Foo Emojis & Symbols

⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠠⠀⢄
⠀⠀⠐⠀⠂⡤⠁⢘⠁⡀⠀⠀⢀⢀⣀⣸⣇⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠤⣒⠀⣄⢁⡎⠸⡀⠀⠄⠀⠈⠁⠀⠈⠉⢻⣧⡄⠀⠑⠀⠤⠀⠄⠤⠀⠊⠁⠀⠐⠠⡄⣀
⠀⠀⠀⡀⢤⢫⡦⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠈⠳⣅⣏⣙⢀⡂⣢⡸⠃
⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠂⠀⢠⠀⠀⠀⣰⣿⣿⠁⠀⠀⠀⠉⠉⠉⠉⢀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣾⣧⣤⣴⣿⣿⡏⠀⠀⡀⠁⠄⠄⡀⠀⢸⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⡤⠒⣤⡀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠀⠀⠀⠀⢄⣀⡸⠁⢀⠂⠀⢠⠀⠀⠀⠀⠈⢃
⠀⠀⠀⢀⠀⠀⢸⡇⠀⠀⠀⢠⡄⠀⠀⠀⢠⣄⠀⣀⣤⢀⠀⠀⠀⠀⠴⣯⠀⠀⠈⠲⣦⣴⣶⡿⠃
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠐⠂⠀⠀⠀⠈⠻⠿⢟⣣⠞⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡿⠀⢠⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠸⠀⡏⠀⠀⢤⣀⣠⣀⣴⡼⠀⠀⢰⣶⣼⣧⣶⣄⠀⠀⢠⡇⠀⠘⢷⣄⠀⠀⢀⣤⣼⠏
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠉⠉⠁⠀⠐⠉⠈⠉⠀⠀⠈⢹⡇⠀⠈⢇⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠃⠀⠀⢡⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣸⠇⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⣀⡾⠀⠀⠈⠒⠦⠴⠿⠟⠋⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⢀⣀⣄⣀⣀⣀⠠⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡏⠀⠀⠀⠀⣶⡶⡟⢣⠀⠀⠁
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡦⠀⠰⣆⡀⠀⠀⠀⠀⠀⡀⢄⣽⡷⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠈⠈⠁
⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⣀⣰⠋⢳
⠀⠀⠀⠀⡰⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣠⣬⣇⠀⣞⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣠⠴⠶⡄
⠀⢀⣦⠘⢳⡃⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣸⠉⡥⠶⣏⡛⢯⢷⠀⠀⠀⠀⠀⠀⡜⠁⠀⠈⠉⣉⣀⠀⠀⢧
⣴⣯⡼⠋⠉⠳⣄⠀⠀⠈⠙⠒⠦⡴⡆⠀⠀⢠⣷⣧⣺⠟⠉⢻⣽⠋⠈⣧⠀⠀⠀⠀⠀⠙⢦⡀⢰⠋⠁⠈⠱⡄⠈⠳⣄
⠀⠀⢳⡀⠀⠀⠈⠙⠶⢦⣤⣤⠖⠓⠇⠀⠀⠈⢇⠀⠉⡍⠉⡽⢁⠀⠀⠸⡄⠀⠀⠀⠀⣠⠞⠀⠸⡀⠀⠀⢠⠇⠀⠀⠈⡇
⠀⠀⠀⠙⠢⣄⣀⠀⠀⠀⠀⢀⣽⢻⠃⠀⠀⠀⠘⣆⠀⢀⡜⠁⠀⢠⠀⠀⢳⠀⠀⠀⢸⠁⠀⠀⠀⠉⠛⠛⠁⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠋⠉⠙⠿⠀⠀⠀⠀⠀⠈⢳⡞⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠘⠦⢤⡤⠖⠚⠉⠙⠓⠲⠤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠀⠐⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠹⣄⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⡎⡭⠙⠋⠀⠀⠀⠀⠀⠀⠀⠫⢼⡆⠀⠈⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡀⡠⣠⠓⢲
⠀⠀⠀⠀⠀⠀⢸⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠻⣀⠀⠀⢀⡞⣠⠀⠀⠀⠀⣠⡄⠀⠀⠀⠙⣤⠟⢧⣼⢶⡛⢶⢲
⠀⢠⠶⠶⠶⠒⠛⠛⠒⣒⣒⣲⡄⠀⠀⠀⠀⢰⣛⣛⣛⣛⡇⠀⠘⡇⡧⢠⣤⣄⣼⠟⠁⠀⠀⣟⣓⠻⢤⡏⡏⢸⢷⠈⢻⡀
⠀⠉⢿⠉⠉⠉⠉⠉⠉⠉⠉⡏⠁⠀⠀⠀⢠⠞⠉⠀⠀⠀⠑⢦⠀⢃⣀⣻⡀⠈⣷⠀⠀⠀⠀⢠⣤⣟⣄⠙⢧⡟⣸⣧⡤⣷
⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⣏⠁⠙⣿⠛⠃⠀⠀⠀⠀⠀⢳⡀⠉⠉⠉⠉⠁⠀⢀⡏
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡞⠛⠻⡗⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢸⡄⠀⠀⣠⠖⠶⣿⣴⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢀⣀⠀⢸
⠀⠀⠀⠀⣧⣤⣤⣤⣤⣤⠇⠀⠀⠀⠀⠀⠸⣇⣀⣀⣷⡀⡀⢈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⣿⠟⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢤⣤⣀⡀
⠀⠀⠀⣰⣒⣶⣓⡶⠶⡴⢲⡄⠀⠀⠀⠀⠀⠀⠛⠁⠀⢀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣤⠀⠀⣉⠙⠲⢤⣀
⠀⢀⡴⠋⠀⠂⢀⠈⠳⣍⢹⣛⢯⠓⢦⠀⠀⠀⠀⢀⡴⠋⢥⡀⣤⠙⢠⠍⠳⣄⠀⠀⠀⠀⠀⢸⣯⡉⠓⠲⢧⣀⣀⠀⠈⠳⣄
⠀⢸⡀⣀⠀⠀⠈⠀⠠⠈⠳⡈⣿⣹⡎⣇⠀⠀⠀⢺⣀⠃⠀⠀⠀⠤⠀⠐⠛⠘⡆⠀⠀⠀⠀⢸⣧⢙⡆⠀⣂⣈⣙⠦⣴⠂⠈
⠀⠀⠳⢄⡀⠈⠀⢀⡀⠀⠃⢹⡄⡿⣟⡏⠀⠀⠀⢀⣏⣉⣭⣙⣛⣋⡿⣟⣛⡿⢧⠀⠀⠀⠀⢸⠗⠋⢰⣫⢷⢰⣯⣷⠼⠓⠋
⠀⠀⠀⠀⠙⠲⢤⣀⠁⠀⠄⠀⣷⠷⣿⠃⠀⠀⠀⠘⣧⠤⠴⠶⠿⢶⣶⠶⠶⠶⡏⠀⠀⠀⠀⢸⠦⣄⣸⡬⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⣸⡼⠁⠀⠀⠀⠀⠀⠈⠳⢤⣄⣀⣀⣈⡷⠤⠞⠁⠀⠀⠀⠀⠼⠖⠋⠁
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠁⠀⠀⠡⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⢀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⢤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⡄⠀⠀⠠⠀⠀⠀⠀⠀⢸⣏⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠒⠀⠀⠀⠠⠄⠒⢂⡒⠀⠤⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⢿
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠘
⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠊⠀⠀⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠲⠀⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢄⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠠⠤⠈⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠈⠂⠀⡤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠴⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠌⠀⠀⠀⠀⠔⠂⠐⠲⠀⠒⠒⡀⠀⠀⠀⠀⠀⠄⠤⠀⠦
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠇
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠤⠤⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠐⠂
⢀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠴⡆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠉⠀⠄
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⣠⠸⡆
⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠑⢴⡻⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠀⣁⣀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠂⠀⠄⠀⠴⠂
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⢀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠓⠲⠠⠞⠫⠀⠀⠀⠀⠀⠀⠀⣤⣟⣀⡀⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄
⠀⠀⠈⠠⣐⡄⠀⠀⠀⠀⡴⡦⡶⠀⠀⠨⠛⠃⠀⠘⣷⣦⠤⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠡⡀
⠇⠀⠀⠌⢦⡠⠇⠀⠀⠺⣾⡇⠀⠀⢀⡰⠋⠀⣤⠔⠙⠄⣤⠂⠀⠀⢉⣉⣉⣉⣉⣉⠉⠁⠀⠀⠐⠀⠑
⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠑⠦⠴⢿⡄⠀⢀⠽⠧⠚⠋
⠀⠀⠀⠀⠀⠀⣤⢀⡀⠀⠀⠀⠀⢤⣀⣀⣀⣀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀
⠀⠀⠀⠀⠀⡼⢡⠏⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⠀⠑⠐⠂⢀⠠
⠀⠀⠀⠀⡰⣡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣀⣀⣄⣀⣀⣀⣀⣄
⠀⠀⠀⡰⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⣀⣐⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠁⠀⠀⢀
⠐⠟⠿⠿⠿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠰⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠀⠀⠀⠀⠐⠚⠉⠀⠀⠀⣔⠀⠂
⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡴⣴⠃
⣄⠀⠀⠀⡴⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠉⠐

⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣵⣭⣶⣬⣯⣩⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢀⡆⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠿⠿⠿⠿⠛⠛⠋
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠠⠤⠤⠤⠤⠤⠤⠄⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢴⠀⠀⠀⠀⢀⠤⡠⠤⠐⣒⠒⠚⠤⠤⠤⠤⠀⠀⢤⣀⣄⣀⡀
⠀⠀⠀⠀⢠⠀⡀⢄⠀⠀⠀⡀⢐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⣀⠤⠖⢈⡀⠈⠀⠀⣶⠁⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠐⠀⠀⠠⠊⠁⠒⠲⢄
⠀⠈⡀⠀⣄⡀⠀⠒⠖⠊⠉⢐⣀⡄⠀⠀⡀⠀⢀⠀⠀⣠⣊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⡁⢄⣰⢎⣁⠚⠙⠒⠂⠈⠀⠀⠀⠢
⠀⠀⢏⢶⡌⠀⠀⠛⠚⠙⠁⡀⠙⠁⠀⡠⠄⢠⡁⡢⠀⠈⠃⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⡀⢀⠀⢠⠀⠈⠉⠛⠛⠴⠢⠦⠀⢠⣼⠀⠀⡀
⠀⠀⠈⠣⡉⢢⠄⡠⡄⡀⠠⠂⡌⣐⢅⣰⣁⣣⣬⡇⠀⠀⠀⣠⠤⠈⠀⢰⣁⠀⠂⢮⢳⡦⣤⣀⣀⠄⠁⠀⠀⠀⠀⢡⠎⠀⠈⢸⠀⠀⢹
⠀⠀⠀⠙⠻⣦⣤⣂⢉⣀⠅⣜⣳⣦⠾⡯⠖⠚⠉⠀⠀⠀⠈⡟⠀⣠⢂⡏⠴⢰⣀⡀⢈⣀⡇⠁⠀⢀⡀⠀⠀⡀⣀⠊⢀⡜⠁⣸⠀⠀⢨
⠀⠀⠀⠀⡀⠀⠉⠑⠩⠀⢀⡀⠉⠂⠀⠀⢠⡄⠀⠀⠀⠠⢨⠀⣸⠡⢤⠃⠀⠀⠀⠀⠉⠑⡒⠀⠒⣀⠀⢀⣠⡔⠃⡀⠁⠀⡴⠃⠀⠀⠤
⠀⠀⠀⠀⠀⢀⣀⢀⡠⠤⠄⢤⣤⠐⠠⠀⠀⠀⠀⠀⠀⢀⠀⠂⣼⢢⡞⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⣠⣠⠞⢋⡴⡼⣀⡤⠞⠀⠀⢠⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢀⡈⠁⠈⠙⠒⠾⣖⣩⡏⢭⠤⠀⠀⠀⠐⠀⠀⠴⠀⢳⣠⠟⠂⢀⣤⣤⠤⠤⠴⠶⣞⡻⢛⡁⠀⢈⡘⢋⣉⣀⡴⠒⠊⠁
⠀⠀⠀⠀⠈⠛⠆⠀⠀⢀⡀⠈⠳⡄⠐⢉⣃⠄⠀⠀⠀⠀⠐⡶⢼⡇⠉⢠⣂⠀⢀⣠⠴⠁⠈⠁⡠⠊⠉⠂⠀⠁⠁⠀⠀⢀⠔⠁⠀⠀⠀⠀⠠
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠓⠀⢹⠉⠽⢚⠃⠄⠀⠀⠀⠀⠀⠈⠳⣄⣀⣉⡙⠉⠀⣀⣠⠴⠋⠳⠂⠀⠀⠀⠈⠁⠐⠁⠁⠀⠀⡐⠀⠂⢰
⠀⠀⠀⠀⠈⠀⠀⢠⡆⠀⠀⠀⠀⠈⢇⠀⡟⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⣉⡼⢤⡀⠀⣀⠀⠘⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⠀⢰⡅⠘⡦⢦⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢣⣀⠀⠀⢀⠀⣰
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢈⡈⠙⡿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠒⠲⠓⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠒⠐⠉⠁⠈⠈⠁⠀⠒⠄⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠟⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⣀⣀⣤⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣟⡉⣉⣁⣀⣠⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠻⠛⠛⠛⡿⢿⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠘⠻⢲⣄⠀⠀⠈⠙⠢⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠑⢢⣄⡀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠈⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⢰⡇⠀⠀⢀⠳⣶⣶⣤⣄⠀⠀⠀⠀⠙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢸⠇⠀⡆⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣠⠏⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⡾⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣠⠶⠚⠉⠁⠀⠀⠀⠈⠙⠶⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⠖⠖⠀⠀⠊⢹⣦
⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⣚⡏
⠀⠀⠀⠀⠀⠀⠛⠿⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠛⠋⢀⡤⠀⠀⠀⠀⢴⡇
⠀⠀⢰⣄⡀⠀⠀⠀⠀⠉⠛⠺⠿⢏⣻⣄⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠐⠢⠄⠀⠀⠈⠀⣀⡠⠎⠀⠀⠀⣞⠀⠀⠀⣾⠇⠀⠀⠀⢀⣾
⠀⠀⠸⠿⣽⣲⢤⣄⣀⣀⠀⠀⣦⣀⣠⣬⣤⣿⠋⠉⠀⠀⠀⠀⠀⠠⠤⢄⠀⠀⠈⠁⠀⠀⣀⣠⡤⠒⠋⠁⠀⠀⣠⠺⠇⢳⣤⢀⡤⠂⠀⠀⠀⠀⣰⠏
⠀⠘⣦⣤⣀⠀⠉⠁⠘⠻⠁⢀⣟⠀⠀⠘⠉⠀⠀⠀⠀⠀⠒⠒⠦⠄⠀⠀⠀⠀⠀⡀⠴⠒⠉⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠰⠉⢾⠁⠀⠀⠀⢀⣰⠁
⠀⠀⠈⠙⠛⠿⠇⢰⢦⣤⠀⠼⠃⠀⠀⠀⢀⡀⠀⠉⠉⠓⠀⠀⠀⢀⣤⠤⠐⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⠀⠀⣠⠖⠂⠀⠀⠀⠈⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠐⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢹⡞⠸⡇⠀⠀⠀⠀⡀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠤⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⣀⠀⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⢀⣴⡾⠓⠂⠀⠀⠰⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⢄⠀⠀⠀⠀⠀⠹⣹⡧⠀⣀⣠⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⡀⠀⠀⠀⠹⣿⣿⣿⣿⢿⣦⣄⣀⠀⠀⠀⠀⡀⠀⠐⠛⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠉⠛⠿⣷⣶⣌⣉⡳⠶⠂⠈⠀⣀⣠⡾⠃⠀⠀⠀⠀⣀⡀⠺⠋⠀⠀⠀⠈⠙⢆⡀
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣤⣴⠷⠚⠁⠀⠀⠀⠀⠀⢀⠚⠁⠀⠙⣶⣤⣄⣀⣀⣠⠞⠛⢧⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠊⠉⠁⠽⣍⣹⡥⠀⠀⢘⡇
⠀⠀⠀⠘⢦⣄⣀⣀⠀⡀⠀⠀⠀⠀⠀⣀⣠⣴⠋⠀⠀⠀⠀⠀⠓⠄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣠⡆⠀⠀⠀⠀⢸⡏⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠉⠛⠻⠿⠯⣤⣈⠛⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢤⣄⡀⠀⠀⣀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⡀⠀⢀⡀⠓⠦⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉

⠀⢀⡀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠤⠄⡀⠀⠀⠀⢀⡀⠀⠀⠀⡀⣠⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⠄
⠀⠘⠀⠀⠀⠀⠀⠈⢄⠀⠰⠁⢀⠀⠉⠆⠀⠀⠌⠠⠊⠠⠀⠟⠊⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠈⠀⠡⣈⢀⡄⠐⠰⣲
⠀⠀⠐⠀⠐⠀⠀⢉⠣⠀⠀⠣⡀⠈⠀⠈⠆⠈⢠⠴⡀⠊⠀⠀⠀⠂⠀⠠⠀⠄⠀⠁⠀⠀⡠⠁⠀⠒⠄⠀⠉⠉⠀⢐
⠀⢀⠀⣋⡀⠀⠀⠀⠈⣀⢀⢀⠈⠒⠈⠄⢀⡴⠀⡯⢚⠁⠀⠀⢠⠐⠂⡐⠠⢀⢀⠀⢀⠜⠀⢣⢄⣀⡀⠀⠀⠀⠤
⠀⠘⠀⠀⡆⠀⡠⠊⡁⠀⠃⠂⢌⡑⢄⠀⠸⠋⠀⢸⡵⠀⠀⢸⠃⠀⢀⡅⡀⠘⠄⠐⠁⢀⠀⠠⣀⡀⠀⡀⠠
⠀⢠⠖⢦⠀⢄⣠⠒⡂⢜⣊⠼⠓⢊⠁⢠⠒⠒⠤⡀⠃⠀⠀⠀⠁⠨⠉⠁⠀⠀⠀⠀⠠⠂⢤⠀⠠⠀⠀⠁⠀⠈
⠀⠀⡆⣈⢂⠀⠀⠀⠀⠒⠒⠒⠈⠁⠀⡌⠀⠀⢰⠀⠰⢠⠀⠀⠂⠆⠀⢀⣴⣶⢻⣟⣳⡆⠀⡀⠀⢀⠀⢀⡰⠉⡘
⠀⠀⡄⠂⢠⠀⠀⠀⢖⠒⠀⠠⠀⢲⠆⠑⠀⠲⠈⠀⠀⠁⠃⠀⠀⠀⠀⢀⢀⠽⠉⠉⠉⠉⠀⠀⡀⠐⠀⠀⠉⠉
⠀⠀⠈⠉⠁⠔⢄⠀⡄⠉⠀⠒⠀⠁⢀⠀⣴⡢⡄⠀⠠⠀⠀⠀⢀⠖⡆⠀⠀⠀⠀⠍⠀⠁⠀⡀⠃⠀⠀⡔⠉⢆⠁⢠
⠀⠦⠀⠀⠈⠀⠀⠀⠀⢀⠀⢈⠈⠡⠏⠓⢉⠠⠣⢶⠠⢅⢤⡤⠀⠀⠀⡀⠈⣁⠀⠈⠈⠀⠂⠀⠀⠀⠨⠀⡠⠊⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠐⠀⠀⠂⠈⢀⣐⣃⡠⠤⠗⢉⠀⠀⠀⠀⠰⠀⠀⡀⠼⢑⠀⠉⡂⠲⢀⠑⢀⡱
⠀⠀⠐⠀⠘⢀⠀⠀⠀⠀⠀⠤⠀⠀⠘⠀⠈⠉⣤⠀⠀⢘⠭⠁⣀⠀⠐⣁⠀⠀⠀⠁⠀⠀⠀⠀⠀⢈⠀⠀⠀⠎
⠀⠐⠂⠀⠀⡠⠄⠀⠀⠊⢟⠀⠀⢠⠶⠛⠉⠐⢹⣶⠄⠈⡠⠀⠀⠀⠀⠈⠀⢠⠄⠀⠀⠀⠀⠀⠀⣡⠀⠀⠘⠀⠂⠄
⠀⠰⠠⠍⢀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⢈⠠⠒⠀⠀⠀⠀⠉⠉⠉⠈⠐⠡⠄⢀⣀⠀⠂
⠀⢠⠀⠀⡀⠄⠈⡆⡕⠀⠈⠀⠐⠀⠀⠠⠒⠃⠀⠀⠀⢰⠀⠀⠀⠌⠀⠀⠄⠠⠏⠀⡀⠀⢀⠠⠀⠀⠙⠇
⠀⠀⠀⡀⢀⡄⠀⢡⠁⢀⡀⠌⠀⡄⠂⠂⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡰⠒⠀⠀⠒⢅⡀⢀⠰
⠀⠠⠐⠊⠸⠈⠆⠈⢀⠡⠀⠀⠦⠠⢖⠀⠀⠀⠈⠁⠀⠈⠀⠐⠀⡄⠀⢠⠂⠉⠀⠀⠀⠈⠀⢀⠜⡀⠀⠀⢻⠧⠂⠁
⠀⠀⠠⠨⠄⠀⠂⠀⠀⠒⠈⠀⠀⠀⠀⠄⠀⠀⠀⠠⠒⠃⠀⠀⣀⠀⢌⢀⠢⠤⠬⠔⡀⠤⠔⢊⠈⠃⡀⠈
⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠈⠠⠂⠀⣀⡀⡔⠒⠒⡆⠀⢢⠀⠐⠀⠀⠁⠀⠈⠀⠠⡈⡀⢄⠀⠠⠀⠈⠀⠀⠀⠀⠐⠁
⠀⢀⡀⠐⠀⠀⠀⠀⠂⠄⠁⠀⠀⠘⠄⠂⢘⣀⣸⠀⠀⡀⠀⠐⠄⢤⠆⠀⠀⠈⠚⠁⠡⠊⠈⠠⠁⠀⠤⠀⠐⠀⠒⢤
⠀⠀⣠⡶⢀⡶⠀⢀⠀⠃⡀⠂⠈⠠⠀⠀⡀⠄⠠⣀⠀⠀⠘⠀⢀⠀⠀⠀⠃⠀⠠⣀⣠⣤⠄⠀⠀⠀⢄⠀⠀⠀⠀⠔
⠀⢸⣆⠅⠊⠀⡀⠁⠀⡂⠀⠀⡀⢊⠀⠌⡠⠊⢉⡉⠠⠀⠈⠠⠊⠀⠀⠀⠁⠀⢀⠜⠈⠡⡀⠀⠀⠀⡈⠀⠈⠁⠁⢠
⠀⠀⠁⠂⠀⠀⠃⠀⠀⠈⠀⠉⠀⠈⠀⠋⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠘⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠶⢦⣤⠶⣴⠄⠀⠀⠠⠤⠦⣤⢤⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⣿⡆⢰⡏⣷⠀⠀⠀⢀⠀⣤⣀⢀⣠⡄⣴⣄⠀⣤⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢸⡇⠈⠃⢻⡇⠀⠀⢸⠀⠋⠻⠚⠛⠀⠃⠛⠋⠘⠁⡟⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⢀⡼⠃⢰⠀⣼⠀⡄⠂⡶⣄⡀⡇⢀⡄⢀⠐⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⢁⠀⠇⠀⢁⠇⠰⠁⢸⡇⠈⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢨⠐⠠⠀⠈⠀⠀⠀⠈⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢙⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠁
⠀⠀⠀⠀⠀⠰⡖⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⡄
⠀⡠⠚⣉⠶⠐⢶⣊⣁⠀⠐⠛⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠶⠶⠶⠒⢒⡒⠒⠶⣄⠀⠀⡤⠂⠀⠈⠀⠀⠀⠀⠀⣠⠞⠛⣇
⡞⠳⠶⣅⠀⠀⢘⣃⣈⣹⡄⠀⠀⣧⡀⠀⡀⠀⠀⠀⠀⠀⠠⣏⠀⠀⠀⠀⠀⠀⠀⡀⢉⠙⢢⡌⣧⠀⡈⠠⢒⣤⠀⠀⠀⣴⠟⢫⣾⠷⠋
⡇⠀⠀⠈⠙⠛⠋⠉⠉⠉⢙⡶⣾⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠂⠀⠀⠀⠈⠀⢐⠀⣐⢉⣠⣼⠀⠋⠒⠸⠿⠄⢀⣩⡴⠖⠋⠁
⢰⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢻⠉⠀⠀⡄⠀⠀⠀⠀⢀⠜⢿⣒⣷⡖⢒⣷⣖⣓⣾⣷⡿⢿⣿⡿⠀⠀⠁⠠⠲⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⢸⠀⡆⠀⠀⠀⠀⠀⠠⠂⠀⣀⣨⠇⠀⠀⠣⠤⠤⠌⠀⠸⣆⠤⠌⢉⣉⢉⡉⠩⠭⠄⠒⣊⡥⠞⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⠀⠀⠀⠐⠀⠘⢠
⠀⠦⢤⣤⣤⣄⣀⣤⣠⡴⠞⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠘⠀⠰⢄⡉⠒
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣈⡉⠉⠐⠢⣄⡀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⢠⡏⠀⠀⠐⠀⠀⢀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⣀⠤⠀⠀⠄⠀⠀⠀⠀⠀⠀⢠⠒⠀⠀⠈⠐⢠⡀⠙⠲⣄⠀⠀⠀⢳⢸⠀⠀⠀⠀⡟⠀⠀⠀⠀⢶⠺⠛⠻⠶⡶
⠀⠀⠀⠄⠀⠀⢠⠀⠀⠀⠀⠀⠈⠣⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠈⠢⡀⠙⢢⡀⠀⠘⢸⠀⠀⠀⠰⠁⠀⠀⠀⠀⠈⠐⠀⠢⠑⠆
⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠶⠀⠀⠀⠀⡴⠁⠀⠀⠀⠖⠀⠀⡀⠀⣀⣼⡦⠰⠇⠀⠐⠀⠀⠈⢪⠀⠀⠀⠀⠀⠀⠀⠁⢈⠰⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣼⢃⡀⠀⠀⢀⠀⣀⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢀⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣰⠃⠀⠐⢀⣠⡼⠞⠋⠈⠾⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢨⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⡀⠀⠀⠀⠂⠐⠒⠐⠀⠀⠀⢠⡇⣀⣬⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣄⣀⠀⠀⠀⠤⠆⠀⠀⠀⠀⠀⠀⠞
⠀⠀⣀⠠⢄⡀⠀⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⣀⣤⠶⡾⠛⠓⠶⠦⢤⡀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠐⠁⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⠤⠀⠀⠀⠀⠀⠀⣠⠞⠃⠀⠰⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⡀⠠⣬⣱⣧⠱⡀⠠⠄⠀⠀⠀⠀⡀⠀⠀⠤
⠀⡆⠀⡇⠀⠈⡇⠀⠀⠀⣠⡾⠛⢘⠿⠒⠓⠒⠲⢦⣀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣛⡷⠀⠀⢉⣳⡌⠈⢩⡆⢿⢠⣠⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⡇⣤⠃⠀⠀⡇⠀⠀⢴⣿⠃⡠⠋⠀⠀⠀⠀⠀⠀⠙⡃⠀⢼⠀⠀⠃⢀⣀⣤⣴⣾⡿⠛⠉⣭⠿⠀⣄⠀⣿⠃⣄⣨⢱⣿⣾⡟
⠀⢛⠺⡀⠀⢠⡇⠀⠀⠲⣝⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠈⠻⡿⡟⠋⢁⣬⡥⠔⢿⣛⣾⢴⠖⣿⠁⠀⢰⠀⠉⠙⠛⠉⢩⡇⠀⠀⠀⠀⠀⢠⠀⠚⠒
⠀⢸⣄⡇⠀⢸⡇⠀⠀⠀⠈⠉⠑⠒⠒⠤⠤⠤⠤⠄⠐⠃⠀⠀⠀⢱⣾⣤⣸⣤⣶⡿⠿⠏⠈⣀⡾⠃⠀⠀⠸⡆⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⡌⢀⡠⠂
⠀⠈⡇⠀⠀⣾⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠮⣀⣀⣈⣉⣀⠤⠔⠚⠉⠀⠀⠀⠀⠀⠏⠀⠀⠀⠜⠇⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠹⣄⡸⠃⠀⠀⠀⠀⠀⠀⠈⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⣀⠀⠀⠀⠀⠀⠒⠀⠒⠒⠀⠀⠀⢀⡀⠠⢄
⠀⠀⠀⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣨⣤⡼⠿⠫⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠠⠄⢀⣄⠑⢄
⠀⠀⠀⠀⡇⠀⠀⠀⢠⡄⠀⠀⠄⣤⡠⢤⣄⣀⢀⣁⣠⠀⠀⠀⠀⣀⢀⣤⣤⡴⠿⠛⠋⠁⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣯⠀⠈⣳⣄
⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣈⣁⣀⣈⣁⠀⠀⠐⠀⠸⠉⠁⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⣦⣀⡀⠀⠀⠤⠶⠛⣽⢠⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⡠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠀⠀⠁
⣿⣾⠾⠷⣿⣿⣿⣾⣿⣿⣾⣷⣷⣾⣿⣷⣶⣿⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣶⣷⣾⣷⣿⣶⣶⣾⣷⣷⣷⣶⣷⣶⣾⣶⣶⣿⣷⣾⣿⣿⣿⣿⣶⣿⣷
⣿⣷⣏⣻⣧⣤⣤⣤⣤⣦⣤⣾⣦⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡤⣤
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠙⠲⡟⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⡀⣤⣋⡷⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣤⠤⠞⣻⡥⣤⡷⣄⠀⠀⠀⠀⠀⠀⢀⡴⠒⠲⠦⣤⠴⠚⠉⠉⡇
⠀⠀⢀⡼⢣⡤⣼⣆⠀⠀⠙⠢⣄⣀⠀⠀⣀⠀⠀⠀⢸⣡⢇⣴⣏⣭⣷⢯⡽⠛⡆⠀⠀⠀⠀⠀⠸⣅⠀⠀⢀⡤⠶⠦⣄⠀⢳⣀
⠀⠐⠛⠲⡏⠀⠀⠉⠳⣄⡀⠀⠀⠈⠉⣻⣹⠀⠀⠀⢾⠻⠿⢾⣁⣄⣽⡞⠁⠀⢻⠀⠀⠀⠀⠀⠀⠈⡷⠀⡏⠀⠀⠀⢸⡆⠀⠈⢳⡀
⠀⠀⠀⠀⠹⣄⠀⠀⠀⠈⠙⠛⠻⠿⣏⣁⡍⠀⠀⠀⠘⣆⠀⠐⠂⢠⠏⠐⠀⠀⠈⣇⠀⠀⠀⠀⣠⠞⠁⠀⠳⣄⣀⣀⡼⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠙⠦⢤⣀⣀⣀⣀⣀⣼⣁⡇⠀⠀⠀⠀⠘⢦⠀⢠⠏⠀⠀⠰⠀⠀⠸⡄⠀⠀⠀⡇⠀⠀⠀⠀⣀⣉⣁⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠙⠃⠀⠀⠀⠀⠀⠈⢳⠇⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠙⠲⠶⠒⠋⠉⠁⠉⠉⠓⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⡀⠀⠘⠀⠀⢂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠹⣄⡀⠀⣄⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠘⠧⣽⡀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢦⢠⡤⣼⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢳⡀⠀⠀⢠⡞⣠⠀⠀⠀⠀⢀⣄⠀⠀⠀⠈⢳⡼⠛⢦⡼⢾⠙⢶⣳
⠀⠀⠀⣠⠶⠶⠶⠖⠛⠛⠒⠒⠒⠒⣦⠀⠀⠀⠀⠀⣾⣛⣚⣛⣛⡇⠀⠘⣇⢳⢀⣤⣄⣴⡿⠋⠀⠀⢸⣛⡛⠳⣴⡋⡇⣾⢧⠈⢻⡀
⠀⠀⠀⠙⣟⠉⠉⠉⠉⠉⠉⠉⠉⡿⠉⠀⠀⠀⠀⣠⠟⠉⠉⠉⠉⠓⢦⠀⠟⣀⣻⡀⠈⢿⠄⠀⠀⠀⠈⣠⣸⣳⡀⠙⣧⡏⣸⣇⣠⣷⠆
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⡞⠉⠙⢿⠳⠛⠀⠀⠀⠀⠀⠘⣏⠉⠉⠛⠋⠉⠉⠁⠀⡟
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡾⠶⢿⡶⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣠⡤⣤⣷⣠⣁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣹⠀⠀⠰⣇⠐⠀⠙⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠚⠛⠛⠓⠛
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⠛⢛⣿⡿⠲⠵⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢀⡤⣤⠤⣀⣠⣀⣠⣀⠀⠀⠀⠀⠀⠀⠰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡉⠉⠛⠲⠦⣄⡀
⠀⠀⠀⠀⣠⠟⠛⠉⠛⠲⢤⡿⠶⣿⣶⠦⣄⠀⠀⠀⠀⠀⠀⣠⠶⡛⠉⠉⠯⠛⠲⣤⡀⠀⠀⠀⠀⠀⠀⢸⠾⠧⣤⣠⠆⠀⠀⠉⠳⣄
⠀⠀⠀⣼⠁⠀⠀⠀⠰⠀⠀⠙⢾⠓⣼⡧⣌⢧⠀⠀⠀⠀⡾⢡⠆⠙⠀⠛⠀⠘⢁⣤⠹⡄⠀⠀⠀⠀⠀⣼⠹⢦⠀⢈⡙⠲⢦⡀⢀⡀⠳⣄
⠀⠀⠀⠹⣄⠂⠀⣤⠀⠀⠈⠀⣌⢳⡘⢾⣻⣸⠄⠀⠀⠀⢹⡦⠤⠤⢤⣼⣭⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀⣿⣃⡾⢀⡴⡒⣒⡶⣝⢻⣄⡤⠿
⠀⠀⠀⠀⠈⠳⢤⣀⠀⠠⠆⠀⠀⠀⢧⣸⣹⣾⠀⠀⠀⠀⢼⡳⠒⠛⣲⣶⣖⣛⣓⣶⣞⣹⠆⠀⠀⠀⠀⣟⠡⠀⣟⢾⣹⣽⠽⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠃⠀⢸⡏⡽⠃⠀⠀⠀⠀⠈⢿⡛⠉⠉⠉⠛⠯⣍⠉⢉⡟⠀⠀⠀⠀⠀⡏⣙⡦⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠶⠶⠚⠛⠋⠀⠀⠀⠀⠀⠀⠛⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡠⠄⠐⠒⠂⢄⠀⠀⠀⠀⠀⣀⠀⠇⢀⡀⠀⠀⠀⡠⠎⠠⠵⢄⠀⠀⠀⢖⠖⣹⡶⢪⡦⣄
⠀⠀⠀⢈⣀⣀⡀⢀⣀⣀⣡⠀⠀⠀⠸⡭⠭⠭⠭⡵⠀⠀⠀⢧⣤⠤⡥⡼⠂⠀⠀⠧⢤⣣⣰⡷⠼⠇
⠀⠀⠀⢱⡭⣴⠦⠽⡮⣽⡽⠀⠀⠀⠀⠃⠀⠀⢰⠀⠀⠀⠀⠈⣴⣉⢱⠃⠀⠀⠀⠸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠑⠂⠛⢇⡵⠓⠁⠀⠀⠀⠀⢸⠀⠀⠘⠀⠀⠀⠀⠀⠰⡊⡏⠀⠀⠀⠀⠀⡆⠀⠀⢀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⢀⠔⡨⠥⠠⢍⢆⣴⢢⠀⠀⠀⢀⠔⠒⢆⠐⡆⠢⡄⠀⢀⠔⠂⠀⠐⠢⣄⠀⠀⠀⢀⠔⠀⠐⢄
⠀⠀⠀⠃⡏⡥⡥⣔⣷⣥⠘⢄⠆⠀⢠⡅⠀⠀⠈⢢⠼⠒⠘⠀⠰⡒⡒⢐⠒⠒⠎⠀⠀⠀⠃⠀⠀⠀⢠
⠀⠀⠀⢃⢧⡡⠠⡀⢈⡜⡁⠀⠀⠀⣦⡈⠢⣀⠔⠃⠀⠀⠀⠀⠀⢁⢠⠸⠠⢠⠀⠀⠀⠀⠤⣀⢀⠔⠁
⠀⠀⠀⠀⠓⠤⠉⠋⠭⠚⠁⠀⠀⠀⢇⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠉⠁⠀⠀⢴⡊⡖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⢠⠀⠀⠀⠀⠀⠀⢠⣒⡆⢰⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⡴⢯⡭⠣⠡⢦⠀⠀⠀⠀⡤⠄⠐⠚⠤⢤⡤⡀⠀⠀⠀⠀⢧⡓⣓⠀⠀⠀⡠⢊⠢⡄⢊⠢⡀
⠀⠀⠀⡌⡜⠁⠀⠈⠉⠙⣵⠀⠀⠀⠐⣀⠀⠀⣠⠿⠓⠁⠀⠀⠔⠀⡟⠁⠈⢲⠀⠐⠁⢠⠁⢸⠘⡄⠈
⠀⠀⠀⣏⣀⣀⡀⣀⢀⣀⠝⠀⠀⠙⠤⠈⠀⠀⠄⠤⠊⠀⠀⠀⠀⠀⡇⠀⠀⠈⠀⠈⢄⠠⢀⠼⡀⢃⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠑⠒⠇⢀⡀⠀⠀⠀⠀⠙⠁⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⢀⢠⡄⡀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⣠⢤⣀
⠀⠀⠀⠀⣀⣀⢰⣧⣾⠗⠛⡄⠀⠀⢀⢋⢘⡀⠀⠀⠀⠀⢀⠞⠙⣾⣬⡣⠀⠀⡤⢤⠄⠢⡤⠤⣄⠀⡀
⠀⠀⢀⢧⣶⡮⠿⠓⠁⠀⢠⠃⠀⠀⢪⠭⡉⢸⠀⠀⠀⡠⠗⠊⠉⠀⡠⠃⠀⢠⡄⣀⡤⠄⣤⠀⣁⣠⣅
⠀⠀⠈⢶⠁⠀⠀⠀⡠⠔⠁⠀⠀⠀⢀⠤⠃⢆⠀⠀⢎⠀⠀⠀⢀⠎⠀⠀⠀⠐⣊⠑⣢⢘⠠⠑⠢⢛⡖
⠀⠀⠀⠀⠑⠒⠂⠉⠀⠀⠀⠀⠀⠀⠨⣀⣀⡸⠀⠀⠀⠉⠢⡠⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣤⡀
⠀⠀⠀⠀⠀⣀⠤⠶⠖⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠩⠀⡀⠈⣈⢳⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠹⡄
⠀⠀⠀⢀⡞⡁⠒⣀⢁⡀⠆⠙⣆⠀⠀⠀⠀⠀⠀⣤⡤⣤⠴⣷⢴⡤⣤⠀⠀⠀⠀⠀⠀⠀⢀⠧⢀⠀⠀⠀⣀⣼⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⡇⠑⢰⠁⠀⢸⠐⠀⣿⠀⠀⠀⠀⠀⠀⢹⡉⠉⠉⠉⢉⠉⡟⠀⠀⠀⠀⠀⠀⠀⠈⢷⠚⡳⠛⡦⣾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⡼⠁
⠀⠀⠀⠘⢧⠈⡀⢙⠛⢣⠀⣠⠇⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠙⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡀⢂⢐⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣸⠃
⠀⠀⠀⠀⠈⠛⠶⠬⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡜⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠓⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠾⠇

⠀⠀⠀⢀⣠⡤⠶⠶⠶⠒⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡦⣤⢤⣄⡀
⠀⠀⠀⣟⡠⠐⢒⢄⠀⣴⠒⠤⣹⠆⠀⠀⠀⠀⠀⠀⣠⠼⠧⠤⠿⣤⡀⠀⠀⠀⠀⠀⠀⢀⡖⠉⠀⠀⠂⠠⠙⢳⡄⠀⠀⠀⠀⠀⠀⣾⣿⣼⣷⣿⣼⠾⣽
⠀⠀⠀⠸⡴⡩⢊⡉⡜⡇⠛⣠⠋⠀⠀⠀⠀⠀⠀⢘⡧⠒⠒⠖⠒⠺⡅⠀⠀⠀⠀⠀⠀⠸⡧⠤⣤⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⢹⣿⡇⣿⢸⢹⣾⠏
⠀⠀⠀⠀⠹⣄⣈⣆⢨⣮⣼⠃⠀⠀⠀⠀⠀⠀⠀⠸⡧⢄⢀⠼⡀⣠⠇⠀⠀⠀⠀⠀⠀⢸⣶⣶⣤⣴⣶⣦⣤⣶⣇⠀⠀⠀⠀⠀⠀⢸⡏⠙⠛⠛⠙⣻
⠀⠀⠀⠀⠀⠹⣏⢡⢦⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣥⣤⡼⠋⠀⠀⠀⠀⠀⠀⠀⠓⣖⡒⠣⠚⠑⠒⠓⣸⠋⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⠿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠶⠶⠶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣆⠀⠀⠀⠀⠀⠀⢀⡤⣤⡴⣲⣤⠦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⣼⠀⣗⣇⡽⢿⡄⢹⡀⠀⠀⠀⠀⠰⣯⡻⣿⣿⡟⣆
⠀⠀⠀⡤⢶⠟⠛⠁⠉⠙⠛⢷⣄⠀⠀⠀⠀⠀⠀⢠⠈⢻⣯⣿⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡏⠃⣧⣾⡀⠘⡇⠀⠀⠀⠀⠀⡇⠱⡘⣿⣿⣾⢦
⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⢴⡶⣶⣚⣛⣛⣒⡒⣶⠀⠀⠀⠀⠀⠀⢘⡇⠀⢿⣥⡷⠗⡆⢀⡇⠀⠀⠀⠀⠀⡇⠀⠘⢞⢷⣿⣿⣆
⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠈⡇⠀⣿⠿⡤⣿⡇⢨⡇⠀⠀⠀⠀⠀⡇⠀⠀⠈⢣⠻⣿⣿⢦
⠀⠀⠙⠛⠛⠛⠓⠛⠓⠒⠒⠒⠛⠋⠀⠀⠀⠀⠀⣿⢿⣾⣿⣶⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⢷⠀⢸⣦⡦⢿⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠱⡙⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⣀⣉⣁⣨⠇⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⢿⣤⠾⠓⠋⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠒⠒⠚⠚⠛⠉
⠀⠀⠀⠀⠀⣀⣀⡀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⢰⠃⠀⠹⡞⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⣀⣀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢹⡄
⠀⠀⠀⠀⣠⣄⣀⣀⣰⣀⣀⣏⠀⠀⠀⠀⠀⠀⣠⠶⠋⠉⠩⠍⠉⠙⠢⣄⠀⠀⠀⠀⠀⠀⣀⡴⡚⢻⠿⠻⡶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢠⡾⡷⠋⠀⠀⠀⠀⠈⠺⣿⡀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⢸⡇
⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣴⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣀⠀⠀⣿⡔⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢺⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠻⣦⣄⣀⣀⠀⠀⣀⣀⣤⣾⠵⠋⠀⠀⢻⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠹⢤⡤⠞
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠈⠙⠢⢭⣉⣉⠽⠛⠉⠁⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢹⡌⢿⡀⠀⠀⠀⢀⡔⠂⠁⠀⠀⠀⠀⠀⠀⢠⡾⣣⠶⣤⡀⠀⠀⠀⠀⠈⠉
⠀⠀⣀⣠⣄⠁⣤⢀⡀⡄⠀⠀⠂⣤⠤⠄⠐⠀⠀⠀⠀⢸⡀⢸⡧⠈⠣⡄⠀⠠⠉⠶⠀⠀⠀⠂⠀⠀⢀⡰⢿⣜⡱⢶⡌⠀⠀⠀⠀⠀⠀⢀⡴⠶⣤
⠀⠀⠉⠉⠉⠀⠸⠼⠃⠇⠀⠀⠺⠶⠒⠺⠛⠁⠀⠀⠀⠘⡗⠈⠡⠀⣰⠇⠀⠀⠤⠼⠒⠈⠤⠀⠀⠀⠚⢵⢏⣺⡷⠋⠀⠀⠀⠀⠀⠂⠀⢺⣗⣤⠟
⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠖⠛⠁⠀⠀⠀⠀⠀⠀⠤⠒⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠰⣦⠙⠃⢰⠀⠀⠀⠛⠿⣿⡿⠛⠁⠀⠀⠀⠃⣀⠈⠓⢄⣤⠀⠀⠀⢠⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⢞⠁⣽⠆⠉⠀⠀⠀⠀⠛⠇⠀⢀⠴⠋⠀⠀⠀⠄⠀⠀⠀⠀⣀⠀⠀⢠⣴⠏⢠⣤⠀⠙⠃⠀⠀⠀⠀⢠⠙⠃
⠀⠀⠀⠀⡀⠻⠀⠀⠀⠀⠀⠧⠀⢠⣠⡤⠀⠁⠀⠀⠠⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠃⠀⠙⣁⣠⣤⣤⣤⡀
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠰⠀⢀⠀⠀⠀⠀⠀⠀⣦⠤⡤⠀⠀⠀⠀⠀⠙⠇⢠⣄⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⢘⠛⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⡉⠀⠀⠈⠀⣀⠀⠐⢦⡀⠀⠛⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⡷
⠀⠀⠀⠀⠀⢾⡧⣴⠄⠀⠀⠧⠀⠁⠀⠈⠀⠀⠛⠀⠀⠀⠁⠀⠊⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⡆⠀⠀⠀⠒⠃⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉
⠀⠀⠀⠀⠀⠘⢷⠜⠃⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⠘⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄
⠀⠀⢀⣴⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⠀⠉⠟⡄⠀⠀⠀⠀⢰⠄⠸⣀⡴⠆⠀⡀⠀⠀⢄⠀⢰⠀⠀⠀⢠⣴⣶⣶⣶⡤⣄⡀
⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⡇⠀⠠⣠⡁⣠⡤⠘⠋⠀⠀⢈⡁⢀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠀⠉⢀⡰⠶⠃
⠀⠀⠆⠀⠀⠀⠏⠀⠀⠀⠀⠀⠈⠀⠀⢸⠁⠀⠀⠀⠀⠈⠁⠈⠈⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⣩⡁⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣶⡗⠀⠀⠰⠟⠆⠀⠀⢀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢤⠄⢨⠀⡀⠚⠁⠀⠀⢀⠀⠀⠈⠁⠀⠠⠀⠀⠀⠀⠈⠀⢀⠟⠀⠀⠀⠂⢀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣟⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠐⢣⠀⠈⠒⠂⠀⠀⠀⠀⠠⢠⡄⢠⣄⢹⡆
⠀⠀⠀⠀⠀⠀⠠⠘⠃⠀⠀⠀⠀⠟⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠯⠜⠃
⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⢠⣴⠶⠿⣷⣶⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣤⣦⠀⠀⢠⣶⡄⠀⠀⠀⢦⠀⠘⢇⠀⠀⠀⠀⠀⢀⣤⣤⣠⡄⠠⠶
⠀⠱⣤⣤⣄⣄⣰⣤⠆⠀⠀⠙⢿⣤⣿⣦⡼⠇⠀⠀⡀⠀⠋⠉⠃⠀⠀⠀⠠⠀⠀⡀⠀⡀⠀⠰⠀⠀⠸⠃⡰⣿⡟⢶⡏⠓⣤⠀⢿⠯⣍⡼⠇
⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠴⠶⠋⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠂⠈⢱⣏⣠⠼⠷⠞⠁⠀⠀⠀⠈⠁

⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡤⣤⡤⠀⠀⠀⠀⠘⠿⣿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⡄⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⣄⠀⠀⠀⠀⠀⠐⠀⡈⠀⠀⠀⠀⠀⠀⠀⠻⠷⠀⠀⠀⠀⠀⠆⣠⠆⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢲⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠺⠀⠀⠠⠀⠀⠀⠈⠻⠶⠶⠶⠟⠁
⠀⠀⠀⠀⣀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠐⠂⠠⠀⠀⢑⠀⠀⠀⠀⠀⠀⣀⣀⡠⠄⠀⠀⠀⢠⣬⡑⠢⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣾⣦⠄⠀⠄
⠀⠀⠀⠼⠃⣀⠴⢟⠀⠀⠠⠖⠐⠒⠀⠈⠆⠀⠀⠀⢴⣬⣿⣷⣤⡈⠀⠀⠀⠀⠀⣰⡀⠊⣱⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠒⠶⠐⠿
⠀⠀⠀⠲⠀⠙⢄⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣬⠋⣹⡄⢣⡷⠀⠀⠀⠀⠂⠙⠁⡟⠁⠀⠀⠀⠘⠛⢃⣀⡄⢶⡄⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠐⢠⣤⣤⣀⡀⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠐⠖⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⢱⡄⠀⠀⠀⠀⣀⣤⣴⠾⠟⠂⢀⠀⠀⡤⠈⠀⡀⠺⠆⠀⠀⠀⠀⠘⠛⠛⠂⠀⡄⠀⠀⠀⢈⠛⡀⠀⠰⣺⠉⣧
⠀⠀⠀⢶⣿⠿⠃⠀⠀⠀⠀⠃⠀⠀⠀⠁⠀⠀⠀⣶⠟⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠦⣿⡶⠀⠀⠀⢄⣠⡀⣀⣸⣀⡲⠐⠀⠀⠀⠀⢀⡀⠀⠀⢑⠊⠁
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠇⠐⠋⠀⠀⠀⠀⣼⡿⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠺⢀⢈

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⡛⠏⠙⢻⡋⠉⡟⠛⢻⡙⠏⣙⡿⢛⡋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣿⣿⣷⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠐⠂⠧⠤⠞⠁⠀⢀⡠⢄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠐⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀
⠀⠀⡠⢀⠀⠃⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⢴⠾⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠘⢈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⣀⠄⠐⠀⠀⠉⢁⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠠⠀⠠⠴⠒⠈⢘⡉⠀⠀⠀⠐⠂⠈⠉⠉⠀⠀⢀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠄⠀⠀⠈⠀⠀⠀⠉⠉⠁⠀⠀⠀⢀⡠⠄⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⡠⠀⠀⡄⡀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠰⡀⢢⡀⠀⣀⢀⠤⠐⠂⢘⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣀⠤⠀⡂⠀⠀⠀⡆⠀⠠⠤⠐⠴⠂⠆⠐
⠀⠀⠀⠐⠄⠀⢀⠘⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⡡⠀⠀⡇⠆⠀⠀⠃⠀⢀⣴⠄⠀⠀⠀⢰⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠋⠡⠀⠀⠠⠀⠀⢙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠂⠀⠀⠀⠚⠉⠁⠀⠀⠤⠄⠐⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠀⠀⠀⢘⢈⢸⡬
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠉⠀⠀⠁⠈⠉
⠀⠀⠀⠂⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠜⠐⠂⡈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⡀⠀⠀⠀⠀⠀⠀⠈⡀⠆⠀⠀⣄⠀⠀⠈⠉⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠁⠀⠀⠀⢐⠀⠀⠀⠀⡂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢠⡀⠁⡄⢀⢈⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡞⡉⢳⡄⠀⠀⠒⠀⠀⠀⠀⠀⠠⠤⡄⠴⠦⠀⠄
⠀⠈⠑⠤⠁⠀⠠⠔⠀⠀⠇⠀⠀⢀⠈⠒⠀⠂⠶⠒⠒⠚⠛⡆⠀⠀⠀⠀⠐⠀⠀⠀⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠈⢁⢀⠁⠒⠤⡀
⠀⠀⠀⠀⣀⡂⠂⠀⠀⠀⠀⠀⠀⠘⣄⠋⠄⠴⠌⡃⠉⠀⢠⡇⠀⠀⠀⠀⠐⠁⢇⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠌⠀⡤⠤⠀⢠⠀⠄⠄⢸
⠀⢠⠀⠀⣘⠑⠀⠀⠀⠔⡃⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠒⠒⠀⠀⡠⠊
⠀⠀⡀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠄⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠑⠂⠂⠀⠀⠀⠀⠀⠀⠀⢤⡀⠉⠑⠒⠚⠊⠉⢀⡠
⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⡀⠀⠀⠀⠎⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠉⠀⠀⠀⠀⠀⠀⢀⣼⣀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠉⠀⠒⠂⠀⠀⠀⠀⠒⠂⠈⠉⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠓⢺⠤⣄⣀⣀⣀⣀⣀⠀⠀⠠⠐⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠲⠚⠒⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⣸⣀⡠⢄
⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠤⠒⠋⠍⢀⡠⠚⣳⢦⡀
⢀⣀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⡀⠀⠀⠁⠀⠉⠀⠉⠙⠳⢄⡀
⠀⢆⣿⡑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣲⠤⢀⣀
⠀⢌⠛⡙⢷⣦⣤⣠⡤⠄⠀⠀⠀⠀⢀⣀⣀⣬⢴⣯⢠⣼⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣾⡷⠤⠒⣟
⠀⢀⣷⡊⠐⠶⠒⠿⣏⣹⣛⣻⠋⢭⣍⣡⣤⣀⣉⢩⣾⠁⠀⠈⠐⢄⠀⣠⠶⣾⡿⠋⣹⣏⣉⣉⡤⣤⡴⣞⣋
⠀⢸⠩⡓⠶⣄⣀⠀⠀⠀⠈⣑⠀⢀⡰⠀⠈⠭⠤⠎⣿⡀⡀⡄⠀⠀⣼⠉⠲⡌⠀⢮⡌⢿⠑⢺⢥⡂⠌⣓⡽
⠀⠈⠳⠄⠀⣄⡈⠛⠀⠤⡄⠀⣄⠉⣀⠀⠀⡀⢠⠞⢱⠙⢤⢣⠆⢸⣿⡇⢸⣌⣵⠪⠷⣘⡆⢘⠶⠼⠷⣧⡂
⠀⠐⡀⠀⠈⠉⠉⠉⠁⠒⠚⠃⠈⠛⠁⠀⠁⠈⠁⡀⠎⠀⠀⠙⢄⣋⠹⣧⠀⢿⠮⣉⡛⢒⠯⡴⣷⠒⠒⠓⠁
⠀⠀⠈⠁⠐⠒⠒⠂⠤⠤⠤⠤⠤⠤⠀⠀⠒⠀⠉⠀⠀⠀⠀⠀⠀⠙⡄⠹⡦⡞⢡⣈⢙⠆⠑⢌⣻⢓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠴⡐⡴⢳⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⠄⠀⠀⢀⠀⠀⠀⠀⠀⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠁⠀⠀⠀⠀⠘⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⠀⢄⠀⠀⠠⠀⠀⠀⡀⠔⠃
⠀⠀⠀⠀⠀⠈⠊⠀⡄⠄⠀⠀⠀⠀⠀⣥⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⢇⠀⠀⠠⠀⠢
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢿⠄⠀⠀⠀⠀⠈⠂⠀⠀⡀⠀⠀⠘⠒⠂⠀⠐⠂⠈⠀⠀⠀⠀⠈⠊⠠⠀⣀⣀⠁⠎⠀⠄
⠀⠀⠀⠀⠀⢐⠀⠀⠀⢀⠁⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣱⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠘⣇⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡆⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠰⣷⣀⠤⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⢁⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⠼⠄⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠰
⠀⠀⠀⠀⠳⠄⠔⠊⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠂⠀⠀⡠⠄⠒⠂⠐⠀⠄⠀⠀⠀⠁⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠐⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⢀⡧⠀⠀⡇
⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⢁⢈⢘⡀⠀⠀⠆⢀⠀⡄⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠱⡀⠀⠀⠀⠈⠀⠀⡰⠀⠀⠀⠀⠰
⠀⠀⠀⠿⢤⣀⣀⠀⠀⠀⠀⢀⡀⠀⠈⠁⠀⠀⢰⡀⢀⠄⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠲⠄⠀⠀⠤⠐⠁
⠀⠀⠀⠀⠀⠀⣉⠉⠉⠉⠉⠉⠀⠀⢠⢀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡂⡒⠠⡀⠀⠄
⠀⠀⠀⠰⢀⡀⠀⠀⠀⠀⢦⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠈⠀⠄⠠⠀⠈⠆
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡉⠀⠀⠀⠈⣆⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⡀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠂⠀⠃⠀⠀⠀⠆⠀⠀⡀⣀⠀⠀⢠⠀⠀⠀⠀⠀⢸⣝⠠⠐⠓⠀⠒⠒⠊⠁
⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣄⣀⣀⡀⠄⠊⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡀⡈
⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⠀⠉⠑⠚⠒⠋
⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠁⠀⠀⠤⠤⠀⠀⠉⠀⠀⠐⠦⡀⠀⠀⢎⠀⣈⡀⠠⢀⣠⠀⠀⠀⠀⠤
⠀⠀⠀⡡⣈⢹⡒⠒⡢⡄⠐⠒⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⣀⠙⠃⠀⠠⢠⠈⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠀⠒⠚⠀⠈⠉⠉
⠀⠀⠀⠣⠈⠀⠂⠀⠤⠢⠌⡀⠁⠀⠀⢰⣀⠀⠀⡄⠀⠀⠀⠠⠀⠰⠀⠀⢉⢀⡘⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠳⢄⣇⡀⠐⠂⠂⢀⣆⠀⠄⠐⠁⠀⠀⠀⠀⠈⠐⠄⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⢠⠆⠀⢀⠠⠤⢤⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠠⢀⠤⢲
⠀⢀⠀⠀⠀⠀⠀⢘⠉⠉⠉⡁⠀⠀⠀⠀⠀⢠⠕⠠⢀⡀⠀⠀⠀⠀⢠⠖⠉⠉⣐⣂⠤⠚⠚⠉⣰⠔⡇
⡠⠫⣻⠫⣀⠼⢟⣟⣀⣀⠀⠅⠀⠀⠀⠀⠀⠸⠀⠄⠀⠇⠀⠀⠀⠀⡄⠿⣴⡪⡽⢁⡠⢂⣲⡮⢔⡾⢃
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⠧⠄⠀⠀⠀⠀⠀⠈⠲⢤⣉⣙⠚⠛⠕⢊⣉⣡⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⢀⣤⣄⡠⠊⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠰⢂
⠀⠀⠈⣷⠋⠀⢀⠀⠋⢂⠀⠀⠀⠀⢀⣀⠀⣦⣴⣋⣉⠖⢫⠀⢀⡀⠀⠀⠀⠀⢨⠛⠓⠚⠓⡀
⠀⠀⠐⡯⠒⠒⢒⠚⢓⢿⠇⠀⠀⠘⣄⣦⣏⣏⠁⠀⡘⡾⢞⢳⣿⡌⠀⠀⠀⠀⠸⣶⣦⣤⣾⠇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⣽⢧⢭⣋⠽⠶⢺⣭⣠⠵⢊⡇⠀⠀⠀⠀⠀⡆⠀⠀⢠
⠀⠀⠀⠱⣄⡀⢀⠀⣀⡜⠀⠀⠀⠈⢫⡑⠒⠦⠵⡀⢀⠾⠗⢚⡽⠁⠀⠀⠀⠀⠀⠇⠀⠀⠆
⠀⠀⠀⠀⠘⠛⠋⠛⠛⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠿⠿⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⢰⣀⣀⡆
⠀⠀⣠⢴⠒⠒⢲⣤⠆⣰⡶⣢⠀⠀⠀⠀⠘⠣⣄⣀
⠀⡘⠁⡐⣰⡾⠋⡉⣞⠋⢞⠉⠀⠀⠀⠀⠀⡖⠋⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠢⢄
⢰⣷⣚⢿⣽⠀⠮⣀⠴⢀⣼⡆⠀⠀⠀⠀⠰⠛⠒⠒⠒⠚⢢⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡁
⠘⣟⠻⠿⢶⣿⣶⡶⠿⠟⢻⠇⠀⠀⠀⠀⢸⠸⣄⠀⣀⠆⡀⠀⠀⠀⡤⠎⢠⡀⠁⠀⠀⠀⠀⢁⠀⠘⠄
⠀⠘⢿⣒⠤⠄⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⠀⠑⢲⠛⡗⠊⠁⠀⠀⠀⠀⢇⠻⠿⠟⠀⠀⠀⠀⠰⠀⡠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢠⠀⠀⡲⣄⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⣀⢀⡀⠐⠂⠀⠀⠔⢁⡄⢀⠀⠀⠿
⠀⠀⠂⠀⡤⢈⠀⡀⠀⠤⠀⠀⠀⠠⠀⠈⠐⠀⣠⣄⠄⠀⠀⠀⢈⠀⠀⠀⠀⠰⣇⡠⠙⠛⠨⠚⠁⠆⠀⠈⠄⠀⠈⠂
⠀⠃⠐⠀⡀⠘⢀⠁⠀⠀⠉⠀⠀⠠⠀⠀⠀⠈⢀⡀⠱⠤⡅⠀⢀⠀⠀⠀⠀⢸⠛⠿⣷⣦⣱⠈⠀⠀⠁⠀⡀⠑⠀⠞
⠀⠰⡆⠀⠀⠣⠀⠀⢂⠀⢀⠤⠍⠐⣀⠀⠀⠀⠀⠀⠀⢀⣄⠈⠁⠀⠀⠀⠀⠻⣷⡢⢄⠉⠛⠈⠀⠀⠀⠈⠋⠀⡀
⠀⠀⠈⠀⠀⠀⠀⠀⠁⢀⡁⢤⠀⠀⠀⠄⠀⠀⠈⠀⠘⠻⠿⠀⠀⠀⠀⠀⠀⣀⠈⠛⢷⡽⢀⠁⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠂⢀⠃⠀⠒⠀⠂⠀⠀⠂⠀⠀⠀⠀⢠⠀⠄⠖⡀⠈⠐⠂⢁⠐⣄⠘⠛⠀⠀⠈⠀⠀⠀⠀⠄⠀⠠⠀⠀⠠
⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⡀⠀⠀⠀⠁⠁⠒⠂⠀⠠⠀⠀⠀⠀⠀⢡⠀⠀⠀⠂⣠⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠
⠀⠀⠁⠀⠴⠆⠠⢠⡀⠀⠀⠀⠀⠀⠀⡀⠀⠢⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠠⠀⢰⢹⡿⡏
⠀⠀⠄⠀⠀⠀⠀⠀⠙⢖⡂⢁⡀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣀⣀⣀⣤⣤⣤⣤⡀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⣸⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⡠⠀⠀⠀⣰⠻⢿⣿⣿⣷⣭⣭⣏⣨⣿⣿⣿⣿⠛⡆⠀⠀⠆⠀⠀⠀⠀⡔⠀⢿⠀⠀⡄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠂⠙⠀⠀⠀⢿⢘⣻⠻⠛⣿⢸⣿⡇⠾⢛⠛⡍⠿⡃⡇⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠰⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⣀⠀⠘⢼⣧⣄⣷⣾⣬⠿⠧⠿⠶⠿⠾⠷⢖⣁⠀⠀⠠⣀⠀⠀⡀⠴⠀⠀⠠⠢⡀
⠀⡐⠁⠄⠂⠀⢄⠀⠁⠀⠠⠀⢠⡾⠻⠎⠁⠠⠀⠀⠀⠤⢄⠀⢤⠀⠀⠀⠀⠊⠀⠌⠐⠀⠀⠤⠀⠘⠂⣀⣠⣤⣤⣤⠁
⢰⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠁⢳⡤⢈⢤⠀⠂⡀⠀⠀⠀⡁⠁⠀⠀⠀⠀⠀⢀⠀⠂⠔⠀⠀⠀⠀⠀⢰⡷⠲⠴⠞⣩⡷
⠈⡀⠀⠂⠤⠀⠁⠀⢠⠃⠀⠀⠐⢀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠑⠀⠉⣠⠂⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠰⠀⠀⡔⠡⠘⠀⠀⠀⠁⢀⡀⠀⠀⠀⠀⢠⠓⠄⠔⠲⠒⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⡰⠀⠄⠁⠀⠀⢪⠒⢹⠂⡄⠀⠑⠲⠷⢦⣤⡤⠠⠜
⠀⠀⡀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⢨⠉⠁⠀⠀⡀⠘⢐⠀⠀⠅⠀⠀⠰
⠀⠀⠙⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠙⠃⡀⠀⠀⠒⠀⠈⠀⠒⠀⠀⡀⠀⠀⢂⠀⠀⠒⠀⢀⠈⠀⠢⠤⠂⠀⠂
⠀⠀⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⠀⠆⠀⠀⠃⠀⠀⠁⠀⠰⠀⠀⠀⠀⢂⠀⠀⠀⠈
⠀⠀⠀⠀⣠⣄⡈⠘⠲⣄⣄⠞⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠿⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠉⠂⠀⡛⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠈⠒⢤⡀⠘⣜⣷⣦⣭⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⡿⢶⣄⠀⠀⠀⠉⢦⡈⠛⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⣀⣼⣿⡻⢇⢤⡀⠀⠀⠀⠹⣄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣧⠀⠀⠀⠀⠀⠀⠀⢀⣤⣯⣛⠇⠫⠻⠏⠁⠀⠹⢿⣶⣄⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣧⡀⠀⠀⠠⡤⣤⣸⡟⠋⠉⠛⢯⠈⠳⣄⡄⡀⣼⣿⣿⡆⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠈⣡⣶⣺⡟⢶⣜⠦⣴⣿⡝⢯⣾⣺⣿⠇⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⣴⡾⠟⣿⣿⠷⢋⣙⣷⠉⠿⠻⡾⠉⠉⠀⠀⢲⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⢀⣨⡍⠀⠜⠁⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⡀⠀⣤⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡳⣄⠀⠈⢛⡞⠁⠀⠀⠀⠀⢠⠾⠋⡀⠄⣠⣾⣿⣬⣾⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⢠⡛⢦⣄⡀⠀⠏⠀⠀⠉⠀⣘⣿⡿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣦⡀⢷⣄⠈⠙⠛⠓⠒⠚⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡄

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠤⠄⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠
⠀⠰⠀⠀⠀⠀⠀⠀⢑⣄⠉⢠⠁⠔⠀⠈⢢⠀⠀⢀⠇⠠⠔⠀⠠⠝⠀⠁⠀⠀⠀⠈⠀⠄⠀⠐⠀⠐⢈⠀⠩⣎⡀⢀⠄⠒⣢⢠
⠀⠀⠀⠀⠠⠄⠒⠀⠒⣆⠀⠈⢆⠀⠰⠠⡀⢣⠀⠢⣀⣤⠠⠄⠀⠀⠀⠄⠀⠀⡀⢀⠀⠀⠁⠀⡀⢁⠎⠀⠤⡌⠀⠙⠒⠒⠊⠉
⠀⠀⠀⡦⠄⠀⠀⠀⠨⠐⠀⠀⠀⠑⠠⡐⢈⠐⠀⣀⢸⢞⠵⠀⠀⠀⠠⡡⠤⠀⠇⡀⠀⠁⠀⠀⡰⠁⢎⡀⠀⠀⠀⢀⠀⠀⣀
⠀⢸⡀⠈⢈⠀⠀⣀⠴⠲⢙⠌⠜⡐⠢⡀⠀⠀⣾⠆⠀⣧⣟⠀⢀⣢⡌⠀⠀⠘⠈⠀⠇⠐⡠⢊⠀⠀⢘⠈⠉⠉⠀⠀⠀⠀⠀⢤
⠀⠀⣀⡀⠈⠀⡘⢑⣠⡀⣄⡄⠰⣔⡢⠽⠀⣀⣁⡀⡀⠘⡇⠀⠀⠈⠒⠠⠤⠻⠑⠀⠀⠁⠀⠈⠜⢀⠈⠁⠉⠀⠰⠀⠁⠆
⠀⠀⡇⠘⣆⠈⠐⠂⠀⠊⠐⢒⣉⡠⠔⠁⠸⠇⠀⠈⣡⠂⢀⠀⠀⠀⢀⢈⠁⠀⠀⣀⣠⣤⣤⣌⠀⠙⠀⠀⠑⠀⠀⠀⠀⠄⣀
⠀⠀⡇⡔⠈⡆⠀⠉⠈⢉⠉⠁⠀⠀⠀⠀⢺⡀⠀⠀⠟⠀⠘⢐⡀⠐⠁⠈⠀⠀⠺⠿⣯⠿⠷⠽⢧⠀⠆⠀⠀⠆⠀⢰⣅⡠⠂
⠀⠀⠣⡈⣠⠇⢀⠀⠈⠧⣈⠁⠐⠈⡩⠃⠀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠤⠔⠁⢀⣀⠀⠤⠂⠁⠠⠒⠁⠀⢀⣀⠀⡀
⠀⢀⠀⡀⠀⡐⠑⠄⠈⠆⠀⠀⠈⠀⡀⢀⡄⢴⣯⠒⡄⢀⢔⡀⠄⠀⠠⢏⠝⠀⠀⣀⠀⠀⣀⢀⠀⠀⠔⠈⠄⠀⡴⠁⠈⣆⣄⡅
⠀⠓⠒⠀⡐⠀⠀⠀⠀⠀⣀⠀⠨⠌⠰⠖⠘⢁⡠⠊⠔⠗⠐⠠⢤⡶⠂⠀⠀⢄⠀⢠⡄⠀⢀⠀⠀⢁⠀⠀⠀⠐⠠⢀⠔⠁⠀⠁
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠚⠀⠐⠂⠀⠒⠈⠀⣀⣩⣄⠦⠔⠛⣡⡀⠀⠀⠀⢀⠇⠀⢀⠀⠮⠩⠠⠍⢡⠘⠂⡈⢒⣈⠦⠀⡀
⠀⢀⠀⠆⠊⠣⡀⠀⠀⠀⡰⠀⠤⠀⠀⠘⠃⠀⠉⢠⡄⠀⠀⣚⠭⠁⣄⡀⠐⢁⡀⠀⠀⠈⠡⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠁
⠀⠘⠦⠀⠀⠀⡤⠀⠀⠀⠚⡟⠠⠈⢀⡴⠖⠋⠃⠚⣳⣠⡄⠈⡀⠄⠈⠀⠀⠈⠁⠀⣰⠀⠀⠀⠀⠀⠀⠀⢩⡀⠀⠀⠖⡄⡠⡄
⠀⠠⢄⡈⠡⠊⠀⠃⠀⠀⠀⠈⠂⠀⠈⠀⡀⠀⠀⠀⠀⡀⠀⠈⠐⠄⠂⡄⠀⠂⡬⠂⠀⠁⠐⠒⠒⠒⠒⠊⠉⠃⡀⠀⠀⠀⠀⠃
⠀⠐⠀⡀⠀⢁⠀⢊⠔⡠⢄⠐⠀⠠⠄⠀⠀⡠⡴⠄⡈⠀⠀⢠⠀⠀⠀⢀⠋⡀⢄⠀⢠⠆⠀⠀⠀⠀⢀⢀⠀⠸⣰⠀⢨⠙⠈
⠀⠀⠂⠒⠈⠀⠀⠘⡌⠃⠈⠀⢑⠀⡄⠄⠠⡀⠀⠀⠀⠀⡀⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⠪⠩⠉⢬⡇⠈⠀⠠⡀⠀⠀⠂
⠀⢀⠀⡒⠒⡋⢆⠀⠣⠠⠊⠀⠁⡐⠁⣀⠄⠀⠀⠀⡐⠀⠀⠻⠀⠈⠐⠂⠀⠀⢀⠤⠊⠁⠀⢀⠤⠀⠘⢲⠔⠁⠀⠰⣶⢂⠡⠄
⠀⠈⠀⠀⡄⠀⢈⠀⠀⠊⣉⠢⠀⠈⠁⠃⠃⠀⠢⠀⠀⢀⣀⠄⠀⠀⠀⠃⢀⠄⢃⠀⠀⠠⢀⠀⠀⢀⡠⠃⡆⠀⠀⠄⠋⠉
⠀⠀⠈⠀⠉⢀⠀⠀⠀⡈⠀⢠⠀⢀⠀⠀⠀⠀⢀⣀⣀⠉⢀⠀⠀⠀⠕⠀⢘⠠⠂⠉⠁⠉⠡⠊⠛⠩⠐⠊⠀⣐⠀⠀⠀⠀⢠
⠀⠀⠀⠄⠀⠀⠀⠀⢀⠰⠀⣀⠉⠂⢠⠔⢠⠸⡁⠀⡩⠆⠀⡜⠀⠈⠀⠀⠀⠀⠀⠀⡴⣲⠀⠔⠢⢠⠐⡆⠀⠀⠀⢀⣀⡀⠀⠁
⠀⠠⠴⠀⢁⠈⠀⠀⠀⠑⡃⠀⢀⣀⡀⠙⠉⠀⠥⠤⠧⠀⠠⠀⣀⠈⠂⠒⠃⠀⢀⠀⠈⠁⠀⠂⠁⠀⠘⠀⠀⡚⠃⠀⠀⠀⠑⢲
⠀⠀⡴⡺⠀⡼⠃⢀⣄⡀⢀⠄⠁⠀⢘⠀⠀⡠⠐⠀⣂⣄⠀⠀⠈⠀⢠⠄⠀⠀⠈⠠⠄⠂⣤⣴⣴⠀⠀⠀⠀⠱⡀⠀⠀⠀⡠⠋
⠀⠐⣇⠤⠑⠁⢠⠀⠀⠀⡁⠀⠀⡠⢊⡀⠈⢠⠊⠁⡀⠀⠂⠤⠤⠄⠊⠀⠠⠀⠁⢀⣀⡠⠂⠀⠠⠀⠀⠀⠀⢀⠁⠀⠀⠀⡀⢴
⠀⠀⠈⠐⠒⠂⠚⠀⠀⠀⠈⠀⠀⠀⠈⠀⠘⠁⠀⠀⠈⠀⠀⠀⠀⠀⠐⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠰⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⡀⠀⠀⠀⠀⠠⢒⠀⠀⠀⠀⠀⠀⢀⣞⠁
⠀⠖⠶⠖⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⡜⠁⠀⠐⢤⡹⠀⠈⡀⠀⠀⠼⠉⠉⠉⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⡀⠀⠀⢠⡄⠀⡠⠀⠀⠀⠀⠀⠉⠡⠀⢁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⡀⠂⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⠀⠀⠀⠀⠀⡀⢤⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠠⠄⠀⠀⠀⠰
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⣭⡢⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠈⡀
⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈

⠀⡀⠠⠀⠤⢠⠀⠀⠀⣀⡀⢠⣠⠄⠀⠀⠀⠀⠀⡀
⠈⢀⠰⢒⣶⠀⠀⠀⠀⢘⠓⢀⠿⡅⠀⠀⠀⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠐⠻⠋
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀⠀⠀⠀⠀⣠⡄⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠐⠀⢀⣀⣀⠀⡀⠀⠀⠀⢀⠁⠈⠀⠀⠀⣼⠁⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠂⠀⢀⠁⡀
⠀⠢⠀⠀⠀⠀⠘⠁⠀⠰⡄⡀⠁⠀⠀⠀⠀⢉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠔⠈⠀⠈⠐⠠

⠀⠀⢀⣀
⠀⠀⠹⡿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠆
⠀⢰⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠟⠉⠀⠀⠀⠂⠀⠀⢠⣄
⠀⠸⠀⢸⠀⠁⠀⢀⣀⣀⣀⣀⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚
⠀⠀⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢤⡐⠓⠒⠓⠒⠓⠒⠒⠒⠢⢤⣶⡄⠀⠀⠀⢀⣤⡴⢲⠖⢢⣄
⠀⠀⠀⢀⣴⠞⠋⢉⠉⠛⢦⡀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠒⠚⠒⠚⠛⠓⠉⠁⠀⠀⠀⠀⠀⢀⡾⣠⣤⣼⣄⣤⣼⢳⠀⠀⠀⠀⠀⢰⠨⠤⠤⢼⡀
⠀⠀⠀⣾⠁⠀⠀⣀⡀⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⡞⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠟⠀⠒⡒⠚⣣⡀
⠀⠀⠀⣟⠁⠀⢰⠋⠙⠂⠂⣸⠃⠀⠀⠀⠀⠀⣰⡟⠀⠁⠀⠀⢀⢄⡀⣸⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠉⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠘⢦⣀⡉⡄⣀⣠⡴⠋⠀⠀⢠⣀⡆⠀⣿⡅⠀⣾⠙⡶⠻⠼⠋⢹⣿⡃⣠⡏⢰⡟⡇⣾⣹⡀⠀⠀⠀⠰⠄⠀⠀⠀⢀⣇⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⣀⣤⠞⣿⡀⠀⠘⠳⠔⠛⠚⠁⠀⠀⠀⠈⠁⠉⠉⠛⠉⠀⠉⢉⢽⠇⠀⠀⣠⠶⣦⡀⠀⠀⠘⠛⠋⢥⢈⡭⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡋⠀⠄⠊⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠒⠀⢀⠀⠈⠋⠀⢀⡾⢥⣬⣏⣝⣷⡄⠀⣀⣴⠟⠀⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣐⡡⢀⠁⡆⣿⡄⠀⠀⠀⠀⢀⣀⠤⠔⠒⠀⢐⠒⠤⣀⠀⠀⠄⠀⠀⣿⠄⣺⢲⠓⡇⢁⡟⠀⠉⠉⠉⠉⠉⠉⠁
⠀⠀⣠⠶⠛⠛⠛⠛⠓⢦⠀⠘⠿⢻⣄⢀⠢⢀⡇⠀⢀⡤⠚⠉⠀⠀⠴⠀⠀⠀⠉⣢⡈⠡⠀⠐⠢⡀⠙⠶⣍⣹⢙⣳⠟
⠀⠀⡯⢏⠉⠉⣢⠀⠀⢸⠀⠀⠀⠀⠙⠳⠾⠛⠀⡴⠉⠀⠀⠀⠀⠀⠀⡐⣈⠀⠂⠀⢌⠀⠀⠀⠀⠈⠢⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠈⠓⠚⠛⢶⠖⣾⠋⠀⠀⠀⠀⠀⠀⠀⢀⡞⢠⡦⠀⠀⠀⠀⠀⠀⡀⠁⠀⠁⠐⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣴⣲⣶⣾⣷⣰⣶⣶⡄
⠀⠀⠀⠀⠀⠀⣼⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠘⠀⠻⠀⠀⠀⠀⠀⠹⡛⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠨⡇⠆
⠀⠀⠀⠀⠀⠀⠳⠛⠾⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠄⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⢀⡠⠤⠤⣄⠤⡤⢤⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒⢈⡶⠤⢴⡄⢰⠋⠁⠀⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠧⠤⠤⠤⠤⠤⠤⠼⠂
⠀⠀⠀⠀⢀⠎⠁⢰⢏⠤⠂⠑⠀⢸⠆⠀⠀⡆⠀⠀⠀⠉⠢⠤⠄⢀⣀⡜⠙⠀⠸⡁⢙⠀⠀⢀⡄⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠘⣄⠐⠬⢀⡀⠠⠊⣠⠞⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⢈⡃⠀⠀⠀⡇⠀⠀⠀⡄⠀⠀⠀⠀⡼⠀⠀⠀⡀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠑⠒⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⢠⣤⢴⠶⣀⣲⠶⣤⣼⣄⠀⠀⠀⡧⠀⠀⡠⠇⠀⠀⠀⡴⠁⠀⠀⠀⠀⢿⠀⠀⠆⠀⢀⡿⢶⡆
⠀⠀⠀⠀⠀⣤⠤⢤⠤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠈⠓⢧⠤⠭⠥⢴⣎⡓⢋⠁⠀⠀⣤⠤⠚⠀⠀⠀⢀⠜⠁⠀⠀⢲⠀⠀⠸⡄⠀⠂⠀⢠⣧⠟⠁
⠀⠀⠀⠀⠀⢷⠋⠉⠉⠙⢲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⢩⠀⡀⠀⠀⠤⠀⠀⢀⡀⠞⠁⠀⠀⠀⣴⠀⠀⠀⠀⢇⠀⠥⠀⢸
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠈⡇⠀⠀⠀⣀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠀⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⠒⠒⠒⠃
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣧⠀⠀⠀⣧⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⡀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣤⠤⢤⣤⣤⣤
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⡸⠀⠀⠀⢸⠀⠀⢰⠃⠀⢺⣯⣭⣭⣝⣳⠀⠀⠀⠀⠰⣽⣿⣿⣯⡿⠀⠀⠀⢠⢻⣷⠀⠀⠀⠀⠀⠀⠈⠉⠛⢛⠉⠉
⠀⠀⠀⠀⠀⠈⠲⠶⠦⠤⠞⠁⠀⠀⠀⠈⠈⠉⠉⠀⠀⢠⠇⠀⠀⠀⣇⣠⣤⣄⠀⠀⠘⢼⣿⡿⠀⠀⠀⠀⠘⠾⠟⠀⠀⠀⠀⠀⠀⢠⠴⠚⡚⠒⢄
⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⠀⣀⡀⣹⣇⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣿⣫⠄⠠⢑⡊⡇
⠀⠀⠀⣔⣒⣒⣚⣛⣒⣒⣒⣆⣀⣀⣀⣠⡤⣤⡄⠀⢸⣇⠀⠀⠀⠀⢨⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⡔⣊⣉⣀⣀⣀⣉⣑⣦⡀⠀⠘⠰⠷⠶⠶⠶⠥⠗
⠀⠀⠀⣇⣭⣄⣬⣡⣤⣄⣤⡟⠉⠁⠓⠛⠉⠉⠁⠀⠀⠛⢷⣦⣤⣴⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢫⣿⣭⣭⣥⣭⣭⣭⣭⣭⠇

⠀⠧⠀⠀⠀⡠⠒⠉⠀⠀⠁⠐⢀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⡈⢡⠀⠰⠁⠀⠀⠀⡀⠀⠀⠀⠡⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢧
⠀⠀⠀⠀⢈⠀⠀⠀⠈⠋⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠈⠓⠦⣤⣤⠴⠋⠀⠀⠄⠀⢀
⠀⢀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⡠⢃⣀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢈⠦⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⢀⠀⠀⠀⢸
⢠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⠂⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⢀⡀⠀⢀⠠
⠀⠀⠀⠀⢀⠄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠄⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈
⠀⠀⠀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡛⢂⡶⠛⠲⡄⣴⠚⠳⣆⢰⡗⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠙⢧⣀⣰⠇⢷⣄⣠⠟⢸⣄⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢠⡀⢀⡤⣄⢀⣀⠀⣠⢤⠀⣤⣄⢀⡤⡀⢠⢀⠀⣄⢠⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠂⠞⠳⠸⢤⡤⠸⠣⠀⠧⡶⠆⠿⠇⠻⣤⠟⠸⡼⠀⠏⠾⠸⡦⠇

⠀⢀⣀⣀
⠀⠘⡔⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠄⠀⠀⠀⠇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠠
⠀⡡⠂⠀⠑⠂⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈⠑⠂⠤⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡠⠀⠀⠀⡠⠀⡀⠀⠀⣀⠀⠀⠀⠲⢁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠔⠁⠀⠀⠀⠀⠉⠐⡄
⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠄⠀⢀⣠⠴⠶⠦⣄⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⣄⠠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⢳⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢐⠀⠀⠀⠀⠁⠀⠀⠀⡘⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢐⡀⠑⠄⢀⠀⠀⢀⠠⠞⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢸⣯⣓⢦⡀
⠀⠀⠀⢀⡴⢋⠡⠈⠄⡀⠍⠙⣦⠀⠀⠀⠀⠀⣰⣒⣚⣛⣛⣶⡀⠀⠀⠀⠀⠀⢸⡇⢸⡀⠀⠀⠀⠀⠀⣠⢞⣩⠴⣿⣼⣚⣍⣳⣽
⠀⠀⠀⢸⡧⠬⠤⠤⠤⠤⠤⠤⣼⠆⠀⠀⠀⠘⣧⡤⠤⠤⠤⣤⠇⠀⠀⠀⠀⠀⣞⡉⠉⣧⠀⠀⠀⠀⣼⢡⢏⠤⡅⡏⠿⢟⣫⡵⣆
⠀⠀⠀⢸⡗⠛⢒⣒⣛⣒⠒⠓⢺⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⡟⠀⠀⠀⠀⠀⠸⡇⢹⡇⣸⠀⠀⠀⠀⣇⢸⠘⢒⠋⠷⢚⣭⡀⡇⣿
⠀⠀⠀⠀⢿⣙⣯⡉⠉⢉⣽⣋⡟⠀⠀⠀⠀⠀⠈⡇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡟⠉⠀⣿⠀⠀⠀⠀⠹⡜⢧⡻⠗⣡⣌⣋⡼⣡⠏
⠀⠀⠀⠀⠀⠉⠉⠙⠶⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣸⠃⠀⠀⠀⠀⠀⢠⣇⣀⣀⣻⠀⠀⠀⠀⠀⠙⠦⣍⣛⣓⣛⣩⠖⠋
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⣠⣞⢻⡏⣿⢓⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢿⡳⣄
⠀⠀⠀⢸⠷⠾⠮⠷⠧⠾⠶⣿⠀⠀⠀⠀⠀⠀⣤⣤⣯⣯⣤⣄⠀⠀⠀⠀⠀⣠⠖⠋⡀⢀⠐⡈⠓⢦⡀⠀⠀⠀⠀⣰⢋⠀⡁⢈⠙⣿
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡿⢛⡧⠀⠀⠀⠙⣶⠓⡶⠚⠲⡖⢳⡞⠁⠀⠀⠀⠀⣏⠠⠀⠄⣠⡼⠁
⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣀⣀⣿⣀⣀⣀⣀⣟⣋⣀⠀⠀⠀⠀⢸⡄⢹⠀⢸⠃⣼⠀⠀⠀⢀⣤⠞⣩⠷⠖⠛⠁
⠀⠀⠀⠀⠸⢤⡤⠤⠤⢤⠼⠀⠀⠀⠀⠈⠧⣄⣀⣀⣀⣀⣀⣀⣤⠟⠀⠀⠀⠀⠀⠳⣼⣧⡾⡴⠃⠀⠀⠀⠘⢦⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣉⣳⣆
⠀⠀⠀⠀⠀⢀⣀⡤⠞⣧⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣀⣄⣀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠻⡄⠀⠀⠀⣸⣥⣤⣽⣧⣬⣧
⠀⠀⠀⠀⣰⠯⠤⠤⠤⠬⢷⡀⠀⠀⠀⣰⠋⠀⠀⠏⠀⠀⠟⠁⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⣠⡏⠙⠓⢿⠀⠀⠀⠹⡞⠛⢚⣷⢶⡏
⠀⠀⠀⠀⡷⠶⣤⠴⢤⡴⢶⡇⠀⠀⠀⣟⣶⣒⣲⣒⣲⣒⣒⣖⣒⣶⣻⠀⠀⠀⠀⠀⢀⡞⠉⠙⠦⣄⣸⠁⠀⠀⠀⢻⣚⣩⡴⡾
⠀⠀⠀⠀⢹⡀⢸⠀⢸⠀⣸⠁⠀⠀⠀⣿⠦⠭⡽⠯⢥⡬⠵⠮⡭⠴⣻⠀⠀⢀⣠⢾⡉⠙⢦⡀⠀⢈⡗⠀⠀⠀⠀⠈⣏⣡⢴⠃
⠀⠀⠀⠀⠈⣧⣸⣄⣼⣠⡇⠀⠀⠀⠀⠈⠉⠙⠛⠓⠒⠒⠚⠛⠛⠉⠁⠀⠀⠘⠲⢤⣷⣀⣠⠿⠖⠋⠀⠀⠀⠀⠀⠀⠹⣄⡟
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢴⢶⣤⡀⠀⠀⠀⠀⢀⣤⡀⠀⢀⣤⡀⠀⠀⠀⠀⢠⡤⠤⣤⢀⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡿⢦⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠛⣧⡾⡶⣴⢧⡀⠀⠀⣴⠋⣄⠙⣶⠋⣄⠙⣆⠀⠀⠀⠈⡏⠉⡇⠸⡷⢾⡇⠀⠀⠀⠀⠀⠀⣠⢞⡼⣳⠋⠈⢹⡄
⠀⠀⠀⠀⢀⡴⠋⠀⠀⣿⠶⢿⣹⠋⠀⠀⠰⡇⢀⡼⠀⢸⢀⡞⠀⢸⠀⠀⠀⢀⡇⠸⣧⡞⠁⠈⢳⡆⠀⠀⢀⡴⢞⡵⣫⠟⠁⠀⠀⣸⠃
⠀⠀⠀⣴⠋⠀⠀⢀⡴⠃⣠⠞⠁⠀⠀⠀⠀⢳⡈⠃⣠⢾⡈⠇⣠⠟⠀⠀⠀⡏⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢿⢚⡿⠞⠁⠀⠀⣠⠞⠁
⠀⠀⠀⠘⢦⣀⡴⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⠶⠋⠀⠙⠶⠃⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠈⠻⣄⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠙⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠲⠚⠓⠒⠶⠚⠃⠀⠀⠀⠀⠈⠉⠉

⡿⢿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣻⣛⣿⣿⡿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠠⢄⠄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠻⣷⡶⢀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣀⢆⣂⡠⠧⠄⢀⡀⠀⠀⠀⠀⠈⠐⠨⠻⣭⣑⢲⣤⡀⠀⠀⠀⢰⣿⡒⢂⡀⠀⢀⣴⡿⡀⠀⠀⠀⠀⡄⠐⠀⡀
⠀⠀⢹⡀⢙⢴⣤⣾⣾⣿⣽⡁⠀⠀⠀⠫⡇⣰⠶⡧⢢⣜⣰⠂⠀⠀⠐⣭⣛⡻⢟⠶⠗⠚⣡⠀⠀⠀⢀⡀⡀⠁⠠⠁⡀
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠉⠍⠋⠀⠠⠀⠀⠀⠀⠀⠚⢦⣄⡔⢌⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠒⠆⠀⠐⠂⡀⠀⠀⠀⠀⢠⣶⣦⣄⡔⠦⢤
⠀⠀⢀⣄⡟⠛⠂⣸⢻⣵⠦⡀⠀⠀⡀⢂⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠈⢻⢿⢿⣷⣞⠨⣧⡄⠀⠀⠈
⠀⠀⠿⣀⠀⠀⠰⣿⢲⢵⣡⡶⠀⠀⠀⠀⡈⠐⠀⠀⠚⠈⢠⠀⠀⠀⠀⠀⠀⠐⠯⠷⠏⠉⠛⢳
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠲⠤⠠⠠⠤⠶⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⡐⠀⢄⠀⠂⠈⠁⣀⠀⠀⠀⠠⡚⠢⠈⠙⠴⠿⠆⠀⠀⠀⠀⢀⠀⢔⠂⠀⠂⠀⠀⠀⢰⡎⣻⣷⢿⣯⣗⣦⣄⡀
⠀⠀⠀⠣⠩⠄⢄⢠⣤⠔⠀⠛⠀⠀⠀⢷⡖⢂⣂⠀⠀⡀⠢⠂⠀⠀⠆⡀⢀⠀⠐⠀⡀⠀⠀⡀⠀⠉⠉⠦⢤⠿⠒⠣⣴⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠀⠁⠀⠀⠀⠈⠑⠦⢄⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠈⠉⠉⠉⠉⠉⠐⠒⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⢀⣤⡶⠾⠛⠛⠉⠉⠉⠙⠛⠛⠷⢶⣤⣄⡀⠀⠀⠈⠲⣄
⠀⠀⢠⢀⡄⣠⣠⡀⠀⠀⠀⠀⢀⡔⠁⠀⠀⣠⣾⣟⠥⠒⠈⠉⠁⠒⢤⡀⡰⠉⠉⠓⣄⠀⠉⠻⢷⣄⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⢀⢄
⠀⠀⢸⣾⣿⣿⢻⡇⠀⠀⠀⢠⠊⠀⠀⢀⣾⢫⠊⠀⠀⠀⠀⠪⠕⠘⠓⢹⣧⠀⠀⠀⢨⠗⠲⣦⡴⠋⠙⣆⠀⠀⠈⠣⡀⠀⠀⠀⠀⢸⠀⠑⡄
⠀⠀⢸⣧⣿⣿⣾⡇⠀⠀⢠⠃⠀⠀⣰⡟⡱⠁⠀⠀⠀⠀⠰⠆⠀⠆⢰⡆⡟⠀⠀⠀⠈⢦⣁⣎⣣⣌⣰⠽⣷⡄⠀⠀⠱⡀⠀⠀⠀⢸⠀⠀⠸⡀
⠀⠀⠘⣿⢿⠿⣿⠃⠀⢀⠃⠀⠀⢰⡟⢠⠃⠀⠀⠀⠀⠀⠀⠀⢰⡲⠀⢀⠃⠀⣀⡀⣀⠀⣃⠤⠈⣧⠶⣀⣠⢿⡄⠀⠀⠱⠀⠀⠀⢸⠀⠀⢀
⠀⠀⠀⠈⢲⡖⠁⠀⠀⡎⠀⠀⢀⡿⠁⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢉⡉⢡⣒⡄⢍⠙⠶⡴⣿⡯⠟⠀⠀⢿⡄⠀⠀⠇⠀⠀⢸⠀⠀⡸
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠇⠀⠀⢸⡇⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⡳⠞⢔⡣⠈⠒⢁⠼⢄⣩⠧⠀⢀⡀⠘⣷⠀⠀⢸⠀⠀⢸⢀⠜
⠀⠀⠀⠀⢸⡇⠀⠀⢰⠀⠀⠀⣼⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢣⠃⢞⡆⣀⡰⠽⠃⠀⠀⠀⠀⠀⠀⠘⡄⣿⡀⠀⠈⠀⠀⢸⡏
⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⠀⢿⢀⠎⠀⠀⠀⠀⠀⠀⡀⠔⠊⠀⢔⡲⠣⠗⠭⡼⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣿⡇⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⢸⢰⠀⠀⠀⡇⠀⠀⡼⠋⠀⠀⠀⠀⢠⠔⠉⠀⠀⡴⠒⠲⢤⡀⠪⢵⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣿⠀⠀⢸⠀⠀⢈⣿
⠀⠀⠀⠀⢸⢸⠀⠀⠀⢡⠀⠀⠑⣾⣄⣀⡀⢠⠃⢠⣊⠉⢆⠙⢅⠠⠀⠛⡄⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢫⡟⠀⠀⡆⠀⠀⠸⢨
⠀⠀⠀⠀⢸⠸⠀⠀⠀⠀⢇⢰⠒⠛⠀⡇⠈⠁⠀⡆⠀⠐⡎⣰⠫⢿⠒⠛⢁⢴⠦⢕⠢⢤⡀⠀⠀⠀⠀⢀⠞⢠⡿⠀⠀⡸⠀⠀⠀⡆⢸
⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⠈⢎⠒⠢⣀⣼⡀⠀⠀⣇⠄⢸⠃⡌⠀⠬⡆⠀⢂⢏⠔⣹⡤⡖⠸⡂⠤⠤⠔⠉⣰⡟⠁⠀⡰⠁⠀⠀⠀⡇⢸
⠀⠄⠀⠀⢸⠀⡇⠀⠀⠀⠀⠈⠣⡀⠀⠈⢿⣦⡀⠈⠋⠁⠀⠹⡀⣴⠀⢀⡤⠹⢏⠐⡤⠬⡷⡝⠀⠀⣠⡾⠋⠀⢀⠔⠁⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⢸⠀⢡⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠈⠻⣦⣄⡀⠀⠀⠈⠁⠀⢺⡈⢆⣲⠇⠈⠑⢉⣠⣴⠟⠋⠀⢀⡤⠋⠀⠀⠀⠀⠀⠀⡄⢸
⠀⠂⠀⠀⠈⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠉⠛⠷⢶⣤⣤⣄⣀⣑⣶⣥⣴⠶⠞⠛⠉⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠉
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⠒⠒⠒⠂⠉⠉

⠀⠀⠀⠀⠈⠀⢀⠀⠀⢀⠀⠀⠀⢀⡍⠑⢖⠓⢀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠈⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠜⠁
⠐⠄⡈⠒⠀⠐⠂⡁⠀⠀⠀⠀⠀⠀⠁⠉⢀⡙⢌⡁⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢄⠆
⠀⠀⠰⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⣀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠄⠀⠄⠒⠂
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⢀⠄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⣀⠀⠀⠀⠀⠀⠀⡠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⣤⡖
⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⣠⢠⡾⣞⣷⢠⠃⠀⠀⠀⠀⠁⡉⢀⠀⠐⠀⡎⠉⢲⠀⠈⡓
⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠃⠀⠀⡽⠐⠑⠡⠋⢈⠆⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄⠓⠒⠚⠁⢀⠁
⠀⡀⠐⢠⠀⠀⢀⡂⣀⠤⠂⠀⠀⠈⡀⠀⠀⠀⡘⢸⠀⠀⠀⠠⡴⠀⠀⠀⢀⣤⣄⠀⣀⡤⠖⠁⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠆⠀⢀⢠⠟⠁⠂⠀⣁⡀⠀⠀⠀⠀⠀⠀⢀⠑⠂⠀⠁⠀⠑
⠀⠀⡄⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⠔⢬⡀⠤⠂⠉⠀⢀⣀⣀⡀⠀⠀⠀⠙⠀⠻⡄⠀⢀⡄
⢀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡈⠀⠀⠀⠈⠉⠂⠄⠀⠀⠀⢣⡐⠉
⠈⠃⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⢀⡀⠢⠀⢀⠀⠀⠠⠄⠀⡀⠁⡀⠌⠀⠀⠀⠀⠀⠈⠂⡀⠐⠀⠀⠪⢠⠀⠐
⠀⠀⠀⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠈⠑⠀⠀⠄⠀⠀⠀⠀⠘⢀⠀⠀⠐⠀⡈⠐⠀⠀⠄⠀⠈⡄⠰⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠄⠀⠀⠐⣤⠀⠀⠆⠀⠀⠈⢢⠈⡇⠀⠀⠀⡅⠀⠀⠘⠀⠀⠀⢀⠀⠀⠀⠀⠀⡁⠀⡅⠀⠀⠀⠨⠃
⠀⠀⠀⠐⠋⠀⠀⠀⠂⠈⠁⠄⠀⠱⡀⠀⠀⠀⡇⠀⠀⠀⢃⠀⠀⡓⠂⠀⠀⠀⠀⠁⠀⠀⠐⠀⢰⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡙⠓⢄⢀⡇⠀⠀⠁⠨⢆⠐⢀⠀⠐⠀⠠⠀⠀⠀⠄⠀⠤⠁⠀⠀⠠
⠀⠀⠀⠰⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠄⠀⠀⠱⠤⡈⠀⠀⠀⠂⢀⣀⠴⠊
⠁⣀⡀⣠⣶⣿⣧⣴⣾⡟⠀⠀⠀⠀⢀⡀⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⡄⠀⢠⠀⠀⠀⠀⠀⠀⠠
⣈⣿⣿⣍⣟⣿⣿⣿⣯⣷⣤⠤⠄⠒⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡲
⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣛⠆⠀⠀⠀⠄⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠟⠛⢻⢿⣿⣿⠂⠃⠀⠙⠋⠀⠀⠀⠀⠀⠈⠂⠈⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠘
⠀⠀⠀⠛⡙⠉⠀⠀⠀⠀⠀⠀⠠⠔⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⣀⡤⠄⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣤⡆⢀⠀⠲⠒⢲⡶⠶⠶⣶⠶⠖⠠⢀⣀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠓⠀⠈⠀⡀⠈⠀⠀⠀⠈⠀⠀⠀⠤⠀⠀⠰⠀⠈⢩⣟⠻⡿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠞⠃⠉⡀⠀⠀⠊⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠅⠀⠐⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠤⠀⠀⠀⠙⠁⣽⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠛⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢤⣿⣿⢦⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⣘⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄⠐⣻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣟⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣷⣤⣼⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢛⠿⢶⣦⣤⣀⣀⣀⣀⣄⣀⣀⣠⣤⣀⡀⠀⢀⣀⣀⣀⣀⣀⣤⣀⣀⣤⣤⣤⣤⣶⣿⣿⣿⠿⣟⣛⡭⣉⣠⢶
⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣷⣦⣈⠉⢉⣛⣛⠛⢛⣻⣟⠛⠟⠻⢿⢿⣿⣯⣿⣯⣍⣭⣭⠽⠈⢦⡉⠁⢀⣰⡟⢉⠾⠋⢗⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠰⠚⣉⡙⠿⠿⠍⣉⣿⣿⣿⡟⢻⣿⣿⣦⣤⣤⣴⠿⣷⠾⡯⠟⠛⠿⢿⡴⠋⠳⢍⣻⡿⠻⠷⠁⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣭⡥⣄⡀⠀⠋⠙⠿⠻⠿⠛⢻⠿⢻⡿⡯⠋⠀⠋⠉⠀⠐⠂⠒⠉⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣶⣶⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠧⣿⣿⣷⣶⣏⡋⠉⠀⠀⠒⠓⠀⠊⢀⣠⣤⣴⣶⣶⠶⣶⣶⣶⣾⣿⣿⣿⣿⡿⢛⣽⣿⣇⣼⢧⣼⡏⣨⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣌⢙⣧⣄⡙⢟⣷⣄⠀⠀⢀⣠⣾⣿⣯⣤⣶⣿⣭⣼⡿⢃⣾⠏⢀⣾⠿⣿⢹⣟⠉⣸⣿⣏⣾⡯⣴⡏⢀⡀⠘
⠀⠀⠀⠀⠀⠀⠂⠈⠉⡃⠛⢮⠛⠿⢙⣛⢻⣿⣧⣴⣿⣿⣛⠉⢻⢿⣭⣼⣿⣋⣾⡿⠿⠿⠿⢛⣴⣟⣨⡿⣿⣿⠿⡿⡗⠓⢄⣁⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠶⡥⢄⡠⢀⣀⠀⠀⣈⡉⣉⣉⣤⣤⣞⡀⠒⡢⠈⠟⠀⢐⠊⣀⣀⣉⣡⣽⣄⣤⣤⣏⣀⣿⡿⠶⠾⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠙⠛⠻⠙⠿⠟⠋⠛⠻⠗⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠁⠉⠹⡟⠀⡀⢠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⣄⠀⠀⠀⣰⣀⣼⣦⣼⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠤⠤⠤⠤⣤⣤⣤⣄⣤⢀⣀⣠⣤⣄⣴⣶⣴⣤⠤⠴⠾⠿⠿⠒⠶⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠈⣃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⠀⠀⢀⡝⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀⠀⠀⠀⠘⠈⠛⠶⠖⠛⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠰⠂⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠴⠦⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⠀⠀⠀⠀⠋⣼⢈⠄⠀⠀⢠⡀⢀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠜⠳⠂⢸⠂⠀⠀⡅⠀⠁⠂⠀⠀⠀⠀⡀⠀⠀⠂⡇⠀⠀⠀⠀⡌⠘⠲⢖⠀⠀⠀⢠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠋⠀⠀⠀⠀⠀⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⢤⣀⣠⡶⠀⠂⠀⠀⠀⠚⠛⠂⠀⢀⠎⠁⡔⠀⠀⠀⢀⣀⣀⠀⠀⠐⢥⣀⡀⣀⡬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢀⠴⠊⠀⠀⠀⠀⠀⢀⡀⢠⠆⠰⠋⠀⠀⠀⢠⡏⠠⢈⠂⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⢤⠀⠀⠀⠁⠈⠀⠀⢄⡀⣹⠆⠀⠉⠐⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⢂⡘⠀⠀⠀⠀⠀⠀⠀⠀⢤⠗⠀⠀⠀⠀⠀⠺⡄⠀⠀⠤⢴⡾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠠⠀⠀⢀⠀⢀⠟⠀⠀⢘⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢨⠀⢀⡀⠀⢷⣀⡀⠀⣀⡜⠁⠀⠀⠐⠉⠀⠀⠀⢸⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢤⡤⠚⠀⠀⠄⡁⠔⠨⠀⠀⠀⠉⠙⠉⠉⢠⡀⢨⡷⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⣀⣤⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠉⠐⠠⡀⠀⠀⠈⠰⠋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢺⣷⣿⡿⠃⠀⠀⣠⣄⣀⠀⠀⠔⠀⠈⠑⢦⡤⠤⠂⠀⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⢀⡀⢠⡤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠛⠉⠉⠉⠉⠉⠋⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣷⡄⠀⠀⠾⠂⠀⠀⠀⠛⠆⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⢀⡀⠀⢀⢄⣀⠀⠀⢧⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢛⣻⣿⡀⠀⠀⠀⠉⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⣣⡙⠃⠀⠀⢰⠀⠘⠲⠼⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⠙⣧⠀⠀⠈⠙⠦⣀⣀⣀⣀⠴⠀⠀⡟⠀⠀⠀⢹⡃
⠀⠀⠀⠀⠀⠀⠀⠚⠃⣤⣀⠉⣻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢀⣸⣯⢳
⠀⠀⠀⠀⠀⠀⠀⡴⠯⣀⣨⠟⠃⡏⠙⢦⣄⣀⡈⢀⣓⣃⡤⢾⣅⠀⠀⠀⠁⣽⢛⠿⣀⡴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢉⣀⡂⠇⠀⠀⣼⠋⡏⠉⢫⠀⠱⠸⣏⢦⡀⠀⠘⣌⠷⢂⣩⠟
⠀⠀⠀⠀⠀⠀⠀⣰⠯⢻⢩⢉⡟⣧⢀⣼⠃⠀⠃⠀⠘⡀⣄⢤⡹⣆⡛⣤⠀⢸⠀⡎
⠀⠀⠀⠀⠀⠀⢰⡇⡇⠘⢸⢸⡇⡎⢹⡃⠀⠀⢞⢢⣠⠁⠟⢌⡇⠙⢟⠁⠀⡸⠀⡇
⠀⠀⠀⠀⠀⢠⡏⡇⣧⠀⢸⢸⡇⠃⣨⡧⠀⢠⠈⡇⠁⠀⢀⣘⡵⠁⠈⡇⢠⠃⠀⢹
⠀⠀⠀⠀⠀⣸⡃⡇⢹⣧⢐⣨⡷⠟⢫⡀⠀⣸⣅⡇⢠⠞⠉⣡⣤⣤⡼⠱⡾⠀⠀⡼
⠀⠀⠀⠀⠀⣿⡇⡇⠀⢹⠻⣿⡄⠀⠀⣿⡛⢫⠟⢠⢻⢳⢻⣽⠀⠳⣄⢀⡠⠄⠰⠳⢤⡄⡀
⠀⠀⠀⠀⠀⣿⠁⠇⠈⢸⢀⠀⢷⡄⠀⠘⠷⠋⠀⣾⢸⢸⣹⡇⠀⠀⢠⠋⠐⠒⠀⣀⣠⠤⠈⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⣿⠷⢿⣦⣼⣬⣀⣆⣻⣄⠀⠀⠀⣸⣃⣸⣴⣿⣡⣤⣶⠾⡎⠁⠐⠁⠀⠀⠀⣠⠏⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠉⠉⠉⠙⠛⢧⣀⣴⣯⣿⣿⣿⣿⣿⣿⣿⣄⠈⠒⠤⠤⠤⠔⠚⢁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠃
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠤⠴⠶⢦⣤⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠻⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠻⣆⠉⠻⣿⣿⣿⣿⣿⣿⣿⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⣤⣤⣤⣤⣤⣼⣿⣀⡀⠀⠀⠈⢷⡀⢿⢀⣩⣿⣿⠋⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠉⠛⢦⡀⠀⠀⢳⣾⣿⣿⣿⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠻⣄⣴⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣿⣿⡿⢫⣉⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠘⠿⣿⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠐⠀⢀⠀⠀⠀⠀⡄⡀⠀⠀⢀⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠓⠀⠃
⠀⠀⠀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⢓⠀⠀⠐⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠱⡀⠀⢀⣀⠀⣴⠂⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⢡⠶⠂⢠⠆⠀⠀⠀⠀⠜⡁⣈⡈⠀⠀⣀⢠⡀⡀⣄⣀⡠⠀⠀⠀⢰⡆⠀⠄⠈⠀⠉⠁⠈⠀⠀⢻⣄⡀⠀⢀
⢀⠀⠀⠀⠀⠂⠀⣄⠀⠀⠀⠡⠆⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠁⠈⠀⠀⢠⡄⡒⠚⠀⠀⠀⠉⠁⠄
⣄⠀⡆⠀⠀⢀⡀⠀⠶⠀⡠⠐⠁⣀⣄⣰⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠸⣾⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠁⠸⠛⠓⠲⡀⠀⠀⠀⠉⠈⠈⠀⠀⠀⠀⠀⠀⠀⠛⠀⠄⠀⠀⠛⣠⠄⠠⠆⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⢰⡀⢠⣰⡀⡠⠀⠀⠀⡀⠀⠀⠀⠀⠤⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡘
⠀⠀⠠⠤⣭⣿⣿⢿⣤⡤⠀⠀⠻⡏⠀⠀⠀⣷⡞⠀⠠⠰⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⡾⢠⣉⠅⣿⡀⠀⠙
⠀⠀⠀⠰⠤⠞⠸⠦⠤⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠐⠀⠠⠁⠰⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠸⠉⠐⠤⠗⠹⠇⠀⠈⠡

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠰⠏⢀⠀⠀⠀⠈⠉⠑⡄⠈⠁⡜⠀⠤⠀⠘⢂⠀⠀⠀⢰⠉⣀⠴⢄⠀⡼⠮⠑⠀⠀⠀⠀⠀⠁⠰⠀⢀⢄⠈⠀⠈⡆⠸⣡⠑⠀⢀⡠⠤⣤⣤⡀
⠀⠀⠀⡀⠀⢀⣀⠠⠄⠊⡍⠀⠀⢱⠀⠈⢠⢄⠀⠡⠀⠠⡁⠀⣁⠀⡈⠀⠀⠀⠀⡄⠁⠀⠐⠀⠀⠀⠐⠅⠀⠁⠂⡜⠀⢀⡈⠙⠀⠷⠦⠄⡸⢺⠁
⠀⠀⠀⢥⣁⡐⠠⠀⠀⠐⢈⠇⠀⠀⠑⢄⠀⠢⡑⢄⠇⠀⠈⠍⡹⢪⠅⠀⠀⡀⡰⠀⠀⠀⠇⠀⠂⠨⠀⠀⠀⢢⠎⡀⠀⠀⠈⠢⠀⠀⠀⠀⠀⢰
⠀⢠⡄⠸⠄⠤⠀⠈⠑⠈⣀⣤⡀⠄⡤⢀⠉⠁⠐⠀⢠⣞⡃⢸⡞⣵⠀⠀⢀⠀⡕⠉⠈⣄⠣⠂⠰⢀⡈⢈⠔⠁⠀⢱⠶⠤⢤⡄⠀⠐⠀⠀⠒
⠀⠈⠃⠀⠠⡆⠀⢀⠖⠍⡀⠀⠌⡐⠠⠄⣘⢦⡀⠀⠸⠋⠀⠀⢯⡖⠀⠀⠀⡟⠀⠀⠀⣦⠀⠄⠐⠄⠐⠁⡐⠀⠀⠸⣄⣀⠀⠀⡀⠈⡅⠀⠀⠋⠂
⠀⠀⣠⠦⡄⠀⡠⢁⡨⠴⢤⡸⣒⣒⣫⠭⠒⡏⠀⡤⠴⠦⡐⡀⠸⠇⠀⠀⠀⠈⠉⢁⠊⠙⠊⠁⠀⠀⠀⠐⡠⠁⣤⠀⠀⠀⠀⠀⠁⠂⠂⠁
⠀⠀⢷⠀⠸⡄⠈⠣⣉⢈⢉⣉⣍⣍⠤⠴⠚⠀⠀⡇⠀⠀⢀⡜⠀⠠⠈⠐⠀⢀⣀⡀⠀⠀⠀⣀⣴⣶⣶⢾⣄⠀⠈⠀⠈⠀⠁⠀⠀⠀⡠⠆⢤
⠀⠀⡯⢀⢢⠘⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⡀⠻⣀⠀⡀⡠⠗⠀⠘⢜⡥⠀⠃⠀⠈⠀⢀⠚⠿⣶⠽⠿⠿⠿⢧⠀⡂⠀⠀⣐⠀⠀⠶⠤⠠⠂
⠀⠀⠹⣄⣉⡰⠃⢀⠀⠈⠣⢀⡉⠀⠒⢉⡹⠋⠀⠀⠈⠉⠁⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠰⡤⠤⠙⠄⣀⡀⠠⡤⠀⠁⢠⠐⠂⠀⠀⢀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠄⠑⡤⠀⢆⠀⠀⠈⠉⠀⠀⣀⣠⢴⢮⡫⢆⠀⢀⡔⠠⠀⣀⡈⣩⢋⠕⠀⢀⠀⠀⠀⠀⠁⢰⠀⠀⠤⠘⠠⠀⢀⡜⠀⠘⡄⡅⢰
⠀⠪⡤⠔⠀⡌⠀⠀⠀⠀⡔⠀⠀⢠⠉⡈⣷⡼⠽⠞⠉⡠⢊⠴⣎⠨⢅⡠⣥⡤⠀⢀⢀⡀⠀⠀⣉⠉⠀⠉⠁⠀⠃⠀⠀⠀⠀⠬⡀⢀⡴⠃⠈⠓⠁
⠀⠀⠀⠀⡘⠀⠠⠠⠁⠈⠀⠪⠇⠀⠅⣀⡀⠤⠄⠂⠉⡠⡦⢂⣀⣠⡮⠞⠁⢀⠢⠂⠀⠈⡆⠈⠉⢀⣀⠖⡆⠐⠚⠠⠠⡆⠀⢦⠤⠸⡀
⠀⠀⠀⢀⠠⢤⡐⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⢰⡦⠀⠾⠒⠋⠉⠉⠀⢠⡺⡷⠀⠀⠀⢄⠜⠀⠀⢠⠛⠘⠁⠭⠬⠁⠨⠤⠌⠶⠀⠀⠈⢉⠔⠀⢄
⠀⢰⠀⠈⠀⠀⠱⠂⠀⠀⠠⡐⣥⣬⠁⠠⠀⢀⣀⣀⣠⠀⣿⣆⠀⠀⠹⠏⠁⡐⠦⠂⠁⢰⠦⠀⢘⢂⠀⠀⠀⠤⠄⠤⠐⢠⡄⠀⠀⠀⣌⠀⠀⢸
⠀⠀⠉⢀⣀⠀⣰⠚⡀⠀⠀⠀⠼⠁⠡⠀⠠⠟⠋⠁⠀⠈⠱⠿⠿⠃⠀⡄⠊⠀⠀⠀⠀⠀⢠⠀⡸⢄⣂⡈⠀⠀⠀⠀⣀⣠⠦⠀⠀⢠⠁⠀⠔⠺
⠀⠰⠢⠤⠤⠊⡀⠀⢁⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠃⢀⠄⠠⠀⠀⠑⠀⢠⠀⣉⡠⠖⠂⠀⠀⠀⠀⠩⠉⠭⠭⠀⠐⠈⠠⠄⠠⡀⠀⢀⠇
⠀⠘⡆⠠⠀⣀⡠⠈⢁⠊⡥⠀⡁⢱⠀⠢⢄⣀⡀⠤⠶⠗⢠⠃⠀⠀⢀⡀⢠⠀⠀⡘⠀⠀⢠⠀⢠⡟⠩⠀⠀⠀⠀⢀⠠⠀⠀⠳⡟⠀⠈⢸⠁
⠀⠀⠑⠐⠀⠁⠀⠀⠘⡄⠃⠐⠁⠀⡃⢀⠄⠄⠠⡀⠀⠀⠁⠂⠀⠀⢨⠇⠀⡁⠀⠀⠀⠠⠀⠁⠀⢀⡄⠭⠈⠡⢬⡇⠀⠀⠐⢄⠀⠀⠐⠂
⠀⠠⠂⡐⡢⢲⠁⠄⠀⠡⣀⠔⠂⠈⠀⡘⠁⢀⠠⠀⠈⠀⢀⠶⠀⠀⢹⠀⠐⡀⠀⠀⠀⠀⢀⡠⠔⠋⠀⠈⢀⠤⠤⠜⠒⡥⠂⠉⠀⢤⡔⠀⡈⠄
⠀⠐⠃⠈⢰⠈⠃⠚⠁⠀⡔⠀⠒⡄⠀⠒⠉⡯⠆⠀⠠⡀⠀⠉⠐⢀⡘⠀⠀⠀⠸⠆⠀⡠⠏⠀⠀⠀⠀⠀⠁⠀⠀⢀⡞⢰⠀⠀⢀⠘⠛⠉
⠀⠀⠠⠤⠘⠒⠐⠉⠃⠀⠈⠃⠁⠀⠀⠀⠀⠇⡈⠀⠀⠈⠐⠒⠒⠉⠀⠀⠀⢒⣄⠀⠪⣁⠌⠒⠠⠄⠶⡉⠐⠶⢚⣁⠤⠊⢀⡀⠐⡀⠀⠠⠂⣀
⠀⠀⠀⠀⠀⠉⠑⠀⠀⢀⢀⡀⠀⠣⢄⡊⠀⣀⡀⢀⡖⠒⠚⢳⠀⠀⢠⠀⠀⡄⠀⠀⠑⡄⠀⠉⠁⡠⡀⠀⣠⠄⠀⡠⡀⠀⠈⠀⠀⠀⠀⠀⠘⠐
⠀⠀⠀⡀⠠⠀⠁⠐⠀⠘⢄⣢⠐⠂⠀⠀⠈⠥⡬⠂⠹⠀⠀⡏⠀⠀⡁⠀⠀⢄⣀⣀⡔⠀⠀⠀⠸⠬⠋⠋⠰⠋⢸⢠⡘⠀⢁⣀⠔⠐⠒⠂⠄⠀⡀
⠀⠀⠒⢀⡠⠤⢄⡀⠀⡀⡄⠄⠀⢀⠄⠂⢄⠈⠀⠀⠙⠒⠚⠓⠒⠒⠁⠠⠄⠀⠀⠈⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡉⠈⠉⠉⢩⠃
⠀⠀⡴⢯⣗⢸⠎⢁⠀⡷⠄⡠⠐⠁⠈⠀⢸⠀⠀⡴⠊⣀⡀⠱⠆⠀⠀⠀⠠⠐⡖⠀⠀⠀⡠⠔⠈⠉⠑⡾⠿⠷⣂⠉⠁⠀⠀⢱⠤⠀⠀⠀⡔⠃
⠀⠀⢿⠷⠑⠁⠀⢸⠀⠀⠀⢀⡀⠀⣀⠔⢡⡀⢸⢠⠎⠁⠀⢤⠈⠐⠂⠀⠐⠊⠁⠀⠐⠀⡀⣀⡄⠤⠔⠀⠀⠑⢄⠀⠀⠀⠠⠄⠀⠀⠀⢈⣁⣰⠆
⠀⠀⠀⠁⠀⠀⠂⠈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢄⡀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠠⡏⠀⠀⠀⠀⠈⠉⠑⢆⠀⠋⢰⠋⡠⠄⠀⠓⣄⠀⠀⠀⢘⠁⣀⠥⠀⠀⣌⢮⠑⠁⢀⠀⠀⠀⠊⢄⡊⠀⠠⠀⠁⠄⢱⠀⢛⣌⠂⠀⢀⡠⠤⣤⣄⡁
⠀⠀⠀⠀⠀⠀⡀⣀⠠⢤⣋⠃⠀⠘⡄⠈⠂⡄⡀⠈⠆⠀⢠⠁⠀⣁⠀⡸⠀⠀⠀⠐⡂⠀⠐⠀⠠⠀⠀⠀⠆⠀⠀⠐⢀⠆⠀⣀⠑⠃⠰⡯⡤⠄⡹⢺⠁
⠀⠀⠀⠌⡄⠡⠀⠀⠔⡠⠌⡳⠀⠀⠘⢆⡀⠠⣈⠢⣘⠀⠀⠙⡝⡣⢬⠁⠀⠀⠀⠠⠅⠀⠀⠸⠀⠀⠠⠁⠀⠀⠑⡠⠋⠀⠀⠉⠓⢄⠀⡄⠀⠀⠀⢸
⠀⢀⡀⠰⣉⣉⡀⠤⠂⠂⠉⣀⣀⢀⣀⡀⠈⠒⠈⠔⠀⢠⢶⠀⢛⠽⣳⠀⠀⠀⠡⡡⠊⠘⢄⢀⠰⢀⠅⡀⠀⢂⠜⠁⠈⠦⢇⣀⣀⡘⠀⠃⠠⠤⠔⠈
⠀⠈⠇⠀⠀⣤⠀⠀⡠⠔⠋⠃⢠⠃⠌⠠⠉⢲⡀⠀⠀⣿⠙⠀⠈⣞⡜⠀⠠⠬⡶⠁⠀⠀⣸⡀⢀⠐⢄⡩⠔⢁⠄⡀⠀⣀⠀⣀⠌⠀⠄⢠⡀⠀⠀⢒⠄
⠀⠀⢀⣄⡀⠁⠀⡈⢁⣀⣎⡀⠦⠬⠐⡦⣮⠵⡎⠀⣀⣤⣄⢀⠀⢻⡃⠀⠀⠀⠙⡂⠐⡦⠛⠬⠂⠀⠀⠀⠀⠌⡔⢀⣀⠀⠉⠉⠀⠐⠂⠁⠀⠆
⠀⠀⢿⠀⢹⡄⠘⠰⠒⠠⠐⠚⠒⠒⣉⣀⡤⠞⠀⢘⠇⠀⠀⢉⡗⠀⢠⠄⢠⠀⠀⡀⠼⠀⠀⠀⠀⢀⣤⣄⣤⣎⠀⠈⠋⠀⠊⠑⠀⠀⠈⠀⣀⡀⣀⠂
⠀⠀⢸⢀⠤⠑⡄⠀⠉⠓⠃⠉⠉⠉⠉⠀⠀⠀⠐⡼⠀⠀⠀⢸⡇⠀⢠⠰⠀⠀⠎⠁⠃⠀⠀⠠⣿⣿⣝⣿⣵⣿⣷⠀⢠⠄⠀⠀⡆⠀⠤⣼⡁⢠⠍
⠀⠀⢱⡈⠒⢀⡇⠀⠀⠀⢳⠚⠒⠀⠤⠄⠒⢶⠂⠈⠃⠒⠶⠃⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢠⡀⠀⡼⡅⠀⠀⠀⠀⢃⠀⢄⣀⡠⠃⠀⠀⠉⠉
⠀⠀⠀⠙⠙⠋⢀⠴⡀⡀⢄⠉⠀⠐⠒⠒⠊⠁⠀⢀⢠⡠⢂⡀⠀⠀⣀⠁⠀⠀⠒⠒⡶⢦⠀⠉⠉⠀⠀⢘⠻⠀⠉⠁⠀⢀⠇⠀⠀⠀⡀⠀⢣⠈⠂⢢
⠀⣰⠂⢐⠀⢠⠃⠀⠉⠁⢈⠀⠀⠀⠠⠄⠤⡄⡖⣆⡿⠿⢉⡕⢀⡔⢱⠊⠉⠌⠉⠉⠐⠁⠀⠈⠒⠀⠤⠀⠀⠐⠀⢠⠌⠁⠀⠁⠀⠞⠁⠀⢀⠗⠲⣎⠄
⠀⠈⠉⠀⢀⠆⠀⠀⠀⠀⠄⢠⢤⠀⢲⠒⠀⠛⠁⣀⠠⠔⢋⡔⠹⠃⠈⣰⣹⠟⠉⠀⠒⠀⠒⡄⠀⠶⠀⠀⣠⣀⡀⣠⡄⠀⣀⠀⢰⠁⠂⣰⠁
⠀⠀⠀⢀⠎⠀⠀⠐⠀⠈⠀⠀⠁⠀⠈⠁⠀⠈⢉⡀⠀⣠⣈⡥⠴⠖⠚⠋⣡⣄⢠⠀⠀⠀⢀⠇⠀⠀⣤⢒⠇⠨⠄⠤⠀⠅⠘⠠⡀⠙⢁⠼⠂⡀⣀
⠀⢀⠀⠰⢈⠋⠣⣀⠄⠀⠀⢀⡂⠀⠤⠄⠀⠀⠙⠁⠀⠁⠀⣤⠀⠀⠀⢞⣭⠍⢸⡀⣀⠔⠁⣀⠀⠀⡀⠀⠠⡈⠉⠉⠁⠉⠉⠁⡁⠀⠀⠀⡘⠀⠀⢁
⠀⠘⢤⡀⠀⠈⠁⣁⡀⠀⠀⠰⠺⣾⠪⠀⠁⢠⣶⠶⠒⠒⠠⢟⡦⣄⡀⠘⠁⡠⠀⠉⠀⠀⠈⠊⠀⠀⡆⠁⠀⠀⠀⠉⠀⠁⠀⢹⠁⠀⠀⠀⠇⠀⢀⡘
⠀⠀⡀⠄⠲⢈⠜⠁⢀⠀⠀⠀⠀⠑⠄⠀⠠⠋⠀⠀⠀⠀⠂⡈⠉⠉⠀⠐⠏⠄⢀⠀⠄⠠⠔⢈⣆⠈⠑⠂⠠⠤⠤⠤⠤⠤⠔⢚⠳⠀⠀⠰⠈⠀⠁⡇
⠀⢨⠁⠙⠀⡁⠆⠀⡠⢀⡠⠄⠤⢄⠀⠀⠁⠀⠀⠀⠀⢈⡄⠀⠔⠈⠉⢂⠀⠈⠁⠐⠀⠄⠂⠉⠀⠀⢀⡄⡄⠀⠀⠀⠀⠀⠈⠀⢀⣎⡆⠐⠤⢤⠰
⠀⠀⢅⢐⡂⠠⠔⠁⠠⡃⣰⠉⢱⠀⢧⠀⠛⠀⠀⠐⠚⠛⠁⠜⠀⠀⠐⠸⡄⠐⡄⠠⠜⠀⢂⠉⠆⠀⠏⠐⡀⠄⠀⠀⣀⠐⠠⠀⠀⠓⠇⠀⡇⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢱⠈⠈⢁⢀⡠⠃⣾⠑⠒⠒⠄⠠⠊⠈⠀⠀⠀⣸⠃⢀⠀⠀⠀⠀⠘⠁⠀⠀⣀⠼⠒⠀⠀⠒⠺⡀⠀⠀⣈⡆⠀⠀⠀⠀⡀
⠀⠀⡁⢨⠽⢹⣀⢓⡀⠈⠢⠚⠁⠀⠀⢰⠁⣀⡤⠊⠀⡇⡀⠰⠿⠀⠃⢸⠀⠈⠄⠉⡁⠀⠀⢀⠴⠊⠁⠀⠀⢀⠔⠂⠀⠉⡹⠊⠀⠀⠀⢾⣟⣀⠤⠂
⠀⠈⠁⠀⠠⡀⠸⢘⡀⠀⠰⣉⣈⡳⠀⠀⠁⠘⠘⡄⠀⠡⡐⠀⠀⢈⣠⠎⠀⠀⠀⠈⠁⢀⠄⢃⠀⠀⠀⠤⢀⠀⠀⠀⢀⡼⠡⡮⠀⠀⠒⠊⠉
⠀⠀⠀⠓⠀⠃⣉⠉⠁⠀⠀⠁⠀⢠⠄⠀⡄⠀⠤⠂⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⠨⠦⠀⣑⠬⠤⣉⣒⣒⠚⣥⢊⡛⠋⠥⠐⠊⠁⡄⠄⠀⠄⠀⠀⢀⡀
⠀⠀⠀⢀⠀⠁⢈⠀⠀⠀⡉⡕⢀⠈⠒⠬⠀⢀⣤⡀⢰⡋⠉⠉⣷⠀⠉⢱⠀⠀⠃⠀⠀⠀⡀⠀⠀⢀⡠⣤⠀⡠⢦⡀⣀⠤⡀⢀⠉⠀⠀⠀⠀⠀⠈⠖
⠀⢠⠀⡀⠢⠀⠠⠐⠀⠀⠱⢡⠞⠁⠀⠀⠀⠱⡤⠜⠀⠇⠀⢸⠇⠀⠀⡆⠀⠈⠢⠀⣠⡔⠁⠀⠀⠈⠠⠋⠈⠄⠎⠀⠅⠠⠁⠀⣴⣤⢂⡘⠃⠁⢆⣀⡄
⠀⠀⠉⣀⣤⠐⠤⡀⠀⠀⢀⢰⠀⠀⡠⠒⠒⡄⠀⠀⠀⠉⠉⠉⠉⠀⠈⠀⠰⠆⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢇⠠⠤⠀⠀⠀⠀⣠⠃
⠀⠀⣼⢳⣽⣐⡟⠉⠀⠼⠄⢈⠔⠉⠀⠀⠂⡄⠀⢀⠔⢁⡀⠤⠵⠆⠀⠄⠠⠄⠂⡚⠀⠀⠀⡀⠔⠈⠈⠉⡶⠻⡿⠥⠀⠀⠀⠀⠈⠒⠂⠤⠤⠤⠔⠁
⠀⠂⢻⡶⠒⠉⠀⠀⡄⠀⠀⠸⢀⠀⣀⡠⠊⣤⠀⡇⡰⠋⠀⢠⢤⠀⠑⠒⠒⠒⠊⠀⠀⠐⠀⣀⣀⠤⠤⠔⠁⠀⠈⠢⣀⠀⡀⠀⠠⠄⠁⠀⠀⣀⣀⢺⠃
⠀⠀⠀⠈⠐⠐⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠀⠀⠀⠀⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠐⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠷⠒⠋⠉⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠡⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠁⢀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠠
⠀⠀⠀⢤⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠛⠙⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠂⢀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠠⡀⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣀⡀⠠⠴⠀⠒⡀⠀⠀⠤⠤⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠐⠒⠐⠒⠐
⠀⡀⠀⠀⠀⠈⠄⠠⠴⠒⠈⠀⠀⠀⠀⠀⠀⡄⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠁⠀⠀⠀⣤
⠀⢁⠠⠀⠀⠀⠀⢀⡀⠄⠠⠀⠀⢉⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⢀⡂⠀⠀⠀⠀⡁⠀⢀⡀⣄⡤⢠⠠⠀⠁
⠀⠈⠠⠬⠀⠈⢀⠃⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠁⠀⠘⡁⠀⠁⠀⠀⠀⠇⠀⢀⣤⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠃⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⣙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠠⠤⠀⠂⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠂⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠂⠀⠀⠀⢛⠉⠁⠀⠀⠀⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⡉⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⠂⢀⡀⠸⣁⠘⣴
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢨⢀⢀⡀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡁
⠀⠀⠁⠈⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀
⠀⠆⠀⠀⠀⡀⠀⠀⠀⠃⠀⠀⠲⠠⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠄⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠠⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠘⠇⠘⠓⠂⢂⠀⠀⠀⠀⠀⠀⠤⠄⢙⣒⣂⣉⡠⠤⡆⠀⠀⠀⠀⠀⠉⠉⠈⠀⠁⠀⠀⡀⠀⠀⠐⠀⣀⠤⠀⠠⠠⠤⣀
⠀⠀⠀⠁⠠⠀⠁⠀⠀⠀⠀⠀⠸⡀⠖⣀⣄⠲⠐⢂⠀⡇⠀⠀⠀⠀⠰⢠⠂⠈⠺⠂⠀⠀⠀⠀⠀⢀⡈⠀⣀⡀⢃⡁⣀⣀⢱
⠀⠀⠀⠈⠛⠄⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⠈⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⠠⠤⠄⠀⢀⠜
⠀⠀⠀⠀⠁⠀⠈⠠⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠒⠒⠒⠒⠒⠁⣠
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠂⠀⠀⠁

⠀⢎⠦⡴⡱⠀⠀⠀⠀⠀⠀⠎⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠋⠠⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠭⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈
⠎⠦⡴⠱⢠⢢⠀⠀⠀⠀⠀⡐⢐⠀⢀⠀⠀⠀⠀⠀⡠⠊⡠⠊⡠⠂⠀⠀⠀⠀⡀⠈⠀⠆⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠅⢀⠄⠁⠀⠀⠀⠀⠐⢇⡐⠠⠈⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⢀⠖⠀⠀⠀⠀⢀⡀⠠⠀⠁


⡴⣥⠄⢀⢮⠦⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⠀⠀⠀⠀⢠⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⡀⠀⠀⠀⠀⠀⠀⡠⠀⠀⡄⢊⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠃⠿⠒⠘⢼⠜⠀⠀⠀⠀⢀⠄⠀⡀⠀⠠⠀⠀⠀⠀⠜⠚⠃⠀⠘⠤⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠔⠋
⠈⡏⠀⠀⢸⠀⠀⠀⠀⠀⢄⢀⠔⠁⠈⠁⠀⠀⠀⠀⠀⢀⠀⢀⠠⠂⠀⠀⠀⠀⠀⢄⠀⢀⠆⠀⠀⠀⠀⠀⠑⢄⡀⠀⠜⠀⠀⠀⠀⠐⠆⠀⠘⠃


⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⠀⠀⠢⠀⡉⠁⠀⠀⠀⢀⠔⠈⠀⠈⡐⠄⠀⠀⠀⠀⠀⢀
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⠀⠢⠂⠀⠀⠀⠐⠤⠤⠀⡆⠁⠀⠀⠀⠀⢠⡈⠀⠀⠨
⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠂⠀⠀⠀⠀⠈⠆⠀⢀⠄⠀⠀⠀⠀⢀⡌⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡠⠀⠀⠀⠀⠀⠈⠂⠤⠤⠄


⠀⢊⢠⠈⠐⠀⠀⠀⠀⠀⡄⠀⠧⠃⢄⡠⠀⠀⠀⠀⡐⠁⠀⠀⠁⠄⠀⠀⠀⠀⢀⠠⡄⠠⢀⠀⠀⠀⠀⠀⠀⠈⠀⠢⠤⠀⠀⠀⠀⠀⢀⠠⠤⠄
⢀⠼⠴⢶⠀⠓⠀⠀⠀⠀⡙⠠⠰⠄⡄⠀⠀⠀⠀⠀⠑⠂⣀⠀⠐⠁⠀⠀⠀⠀⠀⡘⠀⠀⠀⠁⠀⠀⠀⢀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠠⠂
⠂⠄⠂⠈⠁⠁⠀⠀⠀⠀⠙⠂⢰⠄⠉⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠁⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠠⢊⠅⠈⠑⡇⠀⠀⠀⠀⠠⠶⡦⢠⡀⠀⠀⠀⠀⠀⠀⢬⢸⠇⠤⠀⠀⠀⠀⠀⠀⢠⣠⢠⠀⠀⠀⠀⠀⠀⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈
⢃⠂⠀⠀⠀⠉⠀⠀⠀⠀⠄⠔⠄⠐⠢⠼⠀⠀⠀⠀⠈⣚⣎⡐⡐⠀⠀⠀⠀⠀⠀⢸⢿⠸⠀⠀⠀⠀⠀⠀⠸⠭⡟⢭⠷⠀⠀⠀⠀⠀⠢⢀⣀
⢀⣀⣐⣁⡀⣀⠀⣀⢀⡀⣀⠀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣑⣞⡒⡁⣀⣀⣀⣀⣀⡀⣀⡝⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣀⣀⡀⣀⣀⡀⡀⡀⢀⣀⣀
⣿⣿⠿⡻⡿⠛⡿⢿⠿⣻⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣠⣴⠖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢷⠃⡆⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠘⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⣿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢠⣤⣀
⠀⡀⠈⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⠀⣸⣿⡿
⠀⣇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⣿⣿⢀⡀⠀⠀⢸⣿⣏⠀⠀⠀⠀⠀⠀⠀⢰⠃⠰⣶⡆⠀⠀⠀⢹⡟⠁
⠀⢹⡄⠀⠀⢥⣀⠀⠀⢰⠆⠐⠰⣿⡇⠀⣿⣿⠸⡧⠀⠀⠘⠛⢿⠀⠀⠙⠛⡟⠾⠆⣺⠂⠀⠛⠇⠀⠀⢀⣿
⠀⠈⣇⠀⠀⠘⣇⠀⠀⠘⡄⠀⠀⢸⠀⠀⣹⠁⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣆⠀⠀⣼⡏

⠐⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠄⡀⢰⣶⠁⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐
⠂⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠐⠀⠈⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⠀⠀⢀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠂⠀⠀⠀⢂⠀⡈⠀⠀⠄
⠀⠐⡆⠀⠀⠀⢀⠀⠈⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠘⠀⠀⠀⢈⡰⠀⠀⠀⠄⠄⠀⠀⠂⠀⠀⠀⠀⢀⣀⠀⠀⣄⠀⡀⠀⠀⠀⠀⠀⠆⠀⠀⠂⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⣷⠉⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠄
⢄⡄⠀⠀⠀⠀⠀⠘⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⢠⣀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡠⠤⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⡘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠃
⠰⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⡄⠒⢢⠀⠿⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡄⠀⠀⠖⠄⠀⠀⠁⠀⠀⠀⠆⠆⠀⠀⠀⢀⠀⠈⠀⠠⠀⢠⠀⠀⠠⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⡀⠀⢄⡰⠀⠀⠀⠄⠄⠀⠀⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠠⠴⠀⠀⠀⠂⠂⠀⠀⠈⠀⠀⠀⠀⠠⡠⠀⠀⣖⣀⡄⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠈⠀⠀⠐⠀⠠
⠀⠀⠀⠀⢀⠀⠀⢀⠂⠀⠀⡀⠌⠀⠀⠀⠀⡀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⢀⠀⠀⠈⠀⠐⠤⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⣌⡅
⠀⠀⠈⠐⠂⠀⣀⣀⠀⠀⠠⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣖⠑⡢⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣤⡔⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠮⠁⠽⠀⠉⠁⠀⠀⠀⢀⠈⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠋⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⡯⠀⠀⠀⠀⠀⠈⢿⡏⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⠟⢛⣛⣁⣀⣀⠀⠀⠀⠉⠉⠘⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣿⣿⣿⣿⡒⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⡀⠀⠤⠀⢰⠂⠀⠀⣀⢀⡀⠀⢀⠀⠀⠀⢸⡏⢻⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠁⣀⠀⠀⣿⡀⠏⢢⡿⣿⡟⢠⡎⠀⠀⠀⠘⣷⢹⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⡇⠈⣿⡆⢇⢹⠀⠀⣿⣿⠀⠀⠀⢸⡇⠨⠀⠀⠀⠀⠀⣿⠠⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣷⣄⢹⣇⣾⡄⡅⡀⢹⡏⠀⢸⣷⣿⠁⢠⡀⠀⠀⠀⠀⢻⡗⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⢿⡸⣿⣿⣻⣧⡀⣷⢸⠇⠀⣼⣿⠇⠀⣼⣧⣤⠄⢰⡄⠚⠓⠼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⣼⠷⠛⠛⠉⢻⣿⣿⣾⡰⢠⣿⣿⣶⣦⣿⣿⣿⣴⣀⣤⣐⣴⣦⡀⠘⠿⡃⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠙⠻⠿⡿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠋⠛⠉⠉⠁⠀⠀⠀⠉⠉⠙⠟⣿⣿⠇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢀⠸⣿⠉⠁⣀⡤⠴⠶⠶⣶⠶⡶⠖⠲⠦⠤⠤⠴⠃⠈⠂⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠘⢦⡨⢛⣩⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⠐⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢀⡈⠉⠘⡿⠿⣛⣋⣻⣍⣉⡋⢉⡉⠙⣛⣻⣛⡛⠛⠃⠲⠂⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠉⢁⣶⣾⣿⣿⣿⣿⣿⠿⠿⠷⢶⣾⣿⣿⣿⣿⣿⠆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⣠⣈⠻⢿⣍⣍⡀⠀⡀⠆⠁⠈⠀⠀⠀⠈⠈⠉⠑⣢⣦⣠⡴⠏
⠀⠀⠀⠀⠤⠤⠶⣶⣾⣿⣿⣤⣤⣤⣤⣤⣼⣇⣤⣤⣤⣤⣴⠿⠶⠞⢛⣟⣓⣛⣛⣻⣟⣀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣻⣟⣿⣿⣿⣿⣷⣶⣶⣶⣷⣿⣾⣿⠿⠿⠿⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠙⠛⠿⠿⠿⠿⠟⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠁⠀⠂⠁⠀⡄⣀
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠇⠀⠀⠀⠀⠠⠀⣀⡄⠀⢀⡇⢸
⠀⠀⠀⠐⠌⡀⠀⡂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠐⠀⠀⠀⢤⠈⡀⠁⢘⣋⠀⠋
⠀⠰⠂⠀⠄⢀⡰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠈⠉⠁⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⣠⠃⠈⠓⡢⠭⢮⣄⡈⠉⠤⠈
⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⡔⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣵⠀⠀⠁⠀⠀⣀⠀⠀⠐⠲⡀
⠀⠀⠀⠈⠠⣀⠀⠀⠢⢄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠘⠀⠂⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡇⠀⢀⡀⠀⠠⡁⠄⠀⠁
⠑⢄⠀⠀⠀⠀⠈⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣤⠠⠔⡀⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⢢⡀⣌⣉⣠⠄⠂⢁⡤
⠀⠀⠉⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠉⠀⠀⡰⠁⠀⠀⠀⠈⠢⡀⠀⠐⠀⠀⠈⠲⣌⡀⠀⠀⠐⠁
⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠢⢄
⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠈⠆⢰⣿⣦⣀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⣀⡀⣀⡀⠈⠛⢿⣿⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠀⠄⠀⠀⠀⠀⠀⠂
⠀⠀⣰⠋⣡⢦⣼⣌⣤⠀⠀⠀⠀⠀⠀⢀⠀⠈⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠈⠁⠒⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠄⠺⣆⡢⣨⡔⢢⡀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠉⠄⠙⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠹⣅⠧⢏⢱⣁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⢰⠁⠐⠈⠻⣔⠣⠤⠀⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈
⠀⠀⠀⠈⠑⠚⠑⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⠀⠀⠸⡀⠀⠀⠚⠉⢀⣰⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⡠⠆⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠀⢳⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⡀⠄⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠐⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠈⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡰⠂⠀⠀⠀⠀⠀⣀⠐⠈⠈⠀⣀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠚⠀⠀⠀⠀⠀⠀⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⣓⣈⡀⠀⠬⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠒⠀⠀⠀⠀⠐⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⡀⢀⡆⢀⠀⣀⠁⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠧⠈⠃⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⡏⠀⠀⢀⣀⣤⠀⢀⡄⠉
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠢⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⣴⣿⣿⠟⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠇⠀⠐⠀⠁⠠⠀⠀⠀⠀⠀⢀⡀⠄⠀⠠⠄⠛⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡈⠐⠒⠛⠀⠀⠘⠛⠁⠀⠀⠀⠀⢰
⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠤⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠈⠒⠒⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠆⠀⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣲⠠⡄⠀⠀⠠⠀⠀⠀⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⠾⣿⣿⡦⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⣥⣲⣤⠁⠀⠀⠀⠀⠀⠀⢀
⠀⢠⠖⠀⠀⠀⠁⠀⠀⣠⣘⡣⢛⠃⠀⠛⠮⠽⠇⠀⠀⠀⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⡀⠀⠀⠉
⠀⠟⠀⠀⠀⠀⠀⠀⠀⢨⢀⠀⠈⠀⢓⠀⠠⠀⠞⠛⢻⣧⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡁⢘
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠐⠋⠁⣿⣾⡇⠀⠀⠀⢀⡵⣣⠂⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⣀⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣸⣿⡁⠀⠀⠀⠀⠢⠥⠙⠃⠀⠄⠀⠀⠀⠈⠈⢁⡨⠿⠏
⠀⠀⢀⣾⣿⣿⣷⡄⠀⠀⠐⠀⠁⠀⠰⠖⠀⠂⠀⠀⠀⠀⣿⣿⡷⢀⢀⣤⣶⡄⠀⠀⠀⠀⠺⠿⠀⠀⠀⢀⠉⠃⠀⠐⠿
⠀⠀⠘⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣤⠄⠰⠀⠄⠂⡀⢻⣿⠇⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⠀⠠⠄⢃⠂⠴
⠀⠀⠀⠀⢉⣉⡁⠀⠀⠃⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠘⠛⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠈
⢶⣶⡆⠀⠀⠛⢀⣤⣴⣆⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⡿⣽⢿⠀⠀⠀⢀
⠈⣀⠀⠀⠀⠀⠸⣄⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠙⠛⠁⠀⠀⢄⠀⠀⣀⡀
⠀⠀⠀⠀⡀⠀⣤⠈⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣤⣶⢿⢿⣿⣶⣄⠘⠂⠀⠀⠠⠇⠘⢴⡿⠁
⠀⠀⢠⣾⣿⠘⠛⠃⠀⠂⠀⠀⠀⡲⣦⣄⠠⣠⠀⠀⠀⠀⠀⠁⠀⠀⠸⣿⣯⣴⣾⣷⣿⣿
⠀⠄⠸⣿⠋⢀⣠⡀⠀⠀⠀⠀⠀⠙⠃⢂⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⡖⠀⠈⠀⣸⣿⣿⡀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣦⠀⠉⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀
⠀⠁⢰⡃⠀⢿⣿⣿⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣷⡯⠀⢀⣤⠀⠀⠀⠀⠀⠀⠙⠛⠁
⠈⠋⠘⠙⠀⠈⠻⠋⠠⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠀⠀⠀⠘⡿⠀⠀⠀⠀⠂⢀⣤⡀⠀⢀⡐⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠂⣠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠘⠋⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠸⠿⠠⠛⠀⠳⡄
⢰⣶⡀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⣀⠀⠀⠠⢲⣶⠀⠀⠀⠀⢸⣿⡷⠀⠀⠀⠰⠀⠀⠀⠀⠐⠀⠂
⠈⠋⠁⠀⠀⠀⢠⣤⡄⠀⢣⠉⡗⠀⢠⠀⠈⠀⠝⠀⠀⠀⠀⠀⠠
⠀⠈⠉⠀⠀⠁⠀⠹⠃⠀⠀⠀⡀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡄⢄⠀⠰⣞⠀⠀⠀⠀⠀⠀⣤
⠀⢰⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡘⠀⠀⢉⣁