Coffee tree Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⡠⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡤⠀⠀⠀⠀⠁⠰⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣴⡆⠀⠓⠋⠀⢾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠈⢣⣀⡀⠀⠀⠌⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠿⡟⠲⠀⠀⠄⠉⠓⠢⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡄⠌⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠀⢀⡀⠀⠠⠈⢃⠀⠘⠆⠀⠤⠄⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠀⡦⠤⠀⠀⠀⠄⠀⠀⡄⠀⡸⠀⠀⠴⠦⠉
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢐⢁⠁⠀⣄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠆⠀⣄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠃⠀⢐⠃⠂⢰⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠂⠀⠀⠀⠀⠀⠀⡀⠀⢀⠅⠁⠀⢀⠀⠀⠒⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠘⠀⠀⣸⠖⠾⠀⢄⠀⠈⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠄⠀⠤⠄⠠⠄
⠀⠀⠀⠀⠀⠀⢠⠈⠀⢀⠀⢠⠂⠁⢀⠦⠄⠀⠀⠀⠀⠁⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠠⠑⠤⠁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠘⠀⠀⠄⠀⠁⠀⠀⠈⠀⠒⠀⠤⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⣶⠾⢶⣶⣤⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣭⠟⢲⣶⣭⡻⣿⠦⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣄⠈⠻⣿⣿⣧⣌⣻⣿⡠⣤⣶⡾⠛⠛⠓⠀⠀⠠⣾⡧⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⣼⣿⣙⣿⡿⠿⢿⣿⣿⣿⡳⠌⠛⠿⢿⣿⢿⣿⠊⢹⣷⣿⣾⣠⣶⡟⣱⣿⡧⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⡻⣿⣿⣦⣄⠀⠀⠀⠙⢿⣟⣻⣏⣅⣀⣙⣿⡇⣿⣿⣿⠀⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷⣭⣿⢿⣿⣮⢻⣿⣿⢳⣾⣟⡀⣀⣈⣻⣿⣿⣿⣿⣿⡅⢻⣿⣿⠀⣾⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣶⣿⡏⣀⣤⣤⣹⣋⣠⣌⣿⣿⣿⣿⣿⣠⣿⣿⣿⡄⢹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠿⡿⠋⣉⣙⢻⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣧⣸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⣛⣿⡿⣿⣿⠛⣛⣻⣿⣿⣿⣿⣿⡟⣿⣿⣿⣏⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⢴⣷⠾⠀⠀⣤⣠⠄⣸⣷⣴⣿⣿⣿⣿⣿⣿⡿⣷⣿⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡿⣛⣢⣤⣄⠀⢀⢠⠄⠂⠃⢠⣿⣷⡟⢻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣷⡈⢿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣫⣿⣆⠙⠟⠛⢛⣿⣤⣾⡿⠖⠛⠉⠉⠉⠁⠀⠠⣭⣭⡍⠛⢿⣿⣿⣿⣿⡷⣿⡇
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣟⣁⡀⠘⠀⠐⣿⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠦⣀⠘⣿⡟⢿⣿⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⡃⠘⣟⠀⠟⠙⠇⠀⢀⣀⡤⠤⠤⠶⠶⣶⣿⣿⣿⣿⣶⣶⣽⣿⣺⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⣾⢿⣀⡄⢀⣤⠘⠉⠀⠀⠀⠀⠀⣀⣩⣿⣿⣿⣿⣿⡀⡇⠹⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⢀⣵⣄⣾⣯⣷⣼⡟⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠙⠻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣥⣆⡻⠋⣽⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢀⣾⣿⣾⣿⣆⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⠇⠀⢻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⡄⠀⠀⠀⡾
⠀⠀⠀⠀⠀⣾⣿⣿⣯⡭⠲⠇⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡏⣿⣿⠁⠀⠀⠀⡇
⠀⠀⠀⠀⢀⣿⣼⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠙⠟⠋⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⣷⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠙⠛⠿⠋⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠿⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠶⠶⠶⣿⠟⠛⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠱⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣀⠒⠦⡀⠀⠀⠀⠀⠀⠆⠀⢿⡄⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠙⢦⡆⠘⢤⡀⠀⠐⠁⠀⠡⡾⠀⢀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠰⡄⠀⠹⢷⣀⠙⡄⠀⠁⣈⡳⠁⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡖⠲⠦⣄⠀⠀⠀⢲⠀⠘⠻⣦⠀⠀⠀⣻⠃⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢦⣄⡀⠓⠀⠀⠀⠙⠂⠈⢹⡟⣤⢲⠇⠀⠀⠀⡀⣀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠘⡄⠀⠀⠀⠀⠀⠀⢀⡀⣀⣽⣤⣬⣷⣤⣄⣠⡄⠀⠠⠄⠑⡷⢊⣼⣧⡶⢷⣾⢥⣤⣤⣈⢄⡈⠅⠐
⠀⠀⠀⠀⠀⠀⠀⡏⡜⠁⠀⠈⡆⠀⠀⠀⠚⠋⠙⠓⣲⣦⣤⣤⣄⡬⣉⡙⠓⠀⠓⠤⢴⡷⡉⠉⣻⠑⠄⠈⠀⠀⣀⣀⠶⠤⠋⠁
⠀⠀⠀⠀⠀⢀⠼⡀⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣿⣭⡿⣿⢹⣤⡢⣁⠉⠀⠋
⠀⠀⠀⠀⠀⡄⠀⢇⣿⠀⠀⠀⠀⠇⠀⠀⠀⠀⡀⠀⠀⢀⠀⢀⠀⣴⡏⡜⠰⢾⠿⣬⣃⠁⣀⣠⡖⠒
⠀⠀⠀⠀⠀⠟⠀⠈⢻⣃⡄⠀⠀⡇⠀⡀⠐⢆⠀⢀⣦⡀⣀⠜⠃⠘⣧⡘⠴⣟⣠⣄⠀⡸⠋⠹⡏⠳⡄⠤⠤⠰⠂
⠀⠀⠀⠀⠀⠘⡄⠓⠀⣽⡇⠀⠀⠇⠀⠠⠖⠘⢻⠉⠀⢹⣏⠀⢈⣴⣋⣉⣢⠿⡁⠀⠀⠃⢈⠠⠧⢆⣀⡠
⠀⠀⠀⠀⠀⠀⠘⠆⠀⢘⣷⢀⠀⠘⣀⠂⣁⣀⣈⡥⠶⣞⠈⠉⠻⠙⢿⣿⣿⣶⣤⣆⣤⡠⠦⠶⠓⠉⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣽⣿⡄⠀⡁⠀⠞⠉⠹⡁⠀⠙⠂⠸⡆⣸⠋⣩⡏⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢌⡙⣝⣆⠃⠀⠀⣠⡖⠉⠈⠷⢴⠖⠁⠘⠀⠘⠛⠤⠄⠰⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣽⣸⡶⣻⠛⠙⠲⠒⠠⠄⢸⡦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠋⠀⠀⠐⠀⠀⠀⠀⢀⣸⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠰⢓⣤⡀⡈⢁⣤⡄⠀⠀⣈⠁⠀⠘⠀⠠⠄⠒⠒⠀⠠⠤⡄⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣘⣩⡍⠛⠙⠋⡙⠛⠏⠛⠻⡟⠓⢶⣶⣤⣤⣤⣤⣤⣤⣴⣾⠂⠀⣠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⠞⠁⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⡌⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⢰⣇⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠁⠀⠉⠒⠒⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣶⣴⣾⠋⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡥⣀⡀⠀⠄⠀⠀⢀⣿⣷⣿⠏⠁⠀⠀⣀⣠⡤⢀⣤⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠚⢔⡨⡆⠀⢾⣿⠗⠂⣀⣴⣶⣿⣿⣿⣷⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠾⠿⣿⣷⣶⣴⣌⡁⠈⠌⣰⣶⣾⣿⣿⣿⣿⠿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠚⠉⠁⠀⠒⢊⣽⡿⢿⡇⢸⠰⠋⣿⣿⡿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣴⣾⣟⠁⠀⠀⠀⠀⠒⠛⠿⠗⠀⠘⢦⠘⠘⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣄⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⢻⡇⠄⢈⠁⡀⢠⣤⣴⡞⢳⠄⡀⠀⠀⢀⠀⣀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣍⡉⡀⣙⣧⠉⣰⣀⠱⣾⣿⡿⠞⣚⣣⣬⣷⣾⡴⠏⠀⢀⣠⠃
⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠋⢙⣛⣿⣿⣡⣦⡴⠀⠒⣙⠋⠻⢿⣿⣯⠋⡟⠻⣦⠍⠬⠉⠁⠀⢴⠏
⠀⠀⠀⠀⠀⠈⢿⣷⣦⣼⠱⣦⡀⠐⢦⣄⡀⡒⣦⣈⡹⣯⡛⠉⠀⠀⠀⢰⡏⠀⠀⠀⠈⠈⠾⠟⠀⠁⠀⠀⠀⠀⠚⠋
⠀⠀⠀⠀⠀⠀⠈⢿⣿⡏⠠⠈⠻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦⠀⠀⠸⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠴⠛⠛⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢹⠃⠰⠀⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠉⢩⡝⢂⠀⡈⠀⠴⣶⣧⣶⣷⢀⡠⠖⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠘⠷⣿⣿⣿⣻⣿⣿⠃⠒⠀⢠⣝⡀⢸⣄⡘⢻⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡌⢰⡇⠀⢀⠀⠀⠈⠋⠙⠛⠀⠀⠖⠀⠂⢹⣄⢀⢡⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠜⠇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠹⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠺⣄⣠⣿⡂⣿⠀⠀⠀⠀⠀⢠⠏⠀⣀⢀⣀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣚⣿⣿⣿⣿⣿⡇⠀⡀⠀⢠⠇⠀⠀⣹⣿⣿⣷⡄⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠟⠉⡻⠛⣃⡴⠇⢀⡄⣰⣬⣴⣿⣿⣿⣷⡾⠶⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠹⣀⠤⣼⡆⠈⢻⣿⣿⡿⠋⠏⠙⠶⣬⠑⠒⠖⠀⠀⠀⡀⠀⣀⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠠⠈⡗⠀⠹⣿⣿⣏⡁⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠙⠒⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠣⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠠⣶⡆⠁⡇⠀⠹⣿⣭⣉⣐⢈⣠⠿⠷⠶
⠀⠀⠀⠀⠀⠀⠀⢀⣸⠷⠶⠶⠞⡺⠉⣡⣴⡿⠘⡀⠽⠄⠉⠉⠣⣄⡀⠀⠠⠤⠦⢦⡀
⠀⠀⠀⠀⠀⠀⡔⣋⡤⠤⢶⣶⠟⢃⢠⡗⢈⢧⡔⠉⣣⠸⡄⠀⠀⠻⠙⢆⠐⠀⠶⠦⠠⣄
⠀⠀⠀⠀⢀⡿⠋⠀⢀⣠⠞⢏⠀⡁⢰⣿⠡⣀⣷⢶⣿⠀⠸⡁⢀⠀⡆⠀⠇⡀⠀⠀⠈⠉⠳
⠀⠀⠀⠀⢸⡇⠁⢀⡠⠋⠀⠀⢠⡀⢹⡟⠋⢹⡟⠁⠁⠀⠀⠙⢬⡸⡇⠀⠀⠈⢻⡐⠂
⠀⠀⠀⢀⡞⠉⢀⣼⠁⠀⠀⠀⢀⣷⠊⢀⡀⡰⠓⢤⡄⠂⠀⠀⠀⠈⠙⠲⢧⣱⠀⠹⡦⠄⠀⣼
⠀⠀⠀⢸⡥⠂⢹⠿⡀⠀⢀⡀⢠⠃⠀⣌⡸⠷⣬⠜⣧⡰⠦⠀⠀⠀⠀⠀⠀⠻⣄⠀⡻⣦⡀⠉
⠀⠀⠀⠘⣇⠔⢹⠀⠱⣄⠀⣷⠃⠀⠀⢸⡡⢸⡇⠠⢨⡃⢀⣟⠒⢒⣦⣤⣀⠀⠙⢆⡇⢷⣼⡀
⠀⠀⠀⠀⡇⠀⣾⠀⠀⡹⠋⠀⠀⢀⣤⣌⣙⣿⣷⣶⣷⣼⡟⠳⢞⣉⠉⠀⠒⠉⠉⠶⠽⡺⣿⡄
⠀⠀⠀⠀⢸⡄⡇⣇⠘⠁⠀⣠⠀⠁⣀⣠⡼⢟⠉⡟⣏⠹⣇⠀⣈⣹⡍⠁⠙⠒⠂⠠⣒⠻⢦⠁
⠀⠀⠀⠀⠀⢿⣿⠟⠀⠀⢀⠟⠉⠁⢀⡼⢃⠈⢢⣧⠜⢦⣬⣻⣭⢸⣷⡀⠀⠀⠀⠀⠈⠓⢤⣳⣄
⠀⠀⠀⠀⠀⠘⠟⠀⠀⡴⢋⠀⠄⣢⡏⠀⠈⢆⡞⣵⣦⠄⣾⡁⠀⠈⠉⠳⢆⣀⠐⣄⢀⣀⠵⠾⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⣀⣴⠃⠈⢀⠀⢸⠇⠻⠃⠀⡟⠉⢡⣴⠁⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡖⠋⢡⠚⡀⠀⢸⡶⠋⠀⠀⠈⠉⠃⠈⣜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⣠⠏⠆⠱⣠⠎⠀⠀⠀⠀⠀⠀⡀⢰⣷⡝⢿⡅⠀⠀⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢯⢐⡏⠀⣠⠴⠃⠀⠀⠀⠀⠀⢠⠿⢁⣼⢣⡕⣄⢢⠉⠐⠂⠤⠌⣂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⡴⠃⠀⠀⠀⠀⠀⠀⢠⡿⠀⢩⣿⢸⡇⠸⡦⠙⠦⢤⣀⣰⡄⠭⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⡾⠁⢳⡇⣴⠘⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⣺⠁⠁⡜⠀⢠⡀⠀⢀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢬⡇⠃⡞⠁⠀⠘⡇⠀⠀⠆⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡗⠁⠀⠀⠀⠀⠘⣦⡆⠈⣎⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢂⠐⠋⣉⠵⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠑⡤⠔⠒⠺⢷⡟⢿⡶⣾⣧⣤⣾⣅⠄⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⢀⠤⠘⠢⡵⠈⢂⠻⣍⠙⠛⠒⢒⠒⠤
⠀⠀⠀⠀⢀⣾⠀⢀⡄⣶⣇⣀⠀⠈⠃⠀⠀⠁⠈⠁⠈⠁
⠀⠀⠀⢀⢺⣇⠋⠉⠉⡟⠉⠉⠉
⠀⠀⠀⢀⠼⣧⠀⡲⠒⠿⠢⠤⡬⢶⡀⠀⠀⠔⠀⢢⠄⠂⡀⠀⠀⠀⠀⠀⠀⠀⡠⠒⡎⣠⡥⣒⠋
⠀⠀⠀⠈⠀⠻⣯⣀⢀⡜⠀⡠⠀⠀⠙⠂⠠⣶⣴⠞⠲⣤⠂⠀⠀⠀⠀⠀⢀⣎⣴⡾⠛⠃⢠⣧⣾⠃
⠀⠀⠀⠀⠙⡀⠜⠻⣯⣉⣉⡁⠀⠀⠀⠚⠛⣾⢧⣀⠀⠂⠀⠀⠀⠀⠀⣠⠚⢿⠛⢉⡈⠘⠹⣿⣷⣤⣠⣠⢀
⠀⠀⠀⠀⠀⠈⠃⡀⡏⠙⢦⡄⡀⠀⠠⠠⠘⠇⠀⠈⠟⠛⠲⠦⠀⢀⣠⣿⣩⣭⣥⣀⣀⣠⣴⣯⣽⣾⣯⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠤⡙⠢⣄⠀⠀⠀⠼⠒⠐⠁⠀⠀⠀⠀⢀⣿⢈⣉⡉⢉⡏⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣔⣢⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣶⠖⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡜⢿⣦⣛⠊⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠸⢻⣖⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠓⢦⠀⠀⠀⢀⣤⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡤⠷⣄⣠⣇⣀⡴⣫⢟⣉⣀⣤⣤⡴⡴⢴⣖⣲⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣄⡽⠛⢳⣄⣼⡉⠉⣧⣾⣽⣧⣤⣊⣭⣽⡿⠛⠟⡻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡅⠈⢹⣧⣤⣼⣿⣿⠟⠛⣏⠈⠛⣿⣧⡙⢿⡆⢁⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⣙⣿⣿⣏⢀⡀⣿⣥⣤⣶⠋⠛⠛⠉⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢿⣌⣀⣼⣶⣾⡟⢥⣉⣉⠓⢦⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣳⣾⡿⡻⣿⡁⢈⡇⠀⠙⢶⣤⡤⠤⠄⠀⠉⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡾⢫⢗⡾⣫⣾⠁⠿⢤⣿⣧⡀⡄⠸⠇⢙⣶⡒⠂⠀⠈⠓⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣥⠂⣿⡿⠛⢹⠋⠷⡄⠈⠑⠘⡿⣇⠀⠀⢸⡇⠙⣯⡙⠂⠀⠈⠙⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡿⡡⣫⣾⣿⡃⠀⢸⡆⢸⣇⠀⢀⠷⢫⢻⣦⣠⠀⠁⠀⢸⡻⢷⡒⠆⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠃⢸⡁⢀⠇⣧⠀⢨⡗⣠⠞⠀⢾⣇⠛⢦⡀⠀⡌⠃⡇⠹⣆⡒⠀⠀⠑⠻⡄
⠀⠀⠀⠀⠀⠀⡠⠶⢻⠉⢧⠀⠀⣇⠀⠘⣿⣅⠙⢶⠁⠀⣀⡈⢿⣆⠀⠷⣄⣤⣄⣀⠀⠈⠙⢶⡔⠋⢀⣽⡆
⠀⠀⠀⠀⠀⡞⣰⠀⣾⠀⠈⢳⠀⠈⢧⡈⠀⢻⣗⢸⡷⢤⡻⠁⣎⠻⣄⠀⠀⠀⠀⠉⢳⣀⣀⣀⡈⠳⣤⡈⢿⡄
⠀⠀⠀⠀⠀⡇⠋⠀⡿⡄⠈⠈⢧⠀⠀⠙⢧⡘⠹⣷⡽⣆⠓⠶⠧⣧⣸⡄⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠿⣷⡀
⠀⠀⠀⠀⠀⠹⡆⠀⠀⢷⡆⠀⠄⠑⣄⠀⠀⠉⠛⠓⠷⣿⠀⠀⠀⠈⠻⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢧⡠⠀⣾⡿⣆⠀⠠⠘⡄⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠈⠻⣅⣀⣀⠘⣧⠈⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠹⣇⢻⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢽⣾⣧⡀⠀⠀⢀⣤⠶⣾⣄⠨⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠘⠧⠴⠾⠟⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡖⢫⡟⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣠⣼⣿⣽⡏⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⣠⠾⠛⠄⠀⣾⣷⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣌⣭⣉⣿⣽⢟⣿⣷⣾⡾⠁⠀⠀⠀⠀⠀⣀⣤⡄⣞⡍⠀⠀⢀⣠⣺⠇⠸⢻⠏⣴⠾⠚⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣦⣤⣴⠿⠿⣿⠿⢾⣻⣿⣿⣿⣷⡙⠁⠀⣤⠆⠠⢰⣿⣿⣿⣷⡿⠃⠀⢠⠎⣱⡟⠀⠐⠁⠶⠶⡔⠆
⠀⠀⠀⠀⠀⢀⣀⠠⠒⠒⣶⡆⠸⢷⣄⣄⣼⡄⢀⡝⠻⢟⡛⠁⣠⣄⡂⣼⣯⠶⣬⢿⣿⠿⠛⢰⣄⠁⠶⢘⠛⣡⣄⠐⠶⠶⠦
⠀⠀⠀⠀⠔⠋⠁⠀⠀⠀⢻⣷⢀⡨⣿⣿⣦⡙⣿⠻⣶⣤⡈⠉⢩⡟⠳⡙⣧⣤⠶⠆⢠⣦⣡⡉⠟⢓⡘⢀⠑⠲⠮⠽⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠆⢘⠿⣾⡍⢿⣷⣌⡈⠻⢧⣜⣦⣼⠍⠃⢛⣷⣤⡤⢌⡻⢿⣿⣿⣱⢞⡣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⢿⣿⡌⣿⣯⣧⠀⠀⠙⡍⢷⡾⠰⣾⣃⢀⣾⣯⣡⣀⢠⠛⠿⠼⠢⠍⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣄⠹⣿⣮⣻⣷⠀⠀⠀⠀⠘⣷⣔⠺⣥⡉⠈⠛⢿⣶⣾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⡌⠋⠷⣝⣧⠀⠀⠀⠀⠉⠻⣷⢦⣟⡦⠀⠀⠈⠉⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣶⣧⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢮⡉⠙⢢⣀⡙⢍⠢⡀⠀⢀⣀⣴⢉⣱⢄⣤⠞⢻⡦⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣩⡖⢂⠟⠉⡩⠋⢉⠜⣉⠝⠓⢮⢼⡁⣠⠥⢄⡸⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠑⠒⠚⠃⠈⠉⠉⠀⠀⠀⣇⠀⡹⢇⣀⣸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⢦⢀⡴⢻⡿⢧⣀⠼⢻⢗⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⡏⠉⢻⠯⣴⠟⠀⠀⠀⠀⣇⠜⢣⠑⠒⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠖⠓⡦⠾⣤⢧⠀⠀⠀⠀⢸⠃⡠⠞⢗⠒⠤⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⣼⣄⣀⡴⠋⠀⠀⠀⠀⠸⡎⠀⠀⣸⣄⣀⣸
⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⡤⡤⠤⣄⠀⠀⠀⣠⣤⠤⢤⣞⣡⡾⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⢶⡊⢀⣄⢀⠇
⠀⠀⠀⠀⠀⠉⠻⠿⠯⢽⣋⠿⣄⡏⣆⠀⢸⡥⢇⡀⢀⠇⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣊⣥⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠒⢚⡥⡟⠀⣸⣄⣰⠋⠓⣶⣃⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⣉⡷⢡⠞⢉⣿⣋⣓⣶⡡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⢁⡴⢋⠴⣺⠟⢀⠽⢋⠽⠓⠒⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⣶⡾⠴⢇⠺⣇⠐⢏⠚⠳⣒⠲⢯⠤⢍⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢠⡖⠁⠀⠀⠀⠑⠬⠷⣌⣳⣄⣈⣳⣄⠵⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠀⠀⠀⠰⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⣄⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⣀⢈⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠐⠒⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠂⣀⠀⣠⣴⠂⠑⠂⠁⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠓⣠⣀⠀⠀⢀⣀⡀⠠⣤⣤⣰⡤⠶⠊⠙⠛⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠄⠈⠙⠷⣦⢉⠉⠳⠈⢀⠉⡰⠖⠁
⠀⠀⠀⠠⢆⣀⠀⡀⠀⡉⢲⣅⠢⠀⣉⡙⢷⡤⡄⠀⠀⢜⡠⢽⠊
⠀⠀⠀⠀⠂⠲⢦⣈⠉⠀⠑⠘⠁⠑⢤⠈⠱⢄⠙⠈⠀⠀⢀⢈
⠀⠀⠀⠀⠀⠈⢄⠉⠳⢶⣤⣤⣀⣄⣀⣀⣹⢊⣐⣱⠀⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠈⠉⢉⡈⢋⢩⠉⡠⠍⠀⣰⠠⠥⠀⠀⠀⠀⣀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⣻⣿⡧⠀⠀⠬⠂⠐⠚⠁⣀⡤⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⣸⣥⠇⣀⣀⡀⣀⣠⣤⠖⠋⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣽⡄⠘⠦⠋⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⢀⣀⡠⠄⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⡔⠀⠈⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠂⠀⣨⡆⠀⠤⠤⠄⠀⠉⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢀⠀⢁⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠈⣡⠊⠀⠀⠀⠀⠀⠀⠀⣤⡤⠀⣅⣠⣀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠿⠆⠀⠀⠒⠀⠀⠀⠀⠀⠴⠈⣀⡁⠐⠂
⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠐⠠⠠⣄⠰⠀⠠⠀⠀⠀⠀⠀⡄⠀⢈⣈⠀⠸⠟⠀⠀⠀⠀⡀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠄⠀⠀⠀⠀⠀⠉⠉⡀⠙⠋⣀⠀⠀⠀⠀⠀⠈⠁
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠉⠂⠀⠐⠀⠀⠀⠀⠀⠈⠁⠆⠀⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠉⠁⠆⠀⢤⠤⠔⢢⢤⠀⠀⠆
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⢠⡄⠽⠀⠀⡈⣁
⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣾⠀⣀⡜⠀⠐⠀⡋⠀⢈
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠈⠂⠈⠄⠀⠀⠐⣤⣤
⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢀⠀⠀⠀⠀⠠⠄⠀⢶⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⣡⣄⠀⣀⠀⠉⠃
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠘⠁⠀⠀⠀⢠⣦⡀⠀⠀⢁⠀⠀⠤⠀⠁⠀⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠓⠀⡀⠀⠀⠠⣤⣶⠄⠀⠀⠀⠀⠀⠀⠐⡾⠇⢀⣀⠀⡀⠈⠉⣤⢉⠉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠠⢾⡷⠠⠆⠈⠆⠴⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠁⠀⠰⠦⠁⠀⣠⣀⠀⠀⣦⣤⠀⠀⠀⠀⠀⠉⢲⠀⠀⢀⠁⠀⣠⣌⠀⠄⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡀⠀⠉⠋⠀⠃⠛⠋⠀⠀⠀⠀⠀⠒⠀⠀⠀⠉⠀⠀⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠁⠀⠀⢀⣴⡄⠤⠀⠐⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢤⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠄⠒⠈⢛⠀⠀⠀⠀⠀⠀⠙⠁⠀⠒⠤⠀⠀⠀⠀⠀⠀⠤⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⢀⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣙⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠐⢀⠐⡆⣠⠆⠀⢲⡀⡶⠀⠀⠐⣶⠀⢀⠀⠀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠁⠀⢶⠀⠹⣇⠀⠀⣀⡼⣇⠸⣤⠞⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢰⣄⡀⢻⠉⣉⠙⢿⡀⢹⠴⠚⠣⣄⠘⣄⣣⠀⠀⢹⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢺⡞⠉⠀⠀⠙⣾⠀⡀⠀⣄⠀⢸⣃⣤⠖⠋⠉⠈⠀⠀⢀⡴⠛⢫⣋⠍⠏⣏⡛⠗⣤⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢐⡧⠚⠁⠀⠘⣦⡏⠁⠈⡆⠀⠀⠀⠀⡴⣋⣤⣤⠀⠙⣷⠶⠶⠶⠾⠾⢷⠆⡇
⠀⠀⠀⠀⠀⠀⢰⠤⠴⠖⠷⠶⠿⠷⠾⠧⢤⠤⣿⣤⣾⣀⣴⣈⣓⣾⠓⣶⠾⣇⢹⠠⢸⠀⠀⣿⣿⢻⢹⡆⠀⢸⡶⡇
⠀⠀⠀⠀⠀⠀⠘⠚⠓⠛⠛⠛⠛⠓⠒⠒⠦⠤⣤⡀⠀⠀⠀⠉⠉⠉⠉⠙⠓⠻⠚⠶⠼⢦⣄⣾⣈⢙⠉⠁⠀⢸⣷⡇
⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣄⣀⣄⣀⣀⣄⣀⣀⣀⡀⡀⠀⠀⠀⠈⠉⠋⠓⠒⢼⣍⡇
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠠⠄⠀⠀⠀⠈⠉⠉⠉⠉⠙⠒⠒⠲⠦⠤⣀⣀⣈⡇
⠀⠀⠀⠀⠀⠀⢸⢀⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡤⠤⠤⠤⢤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⡃
⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⡠⢠⠴⣿⢻⡆⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⡀⢀⣀⢀⠉⠉⠉⠙⠒⠒⠶⠤⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⡋⢳⣯⠭⡇⠀⠀⠀⠀⠀⠀⠀⠹⣟⠿⠿⠉⠩⠉⠍⠉⠙⢛⣺⡶⠦⣤⡀⠀⡅
⠀⠀⠀⠀⠀⠀⠐⠀⢀⣤⠶⣄⠀⢹⡉⡾⠴⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡒⠂⠀⠂⠀⠂⠾⣍⣽⠁⠂⡌⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠻⡞⢩⠷⣤⣳⢷⡊⠀⢀⣤⠞⢻⢉⣯⣿⠃⠀⠠⠀⠀⣽⢷⣮⡀⡂⠐⠀⢾⡆⢄⣅⣠⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠲⢷⠋⣰⢻⠻⣾⢇⡴⡇⢸⣤⠞⠛⡶⠃⠀⠀⠀⠀⠀⣳⠾⠃⢹⣭⣅⣁⣹⡗⠻⣤⡿⠦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣟⠲⠼⡞⠁⡞⠀⣏⣾⣠⠷⢯⣬⠽⠋⠀⠀⠀⢀⠀⠀⠀⣇⣤⡀⠀⣿⡏⠁⢽⡏⣁⣽⡉⡒⡇
⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠦⣧⢞⡁⠘⢿⠛⠛⠉⠉⠀⠀⠀⠀⡀⣹⡛⠻⡆⢸⠿⣼⠇⠀⣿⡧⠰⢾⡇⠦⢿⠀⣤⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠶⢾⡿⠛⢷⣮⣧⣶⣤⡦⠀⠀⠸⠀⠙⡹⢿⡴⠃⢸⠀⢿⠀⠀⡟⡇⠘⣸⡗⢐⢸⠒⠂⡇
⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⠤⠧⠤⠤⠤⠵⠿⠩⠤⠦⠤⠾⠤⠴⠥⠤⠧⠠⠼⠦⠼⠤⠤⠧⠯⠩⠽⠍⠍⠽⠭⠭⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⢠⠙⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣷⣼⡄⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠐⣶⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣺⣿⣿⣿⣿⣽⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠐⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢃⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣍⣉⠉⠉⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣟⡂⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣷⣶⣶⣦⠄⠀⠀⠈⠩⠽⠿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣛⣛⣀⠀⠈⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢇⣀⠀⠀⠀⢤⢀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⢀⣔⣉⣉⣀⣀⣀⠤⠚⠉⠒⠠⣄⠀⠀⠀⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠃⠀⢀⣤⡴⠚⠉⠁⠀⠈⣀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣦⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠲⢤⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢨⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣾⠁⠀⠀⠀⠀⠈⢳⣰⠟⣿⠲⡀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠳⡴⠶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡆⢀⣼⣿⠉⠳⡄⠀⠀⠀⢀⡴⠋⣸⡏⢳⡀⠀⠀⣠⠖⠶⠞⠃⠀⢿⡑⠉⠢⣄⠀⠀⠀⠀⡴⠃⠀⠀⠀⢀⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠙⣦⣠⣴⠟⠀⣾⢧⣙⡢⠙⠲⢮⣁⣀⣀⠀⠀⠀⠈⢿⠂⣀⣈⡷⢾⣧⡾⠁⠀⠀⠀⠀⢺⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣇⢀⡴⣾⠉⠀⠀⠀⠀⠻⣄⠀⠉⠂⠀⠀⠀⠉⠉⠑⠄⠀⠀⠈⠋⠉⠁⠀⢾⡈⠛⠶⢤⣤⣤⠞⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠁⠀⣿⡄⠀⠀⠀⠀⢠⡘⣯⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⢸⡀⠀⠀⣸⠃⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡆⢸⣿⡇⠀⠀⠀⠀⠈⢿⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⡀⢻⡄⣿⡇⠀⢠⢿⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣾⣿⣿⡀⠀⠀⠀⡄⠘⣧⠈⠓⠦⢄⠀⣀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⣿⠀⢹⣿⣿⣠⣯⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣷⠀⣿⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⣿⣿⣧⠀⠀⢸⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣏⢢⡄⣸⣿⡄⠙⢆⠀⠀⠀⢸⣿⡇⠀⠀⢀⣿⣿⣿⠀⠀⣾⣿⣧⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠁⠀⠀⣾⣿⣿⠀⠀⢾⣿⣿⣿⣦⣠⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⡉⢻⠋⢲⠾⣿⣿⣿⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⢀⡀⠀⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⡄⠀⠃⠀⠀⡀⠀⠀⠀⠐⠐⠀⠀⠠⠀⠀⠀⠀⡄⠀⠀⠙⢆⠀⠀⠀⠀⠀⡴⠋⡂⠔⠸⠀⠀⠤⠼⢦⠀⠿⠃⠀⠀⠀⠀⠈⣀⡶⠒⢡⡲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⣤⠀⠀⠀⠀⠀⠀⠤⠀⠒⠀⠀⠰⠀⠀⠈⠃⠀⢐⠀⡸⠏⠀⠀⠀⠀⠀⠀⢠⡤⠀⣶⣶⠐⠿⠂⠀⠀⢯⡈⢇⠀⣠⡏⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⡀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠠⢰⡇⠀⠀⠀⠀⠀⠀⠀⠰⠂⣤⠈⠀⣦⠀⠀⠀⠀⠙⠵⡎⡘⡳⠈
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⡄⠀⢨⠀⠀⢀⡀⠀⠀⢃⠀⠁⠀⠓⠀⡠⠀⠀⠀⠁⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠖⠈⠀⠀⠀⠀⢠⡀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠃⢀⠀⠀⠇⠸⠃⠀⠀⠀⠑⠤⢀⢀⣀⣀⠤⠂⠀⠀⠀⠀⠀⡈⡠⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠰⠄⠤⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣰⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠆⠀⠘⢰
⠀⠀⠀⠀⠠⠀⠀⠠⠐⢤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⡀⠀⠀⠀⢀⠃⠁⣟⡀⠈⠀⠀⠀⠀⢀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠠
⠀⠀⠀⠀⠄⠠⠀⠀⡀⡄⠀⠀⠀⠀⢆⠄⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠉⠄⠀⠀⠈⠁⢸⣏⡀⠀⠀⠀⣀⠀⡀⠀⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠤⠀⢐⢤⠼⠔⠉⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⢀⠀⠀⢀⡀⢰⠀⠀⠀⠀⣶⠋⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢀⠄⠠⢄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠠⢠⠀⠀⠀⠐⠈⠈⠀⠀⠈⢁⡏⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⠞⠀⠀⠀⠀⢇⢒⠆⠀⢱⠀⠀⡈
⠀⠀⠀⠁⠀⠀⠀⠀⡄⢠⡀⠃⠀⠀⠀⠀⠀⣇⠀⠀⠄⠀⠳⠀⠄⠀⠀⢠⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠊⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⢳⡄⠀⡠⠃⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢀⡀⠀⠈⠫⡀⢀⣠⡰⡶⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡃⠄⠁⠀⠀⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣽⠁⠀⠀⠀⠀⠰⢁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢠⠄⠘⢋⣉⠘⠑⠢⡀⠀⠀⠀⠀⠀⠤⠈⠀⡀⠄⠋⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠘⠛⡠⠀⢀⠜⠀⠀⠀⠀⣀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠔⠤⠄⠀⠀⠀⠀⠀⠀⠀⠈⠒⠲⠦⠴⠖⠚⠁⠀⠀⠀⠀⠀⠁⠙⠀⠀⠀⠀⠀⠀⠰⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠐
⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢠⠞⠁⣈⡙⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠚⠀⠄⠰⠀⠀⠄⡡⠆⠀⠀⠀⠀⠀⠀⣤⠀⠈⠒⠀⠀⠑⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠃⠚⠐⠂⢀⠈
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠚⠁⠀⠉⠑⠲⢼⡀⠀⠀⣆⠲⠀⡠⠠⢄⠀⠀⠀⠰⠞⠀⠀⢰⣤⣼⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠘⠄⡃⠀⠚⠃⣀⠨⠵⠤⣀⠉⠀⡟⠀⢶⡸⠀⠀⠀⠀⠀⠀⠘⣿⣭⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠔⡀⠀⠀⠑⢆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡰⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⣀⠀⢇⠀⠲⠆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⢀⠀⠱⣄⠊⠀⠘⢀⡤⠀⠀⠀⠀⠀⠀⡸⢁⣀⠀⠀⠱⢸⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠢⣌⣁⣄⢸⣇⣀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠰⢈⡁⠀⠀⠀⣿⡰⠊⢁⠑⡄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠈⠙⠷⢶⡷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠐⢣⠃⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠀⠀⠀⠀⢀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢼⢸⡆⠀⠀⣷⠀⠀⠀⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⡇⠀⠀⠀⡄⢴⣯⣿⡄⠀⠀⠀⠀⠀⠀⢀⡀⢰⡇⠀⠀⠀⠀⠀⢸⣇⣿⣀⣾⣮⣇⣄⠖⣿⠀⣴⣠⣗⣷⢴⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣇⣸⣷⠸⡀⢀⣇⣿⣿⣿⣷⠂⠀⠀⠠⣄⣀⣸⡧⢸⣧⣰⣆⠀⢀⣈⣿⣿⣿⠟⠻⣿⣿⣿⠤⠿⣞⣻⣷⣹⣿⢉⠿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡂⢰⣿⣿⣿⣿⡈⡒⠘⣿⣿⣟⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⢻⠃⠀⠀⠹⢿⢛⣘⣧⣾⠛⣽⣟⠡⣛⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣆⣷⣿⣿⣿⣿⡿⢳⡏⠀⢻⣿⣿⠁⢅⢠⡀⠀⠀⡙⠈⢿⣿⣿⡿⠋⠃⠰⠴⠦⣴⡏⠀⠀⠀⠀⠼⣟⣡⡿⣟⠛⣿⠋⣸⣿⣗⣠⣿
⠀⠀⠀⠀⣠⣴⣿⣿⣻⣿⣿⣿⣻⣿⢋⣽⠀⠀⠘⣿⠟⣀⠈⣟⣰⣤⣴⡁⠈⠙⣿⣿⠀⠀⠀⠀⠗⠀⢈⡧⠀⠘⠐⠦⠀⣸⣿⠀⢸⣷⣾⠿⣗⡼⠳⣄⡀
⠀⠀⠀⣸⣿⣿⣿⣷⣿⣿⣿⣿⠽⢿⣼⠋⠀⠀⠀⣿⠍⠀⠀⢿⣌⣿⠇⠀⠀⢀⠻⣿⣿⣤⣤⣶⣄⡾⠁⠀⠀⠀⢀⠀⠀⢈⡿⣦⣿⢽⣿⠂⣹⣿⣤⡧⠁
⠀⠀⢠⣿⣿⠿⠟⠛⠋⠁⠀⠀⢀⠀⠀⠀⠀⠀⠐⠏⠀⠑⠒⢘⠛⠟⠀⠈⢁⡠⠄⠈⠀⠀⠀⠙⠘⠳⠀⠀⠰⠛⠻⠟⠟⢿⣤⣾⠸⠯⠐⠂⠉⢧⠀⠈⠆
⠀⠀⠈⠉⠀⠀⢺⠇⠀⠀⠐⠚⢻⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠉⠉⠉⠁⠋⠛⠿⠶⠆⠊⢉⣉⡲⠏⣹⣦⡨⠷⢶⣄⠀⠀⠠⢄⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡀⠤⠤⣄⠀⠐⠶⣦⡀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠛⠓⠒⠚⠛⠛⠻⠓⠒⠺⠿⠀⠀⣀⣄⣀⣀⣀⠛⣫⣉⣱⡖⠂⠉⣳⣀⣀⣸⡧⠄
⠀⢠⠀⠰⠖⠀⢀⣠⣤⣄⠄⠀⠀⢠⡀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠙⠛⠛⠿⣷⣶⣾⣤⣼⣿⣠⡀⠰⣿⣆⢀⡄⣤⢷⣀⡄⡀⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣄⣩⣿⣾⣧⣽⣧⣿⣷⣞⣻⢻⡄⣿⡆⠀⠄⠀⡀⠀⠀⠀⢰⣧⣦⡀⢂⢰⣄⠀⠀⠀⠘⣆⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⢿⡿⢿⣿⣟⣉⣉⣹⣿⣿⣿⡇⠀⢠⡄⣧⣶⣄⣦⢸⡿⣿⡇⠘⡞⣿⠀⠀⠀⡄⢻⢄⠀⢠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⠏⠛⠛⠛⠾⣓⠀⠠⠅⡽⢳⣿⣿⣼⣿⣿⣷⢀⣦⣿⠄⠀⠀⢸⢸⣿⡆⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣉⣉⣁⣈⡁⠀⠀⢰⣉⣉⣩⡍⣻⣿⣿⣭⣄⣀⣦⠚⠀⢺⣿⢿⡟⠋⠁⢓⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠑⠈⠙⠋⠉⠍⠭⢙⣿⣦⡤⢤⣶⣾⣟⡿⣯⣭⡭⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⢶⠲⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠞⡇⢿⢹⣿⠾⡵⠆⢀⣴⣶⣀⣶⣿⣿⣿⣿⣦⠀⠀⠉⠙⠋⠉⠛⠛⠛⠛⠓⠒⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠖⠮⠅⢀⠸⢾⣿⣿⣿⣷⣶⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠌⠛⢻⠛⠛⠟⠋⢩⢥⠌⠟⠗⣠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠛⠚⠻⣶⣌⣁⡋⢠⠭⠬⣿⣶⡆⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠹⠇⡉⠲⠒⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠋⣱⣾⣿⣷⣿⡟⠛⠈⡻⠋⠁⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠈⠛⠋⠀⣿⡀⠀⢀⠀⠀⠠⣿⣇⠀⠀⣾⣇⠀⠀⠀⠀⠃⠀⠀⠀⠀⣧
⣶⣶⣿⡿⠀⠀⠀⠀⢀⡄⠁⠀⣰⣿⠆⠀⠀⣼⣿⡇⠀⣼⡇⠀⣨⣿⣧⡀⢠⣿⣧⡀⠀⢸⡄⠀⠀⠀⠀⣰⣿
⣿⣿⡿⠁⣀⠀⠀⠀⠈⠁⠀⠀⣿⣿⠇⠀⢘⣻⣿⠷⠄⣿⡷⠀⣸⣿⣷⠀⡠⣿⣿⢀⣴⣿⣷⠀⠀⠀⣴⣿⣿
⣿⣿⡇⣼⣿⠀⠀⠀⠀⠀⠀⠠⢿⡿⣦⠀⣈⣿⣿⣁⠰⣿⡟⠒⢻⣿⡏⣾⣿⣿⡷⣶⣿⣿⠷⠀⠀⠀⠻⢿⣿
⣿⣿⣧⣿⡏⠀⠀⠀⠀⠀⢰⣗⢿⣷⣤⠀⢻⣿⣿⣟⣰⣿⣿⢐⣯⣿⣧⣾⣿⣿⡟⠂⢾⣿⣷⠀⠀⠀⠀⠀⣿
⠻⢿⣿⣿⠃⠀⠀⠀⠀⢠⣿⣿⣿⣿⣤⠀⢾⣿⣿⢛⣇⣿⣏⣸⣿⣿⡯⣏⠹⣿⢷⣆⣹⣿⣟⠀⠀⠀⠀⠀⡟
⠀⣼⣿⡏⠀⠠⠀⠀⠀⢼⣿⣿⣿⣿⣼⡹⡒⣿⣿⠘⣿⣿⣿⡟⣿⣻⡆⣰⣶⣿⣰⣏⣽⣿⣏⠁⠀⠀⠀⠀⡇
⢰⣿⣿⠁⢀⠆⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣷⡆⢿⣿⣿⡿⣿⣠⡮⠸⣾⣿⣽⣿⡏⣍⣽⣿⣟⠃⠀⠀⠀⠀⠃
⣾⣿⡟⠀⡼⠀⠀⠀⠀⢸⣿⡏⣼⣿⣿⣿⣿⣤⡟⣿⣾⣿⣿⣿⣷⣶⡏⡗⢸⣿⣨⣽⣿⣿⡌⠁
⣿⣿⡇⢰⠇⠀⠀⠀⠐⠻⣿⡿⡿⠛⠟⣿⢷⢿⠉⢿⣿⣿⡏⢹⣿⣿⣷⠇⢨⣿⣿⣿⣿⡇
⣿⣿⣷⡟⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⢸⣿⠈⠀⢿⣾⠿⡏⣵⡜⣿⣿⣿⣶⡇⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⢸⣿⡄⠀⠘⣿⣾⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⣼
⣿⣿⡏⠀⠀⠀⠀⠀⢰⢠⠏⠀⠀⠀⣿⣿⡇⠀⠀⠸⣿⣀⣼⣿⣿⣿⣿⣿⡿⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⣠⣿
⣿⣿⡇⠀⠀⠀⠀⠀⢛⠿⠻⠿⠶⠶⠿⠿⠳⣤⠀⣀⣿⣿⣿⣿⣛⣋⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⣰⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠐⠿⣿⣷⣲⣶⣶⣶⣷⣶⣠⣶⣶⢶⣶⣼⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠟⠛⡛⠿⠯⠾⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢀⣿
⣿⣿⣷⣤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⢤⣤⣤⠤⠤⠀⣾⣧⣤⣤⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⣀⠘⠒⡀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠹⣄⠀⠈⠂⠀⠀⠀⠀⢠⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢇⠀⠀⠨⣆⠴⠁⠀⠀⠀⠀⠸⡇
⠀⣠⡠⣄⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉⠀⠈⠻⣆⠀⠀⠀⠀⠀⢄⣡⠄
⠀⠀⠀⠮⠿⢦⣀⠀⠀⣀⠠⠝⠓⠦⣀⠀⠀⠀⠀⣀⣹⣆⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠘⣡⢘⡅⠀⠀⠀⠀⠀⠨⠟⠚⠛⠋⠉⠉⣩⠽⠒⠢⠄⣩⡆⠈⠳⣄
⠀⠀⠀⠀⠶⢦⡁⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠖⠛⠛⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⣨⠐⠻⠶⣦⣄⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⡄⠀⠀⢀⠀⠈⠉⠛⠶⠷⢶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠷⣶⣾⣿⣇⠀⠀⠀⠀⠀⠀⢬⠁⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠉⠉⠀⠀⠀⠀⠀⠀⠲⢀⠎⠀⠂⣀⠐⠂
⠀⡀⠀⢸⡄⠀⠀⠀⠀⠐⣄⠀⠀⠀⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠐⠲⠉
⠀⠘⢶⣄⢻⡄⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡷⢸⡿⠿⡗⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠉⠻⣿⣷⣾⣿⣶⣶⡆⠀⠀⠀⠀⠀⣾⣿⣿⣵⠀⣇⣴⣿⣿⣧⠀⠀⠀⠀⠀⠸⣯⠸⠇⣀⣴⣿⠁
⠀⠀⠀⠀⢀⣀⣠⣴⣿⡿⠛⠛⢋⠝⠀⠀⠀⠀⠀⠘⠛⠁⢷⡼⢁⠜⢻⡿⠋⠀⠀⠀⠀⠀⠀⠘⢆⢸⣿⡟⢃⡀
⠀⠈⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣤⣶⣿⢪⣷⠟⢁⡀⠀⠀⠀⠀⠀⠉⠛⠉⠙⠛⠛⠛⠛⠛⠛⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣠⣿⣿⡿⣾⠁⠾⣿⡿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣤⡜⢿⣿⣿⠙⣷⡴⠻⣍⡙⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣯⢟⠻⠛⠀⠀⠀⢠⣿⠀⢀⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠙⢦⣰⣆⠀⢸⣇⠠⣶⣿⣿⣿⡗⠉
⠀⠀⠀⠀⠀⠀⠀⠠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣼⡟⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⡟⠟⠀⠒⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠉⠊⠓
⠀⠀⠀⠀⠀⠸⣶⣄⠸⢆⠀⠀⠀⠈⠉⠋⠀⠀⠀⢹⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⢙⣻⣧⣼⣤⣶⣶⣦⣤⣄⠀⠀⠀⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⠿⠿⠖⠚⠛⠂
⠀⠀⠀⣴⣾⣿⣿⡟⠉⠙⠻⠀⠈⠉⠉⠀⠀⠀⠀⢀⣀⣻⣿⣀⣀⣀⣀⣠⢔⣒⠼⠟⠋⠁
⠀⠀⠰⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠴⠖⠚⠛⢉⣉⣉⣉⣹⣿⣿⣯⣉⣉⣉⠉⠙⠛⠛⢷⣶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠙⠿⢿⠷⣶⣤⣙⡛⠿⣶⣶⢶⣦⣤⣤⣄⡀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣾⣿⣿⣷⣶⣷⣶⣾⣿⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣛⣿⣻⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠛⠁⠀⠀⣀⡀⣠⣤⢠⣤⠤⠤⠤⣤⢤⣤⣤⣌⣀⠀⠀⠀⠀⢰⡦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠂⠉⠀⠄⠁⢠⡤⠀⠀⠀⠀⠀⡶⠿⠿⠟⠿⣿⣿⣿⣶⣧⣄⡈⠁⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠦⠀⠀⠀⠀⢠⠀⠰⣖⣀⣠⣤⣤⡶⠂⠀⢀⠀⠉⠉⠙⠃⣭⠉⠻⣿⣿⡇⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢦⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⢁⠀⠁⢙⠂⠔⠚⢛⣻⣦⣀⠀⠙⢀⣀⣿⣿⠇⠀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⡙⠒⠤⣀⣀⠀⠀⠀⠛⠁⠈⣉⠑⢀⡀⠀⠀⠶⠿⠿⡶⢶⡯⠟⣁⡴⢳⣾⠃⢀⣀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠙⢶⣦⣮⣍⠁⠀⠀⠀⠀⠠⠶⠿⠷⠤⠰⠿⠒⢛⣍⣡⠀⠀⣿⣿⣰⣿⡟⠉⠉⠻⣖⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⠃⠀⠀⠀⢀⣰⢶⠗⠀⠈⠉⠛⡀⠘⠃⣿⢿⣿⠁⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣼⣏⣀⣠⣴⠿⠋⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣰⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⣿⣅⣉⣉⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠷⠊⠙⠉⠉⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⣿⣟⠿⠿⢷⣶⣤⣄
⠀⠀⠀⠀⠀⠀⢠⠠⠃⠀⠀⠀⠀⠀⠴⣻⣷⣵⣆⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡆⠀⡀⠀⠀⣰⠽⣿⡿⣋⡬⣿⠀⠈⠀⡈⢹⣷⡄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢴⡁⢹⣧⣠⣹⣿⣆⢀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠁⠀⢀⣩⠾⣿⡾⣥⣾⣷⠤⡀⠀⠐⠀⠘⣿⠄
⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠉⣹⣭⣿⡋⠥⣺⠏⣻⣷⣷⣦⣄⣀⡀⠀⣀⠀⡂⢀⣉⣀⣴⣾⣿⣱⢊⣽⣓⣺⣿⣾⡷⠏⠀⠁⠀⢀⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢛⣡⠀⢀⠉⠉⠛⠻⠿⠿⢿⣿⣿⠿⣿⡿⠿⠿⣿⣻⢍⣫⡙⣌⠛⠉⠀⠀⠀⠀⢀⠠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⣥⠬⠋⠀⣴⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠟⠋⠛⠉⠀⠀⢀⣥⢴⢊⡿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣄⣀⣀⣀⣀⠠⣄⣀⠀⡀⠤⣶⢎⢃⠈⠿⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠓⠂⠀⠂⠁⠁⠀⠀⠀⠘⠓⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠂⢀
⠀⠀⠀⠀⣾⣀⣤⣴⣶⣾⣿⣿⡛⢿⣿⣿⣿⣿⣯⣙⣻⣛⣛⣿⣿⠿⣷⣶⣤⣀⠀⢠⡁⠀⠀⠀⢀
⠀⠀⠀⢰⡝⢿⣟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣽⣿⡷⢞⣴⣧⡶⡋⠀⠀⢍⣆
⠀⠀⠀⠘⠃⠀⠊⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣛⣭⣴⣻⣿⣿⡿⠁⠀⠀⠀⣿
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠀⠈⢸⣿⣿⢸⡿⠟⠁⠀⠀⠀⠀⡏
⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⠁⠀⠀⠀⡠⠈
⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣃⣀⡤⠖⣉⠔⠁
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⣿⢟⣋⡡⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠶⠖⠶⠾⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⣀⡄⢄⣀⢐⠀⡀
⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣄⣲⣶⠛⠓⣻⠀⠀⠀⠀⠀⠠⠂⡔⠂⡜⡲⡠⣼⣴⣸⣧⣾⡷⣧⢢⡎⢠⡀
⠀⠀⠀⠀⠀⢿⠛⢦⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡔⣻⣭⡿⣃⣾⠏⠀⠀⠀⠀⠈⠀⢱⣧⣼⣦⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡉⠻⠿⢿⣯⣽⣿⣏⠁⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠛⠶⠶⠿⠳⡟⠃⢹⢻⣧⡀⠀⠀⠀⠀⢠⠴⡻⠛⠀⠸⣿⣿⢿⣿⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣧⣴⣎⠀⠀⠀⠀⠀⠀⠙⢶⡿⠀⠹⣿⣦⠀⠀⠀⠀⠀⠁⠀⠀⠀⢹⡟⠀⣿⠐⠙⢻⡟⣻⡟⠉⠉⢹⡿⢿⣦⡭⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣮⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢳⡀⠀⠀⠀⠀⠀⠠⠀⢸⠗⠾⡟⢀⣰⡟⠀⣿⠁⠀⢀⡟⠀⠀⠗
⠀⠀⠀⠀⠀⠀⢀⣤⣿⡿⠻⠉⠋⣝⠳⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠹⣹⡅⠈⠱⣼⢺⠀⣤⣿⠀⣠⠏
⠀⠀⠀⠀⠀⢴⣛⣿⣿⡃⠀⠀⠀⠀⢻⣿⣿⣷⣦⠄⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠉⢳⡀⠀⠺⠀⠀⣿⢏⠟⠁
⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣶⣄⠀⠘⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠳⣄⠃⣂⠀⢉⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢹⠁⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢪⣾⣷⠎⠙⠓⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠈⢿⣿⢿⣧⣶⣶⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡸⣿⣷⣴⣷⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⣀⣀⣤⣶⣶⣶⠿⠿⠿⠛⠋⠉⠉⠙⢾⣻⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠀⠘⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⠦⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⠀⠀⠀⠀⠀⠀⠀⠏
⠀⡀⣀⣰⠀⢀⡀⡀⣄⠀⢀⣰⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⢠⣷⣿⣿⣾⣾⣿⣷⣿⣷⣿⣿⣿⡿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡆⠀⠠⠄⠀⠀⠀⠀⠀⢬⡧
⠸⠟⠟⠿⣿⡿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢺⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠩⢍⡧⠄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣣⠀⠳⠪⣽⣷⣂
⢀⣰⣷⣠⣼⣥⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⢠⣿⣀⠛⢭⣽⣯⠶
⠀⣿⣿⣿⣿⣿⠛⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡧⠀⠰⢬⣿⠔⠂⠰⣬⣷⠞
⠀⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣥⣷⣄⠨⠽⣿⠭⠄⡼⣿⣿⣟

⠀⠀⠀⠀⠀⠀⣀⣔⡀⠀⠀⠀⠀⠀⠀⠀⠠⠼⢆⠀⠀⠀⠀⠀⡂⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠆⠠⠤⠅⠀⠀⠀⣶⣺⣇⠀⠀⠚⢚⠄⠀⠀⠀⠀⢉⢀⣰⢉⠏⠀⠀⠀⠀⠀⠀⡤⢡⡤⠆
⠀⠀⠀⠀⡄⠲⣚⠃⠀⠀⠀⠀⠸⠍⠇⢀⠰⡶⢰⡋⠀⠀⠀⠀⣟⣬⠁⢸⠁⢠⡖⠀⠀⠀⠔⢂⠀⠰⢭⠡
⠀⠀⠀⠐⠋⠁⠹⣆⠀⠀⠀⠀⠘⠓⣀⠩⠔⣢⠦⠀⠀⠀⠀⠀⠙⣡⣀⣿⡰⠋⠀⠀⠀⠀⠀⡀⢳⠜⠉⣁⡲
⠀⠀⠀⠴⠆⠢⠀⠇⠀⠀⠀⠀⠀⠀⠐⠓⠠⢈⡶⠂⠀⠀⠀⠀⠙⡛⢸⣟⠁⠀⠀⠀⠀⠀⠀⠁⠹⢛⣋⡼⠁
⠀⠀⠀⠀⠀⣀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣀⢂⠈⠀⠀⠀⠀⠀⠀⢠⣼⢟⣡⠀⠀⠀⠀⠀⠀⠀⠀⢘⣭⡈⠁
⠀⠀⣀⡄⠚⠛⠃⠉⠂⠀⠀⠀⠀⠀⠀⠙⢉⡛⠀⠀⠀⠀⠀⠀⠀⠛⠼⠁⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋

⠀⢻⣿⣿⠀⠀⠀⠀⠉⠙⣿⣿⣧⠀⢰⣿⣿⠉⠉⠛⠛⠀⠘⠿⠿⠿⠟⠁⠀⣨⣿⣿⠀⠀⣿⣿⠁⢸⣿⣿⡏
⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⣼⣿⡿⠀⢹⣿⣿⣄⠀⠀⠀⠀⣠⣴⣶⣤⡀⠐⠿⠿⠟⠁⠀⠀⣿⣿⡇⠘⢿⣿⠇
⡀⠘⣿⣿⣧⣄⠀⠀⠀⢰⣿⡿⠃⠀⠈⠻⢿⣿⣷⣦⡀⠰⠿⠿⢿⣿⣿⡄⢀⣄⣀⠀⢀⣠⣿⣿⠀⠀⠀⣠⣤
⣷⠀⠈⠻⣿⣿⣿⣿⣿⡿⠟⠁⠀⢀⡄⠀⠀⠈⠛⣿⣿⡆⠀⠀⢸⣿⣿⠁⠈⠻⠿⠿⠿⠿⠛⠁⠀⣰⣿⡿⣿
⠏⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢿⣷⣀⠀⠀⣠⣾⣿⡏⠀⠀⢿⣿⣿⣄⣀⣤⣄⡀⠀⠀⠀⢀⠀⠙⠿⣴⣿
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠘⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣦⣀⣤⣿⣇⠀⠘⣿⣿
⣿⣿⣷⣆⠀⣼⣿⣿⠟⠛⢿⣿⣷⡀⠀⠀⠉⣁⣀⠀⠀⢀⣠⣤⣄⡀⠉⠉⠁⠀⠙⢿⣿⡿⠛⠻⠋⠀⠀⠸⢿
⠀⣸⣿⡟⠀⣿⣿⣿⣀⢀⣼⣿⣿⠇⠀⢰⣿⣿⣿⣷⠀⠘⠛⢿⣿⣿⡄⠀⠀⠀⠀⢀⣀
⣰⣿⣿⠀⠀⠙⢿⣿⣿⣿⣿⣿⠟⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⣄⠀⢰⣿⣿⣷⣆
⠈⠻⣿⣷⡄⠀⠀⠈⠉⠉⠉⠀⠀⠀⢠⣾⣿⣿⠏⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠘⣿⠈⠻⣿⣿⣿⡏⠉⢿⣿
⠀⠀⠀⣿⡇⠀⢀⣤⡄⠀⢰⣦⣤⡀⢸⣿⣿⣷⣶⣄⠀⠀⠘⣿⣿⣿⣀⡀⠀⠀⠐⠺⠇⠀⢉⠻⠿⠃⠀⢸⣿
⠀⠀⠀⢸⣿⣾⣿⡿⠃⠀⠀⣿⡿⠃⠀⠉⢻⣿⣿⣿⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣦⠀⠀⣾⣿⣿⣷⣦⣴⣿⡟
⣀⡀⠀⠀⠉⠉⢀⣤⣶⣶⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⣄⠀⠀⠀⠀⠉⠉⠛⠻⣿⣿⡇⠀⠿⠏⠙⠛⠛⠛⠋⠁
⣿⣿⣷⣤⡀⠀⣾⣿⣿⠿⠛⠛⠁⣠⣴⣦⣄⠘⠻⣿⣿⣷⣶⣿⣿⠇⠀⠀⢀⣿⣿⠀⠀⠀⠀⢀⣤⣄⡀⢀⣾
⠋⠛⢿⣿⣿⣿⣿⣿⡏⠀⠀⢀⣾⣿⠿⢿⣿⣷⡀⠀⠉⠛⠛⠛⠉⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⣸⣿⣿⡷⠸⣿
⢀⣤⡀⠉⠛⠛⠛⠉⠀⠀⠀⣿⣿⡇⠀⠀⠁⢹⣷⠀⠀⠀⠀⢀⣠⣤⣀⠀⠘⢻⣿⣿⣷⣶⣾⣿⣿⠟⠁⠀⠉
⣹⣿⣿⠀⢠⣶⣿⣿⣦⣄⠀⢸⣿⣷⣄⠀⠀⠈⢿⣧⠀⠀⣼⣿⡿⠿⣿⣷⠀⠀⠈⠙⠿⠿⠟⠛⠁⢠⣴⣤⣄
⣿⣿⠏⠀⣿⣿⡏⠀⣸⣿⠀⠀⠙⣿⣿⣧⠀⠀⠻⣿⣷⣾⣿⡿⠀⠀⠘⠛⠀⠀⢀⣀⠀⠀⠀⠀⠀⢻⣿⠛⠿
⠀⠀⠀⠀⠸⢿⣿⣟⠋⠁⠀⠀⠀⣸⣿⣿⠀⠀⠀⠈⠛⠛⠋⣠⣤⣶⣄⠀⠀⢰⣿⠿⢿⣷⣤⣤⣴⣿⡿
⣶⣤⣀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠘⢿⡫⠃⠀⠀⠀⠀⠀⠀⣼⡿⠛⠻⣿⣷⠀⢿⣿⡀⠀⠀⠈⠙⠛⠉⠀⣠⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣴⢟⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢸⣷⡞⠁⠈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⣸⢾⣿⣯
⠀⠀⠀⠀⠀⠀⣰⢿⣿⣿⣆⣸⣿⣿⣿⣷⠀⠀⠀⢰
⠀⠀⠀⠀⠀⢠⡏⣺⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢠⣾⡀
⠀⠀⠀⠀⠀⣾⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣸⣿⡧
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴
⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣷
⠀⠀⠀⠀⠀⣿⡻⢿⣿⣿⣿⡿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢻⡿⠿⢟⣿⣿⣷⣤⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡏⣹⠿⣿⣦⣴⣦⣀⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠘⣷⣶⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⠿⠯⠀⠀⠈⠉⠁⠉⠁⠀⠀⠁⠀⠉⠉⠉⠻⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⠋⡁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠠⢾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣟⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢻⠇⠀⠀⢀⣀⣤⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⣇⣸⣤⣶⣾⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣾⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢰⠇⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⢠⡏⠀⢠⡟⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⡾⠀⢀⡾⠀⠀⣰⠏⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡿⠀⣸⠇⠀⣼⠃⠀⣰⠏⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠟⠛⠛⢹⡇⠀⣿⠀⢠⡏⠀⢠⡏⠀⢀⡞⠘⠛⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣩⡴⠞⣋⣁⠀⢸⡇⠀⣿⠀⢸⡇⠀⢸⡃⠀⢸⠇⠀⠀⠒⠤⣌⡙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢺⣿⣾⣟⣭⣤⣴⣾⣇⣶⣿⣰⣾⡇⣶⣾⣧⣦⣾⣠⣄⣈⠙⠲⣦⣝⠂⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠈⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠖⠀⣀⣴⠟⢸⣛⡷⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣌⠙⠂⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠋⠉⠉⠉⠉⣁⣀⣠⣤⠶⠟⣫⣴⡇⣚⣛⠲⢤⡈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣝⠓⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠛⢋⣉⣩⣥⣴⡾⠿⣛⣥⠀⠉⠉⠙⢷⣷⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠞⠃⢹⣟⠷⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⣉⣉⣭⣴⣶⠿⢛⡅⠀⠒⢂⣠⢿⢏⠄⣾⠁
⠀⠀⠀⠀⠀⠀⢀⣴⠾⣛⡭⠔⣀⠀⠀⠀⢿⡛⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠛⠛⠛⣛⣋⣩⣥⣶⠾⡛⢡⡶⢞⣫⣵⡿⢋⡾⢣⣄
⠀⠀⠀⠀⢀⣴⠏⣡⠞⢫⡴⢋⣡⠔⠀⠀⠈⢿⡷⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠛⠛⣛⣋⣭⣵⣶⠿⢡⣾⣿⠿⣛⣭⠾⠋⠀⠠⡉⢳⣄
⠀⠀⠀⠀⣼⠃⣸⡏⢰⡏⠠⡟⠁⣴⠉⠀⠀⠈⢻⣷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⣛⣋⣩⣭⣶⠞⣡⣿⣷⣶⣿⣿⣷⡄⢦⡘⢦⢹⡄⢻⡆
⠀⠀⠀⠀⢹⣆⠸⣧⡈⠷⣄⡻⢦⣌⠳⠤⠀⠀⠀⠙⢿⣖⠀⠀⠀⠀⠀⠀⠀⢀⣉⣉⣉⣉⣩⣭⣭⣶⣾⣴⣿⣯⢿⣿⠹⣿⡌⣿⠈⡧⢸⠀⢁⣼⠃
⠀⠀⠀⠀⠀⠙⢦⣝⠻⣶⣌⡛⠶⢬⣝⡓⠀⠀⠀⠀⠀⠙⠿⣷⣶⠦⢤⣤⣤⣤⣬⣭⡭⢷⣿⣿⣿⣿⠿⣣⣿⡟⣸⣿⢀⣿⢣⠏⣰⠃⢈⣤⡞⠁
⠀⠀⠀⠀⠀⠀⠰⠿⠷⢦⣍⣛⠷⠶⣤⣉⡉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠶⠶⠶⢖⣛⣛⣛⣭⣥⡶⠿⢛⣩⣾⠟⠡⠞⠁⢀⣠⣤⣾⣿⡿⠯⠍
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣩⣿⣷⣶⣦⣬⣅⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣉⣭⣭⣭⣭⠵⠶⠶⣛⣛⣉⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣯⣉⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠶⠿⠿⠿⠿⢿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠶⠶⠶⠶⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣉⣉⣉⣉⣉⣩⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣋⣉⣉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⠉⠉⠉⠁

⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⢳⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻
⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⣻⣿⣿⠟⠿⣿⣾⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢠⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣶⣦⣾⣿⣿⣿⣿⣿⣿⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣿⠃⣹⠇⠀⠀⠀⣤⣴⣶⣶⣾⣿⠋⢻⣿⣿⡛⠁⠀⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠃⠰⣿⣷⠀⠀⠀⠀⠈⠉⠙⠋⠹⣷⣴⣿⣿⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠛⠙⠏⣻⣤⣄⣀⣀⡀
⠀⢈⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠙⢿⣿⣿⣧⣄⣬⣤⣆⣤⣤⣴⣿⣿⡿⠟⠋⠉⠁
⢀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⡟⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣻⡿⣧⣤⠀⠀⠀⠀⠀⠀⠀⡿⢹⣿⡿⠛⣿⣿⠿⠿⣿⣿⣿⣧⠀⢀⣴⣶⣄⣢⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣽⣿⣿⠀⠀⠀⠀⠀⢀⣰⡄
⡟⠁⠉⠛⠀⠀⠀⠀⠀⠀⠐⣿⢿⣿⣲⣀⡀⡻⡆⣀⡼⣿⡿⢿⣿⣏⣨⣿⣩⣿⢋⣿⣿⡿⣻⣉⠀⣌⣩⠿⣜⣿⢟⠀⠀⠀⠀⠀⢨⣿⡀
⡁⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⢉⣻⣿⣿⢿⢫⣿⢷⣾⣵⢿⣩⠁⠙⠿⣿⣖⣾⣿⣿⡿⡛⢿⣷⣿⠿⣿⣧⣽⡆⠀⠀⠀⠀⠀⠈⢻⣿⡄
⡶⠂⠠⣷⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣟⣽⡿⣍⡋⠀⠈⢹⣯⣟⣷⣦⣽⣾⣿⣟⡋⣤⣴⣿⡗⣋⣁⣼⣏⣍⣽⡇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆
⠓⠀⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⡻⠭⢩⢩⡗⣈⣻⣿⣷⣶⡿⣿⣿⣿⠿⠯⣽⣿⣾⣿⣻⣍⣥⣹⣿⠭⣿⡵⠤⣷⡄⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⣠⣬⣨⣶⣠⣿⠾⢿⡿⠟⢛⣋⣉⠱⣿⣿⣿⣿⣿⡶⠁⠈⠛⠿⠿⣶⣾⣷⣦⣷⣾⣁⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠹
⢀⣿⣿⡗⣠⣾⡀⠀⠀⠀⠉⣿⣿⣯⣉⣁⣽⣿⠁⠀⢻⡿⠀⣀⣈⣭⣿⣿⣿⣿⣿⣶⡀⣤⣀⣹⣻⡷⣿⠿⣿⣿⣿⣿⠃
⣸⣿⣿⢱⣿⣿⠇⠀⠀⠀⠀⠈⠙⠻⣯⡻⣾⣶⣿⢶⡆⢘⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠁⠨⠭⢁⣈⣠⣨⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⢠⡀
⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⡄⠀⠀⠉⢻⣿⣿⣽⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⢠⣶⣶⣶⣶⡿⣿⣽⡋⠋⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣧
⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢿⠟⢀⡀⠀⢸⡟⢻⡆⣿⣿⣿⣿⡿⢿⣿⣾⡶⢾⡿⢓⢻⣿⢡⣿⣿⠟⠀⣀⡙⠛⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡆
⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⡀⠈⠁⠀⢸⣿⠐⠙⣿⣯⣼⣿⡀⡌⢿⢻⠀⣿⣷⣿⣿⣥⣻⢿⣿⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠚⠸⣿⢠⣶⣿⣿⣿⣿⣿⣧⣸⠀⢂⣿⣿⣿⣿⡟⠁⢸⣿⣀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⣠⣍⠛⠟⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⡿⢿⠋⠀⢸⣿⠛⣿⠿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⠃⢀⣀⡀⠀⠀⠀⠀⠀⠇⠀⠸⣿⣿⠂⠀⣿⣿⣿⡇⠹⣿⣿⣄⣿⣿⠋⠀⠀⠀⠀⢸⣿⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡿
⣿⣿⣿⣿⣠⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⢁⡄⠀⢸⣿⣿⡇⠀⢻⣿⣿⡟⣧⣤⣤⡴⠂⠀⢸⠟⢀⣤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⡇⠀⣿⡏⠋⠀⣿⠿⣿⡅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢀⠈⠙⠛⠛⠀⠘⠃⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣓⢯⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠓⠘⠀⣦⡀
⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠰⠏⢩⣿⡿⣭⠁⠀⢀⣴⣦⡤⣀⠀⠀⠀⣿⣿⣦⣤⣶⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢰⡷⢶⢀⠙⠁⠀⠄⣤⡄⠀⠀⠙⠞⠉⠁⠀⢰⣯⢞⣻⠿⠞⠁⠀⣀⣿⣿⣿⣿⣿⣿⣿⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣦⣸⣿⠦
⠈⠀⠀⠶⠀⠀⡀⠀⠀⠄⣴⣦⣦⠀⠀⠀⠀⠈⢁⣼⣷⠀⠀⠀⠀⠙⣏⠙⠛⠛⠛⠋⠙⢢⣶⡔⠁⢀⡔⠆⠀⠀⠀⠘⠛⠓⠂
⠀⠀⠀⠀⠀⢸⡿⠀⠲⠖⠀⠈⠛⠀⠀⠀⠀⢠⣟⡵⢫⣦⣵⠂⠀⠐⠁⠀⣤⠀⢶⡀⠰⢟⡟⠻⢄⢾⡷⠤⡀
⠀⠀⠀⠀⠀⠠⢆⡆⠀⠀⣠⣶⡆⠀⠿⠿⠆⣼⠅⠀⢸⡿⡟⠀⠀⠀⢀⢤⣽⣶⠀⡿⠠⠈⣟⠀⣿⣎⠀⠀⣻⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠀⠀⢀⣀⣤⣾⣿⣟⣡⠀⠑⠃⠒⡋⡅⡠⢋⢁⠛⣤⠀⠘⡄⡙⠂⣹⠯⠀⠀⠈⠀⣤⣄
⠀⠀⠀⠀⠋⠿⠀⠀⠀⢸⣦⡀⠀⠈⠻⣿⣿⣿⡿⠋⠀⢀⠤⣨⡖⢫⢣⣡⠀⢇⡅⢣⣴⠇⢿⡾⠛⢷⠀⠀⠺⣄⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⡥⠀⠀⠀⠀⠀⠉⠁⢰⣦⣤⠈⢯⣟⡛⠀⠀⠈⠚⠋⠪⣵⣦⣬⡁⠀⠡⠵⢰⠀⠀⠰⣦⠟⠀⠀⢠⡄⡦⠀⠉⡉⠀⠘
⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⣲⣂⣔⡏⠛⢁⠂⣹⣿⠀⢀⡄⢠⡆⢺⣿⣿⣻⡟⣆⡀⠀⣀⠀⠀⠀⣎⢝⡉⢢⣤⠈⡡⢾⠛⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢸⠢⡤⠜⠪⡿⠏⠁⠀⣈⣄⣻⣿⠵⠛⣇⢸⡇⣸⠉⢉⠟⠉⢹⠙⠯⣾⣷⡶⠀⠉⠀⠉⣹⠲⠤⢥⡤⣀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠘⢧⡝⣈⢄⠐⠀⢁⣴⣿⣿⡜⣱⢦⡄⢸⡸⡇⡇⡴⢁⡤⢞⣵⣿⣿⣍⠛⠉⠀⠀⠀⠀⢸⠂⠀⠈⢽⣭⣷⠄⣸
⠀⠀⠀⠀⠀⠀⠀⡈⣧⣬⠀⢀⠿⢿⢉⣿⣿⣿⣻⠀⣌⢢⢟⡉⡉⠳⡫⠴⢾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢿⡀⠀⣰⣾⡿⣷⡰⠁
⠀⠀⠀⠀⡈⠂⠀⠀⠀⠊⠀⠸⡆⢸⠎⡼⠁⠐⢙⡀⠀⠉⠈⣶⠈⠂⠟⠿⡍⡫⢯⠉⠀⠀⣰⣶⣤⡀⠀⠀⠁⠀⠉⠺⣿⠛⠝⠟
⠀⠐⢄⠀⠑⠀⠀⠀⠀⠀⠀⠀⣏⢨⡴⡇⠀⣰⠟⣿⣇⠀⠀⠋⠀⠀⠀⠁⠊⣵⢋⣀⡀⢰⡿⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⠃⠁⠀⠘⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⢙⣋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠠⠠⡄⢀⠀⠀⢒⠒⠒⠯⣷⣢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣬⣜⠋⠀⣤⣉⡻⣿⢦⡀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡙⠋⢘⣿⣿⠄⡀
⠀⠀⠀⠀⢸⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣭⣿⡿⢠⣇⡴⠞⠉⠙⣦
⠀⠀⠀⠀⠘⣿⣮⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⣼⡟⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣶⣭⣟⣛⠻⠿⠿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣻⡍⡋⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣏⡙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⢡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣦⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣽⣇⠁⢤⣀⢀⠀⠀⠀⠀⠀⢀⣀⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⠿⠿⠦⠧⠤⠶⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠊⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢉⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠔⠊⠁⠂⣀⢀⣀⠔⡰⠁⠀⢀⠔⠀⡈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⢰⠁⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡿⠯⣁⡈⠀⠀⠀⠀⠈⠁⠠⠤⠀⠀⠀⠸⣀⡂⠔⠩⠄⢐⡂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣿⣤⣤⣉⣉⣀⣂⡀⠄⠀⠂⠼⠿⠿⠟⠓⠠⠖⢀⣀⣀⣀⣀⡺⠾⣃⠿⠀⠀⣀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢽⠙⠛⠻⠏⠿⠛⠛⠛⠒⠶⠒⠲⣶⣶⣶⣶⣾⡿⣿⣿⣿⣿⠛⣿⠃⢠⠔⠊⠁⠀⣀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣒⢀⣩⣭⠿⠿⣟⣛⠀⢑⡁⢸⠃⣠⠞⠉⠉⠉⢳⡀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⢀⡲⢒⣚⣿⡿⠽⢖⣀⠡⡂⢻⠞⠀⠀⠀⠀⠀⠀⣧⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⣤⠀⠠⠴⠶⣒⣻⡭⠄⣈⠁⣿⠀⠀⠀⠀⠀⠀⢀⡟⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠀⠒⣂⣀⣉⣭⡭⠤⠖⢀⠥⠀⡇⠀⠀⠀⠀⠀⣠⠎⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁⠬⠍⠭⠴⠶⣒⣛⡁⠐⠂⠀⣇⢀⡀⠤⠒⠋⠁⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⢀⣚⣛⣭⡭⠵⠀⢋⠄⢠⡷⠂⢀⣀⣤⠴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⠠⠴⠶⣒⣚⣫⡅⢐⠀⣼⡤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⠈⣉⣭⣭⣵⠖⠤⢋⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⣷⣍⠠⠀⠀⠀⠀⠀⣀⢀⣀⠐⣀⣐⣚⣿⣿⡿⠯⢈⣥⣏⣀⣀⣀⣀⣀
⠀⠀⠀⣀⣤⠴⠖⠒⠚⠹⠏⠉⠀⠀⠠⠤⠤⠿⣗⣦⣔⠀⠀⠀⠐⠀⢛⡀⣺⣿⣿⣿⣯⣧⣴⣿⠿⠿⠿⢿⣯⣍⣍⣉⠛⠛⠲⠶⣦⣤⣀
⠀⠀⢸⡁⣄⢠⡀⠀⠀⢎⠀⠀⠀⠀⠀⠰⠀⠀⠈⠣⠄⣀⣀⣀⣀⣀⣉⣍⣩⣶⣶⣶⣤⡦⠞⠁⣀⡠⠀⠀⡀⠀⠈⠉⣙⠆⠀⣠⢈⣹⣹⡇
⠀⠀⠀⠙⠳⢭⣛⡒⠶⠦⠤⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢉⠉⠉⠉⣉⣉⣡⣄⣀⣀⣀⣰⣶⣶⣶⣦⣤⣤⠤⠤⠶⠖⢛⣫⡽⠞⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⠦⣤⣤⣤⣀⣈⣉⣉⣉⡉⠉⠉⠉⠩⠉⠉⠩⠭⠉⠉⠩⠉⠉⣉⣉⣉⣉⣀⣤⣤⣤⠴⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣮⣵⣌⡥⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⡿⠀⣾⣿⣿⣍⣧⡄⠀⢠⣄⠧⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠶⠦⢀⣠⡶⢿⣜⣴⢗⠛⠋⠙⠋⠉⠟⠒⣦⡽⣶⣾⣤⣼⡝⢲⡆
⠀⠀⠀⠀⠀⠀⠀⢰⡶⣳⢎⣰⣟⣩⣿⠛⣴⣿⣏⣉⣹⡿⠚⣩⡑⠖⠶⠍⠛⢿⡽⠿⢣⡀⢘⣠⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⣿⣷⣿⣿⣿⣿⡾⣿⣿⣿⢛⡟⣿⣛⠻⣿⡀⣴⡤⡎⢱⡄⠑⠉⢠⣆⡇⣨⠷
⠀⠀⠀⠀⠀⠀⣀⡖⣄⡊⢠⣥⣴⣿⢿⣿⣿⡾⣿⡟⠓⢿⠶⠿⠶⠿⡷⠿⢷⢹⣷⡞⠀⠀⠈⠉⣷⡁⠒⢒⡆
⠀⠀⠀⠀⠀⠘⠷⣾⣿⣧⣼⣿⣿⣄⣿⡟⡃⢴⣾⠖⢻⣿⠿⠷⠆⠀⣰⠆⠀⠀⢭⣳⣀⡠⣶⣴⡶⠟⢣⡟
⠀⠀⠀⠀⠀⠀⠀⣹⣹⣿⣿⡿⢷⣤⣽⣷⣿⡿⣿⣿⣷⣷⣆⣸⣆⣾⣿⣦⣴⣏⣤⡾⣻⣿⣯⣭⢈⣿⣦⠸⠆
⠀⠀⠀⠀⢀⣠⣾⣿⣏⣿⣿⣶⣆⣹⡟⣿⣯⣗⣋⣿⣟⣝⠿⢿⣿⡿⣿⠆⡼⣿⢿⣿⣻⣿⣿⠋⠀⢳⡄
⠀⠀⠀⠀⠉⠉⠽⢿⣿⣼⣿⣿⣿⣽⣿⣿⣿⣻⣷⣺⣿⣏⣳⢾⣿⢋⣿⡤⠫⣷⣤⠤⠀⠀⠉⢦⣤⣅⡁⢉⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⣋⠀⢀⣝⢿⣿⠿⠫⠋⠉⠻⣿⣿⣄⠛⡾⠻⣿⢶⣶⣈⢘⡛⠁⠀⠠⡤⢀⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠈⠛⡿⠿⠟⠾⠃⠀⠀⢸⣿⡘⡖⢳⠀⢀⠙⠑⠿⠿⠇⠀⣠⣀⣠⣤⡂⣀⡄
⠀⠀⠐⠖⢀⣶⣞⢢⢄⡠⢀⣴⠶⣄⠙⡃⢀⡀⠐⠂⠀⣼⣿⠃⢠⢸⡄⠛⠃⠠⠂⠚⠛⠨⠉⠩⠉⠉⠉⠉⠁⠂
⠀⠀⠙⢃⢸⣿⡷⢿⢦⡇⢺⡿⣿⣼⢫⢱⣿⣬⣱⠺⣲⡿⣿⠀⣾⠴⣇⠰⡄⣰⣖⣓⠢⠀⣤⠦⡀⢀
⠀⠀⠀⠐⠡⠀⠒⠊⠃⠈⠠⠒⠃⠨⠏⠀⣨⣽⣷⣶⣿⣴⠋⣴⣿⣤⡹⠶⣴⢬⣍⣋⡛⡺⣛⡗⢺⢴⣯⣆⢠⣀⣀
⠀⠀⠀⠀⠀⠐⠒⣒⠛⣛⠻⠖⢺⠿⢻⡟⢛⡉⠀⠋⠉⠀⠀⡀⠀⠀⠉⠛⠲⠶⠚⠲⠯⠙⠋⠉⠑⠒⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠛⠂⠲⠴⠀⠠⡬⠛⠛⠂⠂⠂⠤⠤⠌⠒⠐⠂⠀⠀⠈⠐⠀⠀⠀⠁

⡄⠀⠀⢠⠀⠀⠀⠀⠀⠘⠢⢌⣉⡙⠒⠣⣄⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⢘⣷⡂⠀⢻⠀⣇⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢸⡇⠀⡇⠀⠀⠠⡒⡉
⠀⠀⢀⠎⠀⠀⠀⠀⠀⣤⣀⡀⠠⢈⠑⠀⠀⠀⢀⠘⠀⠀⠃⠄⠀⣠⣑⣒⡮⣧⠠⠀⠀⠏⣸⠀⠸⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁⠸⣄⠀⠀⠄⣂⡱⠭⠖
⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠁⠀⢄⠀⠀⠈⢀⠀⢉⠉⠿⣷⣐⠀⠐⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠑⠂⠠⠔⠒⣂⢀
⠉⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠈⠈⠰⢀⠄⠀⠀⠀⠀⠀⠀⠡⠈⠀⡀⠀⠀⠤⡀⠣⠴⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠑⠐⣆⠐⠈⠉⠈
⠄⠀⠀⠄⣀⠤⠴⠶⠌⠀⡢⢂⡤⢖⣠⠴⠤⠀⠑⠀⠠⠀⠀⠨⡐⠀⠀⠀⠀⠄⠄⠔⠉⣤⠶⠖⠛⠐⢤⡤⢊⠔⣝⡲⢤⣄⡀⠀⠀⠀⠐⠀⢀⠀⠈⢦⠀⢀
⠁⠀⢀⡀⠀⠀⠀⠀⠀⢀⡰⠋⡴⠫⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢸⠀⠸⠀⢀⠴⠶⡋⠡⣴⡁⡢⣄⣙⠛⠲⣍⠳⠄⠀⠀⠀⠈⢣⡀⠀⠀⠀⠑
⠁⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠜⡠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢰⢀⠈⠀⠀⠀⠁⠀⠈⠘⠉⠈⡁⠀⡈⠆⠆⠀⠂⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠘⠀⠀⠰⠀⠀⠠⠀⢁⡘⢦⠢⡠⡀⢦⣄⡤⠴⠶⡷⢶⡳⣶⣴⠖⠂⡀⠀⠀⠀⠐⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠠⠀⠂⠀⠀⠈⠀⠠⠂⠀⣀⠤⠶⣤⡀⠄⠀⡆⠀⠀⠀⠀⠀⠀⠈⢿⠀⠂⠙⢦⠤⠠⠤⠀⡊⠠⢫⡾⠃⡀⠐⠄⡀⠀⠀⠀⡀⠀⠀⠀⠠⢀
⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⠀⠀⠔⠀⡠⠋⠀⠀⣀⡈⠙⠧⠊⡑⢀⠈⠀⠀⠀⠀⠂⠲⣆⠀⠀⠀⠀⠀⠀⠀⠠⠐⠹⠉⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⡌⢰⢃⠀⠀⠀⠀⠙⠲⢄⠀⢀⢘⡤⠠⠀⠀⠀⠀⠀⢀⡉⠳⠲⠄⠀⠠⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠤⠀⠀⠀⠀⢀⡀⠀⡀⠠⠤⠤⡊⠀⠈⣸⢡⠐⠄⠀⠀⠀⠀⠔⠡⢂⢚⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠈⠀⠀⠑⡀⠀⡀⠀⠀⠀⠀⣤⠔⠊⠑
⣀⣒⠒⠢⣄⡈⠂⠁⠀⠀⠀⣿⠀⠀⠀⡧⠈⠸⣆⠀⠀⠀⣟⣠⡇⢸⣸⡅⠀⠈⠉⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠁⠀⠀⠁⠀⢠⠔⠁⠊⠀⣀
⡁⠅⠀⠀⠀⠑⣄⠀⠎⠀⠁⣈⢧⠀⠀⠈⠀⠀⠌⠙⢦⡄⠈⠸⠳⠈⢳⢳⡒⠂⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⢀⠂⠈⠀⠂⠤⠀⠀⠀⠐⠊⡀
⠀⠀⢀⣸⠀⢠⡏⡀⠀⢄⠈⠁⠀⠣⡀⠀⠀⠀⠀⢀⣒⣛⡷⡀⠄⠀⢸⢀⠇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠀⠄⠀⠊⠀⠀⠀⢠⠀⠐⡀⡀⢰⠏
⠀⢌⢢⠇⠀⠞⠀⢁⠔⠀⠀⠀⠀⠀⠈⠀⠄⠠⢒⣀⠦⢤⠮⢯⣅⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⢠⠆⢀⡎⣐⠋⠂⠀⢀⣀⠈⣆⢣⠀⢠⡞
⠫⠔⠇⣂⠊⡁⠑⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠜⠁⠀⠀⠀⠀⠋⠉⢀⠔⠈⠀⠀⠀⠀⠆⠀⠠⠁⠀⠀⠂⠀⢠⠏⠀⡚⢀⠁⠠⠀⠀⠀⠍⠈⢿⡌⣦⠟⢁⣰
⡥⠬⡂⡈⠺⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠄⠀⢀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⡟⠃⠀⠠⠞
⠖⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⢠⠀⢀⣚⡀⠀⡃⠰⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠤⠤⢖
⠉⠀⠀⡀⠀⠀⣆⠀⠀⠀⠀⠐⠀⠀⣠⡤⢤⢀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡴⠋⠉⠙⠳⣥⣾⡀⠀⠀⠀⡄⠀⠀⠈⠁⠀⠰⠚⠉
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢀⣠⣾⠗⠋⠱⣸⡇⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠐⡇⣾⡠⠐⢉⣛⢶⣤⢫⡟⣦⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣶⣯⢟⣭⣾⠧⣴⣿⣗⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⡞⠠⢫⢷⣎⠂⠀⠛⢿⣻⡝⡞⡅⠀⠁⠀⠰⠄⠀⡀
⠠⠄⠀⠀⠀⠀⠀⠀⠀⣻⠿⣽⣿⠿⠋⢰⡿⡜⢞⡷⠂⠀⠠⠀⠀⠀⠀⠀⠀⢈⠀⠐⠀⡀⠀⢹⡀⠃⠸⣎⡘⠦⣄⡀⠸⠿⣧⢳⣷⡀⠀⠄⡀
⠀⠀⠀⠀⠁⠐⠠⢄⡀⣿⠁⣿⠉⠀⠀⣾⠀⢃⡘⠇⡁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠈⢱⣄⠀⠈⠈⠂⠈⠻⣦⡀⠙⠀⡽⢻⡀⣀⠀⠀⠀⡀
⠀⠀⠀⠁⠀⠀⠀⢀⠱⣏⠀⠫⣀⢚⣿⣃⡼⠡⠑⡌⠈⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠈⠀⠀⠀⠁⡀⠒⢀⣂⠐⣛⣷⡾⢿⣦⡈⢀⠂⠀⠀⠀⠁⠀⠀⢁⣀⣀
⣲⠀⠄⡀⠀⠀⠄⠀⠁⠈⢓⠶⠤⠽⠷⢁⠐⢀⠾⣍⠀⠄⠀⠀⢀⡠⠖⠐⠚⢶⣄⠄⠈⠀⠀⠀⠈⠀⠀⠈⠀⠈⠀⠁⠠⠈⠀⠉⠁⠀⠀⠀⠀⠀⢀⡜⣩⠄⠂
⣿⡄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠋⠉⠙⠉⠛⠉⠀⠋⠱⢀⡜⢡⢟⠀⠀⠄⢤⡁⠙⢷⡐⢂⠀⠰⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣪⠞⢀⡀
⢣⢳⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠀⠞⠀⡔⠋⠀⢁⡶⣀⠀⠀⠀⠙⠢⠀⠕⡡⢀⠂⠀⠀⠀⠀⠀⠀⠌⠀⢀⠀⠀⠀⠀⠀⠀⠒⡩⠚⡁⣴⣏⠀⢐
⠀⠃⠋⠱⠀⠀⠀⠓⠆⠀⠀⠀⠀⢀⠀⠀⠀⠉⠀⠰⡇⠀⠀⢞⠐⠈⡆⠀⠀⢠⡄⢡⡎⠀⡟⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠈⠀⢠⠴⡑⢌⠠⡁⡈⠉⠀⣼
⠘⠘⠀⠀⡇⠀⠀⢀⠀⡈⠢⣀⠀⠀⠁⠀⠀⠀⢱⠀⠡⠀⠀⠈⠂⠈⠳⣄⠀⢨⡅⣧⠁⡆⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⢠⡎⠀⡇⠘⠀⠀⠀⣾

⣴⣦⣀⡟⠀⢸⣿⣧⡀⠀⠀⣠⣶⣷⡀⠘⣿⣷⣶⣤⡀⠙⣿⣿⣶⣤⣄⠀⢻⣿⡄⢰⡿⠛⠻⠿⠏⠀⠿⠿⠿⣦
⡟⠉⠉⠳⠶⠟⠉⢹⣟⣿⣿⣿⠁⠉⣿⠏⠁⠀⠀⠙⣿⣿⠟⠉⠙⣿⡟⠀⠀⠙⣷⣾⡄⠀⠀⠀⢀⣤⣄⡀⢀⣏⣸
⠿⣦⣶⣶⡆⢠⡎⠙⣟⣿⣬⣿⠀⣴⡏⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⢸⣧⠀⠀⢀⣿⡿⠛⠒⠲⢾⣿⠀⢈⣛⠉⠉⠙
⣠⣿⠟⣨⣤⣴⣿⠀⣿⠉⣠⠟⠀⢿⣿⣦⣀⠀⠀⠀⣿⣿⣦⣄⣀⣀⡛⠿⠿⢛⣡⣀⠀⠀⠀⠀⢻⣿⡿⠛⠛⠶⣾
⢿⣧⣴⡟⠉⣿⠏⠀⠈⣿⠏⠀⠀⠀⠉⢻⣿⣷⠀⣠⡀⠈⠉⠉⠙⢿⣿⡿⠂⣿⠟⠛⢧⠀⠀⠀⢠⡟⠀⠀⢠⣄⠙
⠀⠹⣿⡇⣸⣿⣄⣀⣠⣿⡀⠀⠀⠀⢀⣴⡿⠁⠀⣿⣿⣄⡀⠀⢀⣾⡏⠀⠀⢸⣷⣤⠈⣷⣦⡶⠟⠁⢀⣴⣿⣿⣿
⣀⣴⣿⠇⠈⠉⠉⠉⠉⠙⣧⠀⠀⢰⣿⣿⣧⣀⣠⠟⠉⣹⣿⠟⢋⣿⣷⣤⣴⣿⣁⣿⣷⠋⠀⡾⣿⠇⠘⠋⠀⠈⣿
⠛⠉⠁⢠⡾⠷⣄⠀⠀⠀⣿⠳⣤⣀⠈⠉⣻⡟⣡⣶⣾⠟⠛⠒⣿⡅⣸⡟⠁⠀⠀⠙⣧⡀⣠⣧⡼⣷⣴⣶⣄⢸⣿
⡀⠀⣠⣿⡇⢀⣽⣶⣤⣾⠿⠟⠳⠿⢿⣟⣉⣿⡿⠟⠁⠀⠀⠀⢸⣧⣿⡅⠀⠀⠀⠀⠘⢿⣿⣏⣀⣠⣌⡉⠛⣾⣿
⠿⠛⢿⣿⠋⢸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⣠⣿⣿⡝⣿⡿⠛⠛⢿⡄⠀⠈⠉⠉⠛⣿⡉⢻⣻⡿
⠀⠀⠈⣿⣦⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣾⡿⠋⠉⠉⠙⢿⣷⠠⣤⣾⡇⠀⠀⠀⠀⠀⣼⣧⣾⣿
⠀⠀⠀⣿⣀⣻⣇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠋⠀⠀⠈⠻⣿⣄⠀⠀⠀⣠⣿⠃⠈⠙⢷⣀⠀⠀⢀⣴⣿⠁⠀⢻⣿
⣀⣤⣤⣀⠉⣻⣿⣦⣄⣀⣀⣀⣠⠴⣿⣿⡇⠀⠀⠀⠀⢠⠛⠉⢀⣴⣾⡿⣇⠀⠀⠀⣸⣿⣋⣻⠿⠿⣿⢧⣴⠋
⠻⣿⡟⠉⠙⣿⠉⣿⡏⠉⠉⣫⣥⣴⣾⣿⣿⣤⣀⠀⠀⣿⣦⣤⠞⠛⠛⢦⣀⠙⣶⣿⡟⠙⢿⡁⠀⣠⣿⡾⠋
⣾⡿⠃⠀⣼⣿⡇⠈⠑⢲⣾⡿⣿⠋⠀⠀⠀⠙⢻⣿⣦⡍⠋⠁⠀⠀⠀⠀⠹⣿⣮⠻⠿⠿⣿⣿⡄⠻⣿⠀⠀⣶⣶
⠋⠤⠄⠀⠘⠛⠓⠀⠀⠀⠛⠀⠘⠀⠀⠒⠒⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠐⠛⠛⠂⠀⠀⠀⠛⠁⠀⠙⠂⠀⠘⠂
⠀⠢⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡶⠾⠛⠛⠛⢛⡛⠻⠯⣶⣢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⣻⢟⡭⠚⢁⠠⠤⠀⠠⣄⠈⣉⠉⠑⠲⠬⣙⠪⣝⢶⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢞⣩⢞⣟⡵⢋⠔⡨⠔⠊⠀⠀⢈⡫⡠⠀⠀⠀⠀⠐⠪⡙⠦⡙⢿⣮⣙⡦⠄⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⡴⠋⢠⢯⠞⡀⣠⠊⠀⣠⠄⠀⠀⠀⠘⠁⠀⠀⠀⠀⡀⠀⠈⢢⠘⢎⢫⣧⠀⣀⣄⠘⣇
⠀⠀⠀⠀⠀⠀⠀⢀⡞⣡⠋⠀⢀⡏⡏⡜⠰⠃⠀⠀⠴⠄⠠⠀⠐⠀⠀⠀⠠⠆⠀⠁⠄⠀⠀⠀⠈⠈⡏⣿⠋⠀⢠⢧
⠀⠀⠀⠀⠀⠀⢠⡟⡰⠁⠀⠀⢸⢸⠁⠃⠃⠀⠀⠀⠀⠈⣄⠀⡀⠘⠇⢀⠆⠰⠀⠇⠀⢸⠀⠀⠀⠀⢸⢸⣂⡴⠛⠒⠧⠤⠀⣀
⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⣾⠸⡆⡆⢀⠀⡄⢂⠀⠁⠈⠓⠠⠦⣴⡅⠊⢀⠘⢀⠁⡎⠀⠀⠀⠀⢸⢸⣿⣶⣤⣄⡀⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⢸⠇⠄⠀⠀⠀⠀⢻⡆⢧⠰⡈⢆⢘⣄⡢⣀⠀⠀⠀⠀⡈⢀⡼⢋⠔⡡⢊⠀⠀⠀⢰⢃⡟⣼⣿⡋⠋⠧⠙⢿⡖⠦⠤⠜
⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣷⡘⣆⠀⠀⠀⠙⠻⣶⡛⠷⢶⣤⡙⠈⣴⣵⠟⠊⠀⠀⠀⡰⢃⡞⣰⣿⠙⢃⠀⠀⠀⠠⣇
⠀⠀⠀⠀⠀⣿⠰⠀⠀⠀⠀⠀⠀⡟⣷⣌⢧⡀⠐⢤⡀⠀⠈⠙⠲⢌⠻⢸⠟⠁⠀⠀⠀⡠⠞⣡⢏⣴⡿⠁⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣝⠲⣄⡈⠑⠢⠤⣄⠀⠐⠘⠀⠀⠀⢀⣠⡴⢋⣵⣾⡿⠃⠀⠀⠈⠘⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⡳⠮⣍⣓⠲⠦⠤⠤⠤⠤⠴⠒⣚⣩⡤⠞⣋⡴⠏⢀⢀⠂⠀⢀⠆⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠈⠆⢀⠙⠟⢷⣤⣈⡍⠛⠛⠛⠛⠛⠛⠋⢉⣠⡴⠞⠋⠀⠀⠡⢂⠄⢀⠌⡀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠈⢢⠣⡈⠲⣍⠛⠻⠿⢷⠶⠶⠷⠛⠛⠋⠉⠀⠀⠀⡀⠜⠁⡁⢠⠊⡔⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠢⡀⢑⠢⢀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢐⡨⢐⡡⢊⠔⣡⠎⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⡐⠀⣀⠈⠁⠐⠂⠒⠂⠐⠀⡀⠤⠒⡡⠒⡡⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠨⢐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⢀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣕⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡠⢖⣡⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢽⣳⡶⣤⣄⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⢖⣊⡥⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠾⢭⣭⣭⣽⣭⣭⣭⠭⠶⠖⠛⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡄⠄⠀⠀⡀⠂⠀⠀⠀⠉⠀⣤⠤⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠉⠉⣇⠀⠈⠁⠀⡅⠰⠴⢂⠀⡀⠈⠦⣀⣵⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⠠⠀⠀⠀⠀⢰⠀⣀⡀⠀⠀⠀⢻⠟
⠠⣀⠀⠀⠀⠀⠰⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠙⠓⠀⠀⠈⠀⢀⠇⠠⠇⠋⠀⠀⣀⡀⠀⠀⠀⠀⠰⢮⠋⠽⠓⠀⠀⠀⠀⠀⠀⢀⣤⣼⠿
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣠⠶⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠈⠘⢏⣹⠂⠀⠀⠀⢡
⠀⠚⠁⠀⢙⡀⠀⠀⠈⠲⡄⠀⠈⠀⠀⠀⠀⠀⠐⠚⢁⡀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠁⡀⢀⠀⠁⠀⠀⠀⠀⠘
⠀⠆⠀⠀⠀⠑⠂⠀⠠⠄⠈⠒⠀⠀⠀⠀⠀⠀⠘⢏⣩⡙⠅⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠁⠀⠀⠀⠐⠀⣀⠀⠀⠀⠈⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⢀⠀⠀⠈⠛⠉⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⡋⠁⠀⠀⠀⠘⣶⠯⠃⠂⠀⠰⠂⠼⢻⡾
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠄⢀⠀⠀⢀⣤⣶⣶⣦⡀⠀⠀⠳⠀⠀⠈⢀⣠⠀⠀⡗⠀⠀⡀⠀⠀⠀⠠⡟⠁⠀⠀⠀⠃⠀⠈⠀⠷⢦⣤⠾⠧⠔⠋⠀⠀⣀⡄
⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⢟⣦⡀⢀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠈⠀⠀⢀⠀⠀⢁⠀⣢⡠⡆⠀⠀⢻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠠⠌⠀⢀⠀⠈⣸⣷⠄⠈⢦⣄⡀⠀⠀⠀⠀⠀⢰⣶⢀⡀⠉⠀⣆⡰⠀⠀⣰⠟⣁⡶⢀⣴
⠀⠊⠀⠀⠀⠈⠁⠀⠀⢉⣽⡷⣴⣁⠀⠈⠙⠿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣯⣄⠀⠀⠀⠀⠀⠠⠄⠀⣴⠊⠉⣹⣆⠀⠉⢀⡤⠚⢁⡴⠋⢠⡞⠁
⠀⠀⢄⠀⠉⠀⠀⠀⠀⠁⠹⠙⠆⠈⢠⠤⡀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠈⠀⣀⠠⣿⣥⣀⠀⠀⠂⠀⠀⠀⠀⢹⠆⢀⡡⠀⢀⡴⠟⠀⢠⡞⢁⣴⠏
⠈⣀⠀⠁⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢌⣉⠿⠐⠧⠀⠀⠀⠉⠃⠀⠸⡻⣧⣀⡀⠡⣀⡀⠀⠀⠀⠘⠓⢁⡴⠋⠀⠀⡴⠋⣠⠞
⠰⠀⠀⠠⡀⠐⢀⡀⢢⡀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢠⠄⠀⢄⣀⠀⠀⠿⢿⣥⡀⠀⠀⠀⠀⠀⠠⠔⠉⠀⠀⣠⠞⣡⡾⠃⠀⠀⠈⢲
⠀⠀⠁⠀⠈⠲⡌⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠜⠁⢐⡡⠞⠁⢀⡆⢀⠈⣂⢀⣄
⠀⠀⠀⠀⠀⠰⣇⠓⢄⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠠⢀⠀⠀⠀⠀⠀⠠⢆⣿⠀⠠⠘⠃⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢠⡀⣰⣖⡛⠉⢋
⠀⠀⠐⠀⠀⠀⠀⠁⠀⠉⠂⡀⠀⣀⢴⡇⠀⠀⠀⡘⠿⢧⡄⠈⠀⠀⠀⠀⠰⣋⣳⠏⠀⠐⠆⣤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢊⠙⠃⠀⠅⠀⠈
⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⢈⣦⣾⡟⠁⢀⣄⡀⠀⠐⠂⠀⠀⠄⠐⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠉⠉⠋⠀⠀⠘⠿⠛⠀⠀⠀⠀⢢⠂⢠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⣤⣴⡤
⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⣯⠀⣏⡅⢩⡅⠘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃⠓⠀⠃⠁⠑⠂⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢠⣉⠀⠀⠈⠀⡅⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠒⠈⠂⠀⠚

⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣹⣿⡁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⣛
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠾⠋⠀⢠⣄⢰⣏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣇⠀⠀⠀⠀⢠⣤⣬
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⠄⠀⣾⣿⣶⣧⣤⠀⠀⢰⣆⠀⠀⠀⠀⢌⣧⣄⣤⠤⢶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣶⣆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⣴⣾⣿⣿⣿⡿⠟⠻⠛⠛⠛⠛⢿⡿⡿⣿⣿⣿⣿⣿⣶⣴⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠟⢾⣛⣋⠉⠉⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠨⠙⠙⢻⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⣧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢹⠀⠀⠠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡄⣠⣐⣚⣷⣷⡦⢀⣀⡀⠀⠀⠀⠀⠘⠛⢻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⣤⣴⣦⣦⣽⣿⣿⣿⣿⣿⣿⣶⣽⣿⣿⣶⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠛⠛⠉⠉⢹⣏⠈⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡄⠀⠀⣀⣴⣿⣿⣀⠀⠀⢠⣤⣄⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣷⣾⣴⣦⣤⣤⣤⣤⣤⣶⣾⣿⡛⠭⠥⢤⠤⣴⣶⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣽⣽⡏⣿⡿⢿⣿⣽⣿⣿⡷⠁⠀⠀⠀⠄⠘⠟⢿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡻⣧⠌⣷⢻⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣦⣧⠀⡿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⡷⣧⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢴⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣯⣀⡀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⡷⢜⠂⠀⠀⠀⣀⣴⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠈⣿⣀⣀⣤⣶⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣻⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠾⠿⠿⠿⠿⠿⠿⠶⢶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠋⢁⠀⠠⠠⠐⠐⠐⠀⠀⠀⠀⠄⠀⡉⠙⠻⢶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠁⡠⠔⠈⠀⣤⡰⠒⣄⡎⢹⠄⣤⠀⠀⠀⠀⠀⠁⠢⢀⠈⠛⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⢀⠀⠁⠀⠀⠀⢠⠇⣇⣰⠛⠦⠞⠀⠉⠁⠀⠀⠀⢀⣾⡇⠀⠈⠀⡀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠄⠀⠀⠀⠀⡀⠀⠈⠀⢠⡄⠀⠀⠀⣤⣠⠀⣠⠶⡶⢸⠟⠀⠀⠀⠀⠀⠠⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠃⢀⠈⠀⠀⣼⡇⢸⠇⡤⣴⠌⡟⢡⡇⣸⠃⣯⡟⢰⡏⣼⣃⠿⠤⠃⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣶⣿⣿
⠀⠀⠀⠀⠀⢀⣿⠃⢀⠂⠀⠀⢰⡏⣷⡟⣾⢁⡟⣸⣇⠼⠵⠻⠞⠀⠑⢉⣉⣀⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿
⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠸⠀⠙⠃⠙⠋⣉⣀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⣹⡏⠀⣠⡄⢘⣿⡇
⠀⠀⠀⠀⠠⠿⠀⠐⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣟⣉⠉⠈⢣⡄⠀⣾⣿⡄⠘⣿⡇⠀⣿⣿⠋⢻⣷⡀
⢠⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠟⠉⣉⠉⢻⣿⣿⠀⢠⠀⢻⣿⣿⡀⢰⡄⠙⠀⢻⣿⠇⠀⠛⢻⣄⣈⣁⣠⣾⣿⣿⡄
⠀⠻⣿⣿⣿⡿⠛⠛⠻⣿⣉⡁⢠⣤⠀⢸⣿⠀⢸⡟⠒⠚⢻⡟⠀⣠⡤⠀⠻⠟⠃⢈⣙⣦⣠⣼⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠹⣿⡟⠀⣼⣿⡄⠈⣿⡇⠀⣠⡀⠉⢿⡄⠈⠛⠃⠀⣿⠁⢠⣤⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⣭
⠀⠀⠀⢹⣿⡀⠸⠿⠇⢀⣿⠋⣀⣈⣵⣤⣤⣿⣷⣶⣿⣿⣿⡆⣶⣬⡛⢿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⢀⠁⢰⡿
⠀⠀⠀⣼⣿⣿⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠁⣾⣿⣿⣦⡀⠀⠀⢀⣀⣀⣤⡄⠀⠀⠀⠀⠀⠂⢀⣿⠃
⠀⠀⠀⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⣿⢟⣩⣶⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⠂⢀⣾⠏
⠀⠀⠀⠉⠉⠉⠀⠐⣶⡄⠀⠄⠀⠀⠀⠀⠀⠀⠤⣶⣶⣿⣿⣿⣿⣿⣶⣌⡻⣿⡿⣿⣿⣿⠀⠀⠀⠀⠠⠂⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠐⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣻⡿⠿⠿⠿⣿⡔⣿⣿⣿⠇⠀⠀⠀⠂⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠁⠢⠄⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣶⣅⡛⠛⠁⠀⠐⠈⢀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣀⡈⠐⠠⠠⢀⢀⢉⠉⠉⠉⠉⠀⠄⠙⠒⠁⣀⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⢶⣤⣤⣄⣀⣀⣀⣀⣠⣤⣤⣶⠾⠟⠋⠁
⣶⣶⡶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠰⡄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⢤⢈⠛⠓⣠⠿⠁⠀⠀⠀⠀⠀⠀⠀⠼⢿⠁⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⡐⣯⣼⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⣀⡀
⠀⠀⠀⠛⠿⠆⢸⡏⠀⠀⠀⠀⠀⠀⠀⢠⣴⠀⣰⡀⠉⣹⣶⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣶⡦⡧⠀⠀⠀⠀⠀⠶⣆⠈⠙⠁⡀
⠀⠀⠐⠷⠔⣛⡿⣅⠘⠁⠀⠀⠀⠀⠀⠸⣟⣙⣀⢥⡴⠟⠋⠀⠀⠀⠀⠀⣰⣤⣾⢿⡟⣿⣷⣐⣴⠀⠀⠀⢀⣀⠀⢾⣻⣀⠈⠋
⠀⠀⠐⣶⣋⡍⣴⡏⣁⣤⡀⠀⠀⠀⠐⠄⡿⢿⣧⣖⣯⣰⣿⡆⠀⠀⠀⠨⢿⣯⡿⣭⣯⡟⡳⠏⠁⠀⠀⠀⠈⠁⠺⣻⡏⠟⠷
⠀⠀⠰⣯⣻⣿⡿⢹⣿⡿⠀⠀⠀⠀⠐⢼⣿⡟⣿⣿⠶⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠇⠁⠀⠁⠀⠀⠀⠀⠲⣛⣿⣿⣷⡀
⠀⠀⠀⠀⠐⠾⡿⠊⠉⠁⠀⠀⠀⠀⠀⠘⣿⣷⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡸⢿⣯⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠛⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠃
⠀⠀⠀⠀⠀⠀⣰⡆⣀⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣰⣣⣾⡴⣀⡀⠀⠀⠀⠀⢠⣤⣄⣀⠀⡠⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⢨⣿⣹⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⢠⡰⠆⢸⣿⣿⣿⠟⠛⠁⠀⠀⣠⣷⣬⠾⠛⣿⠚⣠⣦⣴⡄⠀⠀⠀⢶⣤⣿⡷⠞
⠀⠀⠀⠀⠀⣾⠷⣿⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⢀⣿⣄⣴⣾⡿⠉⠀⣴⣌⡟⠃⡇⠔⠁⠀⠀⠉⠛⠃⠀⠀⠐⢿⢯⣿⣽⡿⠐
⠀⠀⠀⠀⠀⠃⡞⣙⡾⢧⣤⣤⠭⠉⠀⠀⣤⣤⢀⠀⠘⡧⣀⣉⣩⠅⠀⠀⠀⠙⠷⢶⢠⡏⡰⠆⠀⣠⠆⠀⠀⠀⠀⢻⣿⡘⢦⣙⡁
⠀⠀⣠⡀⢠⣟⣩⡅⠰⣿⡟⠋⠀⠀⠀⠰⣤⡷⣛⣿⣾⣿⣿⠿⠛⠂⠀⠀⣀⣾⠛⣸⠏⠀⡅⣴⣶⡆⠀⠀⠀⠀⠤⢬⣥⡿⣿⣿⡛⠉⠁
⠀⠀⢿⠿⣿⣿⣣⣿⡀⡿⢿⣵⣆⠀⠀⠀⠀⣾⡗⣼⡗⡠⡀⢓⣤⠆⠀⠈⢙⣷⣆⡟⠇⠀⠈⠋⠉⠁⠀⠀⠀⠀⠀⠈⣭⣿⣿⢧⡀
⠀⠀⠀⠘⢿⣭⣟⠻⠷⠤⡀⠀⠀⠁⠀⠀⠀⠛⠿⠿⠋⣷⣾⠏⠁⠀⠀⠀⠀⠁⠘⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⢻⠭⠓⠈
⠀⠀⠀⠀⠀⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣄⠀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣄⠀⠀⣠⠤⠀⠀⠀⠀⠴⠛⡿⠿⠟⢿⣿⣷⣆⣤⣤⣤⡤
⠀⠀⠀⠀⠀⠰⣷⢠⣴⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠈⠳⣧⣮⣿⣷⣶⣖⠚⠀⠀⢀⣿⣿⣿⠙⣿⢫⣝⠏⠉⣥⣄
⠀⠀⠀⠀⣀⣸⡿⠿⠟⢶⣻⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣀⣘⣿⡓⠈⠃⣠⣠⣀⡀⠀⠛⠉⠉⢠⣶⢧⠰⡟⠂⢀⠈⠹⡇
⠀⠀⠀⠀⢩⣷⡿⣾⡼⣿⠯⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠨⣽⣿⣿⢷⡝⠧⠉⠉⠀⠀⠀⠀⠀⠀⣸⣯⠆⡞⠉⠓⠈⢡⣶⣄
⠀⠀⢀⣶⣮⣛⡸⣿⣿⡏⢯⣿⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠦⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⢻⣷⠇⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠚⠉⠁⠸⠇⢷⢾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⢀⡿⠀⠐⢾⣿⣿⣦⡀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣾⣿⡄⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⡀⠰⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⢲⣼⣿⠿⠀⠀⠀⢀⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⢠⣇⠀⢀
⢀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣸⡼⠛⠀⠀⠀⠀⠀⠀⠸⣿⣷⡄⠀⠀⠀⢸⣿⣦⡙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⣸⣷⠀⣼
⣿⡀⠀⣼⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠁⠀⠀⣴⣿⠿⣿⣿⣷⣦⡀⠀⠀⠀⠈⠻⠿⠛⣿⣿⠟⠟⢛⣿⣿⣁⣼
⣿⡆⢐⣿⡆⢸⡆⠀⠀⣘⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣴⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⢀⣿⣿⡂⠀⠰⣿⣿⠷⣿
⣿⣗⣸⣿⣇⣼⡧⠀⠀⢽⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⣨⣿⣿⣧⠀⠻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠐⢿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣷⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⣀⡤⠚⣀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⠋⢡⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⢾⡁⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠇⠈⢻⡆⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⣠⠞⢡⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡚⠉⠉⠀⣀⣀⣀⣀⣠⣤⣤⣀⣀⣀⣀⠀⠀⠉⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⢸⠱⣏⣤⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣭⣭⣿⣲⣦⣍⣦⢸⠶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⢸⠦⢤⡀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⡟⠀⠀⡷⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠻⠿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⠿⣿⠃⢀⡼⠁⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⣰⡧⠖⠋⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⢧⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣁⣀⣤⠴⠋⠁
⠀⠀⠀⠀⠀⢠⠞⠁⠀⢠⠞⢡⡞⣽⣧⣤⣤⣀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⢸⡄⠀⠀⣿⢠⣿⣾⡭⠴⠖⣒⣿⣧⣤⡤⠴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠙⠲⣤⣙⠿⡴⠿⣍⣉⣉⣡⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠾⠭⠭⣤⣤⣤⣤⣤⣤⣤⠤⠤⠶⠖⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠉⠓⠶⣄⡀⠀⠀⠀⣠⠴⠒⠋⠉⠙⠓⠦⣄
⠀⠀⠀⠀⠀⠀⡰⠁⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⢰⡇⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠃⠀⢸⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠐⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢀⣠⠤⠴⠖⠒⠛⠛⠋⠉⢉⣉⣉⣉⣉⣩⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣍⣛⣛⣓⣒⣲⠦⠤⢄⣀
⣿⢶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇
⣿⠀⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠁⢸⡇
⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡤⠤⠤⠤⠤⣄⡀
⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣀⡀⠀⠀⠙⢦⡀
⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠔⠋⠉⠀⠉⠳⣄⠀⠀⢳
⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢸⡄⠀⠈
⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢀
⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⢀⣤⣤⡀⢰⡷⢰⣿⢠⣿⣴⢏⡼⠁⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⢀⡜
⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⣾⢷⣼⣧⣾⢃⣾⠛⠛⢧⡴⠟⠁⠀⠀⠀⠀⠀⢀⡾⠁⢀⣀⣀⡤⠴⠒⠋⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⣼⡟⠀⢀⣀⣿⣠⠟⠁⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⠉⠉⠁⠀⢀⣀⡠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠠⣿⣷⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠯⠤⠴⠖⠒⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠊⠁⠀⢀⣠⠟

⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⣶⣶⣶⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⣶⣶⣶⣶⣶⣶⣶⡶⠆⠘⢛⠿⢿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠘⠀⠈⢻⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠉⣀⣸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠽⣿⠿⠛⠃⢹⣟⠿⣷⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠠⠄⠒⠒⠀⢘⠛⠛⠛⢿⣿⡯⠛⠹⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣀⣀⣀⣀⡀⢀⣀⣀⣿⣦⣀⣠⣤⣀⣤⡀⢀⣀⣀⣀⢀⣿⣇⣠⣄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠛⡛⠋⠉⠉⠉⠉⠉⠁⠈⠉⠉⢿⣿⡟⠉⠉⠉⠉⠁⠈⠉⣩⣯⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣾⣿⠶⠤⠤⠤⠀⠀⠀⠀⠀⢀⣸⣋⣤⣤⣴⣦⣶⡄⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣯⠥⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣯⣭⣭⣭⣿⡿⠇⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣮⣭⠀⠀⠀⠀⠀⠀⠐⣿⠟⠀⣛⠀⠀⠀⠀⢀⢈⣛⣡⣿⣿⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠿⠀⣬⡭⠅⠀⢠⡀⠙⠉⠉⠉⠉⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⠶⠶⣖⡒⠒⠓⣟⣛⣷⣶⢦⣶⣦⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⠟⠋⠉⠴⠞⠁⣾⡶⠊⠉⠻⠋⠁⠹⣮⣿⣿⣿⠿⣙⣿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡟⠁⠀⡜⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⣠⣿⡿⠛⠁⠀⢸⣯⡝⠻⢿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠈⢣⠀⠀⠀⠀⠈⠛⠻⢦⠀⣴⠿⠋⠁⠀⠀⢀⣠⣾⠏⠀⠀⢸⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⢻⣿⣿⢿⣿⡟⠀⠀⠈⠢⠐⠠⠔⠒⣒⠠⡀⠀⠋⢀⣤⣤⠶⠶⠛⠉⠀⠀⠀⣠⣿⣿⣿⣿⣿⠏⣄
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣄⡀⠠⣀⣠⣤⣤⣠⣠⣭⡻⣤⣶⠟⢉⣀⣤⣤⣤⣴⣾⣷⣿⣿⣿⣿⣿⠿⡫⣾⣿⠟⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣴⣭⣭⣯⣉⣉⠉⠛⣿⣾⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠈⠛⢻⣿⠁⡀⠴⠷⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠄⠠⠀⠀⠀⠀⠀⠐⣾⠆⠀⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⡏⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⡟⠀⠀⠀⠀⣠⠔⢋⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⡏⠀⠢⠐⠚⠉⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠎⠀⠀⣀⣀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠻⠦⠴⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣠⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠩⠿⡖⣶⣶⣶⣶⣶⣿⣿⡿⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⢶⣒⠻⣯⡙⠻⣯⡉⠙⢯⡙⢿⠲⡖⢦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣚⠛⠻⠶⣬⣙⠳⠮⣝⡲⢍⡓⠤⣙⠲⣄⠑⢌⠣⡙⠸⠸⠸⢩⢟⡷⢦⣄⡀
⠀⠀⠀⠀⠀⣠⡶⠛⠲⢟⠉⠉⢓⡛⠒⠬⢝⡓⠦⢍⣓⠮⣕⡊⠑⠢⠑⠀⠀⣀⠤⠤⢄⡁⠊⠐⠩⠔⢛⣲⣄
⠀⠀⠀⡴⣛⣟⠋⢀⡤⠮⡃⠀⠺⠀⠐⠃⠀⢹⣷⢶⣮⣍⡒⠨⠁⠀⢀⣠⣴⠁⠀⠀⠀⠙⡄⠀⡴⢯⡭⠵⠒⣛⣦
⠀⢠⣾⣯⣥⣶⣿⣿⣤⡀⡬⠒⣤⡤⠶⣤⠔⠋⠀⢻⣿⠃⠙⠢⢤⣖⡛⠀⣿⣠⠴⠦⣄⣠⣿⡟⠁⣼⡿⢶⣛⣯⠽⠳⡄
⢠⣿⣿⣿⣿⣇⣨⡍⣙⠳⢾⡉⣀⣤⡚⠁⠀⠀⠀⣣⣿⡇⠀⡾⠛⠦⡉⠛⠤⣤⣶⢶⡿⢿⠍⠁⠀⢹⣇⠀⠙⣾⣵⣴⣿
⣾⣿⣿⣿⣿⣞⢿⣿⢿⡿⣶⣌⠛⠿⣿⣷⣤⠀⣼⠟⠁⣠⣾⣵⣤⣰⢃⣀⣠⣬⣽⣯⣄⠁⠀⣀⣤⣿⣷⣴⣿⣿⣻⣿⣿
⣿⣿⣹⣿⢻⣻⣞⣿⣿⣿⣿⣿⣿⠦⢤⣙⠻⢾⣷⣶⣾⣿⣯⣭⡿⣿⣿⣿⣿⣿⣿⠿⠟⣛⣲⣿⣿⢻⣯⢿⣿⣿⣿⣷⣿
⢿⣟⣿⣿⡻⣭⡟⣿⢾⣿⢿⣿⣿⣷⣆⡉⠳⣦⣮⣉⡟⢿⡿⢿⠟⠋⣩⣭⣴⣒⡺⣿⢟⣿⣿⣛⣯⣿⣿⣽⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣼⣿⣿⣿⣿⣦⡌⠙⠫⣽⣿⡀⠙⠶⢦⣤⣉⡭⣩⣭⣽⣯⣷⣿⣛⣯⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⢿⣟⡿⣿⣿⣿⣿⣿⣿⣷⣿⣽⢿⣿⣾⣿⣿⣵⣮⣿⣯⣳⣦⠀⠀⠉⠻⣿⣿⣿⣾⣿⣿⣿⡭⣽⣛⡳⢿⣿⣿⡿⠃
⠀⠀⠀⠻⣿⣷⣿⣻⣿⣿⣿⣿⣿⣻⢿⣶⠭⣒⢭⣻⣿⠿⠛⠉⠀⠀⠀⠀⠐⢸⣿⢿⣿⣿⣷⠾⣿⣛⣻⣯⣭⣭⠟
⠀⠀⠀⠀⠀⠙⠿⣿⣫⢯⣯⣽⣿⡿⣯⣺⣽⠾⠛⠉⠀⠀⠠⠀⠀⠀⠀⠀⢀⣼⣿⣻⠿⢟⣻⡭⢭⣖⣲⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢾⣽⣷⣿⣻⣿⡀⠀⣀⠀⠀⠰⡀⠀⠀⠂⣠⢞⡯⣟⣭⢖⣻⣽⣒⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⢭⣤⣾⣏⣈⣀⣀⣼⣿⡿⠾⠿⠞⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿⡿⠁⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣃⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢿⠿⠃⢀⣄⡸⠆⠀⠀⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⠝⠟⣣⠀⢐⣿⣾⣿⣵⣐⣿⣷⣶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣦⣶⡆⠀⢰⠟⠿⠏⢲⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⢠⠛⣿⠀⠋⠈⣴⣤⣾⣿⣦⣾⣿⣵⣿⣿⣿⣿⣿⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⢀⠸⠁⠀⡀⣾⣿⣿⠟⢙⡻⣿⣿⠝⠿⢛⠛⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⡴⠉⠀⠿⢋⢛⣿⣿⠋⣰⣿⣦⣝⣿⣶⣾⣿⡖⠀⠰⠖⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠚⠿⣿⠿⢛⠀⠠⢿⣬⣻⣿⣡⣿⣿⣿⡿⣿⣿⣿⢋⡠⠤⠀⠀⠁⠀⠘⠛⠀⢀
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠈⡻⣶⣄⡠⣄⡄⠀⣠⠔⠃⢁⡀⣹⣿⣶⣿⣇⠀⢉⡋⠙⠛⠛⠛⠚⠳⠍⠀⠀⠄⠀⠀⠀⠀⠀⠐⠊
⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⢀⡔⣿⣿⣼⣿⡼⠿⠝⠉⠀⠀⢹⣿⣿⣿⣿⣿⢛⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⡀⠀⣠⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⢀⣀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⣾⣿⣿⣷⣴⣶⣷⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣄⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠊⠀⠉⠈⠀⠈⠻⣿⣿⣿⣿⣟⣻⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⠷
⠀⡔⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠁
⠀⠄

⠀⠀⠀⠀⠀⢀⡠⡆⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠢⡴⠀⠀⠀⠀⠀⠀⠀⠀⡠⣠⣔⠦⣰⣆⡀
⠀⠀⠀⠀⠀⠠⢸⣹⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢀⠀⠏⢄⠀⠀⠀⠀⠀⠀⢐⡉⠘⡄⣹⣿⣏⠃
⠀⠀⠀⠀⠀⢀⡿⢿⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡈⠀⠀⠀⠀⠀⠀⠀⢩⠉⠒⠣⢿⠏⡔⠁
⠀⠀⢀⠤⠂⢺⡗⠒⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣻⠀⠀⠀⠀⠀⠀⢀⡟⠶⢶⣠⣮⣼⠄
⠀⠀⠙⢓⣻⠿⡏⠓⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣤⡎⠀⠀⠀⠀⠀⠀⣠⠁⠀⠈⠁⠀⠀⢀⣀
⠀⠀⠘⠙⠏⢰⡾⡄⡠⠀⠀⠀⠀⠀⠀⠀⠤⠄⡴⢊⣸⢸⣿⢠⢀⠀⠀⠀⠀⡏⠶⣄⡀⣀⠤⡊⠕⠃
⠀⠀⠀⠀⠀⢸⠙⢇⢱⡇⠀⠀⠀⢠⠗⠘⠀⡺⡳⢋⣷⡾⢻⡆⠅⢓⡀⠀⢨⣀⣠⠴⠟⠛⠣⠤⡄⡄
⠀⠀⠈⠂⠀⢙⢦⠣⡷⠟⠆⠀⠀⡠⠒⣸⡛⢲⣋⡚⡏⠡⡼⣌⠵⣀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡠⠀⠀⠻⣤⡛⣿⡄⠀⠀⠋⠠⣧⠴⣯⡛⢻⡝⣦⣱⢦⣟⡿⠕⠄⢘⣉⡑⡓⢒⣶⣶⡶⠶⠟
⠀⠀⡨⣬⣄⠆⡘⠾⡟⡿⡇⢀⠀⢘⢠⡑⢹⠹⣹⠊⣻⣽⠋⣽⢥⡀⠪⠀⠘⠋⠁⠈⠉⠀⠀⠀⠀⡀
⠀⠀⢤⠥⢼⡤⡞⢄⢴⡤⢇⣉⠀⠘⠋⠀⡎⡇⢁⢂⢟⣹⠚⣵⢆⠢⠀⠀⠈⡓⠆⡤⠠⠀⢀⣤⠚⠓⠄
⠀⠀⠀⠀⠠⠤⢷⢦⣬⠧⡞⣘⠄⠀⠀⠀⢧⣿⠡⠎⢘⠹⣿⡰⠀⠂⠀⠀⢄⣱⠶⠉⠀⣶⡎⠸⡄⡳⠂
⠀⠀⠀⠀⠀⠀⢮⣼⣄⠂⠈⠈⠀⠀⠀⠀⠀⠁⠀⠀⠈⢾⠁⠁⠀⠀⠀⠀⠈⠉⠢⡴⢷⢯⠛⡫⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⢒⡀⡠⠄⠨⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⠀⠂⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⣥⣶⣿⡻⢕⣃⠰⠄⠙⠂⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢍⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⣿⣿⣿⣷⣾⣷⣾⣙⣄⢀⣐⢂⡤⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⢼⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠷⣌⡻⢿⣿⣿⣭⣭⣭⣿⣧⣴⣶⣍⡉⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⠜⣣⣞⣿⢀⣍⣡⣍⣀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠉⠓⠪⢝⡛⠿⠿⠿⣯⣿⣽⣿⣿⣿⣷⣦⣵⠶⠤⠶⢚⣛⣋⣭⠶⠛⡫⣰⣿⡿⠋⠈⠉⠙⢲⣟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠘⠀⠐⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⢉⡋⢩⣭⡵⢶⣻⣽⠾⣻⣿⡇⠀⠀⠀⠀⣸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⡠⣤⣒⢚⣿⡀⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠒⠦⣍⣒⣭⣲⣽⣿⣻⣿⣿⢛⣲⠖⢁⡞
⠀⠀⠀⠀⡠⠂⢴⣪⢏⣩⣿⣼⣧⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠼⠿⣛⣻⣿⣿⣿⣿⣿⡿⠟⢋⣥⣾⣿⣯⡔⠄
⠀⠀⠀⠈⢔⠖⢚⢱⡟⢀⢿⠻⣿⣧⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢁⣚⠿⣿⣳⣿⣿⣿⣛⣩⣴⣾⣿⣥⠪⠁⠣⢸⡄
⠀⠀⠀⡀⡘⠸⢣⠓⠁⠁⠁⠉⠀⠛⢷⡈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣾⣿⣿⣿⣿⣳⠟⠋⢝⠷⠛⠛⠏⡡⠁⠀⡐⠰
⠀⠀⠀⠠⡘⠂⠀⢰⡄⠀⠀⠀⠀⠀⠀⠉⢖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢉⡙⢯⣜⢺⣹⣿⡻⠃⠔⠀⠀⠀⠀⠀⠀⠀⠀⠊⡠⠃
⠀⠀⠀⠀⠈⠢⢑⠰⢭⡢⡀⠀⠀⠀⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⢀⡀⢂⣀⣂⣠⣥⡶⠴⣾⡿⠊⠐⠀⠄⠂⠀⠀⢀⡠⠐⣉⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠢⢌⡀⠠⠀⠀⠀⠀⠀⠀⠑⠄⣀⡈⠉⠁⠀⠉⠁⠉⠈⠉⢁⣀⡤⠖⠋⠈⠀⠀⠀⠀⠀⠀⢂⣡⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢦⠤⢀⡀⠒⠀⠀⠄⠉⠉⠉⢉⣉⡀⠉⠉⠉⠉⡁⠀⠠⠄⠐⢂⡈⠤⡐⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠄⠀⢀⣀⡀⢒⠒⠒⠀⢀⣀⣀⠀⠠⠄⠐





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⣉⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⢀
⠀⠛⠟⠀⠀⠈⠉⢀⣶⣦⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢉⣙⣾⠛⢦
⠀⠀⠀⠀⡀⠀⠀⠈⠛⠋⢀⡀⠘⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠤⣤⣀⠀⠀⠀⠘⠉⣻⣿⠰⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠦⠤⢤⣤⣌⣉⣹⣷⣦⣤⣏⣹⣿⢡⢰⡇
⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠁⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠰⠶⣠⣞⣛⢿⠟⣩⣿⣿⣿⣿⠟⣿⡿⠀⢸⡇
⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠶⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡀⠀⠀⠀⠀⢀⡀⠀⠀⠴⠟⠉⠁⢰⣾⠗⣫⣷⠟⣿⣡⣴⣿⠇⠁⡿⠁
⠀⠀⠀⢀⣾⣷⡄⠀⠀⠀⠠⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⢳⣶⢦⣀⡏⠷⠀⡀⠀⢀⣠⠖⢂⣴⣾⠟⠇⠘⣿⡿⠿⢃⣴⠞⠁
⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠐⠂⠀⠀⠀⠀⣮⣿⡀⠝⠡⠀⢤⠀⠐⠋⠀⠰⡯⠞⠁⠊⠀⠀⠛⠿⠷⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⠀⠀⢠⡐⠑⡄⠐⡀⠀⠁⠀⠀⠆⠠⠀⠀⠁⠘⠀⢀⣂⠀⣠⠾⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠂⠀⠀⠀⢄⠀⣄⢀⣿⣼⣷⣿⡇⠈⠙⠀⠇⠈⠀⠀⠀⠀⠲⣦⠀⠉⠉⠀⢀⣠⣼⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⡀⠀⠂⠆⠀⡿⢿⣿⠟⡠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠾⣂⠀⠀⣠⡾⠟⣽⠟⡟⢷⣦⡀⠀⠀⣰⢦⡴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⢀⠀⠈⠶⠁⠘⠿⠀⢠⠀⡷⡀⠀⠀⠀⠀⠠⠎⣡⠄⠉⠷⢶⣄⢀⣾⡟⠰⣿⠀⠙⣣⢀⣴⡾⢋⣌⢇⣼⣥⡤⡀
⠀⠀⣀⣀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢿⠘⠀⠈⠃⡴⡆⠁⢸⢆⡀⠳⠦⣉⡜⣿⣦⣴⣃⣀⡄⠀⡀⢿⠈⣿⠤⠴⢛⣧⢠⢿⡟⣉⣿⣜⡿⣈⣷⡆⣺⣧⣀
⠀⠀⠁⠀⠑⠈⠀⠀⢠⠀⠀⠀⠀⠀⠰⡁⠀⠓⠀⠠⠋⠄⠊⡀⣃⣼⡁⢀⣼⡟⢋⣥⠌⢿⣶⠋⠦⠖⢀⣿⡄⠀⢸⡏⢤⣄⡀⡻⣿⡶⣥⡙⠦⠀⣹⡅⢏⠁
⠀⠀⠀⠀⠀⠰⠄⣄⢀⠋⠀⠠⠀⠘⠀⢁⠀⣠⠄⡀⠈⠤⠀⠀⠁⠆⢁⣿⣿⠀⠟⢤⣤⡰⢮⡴⡦⢠⣾⡿⠀⠢⡈⠳⠟⣹⣿⣷⡌⣴⣻⣙⣧⣀⣤⡴⠎
⠀⠀⠀⠂⠀⠀⣠⠁⣬⣿⡞⠁⠀⠀⠀⠀⠐⠋⠐⠃⢻⡄⠀⠀⣤⠟⣻⣿⣇⠀⠘⠂⠃⣬⡎⠹⠾⠿⠋⠀⠀⣠⣾⣶⣾⠟⠀⠀⠉⠁⢸⣦⢙⣙⡋⠃
⠀⠀⠀⠀⠀⠀⠀⠤⠰⠟⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⡘⣧⠀⠀⢀⡁⠙⣿⣿⠀⡴⣦⠐⣧⠔⠃⠌⢱⡟⠻⠟⡿⠛⡉⠀⠀⠀⠀⠀⠀⠀⠈⠘⠉⠁⢀⣾⣷
⠀⠀⠀⠀⠀⠀⠀⡀⣤⢦⣄⠀⠀⠀⠀⢀⠀⠐⢁⡀⠀⢸⡶⠓⣦⣿⣤⣿⡿⠀⠰⡞⢠⡉⡀⠀⠄⣼⠇⠆⠈⣷⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⠀⠀⠀⢀⠀⠠⠀⢣⡀⠀⠈⠀⣄⠀⣠⣿⣧⣤⣾⡇⠀⢾⣇⠤⣿⡿⣿⣿⣿⣤⢴⣿⠰⢱⣏⣁⣴⠏⢀⠃⣀⠁⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⢀⣼⣿⣿⠟
⠀⠀⠀⠊⢀⡤⠊⠀⠀⠀⢁⡶⠂⠀⠈⠻⣷⠴⢿⣧⠴⠚⣿⡶⠿⣧⠀⢠⠃⢀⡼⣏⠀⢀⣬⣩⡀⠶⠉⣹⠿⠃⢋⠠⢘⣯⠹⠎⠛⢛⠶⠶⣾⠿⠿⠛⠁
⠀⠀⠀⠀⢼⠁⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠙⣷⠛⠻⣷⡞⠙⣷⠶⣿⡇⣸⡀⣼⢀⠉⠃⠀⠈⠿⣁⣴⠛⠛⢠⠢⡌⠀⣸⠃⠀⢬
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢍⠁⢦⠀⠀⠀⠀⣿⠋⠛⣿⡶⢿⡿⢛⣿⠃⠉⠈⢳⣼⠀⠀⠀⡈⢀⠈⠁⠀⠀⠀⡤⡌⠀⢸⡆⡅⠁⠈⠀⠁
⠀⠀⠀⠀⠀⠹⢦⡀⢸⡀⢻⡶⠋⠀⠀⠀⠀⣿⡛⠺⣿⡗⢿⣧⣼⣏⢠⣅⡀⠀⠀⣱⠄⢺⣄⣨⠟⠀⠀⡐⠴⠀⠀⠀⣼⡇⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⢼⡗⠀⠀⠔⠲⠉⢉⢿⡏⠻⣧⡀⢻⡿⣧⡌⢤⡙⢀⢢⡙⠶⠛⢡⡀⠀⠀⠀⠈⠆⡄⠁⢀⣿⡟⢀⠁⠀⠀⠀⠀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠔⠀⢀⠤⢷⡁⠀⢨⢀⡈⢑⠄⣱⡟⠳⡄⣇⠼⣣⡝⠃⠚⠁⠀⠀⠀⠀⠀⠆⠤⢀⣼⡿⠁⠀⠃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢐⠇⠀⠀⠀⠀⠀⠀⠃⣸⣏⠁⠈⠁⠰⣤⣼⠁⣈⠃⠀⠖⠉⠁⣀⠀⠀⠒⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡘⠓⠀⠀⠀⢀⠈⠀⠘⠻⡿⠓⠀⠄⠀⠀⠁⠀⠉⠀⠀⠀⠘⠃⠉⠤⠀⠀⠁⠀⠀⠈⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⠀⠀⠀⢀⠀⢀⣉⠉⠐⣭⡀⢀⠁⠀⢰⠄⠀⠰⣦⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢀⠤⠼⠗⠂⠀⠀⠀⠢⡞⠋⢰⡟⡹⠟⠉⠀⠀⠓⣀⠀⠀⢈⡄⠀⠋⠀⠀⠀⠉⠀⠀⠀⠀⠀⣽⣉⡿⣿⣿⡄⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢽⡖⠒⠳⡄⠁⠀⠀⠰⢀⣀⠀⠀⠀⣧⠥⣼⠿⣴⠂⠀⠀⠈⠀⠈⠀⠀⠀⠀⣀⠀⠀⠘⠀⠀⠈⠃⠀⢠⣼⣿⢨⣷⠿⠇⠀⢀⣼⣿⡿⠃
⠀⠀⠀⠀⠠⠀⠈⠃⠀⠀⠈⢢⠀⠀⢠⠘⢃⠀⠀⣠⠀⡀⢶⠂⠀⣤⠀⠀⠛⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠚⠀⠀⠀⠀⠀⠸⣿⣼⣿⣤⡄⣄⣴⣿⣿⡃
⠀⠀⠀⠀⠀⢷⣄⠀⠀⠀⠀⠀⢣⡔⠂⠀⠀⠉⠾⣽⣔⡷⠛⠓⣡⣟⣦⠤⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⢀⡼⡏⠁⠙⠛⠙⠁
⠀⠀⠀⠀⠀⠀⠉⠣⠀⠀⠀⠀⠀⠱⣄⠀⠀⢈⡁⠈⠋⠿⠾⠾⠷⠋⠀⠀⠀⠈⣁⠀⠀⠀⠀⠠⠶⠀⠀⠀⠰⠆⠀⢀⣴⠛⣬⡇⠈⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠲⣆⠀⠀⠑⠀⣾⢀⡀⢀⠀⠀⠤⠒⠊⠉⠉⠁⠠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠝⠛⢋⢸⣧
⠀⠀⠀⠀⠀⣠⠶⢦⣄⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠻⠦⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠈⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠋⠁⠀⠀⠑⠂⠄⠀⠐⠖⠠⠀⠀⠀⠀⣠⡤⠀⠀⣠⣶⣶⡤⠖⠋⠀⠀⠠
⣆⣠⣤⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠚⠁⠀⠀⠘⣛⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣴⡶⠶⠤
⣿⣿⣿⣷⣶⣷⣶⢀⢀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⣠⡶⠚⠃⠀⠀⠀⠀⠀⢀⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⣾⣴⣾⣦⡆⣶⢀⠀⣿⡀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⣾⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⣿⠟⢿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣠⢸⡇⣦⣿⣿⣷
⠟⠛⠛⠋⠋⠋⠉⠈⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⠀⠀⣾⡀⠀⢀⡄⢀⢠⣀⡀⣶⢀⣆⣿⣿⣤⣦⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⢰⣿⣧⣆⣼⣧⣿⣾⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣿⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⠟⠻⣿⡿⠿⢿⡿⣿⢿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠙⠉⠀⠁⠙⠙⠋⠛⠻⠻⠛
⣿⡿⣿⣿⣿⣿⣧⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⣯⠀⢻⣿⣿⣿⣿⡆⣼⣿⠀⠀⣀⠀⠀⠀⣼⡂⠀⠀⠀⠀⠀⣾⣧
⠃⠀⢺⣿⣿⣿⣿⣿⣿⣿⣗⢠⣿⡀⠀⢠⣿⣧⠀⢠⡄⠀⢰⣿⣿⠆⠀⠀⣄⠀⠀⠀⢠⡄
⠆⠀⠤⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣾⣿⣯⣄⣼⣧⠀⣺⣿⣿⣶⡄⢸⣿⠀⠀⠀⣾⣷
⠀⠀⠈⢻⣿⣿⣿⣿⡟⣿⣿⣿⣿⣷⣼⣿⣿⡿⢻⣿⣿⣬⣿⣿⣿⣿⣥⣿⠿⠇⠀⢸⣿⣿⠂
⠀⠀⠀⢀⣿⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⢰⣦⣿⣿⣿⣶⠄⠀⢠⣇
⠀⠀⠐⠶⠿⣿⣿⡃⠀⢐⣿⣿⣿⡏⢹⣿⣟⠀⠐⣺⣿⣿⣿⣿⣿⣿⣿⡃⠀⢒⣿⣿⣿⣿⣿⣆⠀⣾⣿⠄⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠉⣛⡻⠯⠀⠀⠀⢸⣿⣿⠀⠨⣿⠥⠀⠀⠈⣿⣿⡿⢻⣿⣿⡯⠀⠀⠀⢹⣿⣿⣿⣿⣿⣼⣿⣿⣦⠀⣦⠀⢀⣿⡇
⠀⠀⠀⠀⣀⡤⠂⠀⠀⠈⠭⢿⠇⠀⠀⠘⠀⠀⠀⠉⠽⣿⠁⠸⣿⡿⠃⠀⠀⠈⠭⢿⣿⡿⠉⣿⣿⡿⢿⣿⣲⣿⡂⣸⣿⣷⠄⡄⠀⢀
⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠨⠄⠀⠀⠿⠛⠀⠀⠀⠀⠀⠤⣿⠃⠀⢹⣿⠇⠘⣿⢻⣿⣿⡿⢹⣿⣿⣿⠀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⢉⠉⠀⠀⠈⠋⠀⠀⠃⢘⣿⣿⠃⠈⣿⣿⣿⣷⣿⣿

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


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠆⠀⠀⢀⡴⠆⠀⠀⢀⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⢰⣿⠁⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠸⣿⡀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠹⣿⣆⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠘⣿⡆⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⣿⠃⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠼⠥⠤⠤⠤⠾⠧⠤⠤⠤⠴⠯⠤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢋⣩⣥⣤⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⡶⢶⣤⣤⣭⣉⠓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣶⠾⠿⠛⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠴⠒⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡠⠤⣄⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢧⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡰⠃⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠴⠋⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣣⠴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣸⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⣀⣀⣀⡀
⠀⠀⠀⠀⡤⠖⠚⠉⢉⣥⣤⣶⣶⣾⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣷⣶⣶⣤⣬⡉⠉⠓⠲⢤
⠀⠀⠀⠀⠑⠦⣄⣀⡘⠛⠿⠿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⠿⠿⠛⢁⣀⣠⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠒⢶⡤⠬⠭⠭⢭⣍⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣩⡭⠭⠭⠥⢴⡶⠒⠒⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠲⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠖⠒⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⣄⠀⠀⠘⣆⠙⣆⠀⠀⢳⠀⠆⠀⠀⠀⠀⠀⢄⣺⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⣀⣠⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠈⠳⡈⢢⡀⠈⣆⠀⠀⠻⠁⠠⣼⠟⠉⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠁⠀⠈⢻⢗⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠙⢄⠳⡄⠸⡄⠀⠀⢀⡴⠿⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠐⠁⠀⠀⢿⣧⠀⠀⠀⠀⠀⣼⣦⠀⠀⠀⠀⠀⠀⠠⠖⠀⡌⠣⠱⡀⠻⠀⠀⣛⠿⠀⠀⠀⠀⠀⠀⠰⠘⠀⠀⠀⠀⠀⢈⠇
⠀⠒⠠⠀⠀⠈⢧⠀⠠⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠑⠀⠀⠸⡿⠄⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⡀⠠⠀⠀⡀⠈⠣⡀⣇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂
⠀⣀⣼⠀⠀⠀⠀⡀⠹⣼⡆⢠⡀⠀⠀⠀⡀⠴⠦⠄⠀⠀⠀⠀⠀⠀⡈⠀⢀
⠀⠚⠁⠀⠀⠀⠀⠀⠀⠘⢦⡀⠁⠀⠀⠠⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣆
⠐⣆⠀⠀⠰⠋⠁⠤⣷⣂⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⡀⡀⠠
⠀⠀⠀⡀⠀⠀⠀⠈⠟⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⠆⠠⠄⡤⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠿⠿⠟⠁⠀⠁⠀⠊⠁
⠀⠀⠀⢀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠅⠈⠃⠫⠂⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠠⠉⢋⣡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀
⠀⠈⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⢸⠀⠀⣉⢸⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⣦⣶⣿⣼
⣄⠀⠀⠀⠀⢀⡀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⢀⣻⣿⣿⣿⣷
⠃⣉⠀⠀⡁⠈⡹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⢌⣿⣿⣿
⠈⠉⠛⠃⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⠛⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣉⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠟⠛⠋⣉⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠲⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⣠⣔⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠹⣄⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢶⣤⣄⡴⠋⠗⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠉⠛⠳⠿⢶⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣭⡿⠿⠾⢛⣋⠥⠂⠀⠀⣀⣤⣤⣀⡀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⣭⣭⠭⠉⠠⠔⠒⠊⠉⠁⠀⠀⠀⠀⡞⠀⠀⠀⠀⠈⢳⡀⠆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢠⡇⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⣠⡾⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣀⣤⣴⣶⠿⠋⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠛⠉⢉⣀⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠚⠋⢧⡐⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣃⣀⣠⠤⠴⣞⠉
⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠳⣌⠓⢕⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠤⢄⡀⠀⠉⠲⢄⡀
⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣬⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠉⠆⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠮⣉⡙⠛⠒⠒⠒⠒⠒⠒⠒⣛⣭⣯⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣀⡀⠀⠀⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠉⠀⢀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⢤⣀⣈⡉⠉⠐⠒⠒⠒⠀⠀⠠⠤⠤⠤⠀⠀⠒⠒⠒⠒⠉⠉⢁⣀⣀⡤⠴⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢄⣿⣟⡤⠀⠀⠀⠀⢀⡀⠂⠠⠈⠠
⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀⠾⢿⣿⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠀⠀⠀⠀⠀⠘⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣹⣿⡟⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢸⡀⢀
⠀⠀⠀⠀⠹⢻⣦⣾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣄⣷⠏
⠀⠀⠀⠀⠀⠈⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠲⡄
⠀⠀⠀⠀⠀⠰⣶⣶⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⣠⢲⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠈⠉⡀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠠⣦⣼⣇⣤⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣴⣶
⠀⠀⠀⠀⢛⣿⣯⣿⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠘⠩⣿⠙⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠿

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿