Brunch Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠆⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠘⠓⠀⢠⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⠀⠀⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠌⣀⠀⠀⠀⡀⣀⡼⣯⣄⠀⠴⠀⠀⠀⠀⣤⡄⢤⣤⡵⠶⢻⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠤⠀⠉⠠⠀⠈⠀⠸⣧⠀⠀⠀⠀⠀⠀⡌⠀⠙⠀⠘⠿⢷⡴⠞⣡⣠⠀⠤⡄⠀⠀⠰⢞⡿⢦⠙⠿⣿⣿⠆
⠀⠀⠀⠀⠀⢀⡀⠺⠀⠂⠂⠀⣀⣀⣀⣾⡆⠋⠀⠀⠀⠀⠀⠀⠃⠀⠀⠦⠔⠳⢶⣦⣀⡏⠁⠴⡆⠀⠀⠀⠀⢦⠶⠶⢼⣋⣟⠻⣙⠃⠀⣰
⠀⠀⠀⠀⠂⠈⠙⠧⣦⠀⠐⢢⣀⡎⢍⠀⠈⠃⡰⠀⠀⠀⠀⠀⠨⡀⠀⢠⣤⠓⠂⠉⠀⠀⣠⠶⣴⠇⠀⠀⢠⠘⣴⡆⢯⠘⢣⡋⠼⣧⣾⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠑⠫⠶⠜⣀⠤⠖⠁⠀⠀⠀⠀⠀⡀⢰⣐⣤⠀⣀⣀⣠⣠⡞⠉⠀⠀⠀⠀⠀⠀⠁⠈⠳⠞⠖⠈⠅⠓⠈⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⠀⠀⠔⣊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠁⠘⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠤⠤⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠂⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⣀⡔⠚⣄⠀⠆⠀⠀⠀⣀⡈⠇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⢀⣿⠃⠀⢯⣀⠀⠁⠀⠀⠈⢁⠈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣽⡇⠀⡏⠘⢠⡀⢠⡄⠀⠀⠀⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⣿⡉⡀⢳⠈⠁⠀⠀⠀⢀⠀⢠⡿⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⠈⢻⠁⠘⠀⠈⠧⠀⠀⠙⠁⠞⢁⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠷⢄⠀⢀⡀⠀⠀⠀⢀⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡍⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⣀⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠲⣿⡿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⣀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣷⣼⣿⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠋⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⢁⠋
⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣐⠂⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⡄⠢⠀⠂⠐⠀⠃⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⣠⠀⠀⠀⠐⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡆⣰⡰⡄⠀⠀⡸⠠⠄⠀⠐⠀⠀⠀⠀⠖⠄⠀⡄⠀⢠⠀⠀⠀⠴⠀⠀⢠⠀⠂⠀⠀⠀⠀⠀⢀⠇
⠀⠀⢀⠀⠀⠀⠁⠆⠀⠀⠀⢠⠈⠁⠙⡀⠠⡇⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⢀⡀⠈⠁⠠⠄⡀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠄⠀⠈⢀⠀⠀⠘⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠈⠈⠁⠀⠁⠀⠀⠧⠀⠀⠢⡀⠀⠀⠂
⠀⠀⢀⣀⡤⠀⠈⠀⡠⠄⠀⠐⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠋⠉⠉⠉⠉⠙⠒⠶⣄⠀⠠
⠀⠀⠈⠉⠀⠠⠀⠒⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⡀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠠⡄⠀⠀⠀⠀⠀⢠⡇⠀⠐⠀⡀⠁⠀⠀⢰⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⠁⢀⡀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⣸⠋⠉⠉⠀⢢⡔⠢⠀⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣀⠀⠀⡀⠐⠀⠢⠄⠀⠖⠚⠃⠁⠀⠀⡈⠂
⠀⠀⠀⠀⠀⠀⠒⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠡⠀⢀⠠⠀⠀⠤⢀⣀⠠⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣿⡀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⢀⣀⡙⣁⣤⠤⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠉⢀⠀⠀⡆⠀⠀⠃⠀⠀⣠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠁⣀⠀⡢⠴⠇⠀⠀⠃⠀⠀⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣤⠀⠦⠀⠀⠀⠀⠀⠂⠉⠀⠀⣀⣠⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⣀⣠⠤⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⡀⠂⠀⠓⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠐⠋⠉⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠛⠀⢀⣦⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠦⠀⠀⠀⣸⣿⣿⢻⣿⣟⣿⣿⣿⡟⣿⣿⣿⣿⡇⠀⢀⢨⠾⠡⠁⠀⠀⣠⣶⣾⣿⡄
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣿⣷⣿⣿⣿⣷⣿⣿⣿⣿⠃⠀⠸⡉⠁⠀⠀⠀⠀⠸⣿⣿⣿⠇⠀⠀⠀⠖
⠀⠀⠀⠀⣀⠀⠻⠃⠀⠄⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢀⡀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠈⠃⠀⠀⠀⠼⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠸⠆⠀⢠⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠟⠀⠈⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠰⡆⠀⠀⡀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⡄⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠰⡀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠀⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣤⠀⣀⡀⠀⠰⠀⠀⠀⠀⡀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠐⠀⠂

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⣿⣿⡿⠻⣿⠛⠿⢿⡿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠶⠧⣷⣤⢜⣫⣧
⠒⢬⠂⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢨⠃⠠⠀⠀⠀⠀⠀⠀⠹⣿⣶⣄⣠⠀⠉⠻⠶⠻⠆⠀⠀⠀⠀⡀⠀⡀⢠⡄
⠒⠉⠱⣣⠆⡀⠀⠀⠀⠀⠀⠀⢠⣤⠠⢘⠃⠠⠴⢣⠿⠆⠀⠀⠀⠀⠀⠀⠀⠈⠁⣰⣿⡟⣴⣤⡀⠀⠀⠀⠀⠀⠶⢀⡉⠉⣱⡂
⢁⠀⠈⠡⠘⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢌⠁⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⡇⠏⢻⡿⢿⡦
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣷⣤⡀⠈⠀⠈⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡠⠒⢩⣤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠟⠺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣄⣀⣀
⠀⢰⠁⠈⡙⢿⣷⡀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠉⢹⣏⣉⣀⣢
⠀⠈⠀⢇⠀⠹⣿⣧⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢤⢀⡄⠀⠀⠈⠛⢯⡙
⠀⠀⠀⠀⠀⡀⠙⠛⠃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣴⠖⠀⠀⠀⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⠙⢥⠖⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⡰⠀⠀⠀⠀⢺⣽⠀⠀⠀⠀⠀⠹⠁⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢻⢲⠟⠛
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢡⡶⠠⡄⠀⠀⠀⠀⠀⠀⠀⣋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠀⢸⠁⢀⠆⠀⡐⠂⠲⠀⠀⠀⣿⠁⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⣀⠚⢢⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⢷⠀⠀⠉⠁⠀⠀⢣⣠⣀⠀⠀⠀⠋⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⡀⠶⣀⠺⢂⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠀⠀⠀⠀⠳⠄⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠃⠀⠀⠀⠀⠘⠋⡤⠉⠴⢏⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⣠⡀⠛⠴⠎⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡅⠀⠀⠀⠀⢀⡌⣹⣦⡀⠘⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠇⠀⠀⠀⠀⠀⠤⠉⠁⠛⣷⣟
⠀⠀⠀⠀⠀⠀⣠⠾⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠌

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⢈⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠐⢄⡀⠀⠀⠀⣀⣀⡉⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠇⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠂⠁⠀⠊⠉⠲⡀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠡⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⣈⠉⡆⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⢠⡤⠄⢇⠀⠀⠀⠀⠀⠠⡌⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠆⠠⠂⡐⢦⣍⣠⢟⡀⠀⠀⠀⠐⠐⠠⠀⢀⡔⠁⠀⠐⠀⢑⢠⠔⠀⠀⠀⠀⠑⠄⠀⠀⢁
⠀⠀⠀⠀⠀⠘⠀⠀⢈⡈⠦⡄⠀⣄⠈⠂⡤⠀⠀⠀⠀⠀⣹⡌⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠐⢢⢨⣰⠂⠠⠴⠁⢤⠀⠀⡀⢀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⡀⡙⡘⢣⡗⠀⠰⠀⠀⠠⠁⠀⠀⠁⠀⢄⠤⠟⠃⠐⠐⠀⢀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢸⠀⠦⠀⡀⠈⠁⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⣠⠄⠃⠀⠀⠀⠀⠀⠉⠠⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠂⠐⠒⠒⠃⡀⠂⠀⠐⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠐⡀⢠⠖⠀⠀⠀⠈⠀⠈⠑⠖⠀⠠⠛⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠱⡈⠢⠀⠀⠁⠀⠀⠀⠀⠁⠀⡄⠀⠁⠈⠑⠒⠣⠄⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠂⠄⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠠⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠔⠁⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠁⠒⠒⠈⠀⠂⠀⠀⣀⡠⠤⠚⠋⠀⠁⠀⡀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠁


⣿⣿⠛⢿⠛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠂⣠⡂⣤
⠀⢀⠤⣀⣀⢐⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⠀⡀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⢈⣻⠔⡻
⠀⣧⣿⠿⠿⢷⣅⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣠⠖⠋⢀⠠
⠀⠻⣏⣀⢀⡸⣫⠁⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⢰⠠⠆⠀⠠⠄⢀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡚⠍⠀⠀⠀⣀⣀
⠀⠀⠈⠉⠗⠋⠁⠀⠀⠀⠀⠀⠀⣀⡀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣌⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀
⠀⠀⠀⠀⠀⢐⠀⣠⡤⠴⠖⠒⠂⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡡⠌
⠀⠀⠀⠀⢀⡿⠊⠁⠀⣄⠤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⡼⠁⠀⠀⠀⠈⠗⠒⠀⠀⠀⠀⣤⣳⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠠⠀⠀⠀⠀⣀
⠀⠀⠀⠨⠁⠀⠀⠀⠀⠀⢄⠑⠠⡀⢤⣀⣸⣿⡎⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⠿⣿⣦⡱⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⣄⣌⣙⣿⡇⠆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣧⠀⠀⢸⣿⡇⡁⡀⠀⠀⠀⠀⠀⠀⢢⡀
⠀⠈⠄⠋⠀⠀⠀⠀⠀⠀⢀⠎⠙⢻⡀⢸⣿⡟⣰⠀⠠⠀⠀⠀⠀⢀⡴⠀⠀⠀⠘⢮⡳⢴⣶⠿⠊⠀⡈⠀⠀⠀⠀⠶⠄⠀⠄⠀⢰⣍⣳
⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⣈⠂⡂⢻⣷⣿⠏⡔⠉⠀⠀⠀⠀⠠⠂⠙⠁⠀⠀⠀⠀⠀⠉⠉⠉⠒⠉⠁⠀⠀⠀⠀⠄⣀⠀⠄⠀⢀⣮⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠚⠶⠿⠶⠿⠛⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⠒⠘⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠰⢬⡍
⠀⠀⠀⠀⠉⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠈⠃⠀⡠⢀⣠
⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢀⠀⠀⠀⠀⠂⠄⠈⠀⠀⣈⠅⠀⢠⣾⣦
⠀⣀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠖⠀⢀⠌⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠙⡬⠟⠁

⠰⢀⠉⠀⠀⡀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣉⠒⠀⠀⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠥⢄⣉⠈⠁⠀⢠⡘⠀⠇
⠀⠀⠂⠀⠐⡀⠁⠠⠁⠀⠀⠁⠀⠀⠀⠀⢉⠈⣉⠂⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠈⠲⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡆
⣠⡐⠃⢀⢁⡄⠀⠀⠀⠀⠀⠁⠤⣀⠀⠠⠀⣠⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀
⠋⠁⡉⠡⠀⢠⣄⣐⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠰⠦⠊⠀⢀⠀⠀⠀⢆
⠀⠤⠁⠐⠃⠀⠀⠁⡠⡙⠄⠀⠀⠀⠀⠀⠀⡀⠐⠀⠒⠀⡤⠀⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡀⠤⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠤⣄⠀⢠⡆⡆⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢳⠀⡿⣤⡈⠻⢅⡀⢸⡄⢸⠀⣿⢸⡇⣰⠛⢸⡇⢠⡄⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⢳⡒⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠛⣧⠀⠈⣿⡄⢸⡇⢸⣇⠾⠼⡟⣼⠁⣿⠀⢸⡧⢸⡇⠀⠐⣄⠙⠦⠤⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⣀⠀⠠⠞⠀⠀⠀⠀⠀⠀⠸⡆⢄⡿⠃⠈⠁⠀⠁⠀⠀⠀⠻⠀⠉⠀⠘⠇⢸⡇⠀⠀⠀⠁⠢⠀⠊
⠀⠀⠀⠀⠀⠁⠂⠠⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠚⠁⠀⠀⠄
⣄⠀⠀⠠⠤⠀⠀⠀⢠⠀⠀⠲⢘⠉⠀⠀⠈⠉⠀⠀⠰⣤⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠀⠀⠄⠈⠀⠀⠀⠀⠀⢠⠈
⡍⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠃⠀⠀⠀⢀⣀
⠈⠂⠀⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠠⠾⠄⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄
⠀⠀⠀⡀⠁⠀⠀⢢⠋⣹⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠱⠀⢁⡂
⠔⣂⠸⢟⢠⠄⢀⢹⢰⠄⠉⠴⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠂⠂⢀⠈⣣⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠙⢍⣘⠁⠀⠀⢘⣸⡀⠠⠀⢈⣫⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⢶⠈⣁⠌⠀⠀⠀⠌⠀⠀⠠⠀⠀⠀⠀⠀⠐
⠢⣀⠉⠀⠀⠜⢻⣤⡵⢶⡏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠈⠁⢈⠈⠁⠀⠀⠀⠊⠘⠄⠀⠐⠀⠀⠀⠀⠀⠁⡀
⠀⠈⠪⡰⠄⡀⡊⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠒⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐

⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⣀⠀⠀⣀⡀⠀⠀⢀⣀⢀⣀⡀
⠀⢠⣿⣿⣿⠆⢸⣿⡆⠈⠋⣀⡀⢀⣸⡇⠀⠛⠛⠛⢛⣻⣿⣧⡀⢀⠀⢶⣴⣿⣿⡿⠿⠃⠀⠛⠁⠸⠿⠟⠀⣼⣝⣿⣿⡟⣷⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠐⠄
⠀⠘⠿⠿⠋⠀⠈⠉⠁⠀⠈⠁⠽⠏⠋⡡⠀⠀⠀⠀⢈⢿⣿⠍⠀⡸⠁⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⢀⡀⠀⣤⠘⠿⣿⣼⡽⠟⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢀⠴⠒⠖⣋⣻⣾⣗⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠓⠉⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣧⣀⣿⣄⠀⠀⠀⠀⠀⠀⣤⣶⣤⣶⣶⣶⣾⣶⣄⡀
⠀⢀⡆⠀⢠⣟⢙⠿⣤⣿⡆⠻⢀⠀⠰⢶⣦⣿⣄⢀⣾⣿⣿⣿⣿⣶⡄⢀⠀⢠⡔⠊⠒⠄⠀⠀⡀⠰⢽⡼⣿⣹⣦⠀⠀⠀⠀⣦⣋⣻⣿⠏⠛⠚⣉⣉⣩⣧
⠀⢸⣿⡀⠀⣋⠀⠀⠀⠈⠃⢉⣹⠀⠀⠛⢶⣯⠭⣭⣭⣭⣭⣽⡷⠋⠀⠸⡄⠸⣇⣀⣀⡞⠀⢀⠃⠀⠞⠛⠛⠋⢡⣤⡟⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⢧⣙⣦⣌⣀⣀⣀⣠⣴⣿⡟⠀⠻⠇⠀⠉⠉⠙⠛⠛⠉⣩⢤⡤⠄⢠⠁⡀⠈⠉⠁⠠⠐⠀⠀⠀⠀⠀⠀⠀⢈⣿⠇⢠⣼⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠙⠻⠭⠉⢀⣩⠥⠴⠋⠠⣶⠤⠄⠀⠀⠀⠀⠒⠒⠚⠷⣶⡶⠗⠘⠦⠤⣄⣤⡴⠴⠶⠖⠀⠀⠀⠦⠤⠤⠼⠿⠀⠀⠐⠿⠻⠿⣿⠟⠛⠛⠋⠉⠉⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⣤⢠⡄⢀⡄⢠⡀⢀⡄⢀⡄⢠⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠁⠈⠉⠈⠉⠈⠀⠈⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⠨⠬⠬⠼⠼⠭⠧⠥⠥⠥⠽⠇

⠀⠀⣠⣤⣶⣶⣶⣶⣤⣤⡀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⣶⣦⡀⠀⢀⣀⣀⠀⠀⡠⠢⣀⢀⣀⣠⣤⣀⡀⠀⠀⠀⠀⢀⣤⣶⣦⣄⠀⠀⠀⠀⣤⢀⣤⣄
⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⡇⣠⠒⠒⠤⣀⠀⣀⠀⠰⠀⠙⠻⠟⠠⣿⣿⡿⠀⢀⠈⠠⢿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣍⣐⣶⣶⣷⣶⣶⡇⠀⢤⣙⣺⣻⢿⡀
⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⣠⠤⢄⠀⠀⢡⠄⠀⠻⣃⣤⣤⣤⡤⣄⡀⠛⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣹⣿⣿⣿⠀⠀⠈⠈⠉⠒⢻
⠀⠀⠸⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢧⣀⡀⠁⠀⢀⠀⣠⣾⣁⣿⣿⣿⣟⠉⠹⣔⡀⠸⢿⡿⣿⣿⣿⣿⣿⣿⡏⠀⠐⠐⠚⠛⠟⠟⠛⠀⢠⣤⠀⠀⠀⠁
⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠟⠛⡠⠄⣸⢿⣃⠀⠑⢝⠿⢿⣽⣿⡿⠋⠀⠀⠀⠉⠗⠀⣠⡶⠶⠂⠀⢀⣀⠀⠸⠟
⠀⠀⠀⢑⠀⠀⠀⠀⠀⡀⢀⣄⡀⠀⠀⢀⡀⠀⠀⠄⠀⠈⣿⣿⣿⣷⣶⣶⡴⠟⣱⣾⡟⠀⠀⢀⣀⠀⢀⣠⠴⠒⠀⠀⠀⢀⣔⣛⡋⠉⣳⣦⡑⣬⣷⣄⣤
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⣟⣷⠀⢿⣿⠗⠀⠰⣶⡀⠘⣯⣿⡯⢭⣤⡶⣾⡽⠟⠁⣴⣾⠿⠿⡟⢉⠀⠀⢴⡶⠀⠐⢉⢳⣄⣿⣦⡸⣿⣿⣸⣿⣿⣿⣿⠃
⠀⠀⠀⠈⠛⠒⠀⠀⠈⠀⠀⠙⠛⠁⠐⠀⠁⠈⠀⠀⠀⠀⠀⠀⠉⠁⠓⠘⠛⠉⠁⠀⠀⠛⠓⠒⠉⠀⠀⠀⠀⠀⠈⠀⠈⠘⠛⠛⠻⠟⠛⠛⠛⠛⠋⠉⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣤⣝⣥⣮⣭⣿⣥⣿⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣤⡙⢦⠯⠟⡠⠛⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢸⡼⠧⠤⠄⠂⣆⡀
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⢰⣄⠀⠘⠒⠣⠴⣧⡴⠷⣦⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢠⡀⢈⣀⣀⣀⠀⠀⠀⠛⠁
⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⡀⠘⡉⠩⠗⡆⠀⠀⡸⠛⠚⠣⡴⠀⠀⠀⠀⠰⢯⣬⡷⠀⠀⠀⠀⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠸⣤⣈⡁⠀⠀⠋⡿⢃⡤⠁⠀⠀⠀⠀⠆⢹⣻⡆⠦⠀⠀⠀⠀⠀⠀⢱⣤⡄⠀⠀⠀⢀⠀⠰
⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⠉⠓⠒⠄⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⠀⠀⠀⠀⣤⣛⠀⠀⠀⠀⠀⠀⠛⠂
⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠋⠙⠛⠛⠉⠀⠀⠀⠀⠀⣠⣔⣲⡇⠀⠀⢀⡂⠀⠀⠀⠀⠖⠁⠁
⡷⠉⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⢶⣰⣤⡀⠀⠀⠸⢿⡽⠻⠄⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡷⢦⡙⠾⢷⡷⡽⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠭⣄⣾⠯⠐⠀⡀⢷⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠐⠛⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠠
⡄⡨⠤⠀⠀⠀⠀⠀⠀⠀⠀⠸⠳⠶⣄⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠰⠗⠄⢀⣤⡺⡄⠀⠀⠈⣧⠀⠀⠀⢠⠀⡀
⢦⣤⣠⠆⠀⠀⠀⠀⠀⠀⠀⣟⠳⣶⢶⣆⠀⠀⠀⢰⣶⣾⢿⠿⠂⠀⠀⠀⠀⠀⠰⠂⠀⠱⡤⠀⠀⣴⡇⠀⠀⠀⠀⣆⠙⢏
⠀⣀⣤⠤⠒⠋⠀⠀⠀⠀⠀⠙⠳⠿⠚⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⡀⣤⡴⠟⠁⠀⠀⠀⠀⠘⠀⠴⠖
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⡡⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠐⠘⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢌⡡⠎⡱⢎⡱⢆⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⠌⠡⢞⣹⡃⣱⠎⣡⡶⡀⠀⠀⢠⠀⠀⠀⠀⣠⢖⣶⡶⢶⣄
⠤⢤⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡈⠱⢎⡹⠟⣹⣾⣷⣿⡇⠀⢠⣾⠀⠀⠀⠠⠿⣾⣻⣿⣿⣽⠇⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣽⣦⣌⣩⣾⡿⣯⣿⡤⠄⠀⠈⢸⠀⠀⠀⢠⣲⣈⠉⠙⠻⣬⠀⠰
⠀⠀⠾⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢫⠎⣹⠿⠋⠀⠀⠀⢀⣦⣀⠀⠀⠀⠈⠙⠿⠛⠙⠇⠀⠀⠀⠀⠀⠀⠠⠀⢀
⠴⠼⣣⠿⠗⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠰⣿⣭⣯⡥⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣤⠐⢌
⠁⠉⠈⠋⠀⠀⠀⠀⠀⠀⠀⢫⠐⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣷⣿⣄⠀⠀⠀⡄⠐⠒⢣⡌⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⢁⣀⠀⠀⠐⢄⠀⠀⠀⠀⠐⢿⣿⣿⡻⠃⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣠⠾⠿⣯⠋⣉⡙⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡇⠀⠈⢢⠱⠀⠄⠀⠀⠰⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼⠀⠀⢡⡸⠠⠄⠁
⠀⠀⠀⠀⠀⡠⠀⢐⡂⠀⠀⠀⠀⠀⠀⠀⠂⡀⡂⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡀
⠀⠀⠀⠀⠀⠓⠋⠀⠀⠸⠗⠆⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⠀⠀⠠⠀⠀⣀⢀⠁⣠
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠊⠀⠀⠀⡀⠀⠀⠀⢀⢠⡤⠒⠉⠀⠀⠀⠀⠐⠄⠤⠤⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⡆⢀⠄
⠀⠀⠀⠀⠸⠀⠠⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⠀⠀⡄⢀⠀⡆⠀⠀⠀⠀⠀⢨⠈⡟⣀⣤⠛⣀⠸
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠈⠂⠀⠁⠉
⠀⠀⣠⢄⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⢒⠧⠏⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠂⡤⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⠄⣀⠀⣀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣙⠛⣁⡴⠞⡁
⠀⠀⠀⠀⠀⣀⠤⠛⠁⠀⠀⣠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠀⠈⠁⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠓⢁⣠⠔⠂⠀⠀⢄⠀⠀⠢⠀⠀⣥⢈⣥⣼⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠢⢠⢈⠀⠀⠀⠀⠀⡰⠉⠂⠀⠉⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠤⠊

⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠀⠀⠀⣴⠃
⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣦⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⠞⠁⢀
⠛⠋⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢴⣐⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢂⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢐⡄⠀⠘⠿⠿⢾⡵⠿⠿⠃⠀⠠⡂⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⡀⢀⣀⡀⢀⡀⢀⢀⡀⣀⣀⢀⡀⠀⣀⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢼⢸⣧⠟⢸⠤⠀⣼⣇⢸⣿⠀⣿⠄⢸⣷⠘⢧⡅⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠙⠋⠃⠘⠒⠂⠋⠛⠘⠙⠂⠛⠀⠛⠙⠈⠒⠃⠀⠃
⣄⣀⣀⣤⣄
⣿⣿⣿⡿⠊⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠒⠋⠁⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠚⠛⠀⠀⢈⣀⣤⣴⣶⣤⣀⣤⣦⣄⣀⣠⣔⣂⠀⠀⠟⠏⠁⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⣦⣄⡀
⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠘⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠹⣿⣿⣷
⡟⠁⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⠀⠀⠹⣿⣿
⠀⠀⠀⠀⠀⣤⠶⠃⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘⢀⠀⠄⠁⠃⠀⠈⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷
⠀⠀⠀⠀⠀⠐⠂⠡⣴⠂⠀⢀⠀⠠⠀⠀⡁⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠊⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⣀⠤⠀⠄
⠀⠀⠀⠀⢓⠄⠉⠄⠈⠳⠄⠀⠀⠀⠀⠈⠓⡦⠀⠂⠀⠆⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠐⠂⡤⣄⣠⡇⠀⠀⣢
⠀⠀⠀⠀⠀⠀⠑⠐⠉⣩⣇⠀⠠⠄⠐⣀⠀⠀⠀⡀⠔⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠱⣆⠬⠍⠀⠒⢺⣇⣈⡡⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠤⠤⠤⠤⠤⠤⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⣄⣐⣚⣉⣁⠀⠖⠂⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⠀⠐⠒⠒⠛⠛⢀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠔⠄⠀⠀⠀⠀⠀⡆⠀⠀⠠⡀⠀⠀⠀⣇⡷⢀⢀⠀⠀⠀⡀⡀⣿⠀⢰⡏⠀⢀⠀⠀⡀⣯
⠀⠀⠀⠀⠀⡠⠥⡀⠀⠀⢀⠀⠀⠀⠀⠀⠸⢀⡄⠀⠀⠀⡏⢱⢸⠈⢹⠖⠃⡅⡇⣿⣆⢸⡇⢨⢸⡇⠳⡄⣇⠀⠀⠀⠀⠀⣦⠀⠀⠉⠀⡀⠈
⠀⠀⠀⠀⠀⠀⢄⠀⢂⠀⢀⡆⠀⠤⠘⠀⠀⠁⠀⠀⠀⠈⠉⠁⠈⠀⠀⠁⠀⠀⠁⠉⠈⠀⠁⠀⠈⠁⠀⠀⠈⠀⠁⠀⠀⠀⣽⠀⠀⠀⢨⠁
⠀⠀⠀⠀⠀⠀⢀⠠⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠈⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⣬⢄⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠒⠉
⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠈⠙⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⢀⡴⠘⠂⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⡀⠀⠀⣦⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠈⠉⠳⠄⠀⠀⠀⠄⠸⡄⠀⠈⠛⠈⠀⢀⡟⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠐⢤⣀⣀⣤⡴⠿⠓⠀⠖⠊⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠚⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠔⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠤⠀⣀⣀⣀⣀⡀⠤⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⠖⠂⠀⠉⡉⢀⡇⣄⠀⠈⠉⠀⠀⠀⠀⠀⡠⠀⢢⣼⠖⠒⡂⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀
⠀⠀⠀⡀⠀⠀⢰⠏⢀⠜⠁⢠⣶⣽⡟⢱⡖⣿⢻⠇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡚⠥⠟⠚⠚⣰⠋⣙⢤⣀⡀⢄
⠀⠀⠻⣿⡦⠄⠚⠆⠛⠃⠴⠿⡧⠔⠋⡙⢫⠴⠧⠄⣆⣀⣰⠇⠀⠀⠀⠀⢱⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠔⠚⠛⠋⠸⠔⠒⠓⢒⠊
⠀⠀⠀⠈⠂⠀⠀⠂⠀⢈⡛⠷⣶⡿⠶⠶⠶⠾⠷⠟⠛⠉⢁⡀⠄⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠁⢠⡂⠀⠀⠀⠀⠀⠀⣐⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢍⡛⢛⠒⠢⢤⣤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠈⢠⣀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠶⠖⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠒⠒⠒⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡬⠥⠴⠶⠶⠶⠶⠶⠶⠶⠶⠤⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠉⠉⢀⣴⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢫⡀⣀⣴⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣀⣀⡸⠣⠴⠒⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠉⠛⠻⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠞⣛⠩⠀⠀⣀⣀⣄⣀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠭⠭⠅⠐⠒⠂⠉⠁⠀⠀⠀⢸⠁⠀⠀⠀⠙⡆⢂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢀⡇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⣠⣴⠟⢁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠾⠟⠛⢉⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠳⡀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⣀⣠⠤⣔⠊⠉
⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠀⠀⠙⢦⡙⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠂⢄⠀⠉⠓⢄
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡦⠤⣀⣀⣀⠀⠀⠀⢀⣀⣀⣤⢴⠖⠉⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⢳
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⠤⠬⠭⠭⠭⠭⠴⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⠀⠀⣀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠤⠤⣀⣈⠁⠒⠂⠠⠤⠄⠀⠤⠠⠤⠀⠠⠤⠀⠐⠒⠈⢁⣀⣠⠤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉

⠀⠀⣀⣀⣤⣤⣤⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣶⣤⣤⣤⣤⣀⡀
⠀⣾⣟⡯⠍⠓⠒⠒⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⣽⣿⣧
⠀⣿⠈⠉⠻⠓⠒⢶⣶⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢴⣶⣶⣶⡶⠟⠛⠉⢸⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣀⣠⣤⣤⣀⡀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠟⠋⣉⣉⣉⣙⠻⣷⣄
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣴⠟⠋⠉⠉⠛⣷⡌⢿⣆
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⠃⠀⠀⠀⠀⠀⠘⣿⠸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠃⠀⠀⠀⠀⠀⠀⢀⣿⠀⣿
⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⡟⢸⡿
⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⢀⣼⡟⢠⡿⠃
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⣠⣾⠋⣰⡿⠁
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣠⣴⡾⠋⣡⡾⠋
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⠛⠋⣁⣴⡿⠋
⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣦⣴⡾⠛⠁
⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠋⠁
⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠈⠻⣶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⡾⠟⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣽⣭⣬⣽⣭⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠖⠒⠒⠒⠒⠒⠒⠒⠒⠲⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣚⡭⠵⠖⠒⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠓⠲⠤⣍⣓⠲⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠀⠀⢀⣀⣠⣤⠤⠤⠶⠒⠒⠒⠒⠒⠒⠶⠤⢤⣄⡀⠀⠉⠛⢦⡙⢦
⠀⠀⠀⠀⠀⢠⡏⡏⠀⢀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢤⡀⠀⠀⠀⠉⠙⠲⣄⠀⣿⢸⡆
⠀⠀⠀⠀⠀⢸⣇⢣⡞⠉⠀⠀⠀⠀⠀⢀⡤⠴⠒⠒⠒⠋⠀⡤⠤⡄⢹⡀⠀⠀⠀⠀⠀⢀⡿⣡⢾⡇⣀⣤⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⢸⡈⠳⣌⡳⢤⣀⡀⠀⠀⠸⡄⠀⠀⢰⠖⠒⠚⠁⠀⢹⢸⡇⠀⢀⣠⡴⢞⣡⠞⣡⠞⠋⠁⠀⣀⣀⣀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠉⠓⠮⣍⣛⠒⠶⠿⠦⢤⣬⣷⣤⣤⣤⠤⠿⠾⠒⢋⣩⡤⠖⠉⠀⠀⣧⣀⡤⠖⠋⠁⠀⠉⠙⣦⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠶⠶⠶⠶⠶⠶⠶⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢧⣄⣀⣀⣀⣀⡤⠞⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣨⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠀⠈⠉⠉⠁⣀⡠⠔⠋
⠀⠀⠀⠀⠀⣠⠞⠉⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠻⣍⠛⠋⠉⠉⠁
⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⢸⡷⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡏⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⢦⣌⡙⠲⠦⢤⣄⣀⣀⣀⣀⣀⣀⡤⠤⠖⠚⣋⡥⠞⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠤⠤⠤⠤⠤⠤⠴⠶⠒⠋⠉⠀⠀⠀⠀⢀⣠⣾⠟
⠀⠀⠀⠀⠀⠙⠪⣝⡲⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢴⣚⡭⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠺⠭⣍⣓⣒⠲⠦⠤⠤⠤⠤⠤⠤⠤⠴⣖⣒⣻⠭⠷⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢠⡏⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⠁⠀⡾⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣰⠇⠀⣸⠃⠀⢠⠏⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢠⡟⠀⢰⠇⠀⢠⠏⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠖⣾⠀⢸⠃⠀⡿⠀⢠⡟⠀⢀⡏⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣛⣭⠴⠒⠀⠀⡏⠀⣿⠀⢸⡇⠀⢸⠁⠀⣼⠀⠀⠠⣌⣙⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢾⣿⣶⣞⣋⣥⣤⣿⣤⣿⢠⣼⡇⣤⣼⢠⣤⣿⣀⡀⠒⠦⣭⣛⠆⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠈⢉⣠⠟⢑⣶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣍⠓⠂⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠉⣉⣀⣤⡴⠾⣛⣵⡆⣚⣛⠧⣄⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣝⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⢋⣉⣉⣭⣴⡶⠿⣛⣭⠀⠉⠉⠙⣾⡇⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠛⠃⢸⣟⡳⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣉⣉⣉⣥⣴⡶⠿⣛⡅⠈⠑⣂⡴⣻⡣⢠⡏
⠀⠀⠀⠀⠀⢀⣤⠞⣋⡥⢒⡠⠄⠀⠀⢻⣟⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣉⣉⣉⣩⣭⣴⠶⢟⡋⢡⣞⣛⣽⣾⢟⣵⠟⢶⣄
⠀⠀⠀⠀⣰⠟⣡⡞⢡⡞⢉⡴⠊⡀⠀⠈⢿⣟⠒⠄⠀⠀⠀⠀⠀⠀⠀⣀⣉⣉⣉⣉⣭⣭⣴⡶⢿⡛⢡⡿⢿⣛⣭⡶⠛⠁⣀⢢⡈⢷⡄
⠀⠀⠀⠀⣿⠀⣿⠀⣿⠀⣿⡀⢾⡀⠀⠀⠀⠻⣯⡒⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣭⣥⣤⠴⠶⣞⡛⣱⣿⣿⣿⣿⣿⢿⡌⢳⡈⣆⢳⠈⡇
⠀⠀⠀⠀⠻⣆⠹⣧⣌⠳⢮⣛⠶⣬⣁⠀⠀⠀⠈⠻⣥⣄⣀⠀⠀⠀⠀⠀⠤⠤⠶⢶⣶⣾⣿⣿⣿⣿⣿⢸⣿⡜⣿⢎⡇⢸⠇⡏⢀⡼⠃
⠀⠀⠀⠀⠀⠈⣳⣮⣙⠷⣦⣍⣙⠓⠦⠄⠀⠀⠀⠀⠈⠙⠻⢯⣿⣛⣛⣛⣛⣛⣯⣽⡿⠿⢛⣫⣵⡿⢋⣾⠟⣰⠟⠘⠁⢋⣠⣶⣿⠤
⠀⠀⠀⠀⠀⠀⠀⠨⠽⠿⠶⢮⣭⣙⣓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠽⠷⠶⠶⠶⣚⣛⣋⣭⡵⠾⠛⢁⣈⣡⣤⣶⣾⣿⣿⠿⠭⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣉⣉⣹⣿⣿⣷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣛⣉⣉⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣟⣛⣛⣛⣛⠛⠛⠛⠛⠛⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⣉⣩⣭⣭⣭⣭⣭⣭⣉⣉⡉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣡⠶⠋⡹⠋⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⣠⠞⠂⠀⣼⠁⢠⠀⠀⠀⢈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠛⠀⠀⣴⢃⣠⡦⠄⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠈⠂⠀⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⡤⠚⠀⣠⣦⠰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⢾⠆⠀⠀⠀⠀⠀⠀⠌⠃⠀⠁⠈⠉⢒⡆⠀⠙⣿⠀⡆⠐⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠳⣤⢀⡉⠻⠀⢇⠀⠀⠁⠀⠀⠀⠀⠀⠀⣸⠇⠀⢸⡿⠀⠀⢠⠗⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠱⣤⠦⠈⠢⣀⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠏⣰⡿⠚⠁⠰⠟⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⢀⡤⠃⠀⠀⠉⠻⠆⠐⠶⠚⠾⠃⠀⠀⠶⠀⠀⠒⠛⠉⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠠⡟⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⣦⡀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⢠⠀⠀⠀⠈⠁⠀⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣅⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⣧⠀⠀⠶⣦⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⠶⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⠉⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣧⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠀⠀⠀⠀⠀⠀⠐⠒⠲⠚⠀⠀⠀⠀⠀⠀⢀⣤⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢠⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢤⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠀⠀⠘⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⠀⠀⠀⠘⠀⠀⢸⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣶⣶⣶⣶⣶⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘






⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣾⣶⣶⣶⣾⣶⣾⣶⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⣻⡟⢿⡿⢿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠀⠐⠀⠀⠀⠤⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢠⡰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡈⢿⠧⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⢀⠠⠐⠂⠉⣀⣀⣀⣀⡀⢁⠶⠭⣓⠦⡀⠀⠙⠔⢅⠁⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡠⠖⠀⠠⠖⠛⠉⢉⡔⠣⢌⢙⠣⣍⡒⢌⠳⡄⣄⠀⠀⡀⡀⡢⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠌⠀⠴⠐⠁⠀⠀⠀⠀⠀⠑⠰⢯⡈⠑⠠⣁⠡⡄⢉⠀⢣⠙⣌⠳⣄⠀⠘⠄⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠑⠈⠢⠑⡇⠘⡄⠠⡀⠑⢬⣑⠲⣄⠀⠂⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⡀⠀⠘⡀⠡⡘⢤⡘⠂⡀⡀⠂⢤⡑⣌⢣⠁⡀⠈⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⢀⠂⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠒⠄⡁⠑⣄⠳⡜⢆⠱⢌⠢⢤⡂⠈⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠔⠀⠀⢀⠀⠀⠀⠀⠀⠀⠢⡙⢅⠈⢢⠙⠀⡑⠦⡽⠊⠀⢦⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠄⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠣⡀⢡⠈⠢⢌⡀⠀⠀⠀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⡐⠀⠌⠀⠀⠀⠈⠃⠠⡄⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⢆⡈⠑⢢⠍⠀⠀⠀⠀⠐⠀⠑⡀
⠀⠀⠀⠀⠀⠌⠀⠘⠄⠀⠀⠀⠀⠠⠀⢳⡀⢀⠀⠤⢤⠤⠂⠀⠲⠂⠰⠂⠐⠢⠄⢀⣀⠀⠀⠀⢠⠏⠢⠌⠛⠀⠀⠀⡀⠀⠀⠀⠀⠄⠈⠄
⠀⠀⠀⠀⠌⠀⡐⠀⠘⡀⠀⠀⠀⠀⡡⠤⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠰⣏⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠈⢂⠈⠂
⠀⠀⠀⠐⠀⡐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⠈⢄⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠤⠖⠒⠒⠒⠒⠒⠒⠒⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⠀⡠⠄⠒⠲⢤⣄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠆⠀⠀⠀⢎⠀⠀⠀⠀⠀⣺⡇⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠑⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠤⠤⠶⠒⠛⠛⠛⠛⠛⠒⠲⠒⠚⠋⠁
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣀
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⡾⠒⠋⠉⠉⠉⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⠒⢦⡀
⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣸⣿⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠈⠳⢶⣤⣤⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣮⣿⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣔⢜⣾⠏⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣺⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣶⣤⣴⣤⣤⣼⣶⣿⡷⠟⠁⠀⠀⠀⠀⠀⠀⢸⡀⠀⠂⠀⠠⠤⠤⠤⠤⠴⠷⢿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣳⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⣀⣤⣾⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡟⢻⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢤⠛⠳⠴⠴⢦⣠⢖⡥⢽⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠘⠚⠛⠲⡞⠋⠉⢋⠀⣐⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠂⠀⠀⠸⡄⠰⣼⡇⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠒⠛⠋⢉⠇⠈⢿⡉⠙⠛⠒⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠃⠀⠀⢈⣈⣿⣿⠃⠀⠀⠀⠀⠀⠀⢼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⣀⣩⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠶⠾⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠶⠶⠾⠾⠷⠷⠾⠿⠛⠋⠁


⡿⠿⠿⠿⡿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⡠⠀⡀⠀⢀⠢⢤⡀⠀⠀⡏⠀⢻⢀⡤⣠⠊⠉⠀⣀⠤⠄⠀⢞⢡⠀⠑⢆⠀⠐⠤⡀⠀⠀⡞⢳⡄⠀⢠⠟⠓⠦⣔⠒⠓⠦⣄⣀
⠀⠀⢀⠰⢀⠑⣄⢻⠀⡠⠓⠀⠀⠈⠓⠁⠸⡀⣀⠇⠀⢸⣇⠀⠀⠀⠈⠉⠁⠉⠁⠤⠤⠒⠳⡄⠀⣧⣸⠃⢀⡟⠀⠀⠀⠈⠙⠒⠶⢤⡈⠉⠉⢱⡀
⠀⠀⠀⠂⢢⣽⣿⡻⠋⡠⠔⠒⠉⠉⠓⠦⣀⠀⠀⠀⠀⢸⣧⠤⢄⣀⡀⠀⠀⠀⠈⢉⣀⡈⢽⡃⠀⠼⠁⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⢀⡟⡄
⠀⠀⠀⢊⢀⠔⠁⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⢸⡅⢀⡀⠀⠈⣈⡉⢉⣉⣀⠀⠀⣰⠇⠀⠀⣠⠞⠀⠀⠀⠀⠁⠀⠀⣠⢎⡵⠁⠀⡼⡸
⠀⠀⠀⠀⠁⢀⡎⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠈⣇⠀⠙⠒⠦⠬⠤⠤⠄⠀⢀⣀⠠⠤⠘⠁⠀⠀⣧⣀⠀⠀⠐⠀⠀⠀⣰⢣⠏⠀⠀⢠⢇⡇
⠀⠀⠀⠀⠀⠸⣇⠠⡀⠀⠀⢀⡞⠁⠀⠀⠙⢦⠀⠀⡿⠀⡴⠾⠶⡆⠀⠀⠀⠀⠀⠠⢤⣄⣀⠀⠀⠀⠘⠫⢽⣲⡦⣄⠀⢠⠇⣾⣀⣀⣠⡼⢸⠁
⠀⠀⢀⣤⣄⠀⠙⢦⡀⠀⠀⠘⣇⠀⡀⢀⡄⣸⠀⢠⠇⢸⠁⠀⣰⠏⠀⢠⠒⠒⢦⡀⠀⠀⠈⣧⣀⣀⣀⣀⣀⡈⠙⠲⣝⣫⠞⠓⠶⠶⠶⠖⠋
⠀⠀⣾⠁⠈⠳⣄⠀⠉⢦⡀⠀⠈⠳⠬⠵⠞⠁⢠⠟⠀⠘⠒⠚⠁⠀⠀⠘⢮⣀⣠⡇⠀⢰⣯⣽⣏⣀⣠⣤⠤⠽⠇⠀⠀⠀⠀⠀⢠⠖⠒⠲⡄
⠀⠀⣿⡄⠀⠀⠈⠑⢤⣀⠑⢄⡀⠀⠀⢀⣠⡴⢋⣠⠴⠖⠒⢛⡓⠒⠲⢦⡀⠀⠀⠁⠀⢸⠀⠀⢹⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠏⠀⠀⠠⢹⡀
⠀⠀⠸⣷⡀⠀⢀⣤⣤⡈⠑⢦⡈⠉⠉⠉⠁⡴⢯⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠲⢄⡀⠀⠸⣄⠤⠤⢷⡤⠤⠤⣤⡇⠀⠀⠀⢠⣾⠀⠀⠀⠀⠃⢦⡀
⠀⠀⠀⡟⣧⠀⢻⠀⠀⡝⣦⠀⢹⡄⠀⠀⡞⠀⠈⣧⠈⠀⠀⠀⠀⠀⠀⡎⠀⠀⢠⢙⡆⠀⣟⠒⠒⠚⣷⠚⠛⢉⡇⠀⠀⠀⠸⡍⢙⠋⠙⠉⠉⣩⠁
⠀⠀⠀⢿⠘⣇⠀⠳⢤⣤⠟⠀⢰⠇⠀⢰⠳⣕⠀⠘⣆⢀⣒⣒⣀⣀⣸⣇⣀⠐⣡⠞⢳⠀⢻⠀⠀⠀⠸⣆⠀⢸⠃⠀⣀⡀⠀⠙⠾⣷⣤⡤⠞⠁
⠀⠀⠀⠈⢧⣈⠳⢤⣀⣀⣠⣴⠟⠀⠀⢿⣐⣨⠷⠞⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⢧⣀⣸⠇⠈⢧⣀⣀⣀⣉⣠⠜⠀⢯⠉⢧⠀⢀⣠⡴⠀⠢⣄⡀
⠀⠀⠀⠀⠀⠉⠛⠒⠒⠛⠋⣁⣀⣀⡀⠀⢉⣁⡀⠀⠀⠀⠸⡳⣶⣄⡇⠀⠀⠀⠀⠈⠁⢀⣴⣦⣍⡉⠉⠀⠀⠀⠀⠈⠓⠻⣄⣈⡓⠶⠴⠶⠞⠃
⠀⠀⠀⢰⡒⠦⣴⡒⠋⢉⣉⣀⠠⠀⠉⢶⡁⠀⡝⠀⠀⠀⣠⠽⠾⢿⣧⣠⠤⠤⣄⡀⠀⢸⣝⡻⠷⣯⣭⣍⣉⣉⣉⣛⠲⢤⣀⠈⠉⠓⠦⣄
⠀⠀⠀⠘⣧⠀⠱⢭⣒⣤⣀⠀⠠⠄⠀⠀⠱⡀⢨⠆⠀⣼⢡⠊⠈⠀⠈⠁⠀⠀⢠⠹⡄⠈⠻⢿⣷⣶⣶⣯⣭⣭⣽⣛⡻⠶⣌⢳⡄⠀⠀⠘⣆
⠀⠀⠀⢰⡿⡦⢤⡘⣿⣭⢻⢷⣦⣄⡀⠀⠀⠑⣌⠆⠀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠶⠤⢤⣉⣉⣉⣉⡉⠛⠻⢷⣼⠋⠀⠀⠀⠀⣿
⠀⠀⢀⣀⠓⢬⣒⢵⡀⠛⠉⣟⠀⠛⢿⢗⠦⣄⡈⣧⠀⠸⡆⠀⠀⠀⠏⠘⠆⠀⠀⢰⠁⠀⢸⠭⠶⠶⠶⠶⠶⠦⣭⣍⡓⠤⡉⠀⠀⢰⠋⠉⠉⣹⠂
⠀⠀⠀⠈⣳⡀⠈⠑⠮⣓⢦⣈⠉⠳⡀⢀⡙⠲⠽⠇⠀⠀⠹⣔⠤⡀⠀⠀⠀⠄⣠⠏⠀⠀⠘⠿⢿⣒⣒⣒⣒⣒⠢⠌⡙⣾⠀⠀⢠⡟⡶⠒⢲⣿
⠀⠀⠀⠑⢿⣧⣤⡠⠴⡌⠑⢬⡓⢦⣉⣁⡸⠂⠁⢀⣀⠀⠀⠈⠓⠒⠛⠓⠒⠛⠁⠀⣀⣤⠴⠶⠲⠶⠦⣄⡀⠈⠙⢦⣄⣷⠀⠀⠸⠶⢷⣬⣿⣸
⠀⠀⣠⢾⡿⠋⠛⠒⠋⠀⠀⠀⠈⠓⠖⠋⢀⡠⠞⠉⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⢉⢳⡀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠈⠁
⠀⠀⠉⢁⡤⠤⠤⠄⢤⣄⣤⠤⠤⡀⠀⠀⡿⠤⠤⠤⠤⢤⡴⢦⣄⣈⣓⠲⢄⠀⢸⢿⠀⠀⠀⠀⠀⠀⠀⠀⡰⡠⠃⢀⡴⠞⣻⠋⠉⠉⠉⠓⢦
⠀⠀⡎⢹⠉⣿⠛⠛⠛⠛⠛⠛⠛⡏⠀⠀⣛⣷⠀⠀⣀⠀⠙⠋⠀⠀⠉⠉⢻⠀⠈⢧⡳⢤⡀⠀⠀⠀⠀⠀⢸⠁⢀⡞⠀⢎⠉⣠⠶⢶⣄⠀⠈⢧
⠀⠀⠹⣼⣧⠘⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⣯⡀⠀⠸⠽⠂⠀⣠⣤⣄⠀⠀⢳⠀⠀⠀⠙⣆⢷⠀⠀⠀⠀⠀⠘⡇⠸⡇⣠⠊⠘⣇⠀⣸⣽⠀⠀⣸
⠀⠀⠀⢠⡛⣦⣀⡀⠀⠀⠀⣠⠗⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⠛⠶⠟⠀⠀⢸⠀⠀⠀⠀⢿⢸⡆⠀⠀⠀⠀⠀⢹⠀⢷⡸⢄⣠⣌⢉⣩⣁⡖⣲⠏
⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠙⠒⠒⠒⠒⠒⠚⠙⠒⠒⠒⠒⠚⠀⠀⠀⠀⠈⠳⣧⣄⣀⣠⣤⡤⠞⠀⠀⠙⠶⣤⣈⣉⣠⡭⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⢀⣤⣀⠀⠈⠁⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁⠀⠀⠀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⣴⣿⣿⣿⡆⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠒⠤⣀⣀⣀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠛⠿⠿⠛⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡼⠀⠀⠀⣀⣤⡤⠤⠶⠤⣄⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⢺⡆⠀⠀⠀⠀⠀⢨⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠇
⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠐⠒⠒⠒⠒⢠⡀⠀⠀⠀⠀⠀⢀⡤⠼⠧⠤⠤⠤⠤⠤⠼⠼⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠃
⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⢀⣀⡠⠤⠔⣊⡅⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂
⠀⠀⠀⠐⢬⠭⠉⠉⠭⠭⠁⠤⠐⠂⠉⠀⡂⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠘⡄⢀⣀⣀⡀⠤⠤⠀⠐⠒⠈⢹⠀⠀⠀⠀⢀⣇⣀⣀⣀⣀⣀⢀⣀⣀⣀⠀⠻⣃⣟⠘⠃⠀⣠⠒⠢⠤⠭⠍⠉⠐⢲⠋⡇
⠀⠀⠀⠀⠘⡄⠀⠀⠀⣠⣤⣦⣄⠀⠀⠀⢸⠀⠀⠀⠀⠓⠐⠒⠀⠀⠀⠐⠒⠒⠒⠒⠒⠐⠀⠐⠃⠀⠀⡇⠀⠀⠢⠠⠐⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⢱⠀⠀⠰⣿⢿⣽⣿⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠁⢀⡀⠀⠠⠤⠤⠄⠚⠃⢰
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠙⠻⠟⠋⢀⣀⠠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⣔⡉⣑⢏⡠⢶⠀⠀⠀⠀⠘⠁⢠⢰⡴⠄⠶⠦⠀⡇⢠
⠀⠀⠀⠀⠀⠀⠐⢖⠒⠒⠂⠈⠉⠀⠀⠀⡄⠀⠀⠀⡠⠠⠤⢊⠭⠠⠕⠀⣈⠔⠨⠥⠄⠒⠤⠀⠀⠀⠀⢰⣈⡡⡀⠤⠤⠤⠤⠒⠃⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠄⣀⠀⠀⣀⡠⠄⠊⠀⠀⠀⠀⡗⢒⡒⢁⠔⠒⠊⠀⠀⠀⠀⣀⠀⠀⡀⡀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢰⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠓⠂⠑⢊⣐⢂⡮⠭⠱⢞⢄⡨⠮⡀⢴⠀⠀⠀⠀⠆⠀⠐⠒⠂⠀⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠐⠠⣀⠀⠀⠀⠀⠀⢸⣁⢉⡈⡡⠤⠤⠊⠑⠒⠉⠑⠀⠒⠢⠼⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠈⠐⠠⢄⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢀⠤⡐⠜⠋⠁
⠀⠀⠀⠀⢀⠴⠈⠠⠤⠤⠄⠤⠤⠤⠤⠄⠤⠤⠤⠬⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠄⠧⠤⠶⡈⢁⡀
⠀⠀⠀⠀⠘⣷⣮⡴⡤⠰⢶⣤⣤⣄⣄⣠⣡⣤⣐⣲⣶⠃⠀⠀⠀⠀⠀⠀⠀⣔⠈⡡⠄⠰⡀⠠⡤⢀⣐⠢⠤⣄⡉⢲⡄
⠀⠀⠀⠀⠀⢏⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⢋⡁⠃⠀⠀⠀⠀⠀⠀⠀⢙⠛⠠⠬⢵⣏⣘⣏⣁⣬⣡⠦⠶⠚⢛⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀⠀⠀⠀⠀⠀⣀⣠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⢀⡴⢋⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠉⠙⢿⣯⣡⡀
⠀⠀⠀⠀⠠⡾⠿⠿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠛⣧⣾⣷⣼⣿⣻⣿
⠀⠀⠀⠀⠀⠉⠀⠀⠈⠙⢿⣯⣓⣶⡤⢤⣤⣤⣤⡴⠶⠛⢉⣠⣤⣾⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⣦⣦⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⢠⠔⠉⠡⡶⠚
⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿
⠀⠀⠀⢺⡛⠛⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⣤⣴⣶⣦⣄⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢯⡙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⢫⣴⣷⣙⣿⣏⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠙⠓⡶⠦⣤⣤⣤⣤⡴⠶⠛⣋⢡⣤⡼⠧⢓⡳⢿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠑⢦⣄⣠⣤⣴⣸⣦⣻⣜⡣⣾⢧⢶⣵⡞⠷⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣜⣻⠹⠟⠛⠚⠒⠓⠛⠉⣙⣩⣥⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠂⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠐⠒⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢁⠈⠀⠀⠒⠂⠈⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠒⠂⠀⠈⠐⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠒⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠢⡀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠶⢺⡀⠀⢁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢂⣹⠀⠀⣏⠉⢵⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⢋⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡠⠒⠡⠐⢧⠀⠱⣀⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⣀⡀⠀⡈⡗⢤⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡜⢀⢊⠐⠁⠀⠀⠀⠑⢤⡈⠑⠂⠷⠤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠴⠊⠉⠀⠀⠀⢀⠻⠲⡐⠄⠑⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠆⠀⠀⠀⠀⠀⠀⠀⡼⠉⠑⠂⠠⠀⢤⡀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠡⠁⠀⠀⠀⠀⠀⣠⠞⠀⠃⠀⢨⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢱⡈⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠙⢒⠉⠀⠀⠒⠀⠀⠀⠀⠀⠀⢀⣁⠤⠖⣒⠼⠶⠶⠦⠤⠶⠚⠁⠀⠀⠀⠠⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠠⠆⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⣠⠴⠶⠒⢉⣡⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠂⠌⡁⠂⠠⢀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠉⠀⠀⠔⠊⠁⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⠴⠒⢈⠠⢐⡮⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠄⣀⠀⠀⠀⠈⠉⠁⠒⠒⠀⠤⠤⠤⠤⠤⠤⠠⠤⠤⠶⠶⠾⠛⠛⠓⠊⠉⠉⠠⠀⠂⢀⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠠⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠃⠐⠒⠒⠒⠒⠒⠒⠒⠂⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⣉⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣤⡶⠶⠿⠿⠛⠛⠋⠛⠛⠀⠀⢤⣤⡄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⠉⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠈⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠋⢦⠠⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢾⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢰⠄⠀⢼⣿⡆⠀⠀⠀⠀⠀⣤⠔⠋⠁⠀⠀⠰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣻⠟⠀⠀⠴⢠⣷⣶⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⢾⣯⢀⡄⠀⢀⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠿⣿⣿⣿⣿⣿⡿⣋⣼⠷⣼⠁⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠛⡁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠿⣿⠛⠏⢀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣁⣾⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢻⡧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠉⠛⢀⠀⣹⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢸⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣦⢠⣄⣹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠈⠛⢷⣶⣶⣶⣶⣶⡶⠦⢴⣶⣶⣶⣶⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⡀⠀⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⣀⣰⣹⣀⢤⣠⣄⡤⣤⡄⣍⡤⢠⢤⢠⢶⡀⠀⢸⣍⡷⢘⡏⡱⠀⣯⣱⠆⣻⣙⠆⢹⣍⡶
⠀⠀⠀⠀⢰⡁⢀⠎⢀⣓⠘⠉⢙⠉⠁⠙⠉⠉⠉⠉⠉⠀⠁⠀⠀⠀⣁⣀⣀⡀⠀⣀⠈⠀⠀⠀⢀⣠⣤⣥
⠀⠀⠀⠀⠀⠉⠁⡨⠇⣹⣵⠉⣭⠙⣦⠚⣛⣻⡗⡔⢷⠰⢻⡗⡻⠋⠁⣤⣼⠃⢋⢻⡇⠊⣭⠿⠧⠄⣤⠜⠁
⠀⠀⠀⠀⠀⠀⢠⢠⣆⠉⡟⠠⡍⣴⣁⢀⣛⡟⠀⢸⠺⣷⠀⡰⣇⠀⠀⣥⠛⠄⣽⢸⣧⣕⠌⢳⡀⠀⢻
⠀⠀⠀⠀⠀⠀⠘⠂⠀⠒⠛⠰⠳⠌⠟⠈⠉⠽⠧⠟⠇⠿⠤⠗⠼⠇⠄⠏⠘⠚⠋⠀⠓⠌⠫⠞⠀⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠢⡀⠢⡀⠀⠢⠳⣆⠀⠀⠠⠴⠀⣤⠀⠀⠀⠀⠤⠤⠀⣀⣀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⣠⠀⢀⠀⠢⠀⠀⠙⣦⠀⠀⠚⣠⠞⢩⠅⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠀⠀⠀⣀
⠀⠀⠀⠀⡂⠉⠀⠠⡀⠁⠄⢠⠖⣴⡡⢀⣠⢊⡁⠀⣾⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡖⠉⠀⠉⢦
⠀⠀⠂⠀⠀⠀⠢⠀⠐⢀⡔⢡⡾⠿⠞⠋⠨⠠⣤⠴⠻⠄⠀⠙⠤⢄⠀⠀⠀⠀⣀⡤⠞⢉⠀⠃⣰⠟⠀⠀⠀⢀⡗⢱
⠀⢸⠀⠀⠘⢄⠀⠁⡠⢋⡴⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠵⠒⠙⠁⢰⠀⣀⡴⠟⠸⠀⠀⠀⢀⡞⠁⢸
⠀⠸⣄⠀⠀⠈⢆⡀⣠⠎⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠁⠐⠁⠀⠂⠀⣈⡤⠖⠋⡉⠀⠀⠀⠀⣀⡴⠋⠀⢀⡜
⠀⠀⠩⡢⠀⠀⠀⠉⠑⠂⠸⢦⡀⠀⠀⠀⠈⠒⠤⠀⠀⠠⠄⠀⠐⠀⡤⠚⢩⠁⠀⠇⠀⠁⠀⢀⣠⠞⠁⠀⢀⠀⠑
⠀⠀⠀⠈⠒⠄⡂⠤⣀⡀⠀⠀⠉⠓⠦⢄⣀⠀⠀⠀⠀⣀⡠⠤⠖⠒⠀⠀⠀⠀⠀⠀⣀⣤⠴⠋⠁⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠅⠀⢐⡒⠤⠤⠤⠌⠉⠉⠁⠀⠀⠀⢀⠀⠀⠁⠄⠉⠛⠛⣉⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠈⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⠿⠿⠿⠿⠿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿
⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇
⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿
⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠃
⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠃
⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⣿⣿⣿⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⣀⡤⠶⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣼⠃
⠰⣏⣴⠶⣤⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⡀
⠀⠈⠁⠀⠈⠻⣆⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠈⢧
⠀⠀⠀⠀⠀⠀⠹⣇⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠙⠒⢦⡀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠤⣄⣀⣀⣀⣠⡤⠿⡄
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢀⡿⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠂⢀⡴⠋⠀⢀⣀⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⢸⣃⣀⡀⢀⣄⡀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⣼⠳⠦⠤⠤⢶⠞⠛⠒⢤⡔⠉⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡤⣄⡿⠀⢀⡞⠁⠀⣭⡏⠀⡌⠁⢹⡆⠀⠀⢻
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠃⠀⠶⠀⠀⣷⠘⠃⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢠⡟⠀⠀⠀⠀⠘⣇⠀⠀⠀⣷⣄⣀⣀⠜⠁⣠⠀⢸⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠣⣀⠀⢀⡠⠛⡦⠤⠤⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⣾⠀⠀⠀⠀⠀⠀⠈⣳⣶⣏⣁⣤⣤⠴⠒⠋⢹⠀⢸⠐
⠀⠀⠀⠄⠀⠀⠀⠈⢧⡀⠘⡗⠢⠭⢥⣤⣀⣀⡠⠤⠜⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⣿⠀⠀⠀⠀⠠⠂⠀⠸⣄⣀⡀⠀⢀⣀⠠⠒⡿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢱⣄⣀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⢹⡍⠉⢉⡀⠠⠀⠊⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠂⠀⠀⠀⡼⠳⣤⣀⡀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣿⠟⠋⠉⠉⠹⡍⠉⠻⡇⠀⠀⢀⡤⠒⠒⠾⡁⠀⢀⣈⠉⠉⠋⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢷⠀⠀⠀⠀⠃⠀⠀⡇⠀⠀⡏⠀⠤⠀⠀⢸⠎⠉⢀⠉⠳⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢧⡀⠀⠀⠀⣇⠀⠀⠈⠀⠀⡇⠀⣰⠃⠀⠢⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠈⣆⠀⠀⠀⠀⠀⣰⠃⠃⠀⠀⠉⠒⢲⠋⠙⠦⣀⣀⣠⠔⠁⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⠀⠀⠀⠈⠑⠒⣲⠖⠊⠁⠀⠀⠀⠀⠀⠀⠋⠀⠀⠠⠀⠀⠂⠚⠂⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣤⣤⣤⣴⣶⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠹⠉⠉⠛⣿⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠁⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣤⡤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠆⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠻⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⡿⠟⠋⠁⡀⠈⠛⠿⣿⠿⠛⠉⢀⠈⠙⠻⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⢀⣠⣴⣿⣿⣷⣤⣀⠀⣀⣤⣾⣿⣷⣦⣄⡀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⡀⠀⢀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⡴⠀⠀⠰⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡎⠀⠀⠀⢀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠠⠀⡘⢡⡷⢤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢤⡄⢖⠀⣠⣴⣶⣶⣿⡿⢷⣼⣿⣿⣿⣿⣻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠷⢂⢹⣧⣤⣬⠍⠉⠉⠁⠉⠉⠉⠁⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠑⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⠠⠐⠞⠻⣦⡀⠀⠀⠀⠀⠀⢀⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⠷⣤⣍⣓⣶⣶⡤⠴⡋⠁⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣌⠻⣿⣿⣿⣿⣦⣌⣉⣉⣉⣁⡀⠔⠁⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠈⠀⠀⠀⢠⡴⣿⣿⣿⣿⣷⣿⣿⣿⣿⡟⠋⠉⠉⠀⠀⠀⣀⣀⣤⡔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣟⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠈⠉⠁⠀⠈⠁


⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠈⠙⠫⡑⢤⡀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠒⠢⡀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⢳⣠⠤⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⡻⠐⠁⠀⢠⠀⠀⠀⠈⠀⣽⠀⠀⠀⠀⢀⣤⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⢼⠁⠀⠀⠀⠀⠀⠈⢢⡀⠀⠁⠀⠀⠀⠘⣷⣄⠀⠐⠚⠁⠀⠀⢀⡴⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠘⣆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠳⣷⣄⠀⢀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠹⣶⡈⠉⠐⠚⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡵⠋
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⣠⠊⠀⢀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡬
⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠐⠸⡄⠀⠀⣾⠆⠀⢠⠃⠀⣠⠃⠈⠀⠀⠀⠀⠀⠀⠀⡔⢀⠂⠀⠀⠀⠀⡐⠀⠸⠀⠆⠀⠀⠐⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡟⠀⢀⠆⢀⡴⠁⠀⠄⡀⢠⠀⠀⢠⠀⠀⢀⠊⠀⢀⠘⠀⠀⠁⠠⠀⠀⠀⠄⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣹⠀⠀⠉⠀⡸⠃⢩⠀⠀⠊
⠀⠀⠀⠀⠠⠤⣴⡦⠴⠿⠟⠛⠉⠀⠀⠀⠀⡇⠀⡠⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⣠⡜⠁⠀⠐⠂⠀⡀⠀⠀⠀⠉⠛⢻⣿⣿⣿⣿⠿⢛⠟⢀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠠
⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠒⠚⠉⠁⣀⣀⡴⠂⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢀⠼⠏⠁⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠠⠀⣠⣠⠖⠋
⠀⠀⠀⠀⠠⠤⠄⠉⠀⡀⠀⠠⠴⠀⠚⢉⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⠠⠄⢀⡀⠀⠂⠁⠀⠀⠀⠀⠰⡄⠀⠈⠓⠀⠠⣀⣀⢀⡦⠛⠉
⠀⠀⠀⠀⠀⠀⠈⠚⠓⠓⠠⡄⠀⠀⢀⣸⠇⠀⠀⡀⠀⠀⢃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠦⣐⣷⣄⣾⣍⡗⠀⠀⠀⠑⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡼⠇⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⢸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠉⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠚⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠖⠒⠒⠒⠚⠒⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠂⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡈⠀⠀⠀⠀⠈⠁⠀⠀⠉⠁⠀⠀⠀⡈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠄⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠐⢄⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠦⣍⣘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠀⣸⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣠⠔⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⢀⢤⣶⠿⠛⠉⠀⠀⢀⢠⠃
⠀⠀⠀⠈⢇⠀⣈⣉⠐⠠⣀⢮⠢⡐⠄⠀⠀⠀⠀⠀⠙⠓⠲⢦⡴⢒⡵⠟⠁⠀⠀⠀⠀⢄⡴⠃
⠀⠀⠀⠀⠀⠑⠄⡀⠁⠲⣈⣧⠦⠬⠱⡾⣽⡴⡦⡄⣀⣰⣯⣥⣔⣉⡀⡀⠠⢀⡂⠬⠒⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣉⣗⣾⡿⣿⠬⡯⢑⢔⡉⣀⠛⣧⣶⡖⡖⠒⠂⠀⠀⠉
⠀⠀⠀⠀⠀⠤⠠⡿⠿⠹⣞⣛⢯⡉⣯⣽⣿⣘⢣⢻⣯⢏⣿⣾⣤⢀⡠⡀
⠀⠀⠀⠀⠀⠀⠜⠀⢘⢐⣝⡭⠨⣽⢛⠖⢚⣿⣓⠾⠏⠉⠉⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠤⠂⠈⠑⠋⠉⠒⠃⠘⠯⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣆⣠⣤⣄⣀⣀⡀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⡤⠖⠚⠉⠉⠀⠀⠀⠈⢳⠀⠀⠀⠀⠉⠙⠓⠦⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠇⢀⣠⠤⠴⠖⠒⠒⠛⠛⠛⠛⠛⠛⠒⠲⠦⣤⣀⡀⢻⠲⣄
⠀⠀⠀⠀⠀⣠⠞⢀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣉⣡⣤⣤⣀⠀⠀⢠⣈⡉⠻⢤⣈⠳⣄
⠀⠀⠀⠀⢰⢃⡴⠋⠀⢀⡴⢋⣠⠤⠶⠚⠉⠉⠛⠋⠁⠀⠀⠀⠈⠳⠦⠤⣤⡉⠂⠀⠈⢳⡹⡄
⠀⠀⠀⠀⣿⡞⠀⠀⠐⢁⡴⠋⠀⠀⠀⠀⢀⠴⠊⠉⠉⠉⠲⡄⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢹⣇
⠀⠀⠀⠀⣿⡄⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢯⣀⡀⠀⠀⣀⣠⠇⠀⠀⠀⠀⣀⡼⢁⡇⠀⠀⢰⡿
⠀⠀⠀⠀⢹⠙⢦⡀⠀⠘⢤⣖⣂⡀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⣠⠟⠩⠖⠉⠀⢀⡴⢫⡇
⠀⠀⠀⠀⠈⣧⠀⠙⠳⠦⣤⣀⣂⠙⠶⠤⠴⠿⠿⠧⢤⣤⣤⡤⠴⠚⠁⠀⢀⣠⠴⠚⠉⢀⡞
⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠉⠉⠛⠲⠶⠦⠤⠤⠤⠤⠤⠤⠶⠖⠚⠋⠉⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⢿⢦⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⣄⣀⡀⠈⣿⠀⠀⢸⡟⠀⠀⣀⣀⣠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⣀⣄⣰⡏⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠍⠒⠒⠨⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⠒⢲⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⠛⠚⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠖⠋⠉⠉⠓⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣤⡤⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢦⠹⡌⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠘⡄⣿⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢰⠃⣿⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢀⠏⣸⠇⠀⢰⢿⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡟⠀⠀⡞⢈⡇⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣾⠁⠀⡼⠁⣼⠃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⣰⠏⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡶⠶⠖⠚⢻⡀⠈⠁⣿⠀⠈⠀⠀⠀⠤⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⣋⣥⣤⠴⠶⠶⠒⠈⠻⠦⡘⠙⢧⡘⠛⠳⠶⠶⠤⢤⣀⠉⢻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣿⣥⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠾⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠻⠟⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⣀⣼⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢁⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⡇⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢹⡇⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠖⢋⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣡⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣶⠶⠾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢰⡁
⠀⠀⠀⢀⣀⣤⣶⠾⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀
⠀⢀⣴⡿⠋⠉⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⡶⠶⠖⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡄
⠀⢸⣿⠀⠀⠀⠀⣠⣶⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢤⣄⠀⠀⠀⠀⠀⣹
⠀⠈⢿⣦⡀⠀⠀⢿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠙⠿⣶⣄⣈⠙⠿⢷⣶⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠞⠋⠁⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠿⠶⣶⣤⣬⣉⣉⡙⠛⠛⠛⠻⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠛⠛⠋⠉⠉⠁⣀⣀⣠⡤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠛⠛⠋⠉⠉⠉⠁

⣦⣶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣽⣭⣭⣿⣵⣮⣽⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣶⣶⣾⣷⣶⣶⣶⣿

⠠⠀⠐⠁⠐⠂⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠑⠒⠒⠒⠀⠠⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠁⢀⠀⠠⠉⠀⠐⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠉⠁⠛⠃⠀⠄⠀⠀⠰⠆⢠⠃
⠀⠀⠀⠈⠀⢀⣀⠠⠄⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠠⠄⠀⠀⠀⠃⠀⠀⠀⠀⠈⡈⠓⠒⠂⠀⠀⡀⠚⠇⠈
⠀⠀⠈⠰⠀⠀⠠⠂⠀⠐⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠁⠀⢠⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⡠⠀⠀⠀⠀⣀⠀⢀⣰⡗⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⢸⡅⢠⠆
⠠⠀⠒⠀⠀⠁⣄⠀⠀⠀⠀⠀⠀⠈⠀⢌⡀⠀⠐⣠⠄⢀⡔⢂⠉⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡇⠰⠀⡀
⣯⠛⠰⠒⢋⠈⠁⢀⡐⢀⡦⠀⠁⠀⠀⠀⠉⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠛⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢠⠆⠈⣄⠀⠙⠑⠆⠖⠲⡆⠀⠂⠀⠁⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⡠⠀⢀⠄⠀⠀⠀⠀⠀⠈⠉⡀⠀⠀⠘⠀⠀⠀⠀⠑⡀⠀⠠
⠀⠘⠁⠀⠈⠉⠀⠀⠀⢈⠀⠢⠓⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠁⠀⠤⠚⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠠⠴⠖⠃⠀⠀⠀⠂⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢂
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠻⣦⠀⠀⣿⡁⡇⠀⠀⣄⠀⢀⠀⢠⡄⢀⠀⠀⣀⠀⣿⡿⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡸⡆⢠⡿⢦⣄⡈⠛⢤⣄⠀⣿⠀⣾⠀⣼⡇⣿⠇⢰⡏⠁⣿⡇⢰⣆⠀⠀⠀⠀⢠⠃⠀⠈⠂⠀⠀⠀⠀⢸⣂⠚
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢻⡄⠀⠈⣿⣧⠀⣸⡏⠠⣿⠀⢿⡤⣿⢃⣿⠀⣿⠁⠀⣿⡇⢰⡿⠀⠀⢰⡄⠘⠦⣄⣠⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢸⡿⠀⠙⠗⠀⠙⠁⠀⠀⠁⢸⣿⠀⠛⠃⠀⢿⡇⢸⡇⠀⠀⠀⠉⠓⠠⡀⠠⠔
⠀⠀⠀⠀⠈⠉⢤⢈⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠘⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⢀⡠⠄⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⡐
⣧⠀⠀⠀⠀⠤⠀⠀⠀⠀⢠⠀⠀⠀⠛⠌⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠢⠄⠀⠀⠐⠀⠀⠀⠀⠀⠢⠀⠀⢁⡎
⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⡀
⠙⢤⠀⠀⠀⠀⠀⠀⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠂⠀⢁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁
⠀⠀⠀⠀⠀⢀⠀⠋⠙⠃⣄⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠰⠄⡀⠁
⠀⠀⠀⢀⡆⠀⠀⠀⠀⣱⡒⢠⠽⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⠀⠀⠀⠈⢀⠃⠀⢀⣂
⡠⠶⡀⠿⡝⢀⣤⠀⡀⢻⣠⡄⠘⢋⡴⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠘⠂⠀⠀⠀⠀⠛⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠄⢠⡀⠀⠀⠁⠘⠃
⠠⡞⠃⠔⠉⠀⠀⠀⠠⢸⠃⠱⠀⠀⠰⠞⢃⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣨⡄⠜⠁⢘⠃⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠄⠐⠀⢀
⡀⠀⠡⠆⠀⠀⠂⣤⠼⠚⢆⣀⣩⠄⠒⠂⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀⠀⠴⠃⠐⠰⠖⠁⠀⠀⠀⠠⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠙⠢⡔⡀⠀⠀⠈⠀⣻⠲⡎⠉⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠
⠀⠀⠉⠣⡸⠆⣀⢉⡐⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⢉⣀⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁⠸⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠖⠛⠶⠊⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠋⣀⣤⣤⣀⠀⠀⡀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⢀⡴⠟⣻⣿⠟⢉⡴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⢠⠋⢀⡴⠟⠀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡁⠰⣃⣴⠿⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⡟⠃⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠊⠻⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠁⠀⠀⠀⠙⠷⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣶⠖⠉⠀⠀⠀⠀⢀⣽⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⠟⠁⢀⣀⣀⣀⣀⣀⡿⠹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⢀⣤⣾⣿⣿⣿⡙⡉⠉⠠⠀⢹⠟⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⣾⡇⠀⠀⠸⠃⠐⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠛⠀⠉⢿⣧⠀⠀⠀⠀⠀⠈⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⢀⡏⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡈⠀⠀⠀⠀⠀⢰⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠀⠀⠀⡀⠀⢠⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠛⡏⠸⠋⠈⠉⠀⠀⠀⠀⠀⠀⠈⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⡀⠀⠀⠀⠀⠀⠀⠀⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣄⣠⠀⠀⠀⠀⢀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠉⠿⠻⠗⢿⣿⠁⠀⠀⢀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠐⠀⠀⠀⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠋⠋⠀⠀⠀⠀⠀⢈⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡛⠋⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠧⣒⡄⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠿⣿⣿⣿⠋⠘⢯⣴⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⢈⠁⠋⠀⠀⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⠀⠋⠁⠀⣀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡄⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠿⢿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⢰⣿⣿⣿⢇⣀⣤⡿⠛⠁
⠀⠀⠀⠀⠀⠈⢿⣿⡿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠶⠶⠶⠶⢦⣄⡀
⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠞⠛⠋⠉⠉⠉⠙⠛⠶⣤⡀
⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⣾⣏⣀⡀⠀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⣀⣤⡿⠀⠀⠀⠀⢻⡄⠉⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠶⢻⣏⣹⠃⠀⠀⠀⢀⡾⠁⠀⠀⠀⣷⠀⠀⠀⣀⣺⡄⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⢀⡼⠛⠛⠛⠉⠛⠀⠀⠀⠀⠸⣧⡀⠀⠀⢀⠘⠷⠶⠟⠉⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢠⡟⣀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⢾⡄⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⣠⠟⢉⡽⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⡠⠀⠀⠷⣤⡄⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⣾⣧⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣀⣠⣷⡀⢀⣀⡘⣷⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠙⠉⠉⠙⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣤⣤⣤⣤⣤⠴⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⠤⢤⣤⣄⡀⠀⠀⠈⠻⠶⠶⠶⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⢴⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠘⠞⢁⣤⡾⠃⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃⠀⠀⠀⠀⠀⢀⡠⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠦⣤⣤⣤⣤⣤⣤⠶⠞⠛⠁⠀⠀⠀⠀⠀⢀⣀⣭⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣮⣷⣄⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠾⢛⣛⣿⣿⡶⠶⠶⠶⢶⣝⡲⠶⣤⣂⣤⣤⣤⣤⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣤⡼⠇⠀⣠⢴⡆⠉⠙⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠞⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⢩⡍⣭⠙⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⣀⡤⠤⠤⢤⣄⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⢀⣞⡕⠤⢧⢇⠂⣈⡹⢆⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⣾⣜⢆⠁⠈⢀⠀⠄⠐⠘⣄⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠴⠶⠤⠤⠤⠤⣀⣀⠀⠀⠀⠀⢸⠀⠀⠀⢻⡀⢑⠌⠀⠠⢄⠀⠀⢸⣭⡭⠇⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⣀⣀⣠⣤⣤⣠⣄⡀⠀⠈⠙⠲⢤⡀⠈⣇⠀⠀⠈⠳⣅⣠⠠⡢⢡⣂⡷⠟⠁⠀⣸⠁
⠀⠀⠀⠀⢀⡴⠊⠁⠀⣠⣴⣾⠿⢅⣀⡀⢸⣯⡉⠫⠻⡏⠒⢤⡀⠀⠸⣲⣿⣦⡀⠀⠀⠀⠉⠛⠚⠛⠁⠀⠀⠀⡰⠃
⠀⠀⠀⡰⠋⠀⢀⣴⡟⠉⡿⠛⢶⢾⣅⡕⠀⠙⣼⢄⠀⠙⢦⡀⠈⠓⣄⠉⠈⠻⣿⡦⢄⣀⠀⠤⠰⠆⢀⣀⠴⠊
⠀⢀⡞⠀⢀⣴⠿⣽⠧⢤⡷⢤⣤⠀⡌⠙⢒⣄⠘⣷⢀⣄⠀⠝⡆⠀⠈⠣⡀⠀⠘⣇⠀⠈⠉⠉⠉⠉⠉
⠀⡞⠀⠀⣼⢸⣤⣇⣠⢼⣁⣠⢯⡿⠓⢄⣀⡈⠙⠻⢿⣧⠶⠀⠹⡦⡄⠀⠱⡄⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⡀
⣸⠀⠀⣸⣷⡏⠀⣸⠀⣠⣿⣤⣰⣧⣠⠀⠙⠳⠭⣷⣦⡉⠳⣆⠀⢀⠳⡄⠀⢱⡀⠀⢱⠀⠀⠀⡠⠴⠂⠉⠉⠁⠀⣈⣉⡉⠓⠦⣄
⡇⠀⢀⣿⠁⢳⣎⡽⠋⠁⠀⠀⠀⠀⠈⠙⠓⠦⡀⠀⠙⢿⣗⣿⡂⠀⠀⢻⡦⣼⡇⠀⠘⣦⡴⣪⠓⠀⣠⠤⣶⠶⠋⠁⢠⣧⣠⠋⢣⠑⢤
⡇⠀⢸⡿⢶⡼⠋⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⡀⠷⣿⠀⠀⠈⠛⠻⣄⣀⠀⠹⣭⡽⡆⠀⡏⠀⢀⣴⣋⡴⠊⠁⠀⠀⢀⡞⢸⠏⠀⠘⡄⠀⠳⡀
⡇⠀⠸⡯⢼⡇⠀⠀⠀⡴⠋⠅⠀⠀⠈⡆⢀⣀⣼⡦⠦⠤⣀⠀⠀⠙⣞⠀⠀⢻⡿⠁⢀⠃⣰⡿⠋⠁⠀⠀⠀⠀⠀⡌⢠⠇⠀⠀⠀⣧⠀⠀⠱
⢹⠀⠀⢷⢈⢷⠀⠀⠀⣇⠀⠀⢠⠀⢠⡿⠁⣀⣠⣄⣀⠀⠈⢣⠀⠀⢹⢐⠁⣸⠃⠀⡸⠀⣿⡇⠀⠀⠀⠀⠀⠀⡜⢀⠏⠀⠀⠀⠀⢻⡆
⠀⢧⠀⠈⢦⣘⣧⡀⠀⠈⠓⠶⣴⠶⠋⢠⣞⠀⠀⠄⡙⢦⠀⠀⢹⣐⠌⠙⣿⠃⠀⢠⠃⠸⣟⣷⡀⠀⠀⠀⠀⡸⢁⡎⠀⠀⠀⠀⠀⠘⡇
⠀⠈⢦⠀⠈⢷⡀⠛⡄⠀⠀⠀⡇⠀⠀⢸⡣⠀⠀⠀⡀⢸⠀⠀⠘⢷⣬⡾⠁⠀⣠⣿⠀⠀⢣⣻⣇⡀⠀⠀⢰⢇⡞⠀⠀⠀⠀⠀⠀⠀⢧⠀⢠
⠀⠀⠀⠳⣄⣀⠙⢄⡛⠦⣀⣠⢿⡄⠀⠈⠳⢮⣠⡤⠴⠋⠀⠀⠀⠈⡏⠀⢀⡔⠁⠈⢆⠀⠈⢿⣧⣇⠀⢠⣏⡜⠀⠀⠀⠀⠀⠀⣀⣴⠇⠀⡜
⠀⠀⠀⠀⠈⠻⣇⠀⠉⠲⢄⣀⠀⠙⠢⣤⣀⡀⠀⠀⠀⠀⠀⢀⣀⡤⢋⠴⠋⠀⠀⠀⠈⢦⠀⠀⠹⣾⣀⣿⣴⠁⢀⣀⠤⠤⣴⠾⠛⡕⢃⠞
⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠉⠑⠚⠚⠚⠛⠛⠛⠛⠚⢋⣡⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⠛⠛⠿⠿⠿⠛⠛⠉⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠲⠶⠖⠐⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⣀⣀⣀⣀⣠⠤⠒⠋⠁

⠀⠀⠀⠀⣠⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀⠠⠟⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⠄⠀⢀⡤⣀⠀⠀⠀⠀⠂
⠀⠀⠀⢰⠌⠀⠀⠀⢀⠀⢐⠠⠀⠒⠀⠐⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⢀⣀⡤⠤⠄⣀⠀⠀⠀⠀⠐⢁⠌⡀⠁⠈⡙⠑⢄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠀⠀⡀⠀⠐⠈⡠⠀⠀⠐⠤⠀⠄⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢁⠀⡀
⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠊⠀⠀⡀⠄⠀⠀⠈⠢⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⠀⠀⠀⠀⠈⠂⠈⠠⢂⣱⠆
⠀⠀⠀⠀⠈⠌⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠈⡄⠀⠊⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠂⠐⢄⠀⠀⠂⠀⠊⠠⢤⠀⠄⢠⡤⡀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠈⠀⠀⡠⠀⠀⢄⠀⠀⡀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⣲⢀⢇⢡⠀⠀⠀⠀⠀⠀⠈⠀⠀⠢⢀⡀⠄⠂⠀⠀⢀⡴⠛⢁⠐⠈⡠⠐⠠⠀⠈⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠂⠀⠀⡀⠀⠁⠐⠂⠁⠀⠐⠀⠨⢀⠀⣢⠞⡈⢌⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠘⠀⠀⠀⡀⠀⠀⠀⠀⢰⡩
⠀⠀⠀⠀⠀⡀⠀⠡⢀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠜⠁⡰⠉⠊⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠡⠜⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⠁
⠀⠀⠀⠀⠑⡐⠀⠀⠀⠁⠠⠀⠰⣄⠔⣠⢫⠂⠀⢘⠀⡌⠀⠀⢁⠂⠀⢠⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡀⠀⠀⠂
⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠈⠉⢁⠔⡀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠈⠀⠀⠀⠀⢀⠠⠂⠡⠀⠂⠀⠀⠀⠀⠀⠀⠠⢀⠀⠄⠀⠀⠀⠀⠀⠠⠂⠁⠐⠘⡠
⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠈⠀⠒⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠔⡡⠊⠀⠀⠀⠀⢀⠀⠀⡠⠀⠠⡑⢄⠀⠀⠀⢀⡠⠐⠁⠄⠂⠀⠁⠀⠀⠀⠤
⠀⠀⠀⠘⠶⣠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠄⠀⠀⠀⠈⠀⢀⠊⠀⠀⠈⠀⠀⠀⠁⠂⠀⠄⠈⠀⠀⠊⠂⠰
⠀⠀⠀⠰⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⠁⠀⠠⠄⠀⠀⠀⡐⠀⠀⠀⠀⠄⡆⠀⠀⠀⠀⢠⣀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⠀⢈⠉⠁⠛⠁⠁⠀⠀⢀⣉⠀⠀⠀⠈⢀⢀⠀⠄⡀⠀⠁⢀⠀⠠⠂⠀⠐⠀⢀⠤⠤⠐⡆⠀⠀⠇⠀⠀⠠⠂⠈⠉⠛⠋
⠀⠀⠀⠀⠀⢀⢔⠁⠈⠀⢀⠈⠲⠅⣀⠠⠐⠀⠉⠀⠼⠀⠀⠀⠀⠀⠢⠀⠀⠀⠉⠁⢀⡀⠀⠄⢂⠈⠀⢀⠍⠒⠚⠛⡁⠐⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⡡⠀⢀⠄⠈⠀⠀⠀⠀⠀⠙⠣⡤⠄⠂⠘⡄⠀⠀⠀⠀⠢⡀⠠⢀⠀⠀⠀⠙⠄⠂⠈⠓⠊⠁⠀⠄⠀⠔⠀⠁⠀⠀⠀⠈⠂⠄⠀⠔
⠀⠀⠀⠀⠠⠀⠀⠂⠀⡆⠀⠈⠂⠀⠀⠀⠄⠐⠈⠅⢂⠙⠔⡄⠀⠀⠀⠀⠁⠠⢀⠐⠀⠄⠀⠀⠀⠀⠀⠤⠐⠈⠔⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠈⠄⠠⠈⠂⢠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢀⠈⡑⠢⠠⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⡀⠑⣠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡄⠀⠈⠉⠁⠀⠀⡈⠐
⠀⠀⠀⠀⠐⡀⠀⠠⡀⠀⠀⠀⠀⠀⠉⠁⠀⡀⠉⢂⠁⠂⠀⠀⠀⠀⡄⠀⠀⢠⠂⠐⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠁⠜⠃⠀⢰⠁⢈⡂⢸⡧⠀⠅
⠀⠀⠀⠀⠑⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠠⡀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢠⠀⠐⠊⠀⡘⠁⠐⠄
⠀⠀⠀⠀⠀⠈⠂⠑⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⢀⠀⠉⡵⠤⡄⠘⠍⠡⠊
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⡶⠁⠀⠀⠀⠀⠈⠀⡀⣀⠐⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠐⠀⣀⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠀⠀⠀⠀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⠃⠀⠀⠀⠀⢠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠠⠆⠉⠈⡈⠉⣁⠉⠀⠀⠀⠀⣼⣿⣿⠿⣽⣶⣶⣶⣮⣉⠙⠁⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠴⠀⠀⠀⠀⢀⠀⢲⣂⣀⣤⣤⣶⠂⠀⡀⠀⠁⠘⠛⣩⠉⠿⣿⣿⡆⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠄⠀⣸⠃⠀⠀⠀⠀⠀⢈⡀⠁⣙⡂⠐⠛⢿⢷⣄⡀⠈⠃⣬⣿⡿⠁⢘⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⢌⣙⠀⠤⣄⣀⠀⠈⠉⠀⠩⠁⣠⡀⠀⢐⠛⢛⣛⡻⠞⠋⣤⡞⢾⣏⣀⣄⣈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠻⣶⣶⠄⠀⠀⠀⡀⠐⠓⠛⠓⠂⣙⡋⠩⣷⣴⡀⢠⡿⣧⣿⡟⠁⠀⠙⣯⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠛⠁⠀⠀⠉⠄⠈⢸⠏⣿⠇⠀⠀⣠⡿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠻⠶⠶⠛⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠷⠟⠛⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣿⣷⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⡴⣿⣗⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⢀⣶⣿⡿⢟⣳⡄⠈⠉⠛⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢘⣿⣉⣻⣷⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠘⠀⠀⣛⡾⣿⣟⣩⣿⣥⡀⠀⠱⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⢁⣯⣽⡟⠉⣻⠏⣿⣾⣧⣤⣀⣀⠀⣀⢀⠀⣀⣁⣠⣶⣿⣫⢊⡽⣒⣿⣿⣷⠞⠀⠀⠀⢘⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢛⣥⡀⣌⠉⢙⠛⠻⠿⠿⠿⠿⠿⡿⠿⠿⣿⣟⢍⣯⣱⣝⠋⠁⠀⠀⠀⢀⢰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠞⠁⠰⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠉⠉⢁⠀⢀⡮⢶⡋⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠰⠤⠦⠤⠤⠤⣄⣢⣤⣄⣤⡐⠿⠯⠁⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⠰⠶⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡠⠖⣊⣉⠭⡤⠤⢤⠤⠬⢭⣙⡒⠦⣀⠀⠻⠷⣀⣀
⠀⠀⠀⠀⠀⡰⣡⣶⣋⣭⣥⣴⣶⣶⣶⣶⣧⣔⠀⠈⠑⠪⡻⣄⠀⠀⠈⠑⣄⣀⣠⠄⠀⠤⠄⠠⢄
⠀⠀⠀⠀⢀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣺⠗⠀⠀⠀⡹⣏⣹⠦⠤⠚⡁⠀⣀⡴⠂⠈⠀⠠⠊
⡴⢊⡭⠭⣙⣿⣌⠻⢿⣿⣿⣿⣿⣿⣿⣿⢿⡇⢀⣠⠤⣚⣹⡟⠋⢀⠄⣸⣷⣚⡉⠉⠀⠀⣠⣆
⣇⢸⡀⢀⡼⣿⣿⠀⠀⠈⠉⠉⠛⠛⠛⠛⠉⠉⣍⣴⣿⣿⣿⢧⣤⡷⢞⣉⠁⠀⠀⠀⣴⣉⣠⣄⣙⡢⢄
⠘⢦⡙⠯⣄⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⣿⣿⣿⣿⠀⣌⢧⡀⠭⠀⢠⢶⡉⠻⠀⠉⠈⠉⠂⢘
⠀⣼⠙⡷⠦⣽⣟⠣⠀⠀⠀⠀⠀⠀⠀⠀⣌⠙⣿⣻⣿⣿⠇⢀⡿⣧⢿⣯⣭⣓⢦⣉⣀⣠⠤⠤⠶⠋⠉
⠀⢿⠠⠂⠀⠀⠙⢦⡀⣠⣄⣀⣄⣠⣀⣦⣿⣼⣿⣿⣿⣿⣶⣄⣠⡿⣻⣧⣩⣿⠟⠁
⠀⠘⢆⠠⠀⠀⠀⠀⠙⠺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣶⠤⠆⣱⣿⣍⣧⣽⣀⡀
⠀⠀⠈⠓⢤⡀⠀⢀⡀⠀⠀⠈⠙⠛⠿⠟⠿⠿⠟⠛⠉⠉⢀⣠⣾⣿⠛⢽⣿⣭⣿⢿⡆
⠀⠀⠀⠀⠀⠈⠓⠲⠤⣍⣁⣀⣀⣀⢀⣀⣀⣀⣠⣤⣶⣞⣩⣿⣿⣿⢀⡘⠿⠤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠛⠉⠉⠉⠈⠿⣯⠭⠶⣿⢿⣝⢧⣀⣾⣯⣽⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣎⢿⣼⠏⠳⠬⡅⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡀⠀⢀⡄⠀⢙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⠟⠒⢛⡟⢺⠉⠙⠉⠓⠒⠒⠒⢶⠦⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢻⡄⠀⢰⠃⢸⠀⠀⠀⠀⡀⠀⠀⠈⢳⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠉⠛⠁⠀⠩⠈⢀⠋⠀⣉⡖⢢⡄⢄⢣⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⢠⡏⠡⠶⠏⠉⠁⠀⠀⠀⡇⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⣷⣱⠄⠀⠼⠆⠷⡎⠔⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⡇⢲⡄⠀⠀⠓⠘⠛⠘⠂⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠷⠈⠠⡀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡀⠀⢀⠀⠀⡿⠐⢄⡀⠀⢀⠔⢆⣀⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠑⠢⠀⢀⡀⠀⠀⣾⠨⠭⠉⠭⠁⠀⡇⠀⣤⡀⣩⣁⣀⠀⣀⢀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠈⠁⠛⠛⠠⠥⢄⣉⠀⣠⡆⠀⠰⠔⠦
⠀⠀⢀⣠⡤⣤⠤⠤⣄⡀⠀⠀⢀⣀⣀⣤⡤⠤⢬⣐⠄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠘⠛⠛⠋⠹⡆
⢀⡴⠋⠀⠀⠀⠀⠀⠀⠙⣦⣀⡼⠋⠁⠀⠀⠀⠀⠀⠙⢦⡉⠐⠒⠦⠤⠤⠤⡄⢀⠤⠤⠀⢲⣾⠖⠀⠀⡴⠶⠄⣴
⡜⠀⠀⠀⠀⡤⠲⠦⣤⣤⡟⠽⠁⠀⣠⢤⠤⢤⡀⠀⠀⠀⢻⣦⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣠⣾⡤⠤⠄⠐⠒⠈⠉
⠇⠀⠀⠀⢸⠁⠀⠔⢸⡟⠁⠀⠀⠸⡁⠀⢀⣀⡽⠶⠒⠂⠉⠁⠀⣀⣀⣀⣀⣀⠀⠀⠉⠉⠙⠒⠤⢀⡀⠀⠀⠀⢀⡤⢶⣶⣄⡀
⠠⡀⠀⠀⠀⠒⠤⠶⠿⣇⠀⠀⠀⠀⢹⠗⠋⠁⢀⡠⠴⠒⠊⠉⠉⠀⠀⠀⠀⠀⠈⠉⠁⠒⠦⢄⡀⠀⠉⠒⢄⣠⣻⠗⣫⡤⢼⡿⢦⡀
⠀⠑⠤⡀⠀⠀⠀⠀⠀⢈⡦⢄⡀⠔⠁⠀⡠⠞⡥⣄⣠⠔⠊⠙⣿⠯⣭⢿⣿⢟⣿⢓⡢⡦⢄⡀⠈⠑⢄⠀⠀⠉⢿⣿⢥⡖⠛⣹⠷⢯⣆
⠀⠀⠀⠈⠁⠒⠒⠒⠊⠁⠀⢸⠃⠀⠀⠜⠀⣠⠶⠟⢷⠀⠀⣰⠃⠀⠸⠋⠉⠉⡝⠁⠀⢘⠟⠉⠐⣄⠀⠱⡄⠀⠀⢻⣟⣻⣟⣉⣩⡟⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡘⠀⣐⣻⠀⠀⢠⡿⣩⡽⣧⠶⣇⣀⣠⠊⢹⠦⡔⡿⠄⠠⣤⢊⣧⠀⢺⠀⠀⠀⣧⠾⣍⣴⠁⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢣⢰⣧⣈⠲⣂⡊⠑⠘⢟⣯⣀⣀⣠⣤⣧⠬⠦⣈⣷⠀⠀⣹⠋⣜⡧⢸⠀⠀⠀⣿⣤⠾⣅⣩⠟⠳⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠘⣆⣆⡘⢻⣿⣿⣦⡤⠾⠉⢡⣶⡿⠒⠽⢻⢀⠬⣍⣛⡭⠇⠾⠻⣷⠏⠀⠀⣰⢿⡟⢦⡴⣙⢳⠞⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠴⠷⠶⣖⣛⡛⣯⣭⠿⠰⡶⠂⠲⢦⣤⡭⢅⣀⣠⡜⠛⠓⣇⢀⣷⣦⣤⠼⠃⠀⢀⣴⢿⣀⣸⠷⣤⣼⠛⣶⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠴⠚⠉⠉⠛⢏⡀⠀⠙⠢⠌⣢⣀⣤⡤⢍⢡⡀⠤⢤⡜⠀⢀⣋⡩⠝⠛⠁⠀⣀⣴⠛⠳⣴⠉⠳⣴⣁⠈⣶⣁⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠤⠀⠀⠈⠉⠀⠚⠓⠒⠐⠒⠉⠉⠉⠀⢀⡠⠤⠒⠛⠫⣅⡳⣆⢈⡷⠻⢤⣨⠿⡄⣨⠛⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠂⠐⠒⠒⠒⠐⠒⢈⡁⠀⠀⢠⡛⡢⠀⠈⢣⣨⢛⡿⣧⠖⢧⣀⠘⣧⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣙⡽⢟⠓⡆⢉⡤⣄⠀⠀⠀⠈⠋⢁⣀⠞⠙⢳⡎⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠭⠟⠑⠉⠉⠀⠘⠒⠂⠀⠀⠀⠀⠳⡾⠷⢤⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣍⠗⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠐⠒⠂⠈⠉⠉⠉⠉⠉⠁⠀⠒⠂⠄⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣠⢀⣄⢀⡄⢠⡀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢀⠀⠀⠀⠀⠀⡠⠊⠀⠈⠲⡄
⡇⢸⢰⠀⢨⠀⡇⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠾⠟⠛⠛⠛⠛⠛⠛⠛⠒⠒⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⡘⠀⠀⠀⠀⠀⠘⡄
⡇⢸⢸⠀⢸⠀⡇⠀⡠⠊⠀⠀⠀⠀⢀⣠⠶⠛⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠑⡤⠀⠀⠀⠀⠀⠀⠀⠰
⡇⢸⢸⠀⢨⠀⣇⠌⠀⠀⠀⠀⢠⡶⠋⠁⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢲⢒⣢⣤⣄⣀⠀⠀⠀⠆
⡇⢸⠘⠀⠰⠀⡏⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⣠⡾⠃⣸⠀⠀⠈⠉⠻⠳⣦⠀⡄
⡇⠚⠀⠂⠘⠀⠇⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⣿⠀⠔⢹⡄⠀⠀⠀⣼⠖⠺⣷⠰⡀⠀⠀⠀⠀⠀⠀⡰
⢡⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠈⢳⣦⣄⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣿⢀⡀⠀⣧⠀⣠⠞⠁⠀⠀⢹⣇⠑⢤⡀⠀⠀⣀⠔⠁
⠀⠱⠀⠀⠎⠀⠀⠀⠀⠀⠀⢀⠎⠀⠹⡆⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣿⠈⠉⢳⣍⡹⠧⣤⣤⣀⡀⠸⢸⡶⢄⠈⡄⢰⠁
⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⡄⣬⠤⢊⡩⢿⡄⠀⠀⣿⠀⠀⠀⠀⠀⢡⣀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣿⢨⡴⠃⠘⣆⠀⠀⠀⠀⠀⣄⡆⣠⣀⣿⡇⢸
⠀⠀⡇⢸⠀⠀⠀⠀⠀⠻⠛⡏⡰⠁⢀⠀⢷⡀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⠉⠀⠀⠀⠀⡿⢸⠀⠀⠀⠸⣆⠀⠀⢀⣼⣾⡾⠋⠀⠘⡇⠘⠁
⠀⠀⠇⠈⠀⠀⠀⢀⣠⢃⠔⢀⠇⠀⠀⠀⠈⣧⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡀⠀⠀⠀⠄⠂⣐⡿⣿⡋⠀⠀⠀⠀⡇⢀
⠀⠀⡄⠀⠀⠀⠀⠨⠟⢁⠔⠉⠀⠀⢄⡀⠀⠘⣇⠹⡷⠶⠶⠦⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⠾⠃⡸⣻⠽⠿⠯⠔⠊⣿⢿⠈⠉⠙⠛⠓⢽⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⠀⠄⠀⠀⠀⠉⠲⢄⡙⣶⣬⡼⠟⢓⡡⠖⠒⠀⠐⢶⡖⠒⠒⠒⠒⢲⠞⢶⠉⠛⠛⠒⠶⢒⢩⡜⢧⠀⠀⠀⠀⣰⡇
⠀⠀⠀⠀⡆⠀⠀⠈⠄⡄⠀⠡⡀⠀⠀⠀⠀⠀⠉⠂⠁⠀⣨⣿⠀⠀⠀⠀⠀⠘⣷⡀⢀⡠⡾⠃⠀⠘⣆⠀⠀⠀⠀⣠⣲⠃⢸⠣⡀⣠⣾⡾⡁⢸⠃
⠀⢰⠀⠀⡇⠀⠀⠀⠀⠻⣦⡀⠐⠢⠄⠀⢀⢀⢀⠄⠀⣼⠅⠈⢳⡄⠀⠀⠀⠀⠹⣯⡁⠰⠀⠀⠀⠀⢹⠢⠀⢀⣴⣿⣧⣤⣚⣤⡴⠞⠉⠀⠃⠸
⠀⢸⠀⠀⡇⠀⠀⠀⠀⣄⣺⠛⣧⣢⣄⣈⣀⢀⣀⣤⠞⠁⠈⠠⠀⡏⠀⠀⠀⠀⠀⠈⠛⢾⣶⣤⣤⣤⣜⣀⣭⢾⠋⡠⠋⠈⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠈⠀⠀⢳⡀⠀⠀⠀⢺⠋⢂⠈⡄⠈⠈⣉⡭⠭⠤⠤⠄⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⢁⣨⠏⠀⠕⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸
⠀⠀⠀⠀⢸⠱⡀⠀⠀⠀⣝⡘⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠚⡋⢥⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾
⠀⡇⠀⠀⠈⠀⠘⢄⠀⠀⠛⡇⠸⠀⠠⢀⠀⠀⠀⠀⠀⡀⠔⠀⣠⡏⠀⠀⢀⣀⡤⠶⠚⡋⠥⠒⠂⡡⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⡄⠀⠀⡇
⠀⡇⠀⠀⠀⠃⠀⠈⠢⡀⠀⠘⢄⠣⡀⠀⠁⠁⠃⠀⠘⣀⣠⠶⠏⣻⣗⢚⣋⡥⢐⣊⠡⠤⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⡇
⠀⠇⠀⠀⠀⠇⠀⠀⠀⠈⠢⡀⠀⠉⠊⠓⠒⠒⠒⠊⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⡇⠀⠀⡄
⠀⠘⠦⠀⠔⠁⠀⠀⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠐⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠄⠒⠉
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠈⠀⠀⠁⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠂⠐⠈⠀⠀⠀⢀⠜⢂⠀⠀⠀⠑⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠁⠒⠁⠀⠀⠀⠀⠀⢀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠢⠀⠁⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠐⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠠⠁⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠈⠔⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠦⡐⠄⠀⠄⠀⠀⠀⠈⠂⠀⠠⠂⠐⠀⠀⠐⠁⠀⠀⠀⠢⠀⠠⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄⡀⠂⠠⠀⡐⠀⠀⠁⠀⠀⢀⡀⠀⠀⠈⠀⠀⠂⡀⠀⠐⢈⠠⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⡀⠠⠄⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠤⠀⡀⠀⠀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠈⠶⠀⠀⠀⠀⠀⠀⠑⣀⠀⠐⠂⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠢⡀⠀⡌⠀⠀⠀⠐⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⡀⠀⠀⠀⠀⢈⠤⠇⠀⠀⠀⡠⠆⠌⠀⠀⠀⠀⢀⠄⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⡞⠉⠐⢀⡀⠀⠀⠈⢀⠈⠀⠀⢀⡄⠂⠉⠉⢃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠄⠂⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡟⠛⠛⠻⠿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣛⠻⣦⣈⠛⠶⣤⣤⣄⣨⣽⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⢋⡾⢻⡄⠀⠉⠛⠷⠶⣤⣬⣥⣤⡴⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡛⢷⣌⠙⠛⠃⠀⠀⣠⡶⣆⠀⠀⠀⢠⣄⠀⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠉⠻⣦⡈⠻⣦⣀⠀⠐⢿⣤⡿⠀⠀⣰⡏⣿⡀⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⢤⣄⠀⠈⠙⠷⣤⣉⠛⠶⣤⣤⣀⣀⣀⣈⣹⣿⠶⠞⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠛⢶⡙⣧⡀⠀⣀⣈⡙⠻⠶⣤⣤⣉⣉⣉⣉⣥⣤⠶⠛⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⢈⣿⣌⡛⢛⣉⣉⡛⢦⣀⠀⢀⣩⣭⣍⡉⠀⠀⣠⣤⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣴⠏⣿⠈⠉⠉⠉⠉⠻⣆⠉⠛⢋⣥⡴⣬⡻⠶⠞⣋⣤⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡝⠛⠛⠀⠀⢠⡞⢷⡀⠈⠛⠛⠋⠁⠀⠀⠙⣳⠛⠋⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⡀⠀⠀⠻⣦⡾⠃⠀⠀⣰⠿⣆⠀⠀⣾⠻⣇⠀⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠷⣦⣄⣀⡀⠀⠀⠀⠻⠶⠟⠀⠀⠙⣛⣫⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣌⡉⠙⠛⠛⠲⠶⠶⠶⠞⣛⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣶⣶⣶⣶⣶⣾⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⢉⠄⠂⠈⠁⠀⠐⠤⣀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⢲⣄⠀⠀⠀⢀⡄⠀⢳⠀⠀⠙⠂⠂
⠀⠀⠀⠀⠀⠀⠈⢡⠊⠀⠠⣐⠫⠤⠄⢒⠤⡈⠳⡄⠀⠀⠀⠀⠀⠉⠲⢤⡀⠀⠛⢾⣦⣤⣿⠃⠀⣾⠀⠀⢀⡤⠔⠊⠉⠉⠉⠑⠒⠂⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⠃⠀⢠⣾⠇⠀⠀⠀⠀⠑⠜⢦⠙⠒⢒⣈⣉⡷⠀⠀⠀⠈⠓⢤⣀⣈⣁⣀⣤⡾⠋⢀⠔⠁⠀⠀⣀⠠⠤⠤⠀⠀⠀⠈⠱⣄⠀⠉
⠀⠀⠀⠀⠀⠀⠘⠀⠀⣿⡟⠀⠀⢤⣶⣤⣠⠀⣻⣾⡟⠉⠉⢩⣶⣴⣤⡀⠀⠀⠀⠈⠉⠉⠉⢉⣀⣄⢊⠀⠀⡠⣨⣶⣤⠄⠀⠀⠅⠢⡀⠀⠘⢆
⠀⠀⠀⣠⣄⠀⣀⣴⠀⣻⡁⠀⠀⠘⠻⣿⣧⢆⣿⣿⡇⠀⠀⣿⡏⠍⠉⠛⠀⠀⠀⢤⠤⢂⠤⡘⠢⠄⡐⠀⡐⢸⡿⠉⠀⠀⠀⠀⠳⡀⠐⠀⠀⢸
⠀⠀⠀⠉⠁⠀⠈⠻⡆⠀⠁⠦⡀⠠⡤⣄⣩⣿⣿⠟⠀⠀⠀⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢊⣀⠁⣠⡔⠀⠀⢇⠸⡇⠀⠀⠀⠁⠀⠀⡇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠈⠉⠉⠿⠟⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⡒⠀⠠⠀⣀⠀⠀⠀⠀⢳⠀⠀⠘⡐⠹⠀⠄⠀⠀⠀⠄⠀⡐⠀⠀⠸
⠀⠀⠀⠀⡠⠔⠒⠐⠒⠲⢤⡈⠉⠉⠉⠁⠀⠀⠀⠀⢀⠤⠢⠂⠀⠀⠀⠀⠀⠀⠀⢀⡤⣅⠦⡄⠀⠀⢣⡀⠀⠈⠢⢀⡉⠁⢂⣡⠴⠊⢑⡄⡰⠃
⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⣴⠖⠀⠀⠀⠀⠀⠀⠀⠐⣂⠐⢺⡇⠘⠀⣯⠂⠀⠀⠑⢤⡀⠀⠀⠀⠈⠀⠀⠀⢀⡠⠞⣠⣀⣀
⠀⠀⡇⠀⠀⢠⠔⠒⠢⡄⠀⠀⠈⡄⠀⠀⠀⠀⢼⠂⠀⠀⠐⠀⠀⠀⠀⢀⠀⠀⢀⡾⠳⢰⣦⡇⠀⠁⠀⠀⠀⠈⠑⠒⠶⠶⠒⠒⠊⠉⠀⠀⠸⡽⢾⣤
⠀⠈⡀⠀⠀⠸⡀⠀⢀⠇⠀⠀⠀⡇⠀⠀⠀⢰⠃⠀⡠⠀⠀⠀⠐⠒⢠⡀⠀⠀⠘⣤⡶⣼⢠⠃⠀⠀⢂⠀⠀⠀⠀⠀⢀⠰⣒⠒⠒⠒⠶⣤⣄⠀⠈⠁
⠀⠀⢣⠀⠀⠀⠈⠉⠁⠀⠀⠀⡜⠁⠀⠀⠀⡌⠠⠂⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢀⣄⣇⢠⣸⠀⠀⠀⠸⠀⠀⣀⡀⠀⢠⣴⡅⠄⠀⢁⣲⣦⠙⠷⡄
⠀⠀⠀⠑⠤⣀⠀⠀⢀⣀⠴⠊⠀⠀⠀⠀⠀⠇⠀⠆⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⢣⣘⡘⣸⡇⠀⠀⢰⠀⣿⣉⡡⠀⢘⣷⡀⡠⠐⠀⠀⠈⠦⠀⣷⡀
⢀⡷⠀⠀⠀⠀⠀⠉⠁⠀⢀⣤⣤⢤⡄⠀⠀⠰⠚⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠘⣡⣏⡇⡇⠀⠀⠎⠀⠈⠉⠁⠀⢀⠞⠉⠀⠀⠀⠀⠀⠀⣄⢸⡇
⠘⡄⡇⠀⠀⠀⢀⣤⡾⠷⢿⡻⡀⠀⢉⡃⠀⠀⠣⠠⠂⢤⡀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡽⣭⢛⠇⡐⡄⠀⠀⠀⢀⡄⠊⠀⠀⢀⣠⡀⠀⠀⠀⠀⠴⢸⠇
⠀⠙⣴⠀⠀⠀⣾⡛⠁⠀⠀⠙⠢⣦⠼⠁⠀⠀⠀⠑⣔⠄⡘⠒⠂⠐⠒⠒⠶⠚⠀⠛⠶⠇⡶⠈⠊⠀⢀⠀⢈⠟⠛⠀⠀⠀⠀⠹⣱⢄⣠⠄⣆⣠⠟
⠀⠀⠋⠀⢰⠟⠙⠉⠀⠀⠀⠀⢀⣼⠀⠀⠀⢰⠶⠦⣄⠑⠈⢐⠠⠄⣀⢀⡀⠀⠠⠠⠖⠉⠀⢀⠠⠂⢁⠄⠁⠀⠀⠀⢀⣀⠀⠀⠈⠳⢄⣈⠞⠃
⠀⠀⠀⠀⢼⠂⠀⠀⢐⡿⠶⠷⠞⠁⠀⠀⠀⠹⡀⠀⠈⠆⠀⠀⠈⠁⠐⠀⠂⠒⠀⠀⠀⢀⣀⣀⠤⠒⠁⠀⠀⠀⠀⠘⣧⣼⠇
⠀⠀⠀⠀⠀⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣹⡗⢈⣿⣹⡗⢈⣿⣉⠁⢀⡟⣿⡀⢸⣧⠞⠃⢸⣏⡉⠁⣰⣿⣇⡀⢾⣍⡛⠈⢉⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠼⠇⠸⠏⠳⠆⠸⠧⠴⠄⠿⠉⠿⠁⠿⠙⠷⠄⠾⠇⠀⠸⠟⠹⠿⠐⠷⠼⠟⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣤⢮⠰⡄⢾⡁⠀⡶⡄⠀⢰⡦⠤⢦⣴⠂⢾⠀⢠⡾⣧⡴⡥⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁
⣶⡶⠲⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣭⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠒⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⡁
⠀⠀⢢⠐⠀⠈⢤⠀⠀⠀⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠠⡈⣠⠄⠀⢀
⠀⠀⠀⠀⠀⠈⠸⡀⠀⠀⢀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⠆⠀⠌⠉⠻⠏⠉⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠐⠐⠶⠬⠥⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰⡠⠀⠀⠀⠀⠀⠀⡆⠀⡖⠀⠀⠀⠀⡆
⠀⠀⢀⠬⠄⠀⠀⠀⠀⠀⠀⠀⡂⡀⠀⠀⣸⢱⢼⠈⠗⠂⡄⡇⣷⡀⡇⢨⣺⠐⡄⡇⠀⠀⠀⠀⡅⠀⠀⢀⠀⠁
⠀⠀⠀⠐⠄⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠢
⠀⠀⠀⡀
⠀⠀⠀⠉⠂
⠀⠂⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⡀⠀⢄⡄⠀⠀⠀⠀⡄⠀⢤⡄⡀⠀⣰⠆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠁⠀⠀⢀⠀⠳⡀⠀⠀⢀⣠⡏⢀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠴⣀⣀⢀⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⠀⠀⠀⠀⠀⠀⠀⢈⡛⠛⠋⠉⠀⠀⡀⡀⠄⠂⠀⠀⠀⠀⠀⠀⠠⠀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⣠⠀⠠⠚⣁⢠⡤⢄⣺⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⡐⢀⡀⡀
⢠⣦⢀⡠⠇⠴⠁⣠⣿⡋⠇⠿⣘⡝⢀⡀⠀⡜⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠥⠤⠄⠈⢠⡬⠠⠄
⠀⠉⠀⠀⠀⠀⠐⠲⢤⣵⠶⠤⠤⠶⠞⠛⠋⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠨⡉⠃⠐⠢⠤⠒⠉⠀⠀⠀⠀⠀⠈⠠⡀⠀⢀⣀⠤⠁⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠢⢄⠀⠀⠚⠁⠙⠋⠻⣌⠓⠫⠹⠦⠑⡂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠙⡆⣀⠀⠀⣀⣤⣔⠉⠤⠠⡤⠀⢠⠤⢍⡀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠹⢦⣀⠉⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠓⠛⠉⠉⠉⠁⠈⠁⠉⠀⠉⠉⠉⠙⠒⠦⢤⣐⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠮⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠄⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠆⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣦⣤⣄⣀⣠⣠⣄⣠⣀⡘⠂⠀⠀⠀⠀⢀⠞⠁⣀⡀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣤⠶⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠉⢳⠀⠀⠀⠀⠀⡄⠾⣧⠹⠷⠆⣶⠋
⠀⠀⠀⠀⠀⠁⣠⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢝⠱⠾⠛⠀⠁
⠀⠀⠀⠀⠥⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠋⣿⢤⡝⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⡀⠀⠀⠈⠁⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠠⠚⡽⠀⠀⠀⠀⣴⡏⣹⠿⠀⣶⡞⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠩⠖⠀⠀⠁⣠⠞⠀⠀⠀⠀⢶⣶⠦⠿⠉⢀⣭⠀⠉⠋⠱⠃
⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠚⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠘⢦⣄⣀⣀⠄⠊⠙⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋
⠀⠀⢆⡀⣀⣀⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠿⢿⣤⣀⣀
⠀⠀⠀⠉⠉⠀⠘⠿⣦⣀⣀⣀⣀⣤⣴⠴⠶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠶⣤⣄⣄⣄⣀⣠⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠶⠶⠶⠶⣦⣤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣶⣟⡿⠋⡁⠄⠀⣠⡀⠈⠁⠒⠬⢝⡺⢷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠕⣿⡷⠉⢂⠕⠊⠀⠀⠈⣃⠐⠀⠀⠀⠐⢍⠲⣝⢷⣌⠷⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⡴⣫⠞⠁⣾⠏⡄⡔⠁⠠⠖⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⠈⠎⢿⣦⣤⠖⢘
⠀⠀⠀⠀⠀⢀⡞⡴⠁⠀⢸⣼⠘⠨⠀⠀⠀⠁⡀⠀⠀⣴⠄⡀⢁⠀⠀⠀⠀⠀⠀⠘⣼⡇⣠⢾⣧⡀
⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣿⢿⢀⠀⠐⡀⡀⠀⠘⠦⠄⣀⣄⠀⠈⠀⠀⠸⠀⠀⠀⠀⡇⣿⣥⣀⡀⠀⠈⠀⠒⠄
⠀⠀⠀⠀⢰⠃⠁⠀⠀⠀⢻⠸⡈⠌⢆⢳⣕⢄⡀⠀⠀⢈⠃⡴⣋⢔⠵⠁⠀⠀⡸⢸⢹⣿⠟⠻⠉⢗⡶⠦⠤⠃
⠀⠀⠀⠀⢸⠠⠀⠀⠀⠀⠈⣧⠱⡀⠀⠀⠙⠻⢟⣓⠶⣤⡁⣴⡿⠃⠁⠀⢀⠜⡱⢣⣿⠛⠃⠀⠀⠈⣧
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠘⣷⣙⢦⡈⠲⢄⡀⠀⠉⠢⢱⠇⠀⠀⠀⠔⣡⢞⣵⣿⠁⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⢍⡲⠤⣌⣁⣀⣀⣀⣀⣠⠤⢖⣫⠴⣻⠞⠁⠀⠀⠀⠂⠀⠀⡟
⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢂⠈⠻⡷⣍⣙⡒⠲⠾⠭⠶⠶⠒⢛⣉⡴⠞⠁⠀⡀⠠⠀⠌⠀⠀⢠⡇
⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠠⡣⡈⠮⡛⠻⠷⠶⠶⠶⠖⠛⠋⠉⠀⠀⠠⠊⠀⢀⠌⠄⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠓⠀⢀⠀⠀⠀⠀⠀⠀⡀⠄⡪⢀⠕⡡⠊⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠈⠂⢅⡀⠀⢀⠀⠈⠀⠀⠀⠂⠉⢀⠁⠊⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣔⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢀⠄⣢⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣗⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⣖⣫⠵⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠯⠭⣿⣿⠿⠭⠭⠷⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⢦⡔⢀⠎⠀⣤⢀⠄⠀⡱⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠁⠀⠀⠀⠀⠁⠊⠀⢀⠁⠈⠀⢀⠅⡀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⠀⠀⢤⣡⠎⠀⢀⠀⠄⠀⢀⢎⠜⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⡄⠀⢀⡖⠀⠀⠀⡠⠂⠀⢀⠔⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⡃⢐⠎⠀⢀⠊⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣀⠀⠐⠀⠀⠀⠀⠁⠀⠠⠔⠁⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⡀⠀⠀⠀⡁⠀⢀⢂⠅⢄⠈⠒⠀⢠⠄⢡⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⡀⢖⠁⠄⠀⠀⠁⠀⢨⡌⠓⠃⠀⠀⠀⠈⠡⠂⠀⠀⠇⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠙⠸⠒⢁⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣀⡄⠤⢉⢀⡔⠘⠓⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠈⡀⠀⠀⣰⠆⠀⠀⢠⠀⠀⠀⠀⠀⠀⠰⡀⢉⠀⠀⠄
⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠀⢀⠄⠉⠁⠻⣚⠠⠧⠄⣄⠀⠘⢆⠀⠀⠀⠀⣀⠀⠁⠈
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠈⠄⢀⠀⡠⠇⠀⠀⠀⡁⠀⠀⢄⡀⠀⠀⠀⠉⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠴⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡇
⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠍
⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠎
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⢄⡀⣀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣿⣿⣻⣿⣿⣟⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⢄⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠀⢤⡀⠁⡀⠙⢂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠃⠀⠢⢱⡴⠢⠖⠃⠠
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠒⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡈⠐⠀⢇⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠒⢄⡀⠤
⠀⠀⠀⠀⠀⠀⢸⠤⠖⣋⣉⣉⣐⣦⣤⠀⠀⠀⠀⠀⠀⠀⠑⠛⠒⠀⠀⢀⠀⠀⠀⠀⠀⡠⢂⠑⠀⠀⠀⠈⠒⠄⣀⡀⢀
⠀⠀⠀⠀⢀⠀⠊⠄⠀⠀⠀⠀⠀⢁⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠁⠀⠀⠈⢣⠀⠐⠚⠰⠒⡐⠿⠀⠊⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⠤⠀⠀⠁⠀⠀⠀⠀⠴⠂⠀⠀⠀⢀⣤⠲⠞⠉⠀⠀⠀⠀⠀⠀⠈⠀⠙⠒⠓⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣶⠀⢠⠂
⠀⠀⠀⠀⠀⠀⡄⠀⠀⡁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡆⠂⠀⠀⠀⠀⢀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠋⢷⣴⠏⠐⢻⣖⠂⠠⡄
⠀⠀⠀⠀⠀⠀⠁⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⢻⠈⠀⠀⠃⠁⠀⡇⠀⠀⢸⠀⠢⠀⣇⠀⠀⠀⠀⠀⠀⠀⠸⡆⠰⢠⡶⢯⡯⠁⠶⠒⠁
⠀⠀⠀⡀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⢄⣀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠆⠀⠀⠀⠀⠂⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂
⠀⠀⠠⣡⠆⠵⢂⣄⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠈⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠄⢀⡀
⠀⠀⠀⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠈⠐⢋⡈⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢯⠳⢄⣀⣀⣀⠠⠤⣬⡦
⠀⠀⠀⠀⠀⠀⠤⠒⠀⠀⠀⠀⠖⢐⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⢮⣝⡻⢛⣀⣢⣿⠞⢁⠤
⠀⠀⠀⠀⠀⠀⡀⠀⢀⡶⠜⠉⠀⠀⠁⠈⠀⠀⠀⠀⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠐⠂⠐⠛⠒⠚⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⣀⢀⠀⣠⠼⣣⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢄⡀⠀⠀⠘⠟⠡⠤⠤⢲⡂⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠁⠀⠐⠈⢀⡤⠶⠛⠉⠁⠀⢀⡐⠤⠀⠀⠈⠓⠀⠀⣷⠏⠤⠶⢾⠇⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠄⢀⠔⠧⢢⠤⡀⠐⠀⠀⠀⠀⠀⣰⠋⠘⠃⠈⠁⠰⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⠀⠈⢄⠀⢁⡠⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠐⢄⣀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠒⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠈⠙⣦⡀⠀⠀⠀⠀⢀⣀⣠⣤⡤⠤⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢤⣤⣀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⣀⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠈⣧⠴⠖⠒⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠉⠳⣶⡇⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠶⠿⢥⣄⢀⡤⠞⠛⠉⠙⠓⢦⡤⠋⠁⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢀⡴⠋⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢸⡷⢤⡀
⠀⠀⣸⠁⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢸⣷⡄⣷
⠀⠀⢻⡀⡄⢀⠉⠙⠓⠶⠶⢤⣤⣄⣸⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣀⣠⣤⠞⠋⠀⡟
⠀⠀⠘⢧⡁⠸⠀⡆⠠⡀⢀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠒⠒⠒⠶⠶⠶⠶⠶⠾⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠛⠛⠛⠋⢉⠁⠀⠄⠀⣸⠇
⠀⠀⠀⠈⢻⡶⣤⣀⠀⠀⠈⠀⠘⠀⠀⠆⠀⠀⡄⠀⢠⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠠⠀⠀⠤⣀⠀⠁⢠⠊⠀⠂⢀⣴⠋
⠀⠀⠀⠀⠈⢧⠀⠉⠛⠳⠶⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠈⠀⠙⠂⠀⠙⠀⠈⠣⠀⠀⠀⠒⠀⠁⠒⠀⠀⠁⠀⠈⢀⣀⣠⣤⠶⠞⡿⠁
⠀⠀⠀⠀⠀⠈⢧⠈⠀⠆⠀⡄⠀⢈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠚⠛⠛⠛⠉⠉⠀⠀⡀⣰⠃
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠘⠁⠸⡖⠁⢢⠄⠀⣄⠄⠀⣄⠄⠀⣀⠀⠀⣀⠀⢀⢀⠀⡀⠀⠀⠀⢀⠀⠀⠀⡀⠀⢰⠆⢀⠃⢂⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠈⠂⠀⠱⠔⠙⣦⠔⠙⢦⠔⠛⣤⠖⠉⢢⠂⢀⢶⠁⢈⠦⡀⠠⠓⠀⠌⠀⠱⠃⠀⣁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣤⣤⣀⣀⣀⡀⠀⠑⠀⠀⠁⠀⠁⠀⠂⠀⠐⢀⢀⣈⣀⣀⣀⣤⣤⠴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠁



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣏⣏⣴⣩⣽⣥⣿⣻⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⡞⠁⠀⠀⢀⠀⠤⡀⠀⢡⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢲⢤
⠁⠐⢀⠶⠆⠀⠲⠀⠀⠀⠀⠀⠀⠀⠉⠁⢄⠠⠀⠀⠀⢰⡃⠰⡀⠀⠾⠤⠃⠀⢀⡀⡂⠀⠀⠀⠀⠀⠀⠄⠠⠀⣄⠀⠀⠀⠐
⠀⠀⠈⠀⠐⠀⢶⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣅⡜⠨⠄⠐⠂⠀⠀⡈⢠⠁⠀⢀⠀⠋⠶⠨⠦⠤⠀⠈⡃⢀
⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⠴⠀⠀⠀⠈⠦⣐⠀⡑⠲⠶⠁⠽⠁⠀⠀⢀⠁⠀⠀⠂⠀⢘⠠⢢⡴⠛
⠀⠀⠀⠀⠀⢴⠄⠀⠀⠀⠀⠀⠀⠄⠀⣀⡲⠗⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠊⠁⢀⣀⠀⠀⠱⠀⠀⠀⠄⠄⣭⠄⠉⣆⡡⠊
⠀⠀⣀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⡅⠀⠈⠀⠈⠠⠅⠁⠃⠂⢂⠁⠉
⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡀⠀⠀⠈⠀⠂⠀⠀⠁
⢀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠛⠃⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠀⠀⢀⠁⣀
⠀⢦⠀⠀⢀⠀⠘⠋⠝⠷⠶⠯⡕⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠘⠀⠋
⠐⠋⠀⡐⠀⠀⠀⠀⠀⠀⠐⣠⣾⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠒⠠⣌⣿⠋⠀⠀⠀⣀⡀⠀⠠⠤⠤
⠀⠀⠀⡃⠀⠠⣀⡠⠀⠀⠛⠉⠀⠀⠈⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⠒⠒⠚⠻⠇⢠⠔⠋⠉⠉⠉⠛⠶⣄
⠀⠀⠐⡷⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢁⡠⠖⠒⡾⠋⠀⠁⢀⡴⠛⠛⣻⣶⡄⠈⠳
⠀⠀⠀⢻⣴⠛⠀⠀⠀⠀⠀⠀⠙⠋⠀⢀⡿⠀⠀⠀⡀⠠⠄⠁⠐⢦⣤⠠⠀⠀⠈⢀⢴⠞⠁⠀⠀⠀⣸⡃⠀⢸⠧⠟⢻
⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⣻⣷⢦⣴⠎⠁⠀⠀⠀⠁⠀⠀⠀⠃⠀⣁⢔⠃⠀⠀⠀⢀⠀⢀⡀⠀⠀⢹⣷⡞⠃⠀⢀⡞
⠀⠀⠀⠠⡈⠢⠀⠒⠒⠀⣰⣯⡿⠟⠉⠀⠄⡖⠀⣀⠀⢃⡉⢈⡔⠂⣅⠺⠗⠀⠀⠠⠁⠀⠐⢘⡄⠀⠀⠈⠛⠛⠲⣍
⢀⠀⠁⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠤⠊⠀⠀⠉⠐⠈⠱⠆⠈⣀⠀⠀⢈⠔⠀⠈⠤⣀⣀⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⣠⠄⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⣼⡏⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⢻⣧⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠻⣷⡀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢹⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⡼⠃⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⠀⠒⠒⠂⠒⠒⠒⠒⠐⠒⠒⠒⠒⠐⠒⠀⠠⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡖⢉⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⡍⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⣇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠳⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡰⠁⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣃⠤⠊⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣁⣀⣀⠤⠐⠁
⠀⠀⠀⠀⡠⠄⠒⠒⢈⣉⣭⣤⣬⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣧⣤⣤⣤⣉⡁⠒⠒⠠⢄
⠀⠀⠀⠀⠢⢄⣀⠀⠛⠿⠿⣿⣿⣿⣿⣿⣶⣤⣤⣄⣀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⢀⣀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⢤⡀⠭⠭⠉⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠭⠭⢀⡤⠒⠒⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠂⠀⠤⠤⠤⠤⠤⠤⠀⠐⠒⠒⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡠⠖⠒⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠦⣄⠀⡴⠋⠉⠉⠳⡏⢀⣀⡀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢀⣀⣸⣎⠀⠀⠀⠀⢠⠟⠉⠀⠉⠳⣄⣇⡠⠴⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡤⠚⠉⠀⠀⠀⢳⡀⠀⠀⡏⠀⠀⠀⠀⠀⠘⣏⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠚⠧⡀⠀⠀⠀⠀⠀⣸⣁⣀⠀⢧⠀⠀⠀⠀⠀⣀⡼⠖⠒⠒⠦⡀⣼⠖⠋⠙⡆
⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⢹⠀⠀⣀⠴⠚⠉⠁⠀⠙⣾⡀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⢹⠓⢦⡀⠀⣏⡤⠤⣄
⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢸⡤⠊⠁⠀⠀⠀⠀⢠⠖⠋⠙⠓⠚⠤⣀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠹⡞⠁⠀⠀⠈⡇
⠀⠀⠀⣠⠚⠉⠙⢦⡀⢀⡤⠒⠛⠓⢄⠀⠀⠀⠀⣠⠼⠦⡀⠀⠀⠀⠀⠈⠑⢄⣠⠤⢄⣴⠃⠀⠀⠀⢻⠀⠀⠀⢰⠇
⠀⠀⠀⡇⠀⠀⠀⠀⢹⠏⠀⠀⠀⠀⠘⡆⠀⣠⠊⠁⠀⠀⠘⡄⠀⠀⢀⣀⣠⠋⠀⠀⠀⠘⡶⠋⠉⠉⢻⠀⠀⢠⠞⠒⠲⡄
⠀⠀⠀⡇⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢷⢰⠃⠀⠀⠀⠀⠀⡇⢀⡞⠉⠀⠈⢣⡀⠀⠀⠀⢹⠀⠀⢠⠟⠓⠲⣏⠀⠀⠀⢹
⠀⠀⣴⠛⠓⠒⠲⠾⢤⣀⣀⣀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠈⡇⠀⠀⠀⣸⠀⡴⡏⠀⠀⠀⠈⢧⡀⢀⡞
⠀⠀⠸⡛⠺⠯⣤⣤⡴⠀⠀⢀⡉⠉⠉⢉⡙⠛⠒⠒⠒⠲⠤⠾⠤⠤⠤⠤⠤⠤⠷⣤⣤⣠⣿⣎⣤⠧⠤⠤⠤⠤⠤⣷⡏
⠀⠀⠀⢇⠣⣄⡀⢨⣏⠉⠛⠛⢲⠖⠾⠯⠤⣤⣴⣚⣁⣀⣤⠒⠀⣀⡠⠖⠀⣀⡤⠀⢀⡠⠀⠀⣠⠄⠀⣀⠄⣀⣤⣠⡞
⠀⠀⠀⠸⡴⡀⠀⠘⡇⠉⠋⠁⣿⡈⠳⠶⠀⢸⠐⠶⠘⡏⣍⣉⠍⢻⠒⠚⠛⠳⠖⠚⠛⠒⢺⠛⠓⠚⢻⣟⠋⣉⠉⡿
⠀⠀⠀⠀⢳⢈⡁⠀⡇⠓⠒⠃⣿⠘⠲⠆⠀⡟⠘⠒⠀⣧⣄⢀⡀⢸⠙⠲⠒⠀⡇⠑⠒⠋⢸⣈⠉⠁⢸⢃⠉⣁⢠⡇
⠀⠀⠀⠀⠈⢧⢙⠂⢳⠳⠤⠀⣈⠳⠤⠄⠀⡇⡉⠉⠀⢻⢈⣉⠀⢸⠈⠓⠒⠀⡇⠑⠒⠂⣼⡈⠉⠁⡸⠈⠉⠁⣸
⠀⠀⠀⠀⠀⠈⢆⠓⠈⡶⣄⡄⢸⠲⠤⠤⠀⡇⣈⠉⡀⢸⢤⣁⡀⣼⠙⠒⠒⢰⡇⠒⠶⢀⡇⠙⠒⢡⠇⠙⠚⢀⠏
⠀⠀⠀⠀⠀⠀⠈⠣⡒⢹⣠⣀⠘⡔⠤⡤⠀⣇⠈⠉⠀⣸⣄⠀⠀⡟⠑⠦⠖⢸⠙⠦⡄⣼⠘⠒⠂⡞⡈⠙⢡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣧⣩⡁⢳⠠⠤⠄⡏⠙⠚⠀⣿⡈⠉⢠⡇⠲⠤⠄⡎⠲⠤⢠⠗⠶⠂⣼⡁⢉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⣅⠈⣧⠤⡄⢱⢈⠓⠀⡧⣌⡁⣸⠰⣄⡀⢰⠣⣄⠀⢞⡐⢂⠞⢂⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠾⢶⣒⠘⡎⣉⠀⡇⠤⢀⡏⢦⡀⢠⠏⠢⢀⠎⢀⣴⠿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠾⠧⠤⠼⠤⠤⠤⠿⠶⠒⠛⠈⠁

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⣰⡁⢀⣀⣤⣴⣶⣾⣿⣿⠿⠿⠿⣿⣿⣿⢿⣿⣟⣛⣛⣛⠛⠻⣛⡿⠿⣿⣿⣶⣦⣄⡀⠀⠀⠀⡉
⠀⠀⠀⠀⣦⠻⣿⣿⣿⠿⣿⣿⣿⣿⣷⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⣷⣬⣉⣙⢻⣿⣷⣆⣴⢁⡼⢀⣠⡔⠂⠉⠀⠲⣄
⠀⠀⠀⠀⢻⡷⢈⣛⡷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣥⣾⣿⣿⣣⠴⠀⠀⠈⠙⣿⡄
⠀⠀⠀⠀⢈⠁⠀⠀⠁⠀⠉⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⡛⠛⢋⢡⣴⣾⡯⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠈⠼⣿⣿⡯⢸⣿⡿⠟⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⣻⣿⣧⣾⠇⠀⠀⠀⠀⠀⠀⠊⡀⠁
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣷⡏⠀⠀⠀⣀⠤⠚⣡⠜
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣤⡴⠒⢊⣁⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⡞⣿⣿⡿⣛⣉⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠙⠟⠛⠛⠉⠁

⠀⢠⠊⡽
⠀⢸⠀⡇
⠀⠘⡆⢧
⠀⠀⠘⢎⠢⠄⢀⣀⣀⠤⠄⣒⣒⣒⡒⠒⠀⠤⢀⣀
⠀⠀⠀⠀⢱⠀⠉⠛⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠘⣆⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⡒⠝⡻⡸
⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠒⠒⠋⠉⠁⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢭⡒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡯⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠭⣍⣒⡒⠤⠤⢤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡤⠔⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠐⠒⠒⠒⠒⠒⠒⠒⠊⠉⠉

⠀⠄⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠈⠀⠑⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⢷⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠆⠀⢣
⠀⠀⠀⠘⣦⠰⣻⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠰⢢⢰⢠⠀⢀⡆⠠⠀⠂⣠⠀⡄⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠈⠂⠀⠀⠀⠸
⠀⠀⣴⣦⡤⢖⢿⣄⠀⠀⠄⠀⠀⠀⠮⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠘⣄⠀⠐⠀⢀⡄
⠀⢀⣿⣍⣦⡈⠉⠀⠀⠀⠀⠀⠲⡉⠀⠲⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢡⡄⢰⠏⠙⠲⢄⠀⠀⠢⣀⢀⠜
⠀⠈⠉⢹⣿⡁⠀⠃⢀⡀⠀⠀⠀⠙⠛⠊⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⡀⠀⠀⢀⠀⠀⣄⠀⠌⢆⠀⠀⠀⠁⢀⠈
⠰⠀⠀⠈⢻⣦⣤⣀⠀⠃⠀⢀⡠⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡏⠀⢇⠀⠀⣾⡤⠓⠀⠀⢁⠈⠀⠀⠀⠐⠾⡶
⠀⠀⠀⠀⠉⠁⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⠉⠀⠀⡇⢐⠋⣁⠐⠠⠄⠀⠀⠀⠋⣸⠀⠀⢀⡼⠀⢃
⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⢀⡐⢈⠂⡁⠌⠓⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⡀⠀⠙⢌⠀⡀⠀⢄⣀⣠⡔⠙⡶⠃⠀⣠⣻⠃⠀⠈
⠀⠀⠀⠀⢀⠀⢀⠔⠀⢀⡢⡀⠀⠀⠘⠂⠁⠀⢘⠀⠉⡗⠀⡐⣠⣶⠂⠀⠀⠀⠀⢀⡴⠚⠛⣻⣶⣄⠀⠈⠄⠀⠈⠑⠦⢤⣂⣀⡨⠄⠊⠀⢰⣿⣷⣿⢁⠀⣶
⠀⠀⠀⠈⠀⠀⢈⠀⠀⠄⢠⠇⠀⠀⠔⠀⠀⠀⠐⠰⢰⠆⡡⢾⠁⠄⡂⠀⠀⠀⠀⣾⠀⠀⢘⠇⠽⢻⡆⠀⠘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣷⣯⣿⠘
⠘⢃⣾⠟⢁⠀⠀⠐⠦⠀⠊⠀⠀⠀⠨⠀⠂⠅⡀⠈⢸⠊⢐⠸⠷⡆⠀⠀⠀⠀⠀⣿⣴⡶⠇⠀⠀⣸⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠁
⣠⢾⣯⣷⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠠⡀⠂⡀⠈⠈⠌⠄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠶⢤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠠⠄⣀⢀⠀⠀⠀⠀⠀⠀⠁
⠉⠸⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢠⡚⠉⠿⢩⣽⣍⠋⠉⠲⣄
⠀⢀⠀⠀⠀⠀⠀⠀⠑⠾⠇⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⢀⣀⣀⣤⠤⣤⣖⢀⠀⠀⠀⠀⣰⠏⠁⠄⢀⠆⠂⠁⠛⠒⠦⢸⡆
⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⡀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⣠⣤⠔⠾⢥⡀⠀⠳⢤⣀⣀⠈⠀⠀⠀⠀⢫⡀⣼⡷⠀⠀⠀⢀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠶⠂⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠈⣡⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠘⠦⣀⠀⠀⠉⠀⠀⠀⠀⠐⣎⡈⢻⡇⠀⠀⠀⡇
⠀⠀⠻⠦⠀⠀⣀⡀⠀⠠⠶⠀⠀⠀⡐⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⢰⣨⠇⣀
⠀⡆⠀⠀⠀⢠⡤⠁⠀⠀⢀⡀⣤⠊⠀⠀⢀⠀⠀⠀⢺⡄⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠙⠫⢏⣒⣤⣀⠤⠀⠚⠀⠀⠀⠀⠔
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠘⠁⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡇⠀⡀⠂⠀⠀⠀⠀⠀⠀⣾⣁⣼⣴⣯⠷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢣⣼⣿⡟⣕⣻⠃⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⢁⡤⢤⣀⢀⣀⣀⣀⣀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡠⠚⡵⠓⢄⣈⠓⢤⣀⠀⠈⠉⠓⠦⣄⠈⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣠⠎⢠⠊⢰⣓⠒⢮⡳⢄⠈⠑⣦⡀⠀⠀⠀⠑⢆⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⡰⠁⡴⠡⣞⡡⣞⠒⠺⢭⠉⣀⠞⣠⠞⣠⠟⠀⠀⠀⠀⠀⢳⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⢀⠇⠸⢍⡑⠨⢉⠪⢕⡒⢚⡽⣡⠞⣡⠎⡝⡟⣩⣉⣉⣉⣑⣚⠓⡆⠀⠘⡆
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣿⣥⠢⢍⡲⢝⣋⡔⣡⠜⠁⢀⢁⡇⡇⢀⡖⣶⡄⢹⢱⠃⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⡇⢠⢏⣴⠃⢰⠦⣍⠓⠿⠔⠁⠀⠀⢸⢸⢀⠇⠀⣙⠋⠁⡜⡞⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠹⡜⣎⢻⡀⠀⢣⡀⠩⣒⡒⠒⢲⠆⡞⣸⢨⠀⠸⣙⣿⠆⡇⡇⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠛⠙⢦⣀⠉⠒⠒⠒⠊⣁⡄⣇⣿⣘⠒⢤⡤⠤⠤⢇⡇⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠙⢮⡉⢉⣩⣉⡜⠁⠛⠓⠬⠭⢭⣭⣭⡍⠩⢃⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣤⣈⡉⠉⠉⠉⠉⠙⠛⠉⠉⠉⣀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠉⠉⠉⠉



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

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢰⠁⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠢⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⢆⠀⠀⠀⠐⠠⠀⠀⠄⠂⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠰
⠀⠀⠀⠀⠀⠈⠐⠀⠀⠄⠀⠀⠠⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠐⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠠⠲⠀⠂⠀⠄⢠⠄⠂⠊⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣊⠠⠁⠀⠀⠀⠐⢘⠀⠀⠀⠀⠀⠈⠁⠀⠀⠄⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠡⢉⠀⢀⡀⠀⠀⠀⡀⠈⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡈⠀⠆⡈⠂⠄⡁⠀⢔⠀⡑⠀⡐⡂⠘⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠈⠒⢄
⠀⠀⠀⠈⡄⣆⢱⠀⠀⠀⠀⠀⠀⡄⠁⠀⢠⠀⠈⠀⠈⠚⠋⠄⠉⢉⠁⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠃⢱⠘⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠂⠐⠃⠀⠚⠉⠉⠉⡉⠉⠉⠉⠐⠀⠀⠄⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠈⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠐⠀⠀⠌⠀⠀⠀⠊⠀⠀⠀⢀⣀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠄⠤⠒⠂⠀⠀⢠⠏⠉⠉⡁⠀⠀⠀⠠⠀⠈⠉⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡘⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢶⠰⠀⠒⠂⢀⣶⠚⠈⠉⠉⠉⠉⠉⠉⠂⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⠀⠀⡞⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠂⠠⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢷⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⠤⠠⠬⠙⠶⠤⠤⠤⠤⠤⠤⠔

⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⢠⡏⢀⣠⣤⣄⣀⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⢉⠭⠭⣉⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⢤⣿⠁
⠀⠀⢸⠉⠙⠛⠛⠋⠉⠁⠃⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢞⣀⠤⠃⠀⠀⠈⠱⡀⠀⠙⡄⠀⠀⠀⠀⠀⠠⠤⡄⠀⠀⠀⠀⢸⢤⣀⣀⣀⣀⣼⠿⡆
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣏⢎⡆⠀⠀⠀⠀⢀⡤⠚⡩⢊⠁⠀⠀⡄⠀⢀⡤⠜⠁⠀⢀⡧⠀⠀⠀⠀⠀⠐⢰⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⢩⠞⠀⠀⠀⡴⠊⢡⠒⠉⠀⠈⠀⠀⠀⠀⡰⠁⠀⣀⠤⠴⣋⠇⠀⠀⠀⢀⠄⢠⢼⠀⠀⠀⠀⠀⢸⣆⠒⠊⠁⣄⣀⣲⡇
⠀⠀⠀⣇⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠈⡗⢤⡘⠤⣀⣀⠀⠀⠀⣠⠞⣡⠔⢋⠴⠒⠋⠁⠀⠀⠀⣠⠋⠀⠈⡜⠀⠀⠀⠀⠀⠀⡇⠉⠉⢉⠍⠁⢰⠁
⠀⠀⠀⠈⠉⠑⠒⠒⠈⠁⠀⠀⠀⠀⠀⠓⢤⣈⠓⠦⣄⣉⠀⣁⠴⣊⡠⠖⠁⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⣰⠁⠀⡀⠀⠀⠀⠀⣇⠀⠀⡸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢬⣉⡵⠊⠁⠀⠀⠀⠀⢀⡤⠴⠊⠁⠀⠀⢀⡴⠁⢀⡆⠐⢆⠀⠀⠀⠈⠓⠒⠲⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠘⠳⠤⠤⠤⠤⠖⠉⠀⠀⠀⢯⣠⣃⣑⠄
⠀⠀⠀⠀⢠⠤⢰⠋⠉⠉⠉⠉⡖⠲⣄⡀⠀⠀⠀⡔⠉⠁⣠⣤⡤⢄⡉⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⢄⠀⠈⠉⠁
⠀⠀⠀⣠⢧⡀⠀⢣⡀⠀⠀⢀⡇⠀⣧⠹⡄⠀⠀⠹⠮⣴⡛⢱⣓⣯⣽⢧⠏⠀⠀⡀⠂⠛⠄⠀⠀⠀⠀⠀⠈
⠀⠀⢰⠇⣀⣩⠶⠤⠵⢤⠤⠾⠶⠞⠓⠢⠼⠀⠀⠀⠣⡀⠈⠉⠉⠁⢀⠜⠀⠀⠀⡇⠀⠀⠁⠀⠱⢄⣀⠴⠃⠀⡠⠂⠉⠀⠀⠉⠉⠒⠢⡀⠀⣴⣤⣤
⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⡀⠀⠀⠈⠑⠒⠒⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠉⠉⠉⠀⠀⢀⡇⠀⡟⠛⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⢸⣤⣛⣯⡤⣾⠀⠀⠀⠀⢀⣀⣀⣤⠤⠤⠤⢴⠛⠁⡶⠶⢀⠀⢠⠄⠀⠀⠘⡇⠧⠴⠔⠶⠖⠩⠏⠉⡞⠀⢃⢠⠏
⠀⠀⠀⠀⢀⠔⠋⠉⠁⠈⠉⠙⠢⡈⠦⣀⣀⠴⠃⢀⡤⠖⠋⡉⠄⠠⠄⢐⠶⠭⠭⣉⠑⠓⠤⣞⡤⠀⠀⢱⡀⠀⠉⠒⠀⠀⠠⠠⠀⠀⠊⠀⠀⢸⣰
⠀⠀⠀⠀⡏⠠⠒⠈⠉⠀⣌⠐⢀⢹⠀⠀⠀⠀⣴⠋⣀⡀⡎⠀⠀⠀⠀⠁⠀⠀⠀⠸⠀⠀⠀⠀⠉⣶⣀⠞⠀⠀⠀⡴⢢⡔⢆⠀⠀⠀⠀⠀⠀⢸⢹
⠀⠀⠀⠀⢻⢧⡈⠧⠘⢀⠈⢆⣠⢿⠀⠀⠀⠀⠡⠈⠣⡀⢨⢦⢄⣀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠤⡖⠁⠀⠀⠀⠘⠀⢰⠀⢇⠈⢦⠀⠀⠀⠀⠀⣸⢸
⠀⠀⠀⠀⠘⣆⠈⠁⠒⠒⠋⠉⣠⠏⠀⠀⠀⠀⠑⢅⠄⠈⠓⢡⡀⠚⠉⣉⡉⠩⠭⠥⠤⠒⠒⠒⠃⠀⠀⣀⡴⠂⠀⠀⢣⠘⢦⡀⠑⢤⡀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⢀⠀⣀⡀⠠⠔⠊⠁⠀⠀⠀⠀⠀⠑⢄⡙⠲⣤⠽⠀⠀⢧⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⡠⠲⡄⡄⠀⠠⡄⣇⢰⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢿⣥⣧⣼⡇
⠀⠀⠀⢸⡇⠀⠀⢹⠈⡇⢻⢸⠈⡇⠀⠀⠀⠀⢀⢀⡀⠀⠀⢀⣾⡿⠋⠀⠀⣹⣯⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠰⣿⡦⠔⠸⠆⠙⠸⠃⡥⢉⡠⣄⢠⠒⡌⡇⠀⠀⢀⣾⡿⠁⠀⠀⣰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠛⠙⢿⡷⡄
⠀⠀⠀⠀⠈⠠⣴⠒⡆⢀⡀⢇⠙⡎⣧⢘⡞⢧⡀⠘⢀⣠⣿⠟⠀⣠⣶⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠸⡄⠀⣄⠘⠘⡶⠃⢾⡄⠀⠀⣠⣤⣿⣿⣏⠀⣰⣿⣿⣿⣿⣿⣿⠏⠀⢀⣠⣴⣶⣾⢄⣔⢠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠿⠄⠈⠁⠀⠁⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⣠⣿⡟⠉⠉⠙⣿⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠀⠀⠀⣼⣿⠋⠀⠀⠀⣴⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣿⡿⠟⠂⠀⠀⠀⠀⢠⣾⠿⠃⠀⣤⣤⣶⣿⣿⣿⣿⡟
⠀⠀⠀⣶⣶⣦⣤⣤⣶⣶⣾⣿⣿⣿⡿⠿⠛⣛⣩⡿⠟⠉⠀⣀⣀⣀⣤⣤⣶⣿⡟⠀⢀⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠈⠻⢿⣿⣭⣽⣿⣿⣿⡽⠷⠶⠶⠛⠋⣉⣤⠶⠿⢛⣿⣿⣿⣻⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢾⣋⣥⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣿⡿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠋⠉⠉⠀⠐⠂⠀⡀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠁⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠆⠀⢀⣤⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠁⠈⠈⠀⣈⣿⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡶⠦⣀⢜⠻⡟⢹⢿⡿⠟⠛⠉⠉⠉⠉⠫⢿⣿⣿⡟⠻⢶⣤⣤⣤⣶⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠻⠿⣶⣾⣺⣅⣀⣀⣀⣤⣠⣴⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠐⢿⡿⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⠿⠋


⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⢀⡎⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⢁⣠⡤⠞⢋⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⢀⣶⠟⠁⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⣿⠁⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠻⣦⡀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⣸⡷⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢀⣴⠟⢁⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡾⠃⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠖⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠓⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣫⡭⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣶⣶⣦⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⣈⡙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⣡⣴⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣭⣽⣟⣷⣦⣄⣙⣦⢸⡷⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⢸⣇⣀⡀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⢀⣠⣾⠉⠉⠻⡆⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣶⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣿⡏⠀⠀⢰⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⡿⠀⢀⣴⠏⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⢀⣾⣡⡴⠛⠁⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⣀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠁⣹⡷⢛⡿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠿⠶⠶⢶⣟⠉
⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⣴⠋⢀⡾⢁⣿⡿⠶⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⢰⡏⢀⡾⣿⣯⡥⠶⠶⠚⣛⣿⣧⣀⣤⣤⠴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠈⢷⣾⣡⣽⣟⠒⠒⠛⠛⢉⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢮⣭⣉⣉⡓⠶⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠓⠒⠶⠶⠶⠶⠖⠒⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠐⠑⠊⠟⠐⠀⠔⠁⠀⠀⠁⠀⠘⠐⠃⠁⠸⠘⠃⠐⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⢀⡤⠐⣒⣒⠒⢤⣄⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢀⠞⣡⠞⠉⠉⢙⣯⠓⢌⠙⣦⡄⠀⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡎⢸⠁⠀⠀⡴⠋⠀⠀⠀⠀⢸⣷⣎⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⡄⢸⠐⠂⡿⠁⠀⠀⠀⠁⠀⢸⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡎⡰⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠑⢌⣧⠈⢷⠼⠁⠀⠀⠀⠀⠀⠀⣼⡇⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠐⡰⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣀⠹⢧⡈⠑⠤⠀⠀⠀⠀⣀⣼⠟⠀⠀⠈⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⠇⢆⣅⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⠳⢤⡙⢷⠲⠶⠶⠒⠿⠟⠃⠀⢀⠔⠀⢀⠊⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡓⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡈⠲⢕⠠⠤⣄⡀⠀⣠⠖⠁⠀⠀⠌⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢁⠖⠉⠀⠀⠀⡀⢄⣠⡶⢿⠋⠍⠲⡌⠉⠉⢉⡒⠲⠤⣀⠀⠉⠓⠚⢇⠀⠀⠸⡉⠀⠀⠀⠀⡀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠎⠀⠀⣠⢔⡩⠖⡏⢐⠁⣿⢰⣢⣾⣟⣀⣼⡶⢤⡦⠤⠬⢽⡦⡀⠀⠈⠑⠊⠂⠀⠀⠀⠀⢠⠁⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡜⠀⢠⠞⣠⠋⡁⠀⣇⡸⠗⢛⠉⢩⠀⡇⠀⡎⠙⣇⣤⡖⣶⣦⠙⠊⢢⡀⠀⠀⠀⠀⠀⠀⠀⠜⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡜⠀⡰⠁⣰⢳⠀⠱⣠⡋⠐⡀⢸⡄⣻⡤⠿⠼⢿⡾⢻⣿⣣⣰⠿⠂⡇⠀⠘⢆⠀⠀⠀⠀⠀⢠⠁⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠠⠀⢠⠃⢠⡇⠀⢷⣜⠁⢣⡀⣹⠶⠋⠀⠀⠀⠀⠀⢠⡄⠙⠛⠛⠃⠘⠓⠢⢄⠀⢆⠀⠀⠀⠀⠘⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⠀⡆⠀⢸⡈⠳⣞⡀⠧⢀⡾⢇⣀⠀⠀⠀⠀⠀⠀⠀⢆⠹⠿⠏⣴⡾⡿⢂⡈⢧⠘⡄⠀⠀⠀⣄⠐⠎
⠀⠀⠀⠀⠀⠀⡴⠁⢀⠇⠀⢸⠁⠀⢻⣘⣢⣿⠟⠂⠀⠀⠀⠀⠀⠉⢣⡄⣀⡀⠴⠋⢀⠀⢄⣸⣇⣤⣤⠇⣼⠀⢡⠀⠀⠰⠉⠙⠃
⠀⠀⠀⠀⠀⣼⠀⠀⡜⠀⠀⠸⠀⠀⠁⠀⠀⢹⡀⠀⠀⠀⠀⡀⠀⠀⠀⢦⠀⠀⠀⡰⢿⠀⢸⠯⠏⣉⣡⠼⠻⢶⣸⠀⠀⠂⠀⠘
⠀⠀⠀⠀⣰⠏⠀⡸⠀⠀⠀⢸⡀⢄⣰⡄⠘⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡔⢋⠴⠊⣀⣈⣀⣤⣀⣀⣀⣀⡜⠀⠀⢰⠀⠀⠂
⠀⠀⠀⠐⢍⣄⣠⠁⠀⠀⠀⠀⢇⠀⢸⠋⠀⠀⣹⠆⣀⡠⠔⠀⠀⠀⠀⡾⠯⠀⠀⣀⡾⠳⠶⠤⣀⠀⢀⠀⠌⢁⠁⠀⢈
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠸⡄⠨⣄⣤⠀⠉⡶⠖⠀⡄⠀⢀⣠⡜⠐⡖⡈⢿⣿⠂⠀⠀⣠⣟⣐⡇⠈⠀⡌⠀⠀⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⠳⠊⠁⣠⣶⣉⣨⣉⣢⠶⢫⠄⡜⢐⡽⢠⣖⣛⡤⢬⠿⠃⢀⡞⠀⠀⠰⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠈⠠⢤⣤⠟⡏⢳⠎⣹⠶⡷⠚⠳⣮⢤⠞⣥⣾⠗⠋⠀⣠⠋⠀⠀⠀⠘⠲⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠉⠛⠠⡟⢲⠓⢀⣾⢉⣽⣧⣶⠖⠋⠀⢀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠀⠓⠋⠉⠉⠉⠀⠀⢀⣀⣠⡤⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠀⠀⠐⠛⠓⠈⠉