⣤⢤⣤⠤⡤⢤⣤⣤⣤⣤⣬⣭⣥⣤⣬⣭⣥⣤⣈⣉⣅⣸⡇
⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡧⠀⠀⣴⣀⣀⣂⣆⣀⣀⣀⣠⣀⣀⣒⣲⣒⣒⣒⣚⣓⣚⣛⣛⣛⣛⣛⣛⣛⣿⠍⢹⡇
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡅⠀⠀⠀⠀⡤⠤⠄⣠⡀⣀⢀⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢸⠁
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⣶⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠉⠂⢰⠒⠒⠒⠒⡖⠲⠒⠒⠒⠒⠋⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⡇⠈⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠧⢤⡤⢤⣤⣤⡤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠠⠤⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠙⠲⠤⢧⡀⠘⠒⡤⢄⡀⠠⢄⡀⢀⡀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠒⠛⠛⠋⠛⠓⠛⠛⠃⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣝⠳⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡌⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠘⣿⣆⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⣦⡀⠀⠀⠉⣩⢴⣦⣄⣀⣀⢹⣿⡆⠀⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠈⠛⠘⠋⠁⢸⣿⡇⠀⠀⢸⣿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⢀⣾⠇⡞⢳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⣠⠿⠁⠊⣠⣿⡇⠉⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡀⠀⠀⠀⠀⢀⣾⠟⠀⣠⠞⠁⠀⣠⣾⠟⠉⠀⢀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⠤⠀⠀⣾⡏⠀⣰⢋⠔⣡⡾⠋⢀⣠⣴⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣿⠁⢰⣇⢎⣼⠋⣠⣴⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⢸⡇⣾⢃⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⢸⣷⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠀⠀⠀⠀⠈⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡷⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢲⣦⠀⠀⠀⠀⠀⠀⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠈⠈⠀⠀⠀⠀⠀⠀⠰⢄⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠐⠀⠀⢀⡀⡶⠤⠖⠀⠀⠉⠉⠋⠛⠒⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⢀⡇⣰⠶⠞⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣍⠁⠓⠢⡄⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣰⠆⠀⠀⢹⣆⠀⠀⠘⣦⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⣠⣴⠟⡃⠀⠀⠀⣠⢦⠀⣰⡿⠀⢣⠀⢸⣿⠀⠀⠀⢸⡆⢀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣴⣿⠋⠀⡏⠄⢠⣾⠃⠈⢀⣿⡇⠀⠈⠀⢸⣿⠀⠀⠀⢸⡗⢣⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⡏⠀⠀⠇⢰⣿⡏⠀⠆⣸⣿⠀⠀⠀⣆⠘⡏⠀⠀⠀⡼⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⢿⡇⠀⢀⠀⣸⣿⠃⢠⠀⡿⣿⠀⠀⠀⢹⣨⣧⠀⣠⢾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠈⢿⣷⡀⠎⠀⣿⡿⠀⢸⡶⣿⣿⠀⠀⠀⠈⢿⣿⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⢿⣿⣦⣠⣿⡇⠀⢸⡶⣿⣿⡀⠀⠀⠀⣴⠟⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢⣩⣻⣿⣿⣄⡀⠈⢧⠹⣿⣧⡀⠀⢸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣭⡿⠛⠛⠛⠛⠂⠈⠳⡽⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠠⢴⣆⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡀⠀⢈⣿⣿⣇⢀⡀⠀⢿⡆⠈⣹⡆⢀⣴⣿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠹⣿⣷⡀⢸⣿⣿⣿⣼⡇⠀⠘⣿⡄⠸⡇⠈⠻⢿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠛⠛⠷⠿⠋⠁⠀⢿⣿⣿⣿⡇⠀⠀⠙⢳⡀⠀⡼⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠋⠁⢀⣶⣦⠀⣔⠒⠂⠤⡀⠈⢻⣿⣿⡀⠀⢀⠀⠀⢣⠐⠁⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⢀⣁⠭⠀⠀⠈⢛⠉⠁⠀⢄⠀⠀⠀⠣⠀⡄⠀⠀⣴⣿⣿⡟⠉⢉⣠⣴⠾⠃
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢀⣼⣿⠏⢀⣤⣶⠟⠉⠀⢀⣠⠀⣾⡯⢿⣆⠀⠈⠳⣄⠀⠀⠀⡇⠀⣾⣿⣿⠟⠀⢀⣨⣥⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣿⠿⠃⠀⠀⠑⠁⣀⣤⠾⠛⠉⠀⠘⣿⣋⣿⣆⠀⠀⠹⠇⠀⢀⡇⢰⣿⡿⠋⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢰⡇⠀⢠⡾⠁⠀⠀⠀⢠⣶⣿⠿⠁⠀⠀⠀⠀⠀⠘⣿⣮⣿⡄⠀⠀⠀⠀⢸⡇⠸⠟⠁⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⣠⠋⡅⣰⠏⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⣰⣿⣷⠀⠀⠀⠛⢿⡅⠀⠀⠀⠀⣾⡇⠀⠀⠀⡀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡿⠁
⠀⠀⢠⠚⢃⡰⠇⠀⢀⣴⡇⠀⢀⣠⣤⣤⣴⣶⣾⣿⣿⣿⣿⡦⠀⠀⠀⠈⢻⣄⠀⠀⠀⣿⣿⠀⠀⠈⡇⠰⠶⠦⠤⠙⠛⠿⠛⠋⢁⡀
⠀⠀⠀⠒⠈⢦⠀⠀⣼⡟⢠⣾⣿⣿⣿⣿⣿⣿⡿⠟⠋⣉⠉⠀⠐⣾⣿⣅⠀⢻⡆⠀⠰⣿⣿⣷⠆⠸⠷⠀⠀⢀⡤⢀⣄⠀⠀⣴⣿⢃⣴⡦
⠀⠀⠀⠀⠀⠈⢀⣼⡟⠀⠸⣿⣿⣿⣿⣿⠟⠋⠀⠀⣼⠟⠁⠀⠀⠻⣶⡟⠀⠀⢉⠄⠀⠀⠈⠃⠀⠀⣀⡴⠞⠉⠀⣸⣿⣆⣼⣿⣵⣿⣏⣴⡖
⠀⠀⠀⠀⣠⠚⣿⣿⠂⠀⠀⠉⠛⠻⣿⣷⡆⠀⠀⢰⠃⠀⠀⣄⡀⠀⠘⣇⠀⠀⠀⠀⠀⠁⣀⢤⣶⠟⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤
⠀⠀⠀⠀⠉⢸⣿⠃⠀⠀⡠⠀⠀⠀⢻⣿⣿⡅⠀⠀⠀⠀⣼⣿⠟⠂⠀⢹⡀⠀⡊⢀⡝⢁⡠⠊⠀⠀⣄⣿⡆⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⣼⣿⠃⠀⣠⠎⠀⠀⠀⠀⠀⢻⣿⣷⠀⠀⠀⣼⣿⠋⠀⣠⣀⠈⠇⠀⠀⢸⠉⡹⠁⠀⣤⡀⠘⠿⣿⠘⠻⣿⣿⣿⣿⡿⠛⣁
⠀⠀⠀⢼⣿⠏⢀⣴⠏⠀⢀⣤⡶⠀⠀⠀⠹⣿⠀⠀⣹⡿⠏⠀⣸⣻⠏⠀⠀⠀⠐⠊⠀⣤⠀⠀⢻⣧⠀⠀⢿⡆⠀⠈⠛⠿⠋⢀⣾⡿⢳⠂
⠀⠀⠀⠀⠀⢠⣾⡏⠀⣴⢿⣿⣷⣄⠀⠀⠀⣀⠀⣰⠏⠀⠀⣰⡿⠃⢰⣦⠀⠀⠀⢿⣦⡈⠻⢆⠈⣿⣇⠀⠘⡇⠀⢠⢄⠀⢠⣿⡿⡕
⠀⠀⠀⠀⠰⠿⠻⠁⠈⢻⣾⣅⠀⠉⠑⣠⡾⠋⣰⠋⢠⣀⠀⠋⠀⠀⠅⠀⠐⡀⠀⠀⠻⣷⣄⠀⠀⠸⣿⡄⠀⠇⠀⡄⢨⢀⣿⣿⠎⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⣦⣤⡀⠉⠀⠐⠁⡀⠈⠉⠙⠒⠄⠀⠈⠄⠂⠑⠀⠀⠀⠈⢻⣷⡀⠀⢻⣷⠀⠀⠀⠣⠃⣼⡿⠧⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄⢠⣤⡈⢿⣦⡀⠀⣠⡄⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠙⢿⣦⠀⢻⣧⠀⠀⢀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠁⣤⣝⢿⣮⣿⣷⣄⣿⣷⠀⠀⠀⢸⣿⣿⡆⠀⢤⡀⠀⠈⠻⣦⡀⢻⡆⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⣬⣻⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⣧⠀⠀⠙⢷⣄⡀⠘⢿⣎⡿⡈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣴⡆⢿⣿⣇⠀⠀⠀⠸⡿⣦⡀⠑⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⠟⠁⢰⢿⠀⠘⣿⣿⣆⠀⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠺⠎⠀⠀⠙⠛⠋

⣿⠿⠿⡿⢿⠟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣛⣛⣻⣿⣟⣿⣿⣿⣿⣿⣿⣻⣿⣿⣻⣿