Heart attack Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠛⠉⠁⠀⢹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡀⠹⣿⣿⣿⣿⣿⣧⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠈⠀⠈⠀⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠁⠀⢠⣾⣿⢾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢦⣀⠐⠋⠉⠁⣼⣿⣿⣿⣿⡟⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢏⣽⠃⠘⠉⠀⠀⠠⠾⣿⣿⣿⡟⠁⠀⣈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡿⠃⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⡇⠘⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⢀⣠⣤⣴⣶⣤⣿⣿⣿⣿⡇⠀⢠⠁⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⢥⣄⢷⠀⠀⠀⡏⠀⣠⠜⣚⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⡀⢸⠁⡴⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⣿⣆⡼⠞⠃⠐⠠⣄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⡄⣨⣿⠃⠀⣠⡶⢶⣶⣿⠷⠶⠶⠛⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣿⡿⠀⣸⣷⡄⠀⠀⣀⣤⣤⣶⣾⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⢄⣹⣧⠀⣹⡿⠁⠀⠀⠁⠀⠈⢻⠛⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣆⣴⡶⠟⠻⣿⣯⠆⠀⢰⣧⣴⠂⠢⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠞⣫⠇⡀⠀⠀⠛⠤⠀⢿⣿⢹⠀⢀⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣺⡟⠀⡅⠀⠀⠀⠀⠀⢠⡟⠳⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⡄⠀⠀⠀⠀⡀⢤⠞⠣⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠀⠀⠀⠊⠀⡜⠀⠀⠄⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡂⡄⠀⢀⠞⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣶⡎⠀⠀⠀⣀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣟⣦⣤⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁

⠀⣠⣶⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣀
⣼⣿⡿⠋⠙⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⣠⣶⣿⣿⣿⢿⣿⣿⢿⣿⣷⣄
⣿⣿⡇⠀⣰⣿⣿⠁⠉⠛⠿⣿⣿⣶⣾⣿⠿⠋⠁⠀⢸⣿⣿⠀⠙⣿⣿⡆
⠸⣿⣿⣾⣿⣿⡃⠀⠀⠀⠀⠀⢙⣿⣿⠏⠀⠀⠀⠀⠈⣿⣿⡆⠀⢸⣿⣿
⠀⠀⠉⠛⠿⣿⣿⣦⡄⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠸⣿⣿⣤⣶⣿⣿⣷⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠙⣿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠛⠛⠋⠉⠉⠛⠛⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⣷⣶⣤⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠋⠉⠀⠀⠉⠙⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠁⠀⠀⠀⠀⢀⣾⣿⡿⠛⠛⠻⠿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠛⠛⠻⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠀⠀⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠁⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢀⣤⣶⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⢀⣼⣿⡟⠁⠀⠀⠀⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣷⣾⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣄⡀⠀⠀⠀⣸⣿⣿⠀⠀⢀⣾⣿⣿⣿⣷⡀⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀⢀⣴⣿⣿⠟
⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢀⣾⣿⠏⠀⠹⣿⣿⣄⣠⣿⣿⠇⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⠉⠙⢿⣿⣷⡄⢀⣾⣿⠏⠀⠀⠀⠘⢿⣿⣿⣿⠋⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠏⠀⣠⣄⠀⠀⠀⠻⣿⡷⠀⠀⣠⣾⣿⡿⠃
⠀⠀⠀⠀⢸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠏⠀⣨⣿⣿⣧⡀⠀⠀⠀⠀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⣠⣾⣿⡿⠻⣿⣷⡄⠀⢀⣼⣿⡿⠋
⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣯⣾⣿⣿⣯⠀⠀⠙⣿⣿⣶⣿⡿⠋
⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣆⠀⠀⠀⢠⣿⣿⣿⣿⡿⢻⣿⣿⠀⠀⠀⠈⠛⠛⠋
⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠃⠀⢠⣿⣿⣿⡿⠋⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⢠⣿⣿⡿⠋⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠇⠀⠹⠿⠋⠀⠀⠀⠀⠀⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⢀⡀⠀⠀⠀⠀⠻⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣄⠀⠀⠀⢰⣿⣷⣄⠀⠀⠀⠀⣿⣿⠟⠁⠐⣿⣿⡄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡄⠀⠀⠙⢿⣿⣷⣄⠀⠀⠈⠁⠀⠀⠀⠙⠿⠃⠀⣸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣄⠀⠀⠙⠿⣿⣿⣆⠀⠀⠀⠀⠀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣤⡀⠀⠈⠛⠁⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣤⣀⣀⣠⣴⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⠟⠛⠁
⣿⣿⡿⠻⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠂⠀⠉⠉⠁⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⠀⢀⠀⠺⠆⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡄⠀⠙⠃⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠀⠀⠀⠠⠊⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠄⠐⠐⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠒⠠⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠙⣇⠀⠐⢆⣀⣈⢑⣂⣤⣄
⠀⠀⠀⠀⠀⠄⠀⠐⠂⠐⢦⣀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠂⡰⠂⠠⡀⠀⠠⠁⠀⠀⠀⢰⣿⡍
⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠐⠄⠀⠀⠀⠀⠑⠀⠀⠘⢆⠀⠀⠀⠀⠀⣿⣿⢇
⠀⢰⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⣸⣿⣿⠘⡀
⠀⠂⠉⠙⢦⠀⠀⠀⣀⣀⠀⠀⠀⠀⠘⠀⠴⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣿⣿⡏⠀⠃
⠈⡆⠀⠀⠠⠁⣀⡠⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⣿⣿⡇⠀⠔
⠀⢡⠀⠀⢆⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠐⠁⠀⠀⠻⣿⠃⠀⠸
⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠒⠄⠀⠠⣌⠁⠀⢀⠜⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣄
⠀⠀⠀⠗⣦⡀⠀⠀⠀⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢄⡂
⠀⠀⠀⠠⠈⠳⡀⠀⠀⢈⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠙⠳⣄⠀⠀⠠⡀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⢀⠔⠁⠀⠀⠀⠈⠢⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠄⠀⠀⠀⢀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⢄⠀⡀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣿⣿⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣾⣿⣷⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠛⠉⠉⠀⠀⠀⠈⠉⠛⠻⢿⣷⣤⡀⠀⠀⢀⣤⣾⡿⠟⠛⠉⠉⠀⠀⠀⠉⠉⠛⠿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⡀
⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟
⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠙⣿⣧⠀⠀⠀⢀⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⣠⣤⣤⣾⣿⠃⠀⢻⣿⡆⠀⠀⣼⣿⢿⣿⡄⠀⣠⣤⣤⡀⠀⠀⢀⣾⡿⢿⣿⡄⠀⠀⠀⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠛⠛⠛⠛⠋⠀⠀⠘⣿⣷⠀⢰⣿⡏⠈⢿⣿⣾⣿⠟⠛⠃⠀⢠⣿⡿⠁⠈⢻⣿⣆⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣿⡿⠀⠀⠈⠻⠟⠁⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠻⣿⣦⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⣾⣿⠀⠀⠹⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠋⠀⠀⠀⣿⣿⠀⠀⠀⠘⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠃⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⢸⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠙⢛⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡰⢊⣡⠤⣄⠀⠙⢆
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⠂⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠈⠆⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⢀⠄⠀⡀⠀⠀⠀⠀⠀⠈⠉⠙⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽⠦⠤⠔⠋⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡔⡱⡀⠀⠀⠀⣆⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⡜⢀⡔⡁⠀⠤⠀⠘⢧⡀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢨⠈⠉⠀⠈⠸⢞⠔⣀⡀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⣓⠌⠊⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣤⠤⠒⠁⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠋⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢀⠴⠋⠀⠀⠰⢦⡬⠍⠉⠙⠓⠋⠀⠀⢀⣠⠞⠋⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡤⠔⠊⠀⠀⠀⠀⠀⢴⣩⣴⠊⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠋⢴⣠⣴⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁
⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣟⣛⣿⣟⣿⣻

⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠻⡿⠃⠀⠀⠀⠀⢰⠀⠇⠀⠀⠠⠀⠀⠀⠀⠀⣠⣦⡄⠆⠀⠀⠀⠀⢠⣲⡦⠀⠀⠀⠀⠀⠀⣶⣼⣧⡶
⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⢴⣿⣿⣾⠁⠀⠀⠀⠀⣠⣶⣯⡅⠀⠀⠀⠘⢛⣾⡿⣻⣿⣿⣦⡤
⠀⠀⠉⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠛⠃⠀⠀⠴⠞⢹⣿⣿⢿⡀⠀⠸⣷⣘⣿⣷⣿⠷⣾⣿⣦⡀
⠀⠀⠀⣿⣿⡏⠁⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡄⠀⠀⠀⢠⣿⢻⣿⠈⠷⠀⠀⣱⣿⣽⣿⣟⣿⣯⢿⣿⣷
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢠⠀⠀⠀⠀⠘⠀⠀⠀⣠⣾⠟⣿⡇⠀⠀⢀⣿⠃⢸⣿⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿
⠀⠀⠀⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠉⠀⡀⠙⠁⠀⠀⠺⠃⠀⢸⡏⠀⠀⠤⠀⠈⢻⣿⣾⣿⣿⣟⣿⣿⣿
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠙⠿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢠⣶⣷⡀⠀⠀⠀⣶⣗⣾⡀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⣀⡀⣴⣦⠀⠁⣠⣽⣯⣤⠀⠀⠀⠀⣠⣼⠂⠀⠀⠀⠀⣠⣤⣬⣄⣰⡆⠀⠉⠹⠞⠃⠀⠀⠀⠺⠃⠧⠃⠁
⠀⠀⣴⣿⣿⠃⠉⠉⠀⣠⣿⣿⣿⡿⣇⠀⠀⢰⣿⣿⣧⡤⠰⠖⠰⣿⣿⣿⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠴⠰⠆⠴
⠀⠀⠻⣧⣼⠀⠀⠀⠘⠉⢸⣿⣿⡇⠈⠛⠀⢸⣿⣿⣷⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⡦⣿⣷
⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⢸⡿⢸⣧⠀⠀⠀⠸⢿⡿⠿⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠙⠃
⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢰⣷⣶⣶⣶⡆
⠀⠀⠒⡀⢂⠀⠂⠀⠀⠀⢈⡀⣀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⡀⠀⠁⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣂⠀⠀⠀⠀⠀⠿⠿
⠀⠀⠀⠀⠀⢀⣻⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⢀⣀⣀⣀⣀⡀⠀⠀⠀⢀⠸⣿⣿⣿⠶⢤⡀⢠⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢰⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣬⡛⠃⢸⣿⣉⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢺⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⢰⠀⠀⣾⣿⣧⣤⣬⣭⣹⡋⠉⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⡏⠁
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢸⠀⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢸⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃
⠀⠀⠀⠀⢀⠈⡋⠙⠁⠀⠀⠀⠀⢸⢍⠉⠉⣿⡏⠉⠉⡉⠉⣉⢉⢉⠉⢩⢧⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⣤⡀⠀⣠⣶⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⠁⠘⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠇⢠⡄⠹⣿⡟⠀⠈⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⣉⣀⣾⣧⠀⠻⠀⣰⣄⣈⣉⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣇⠀⣰⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣶⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣆⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠸⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣩⣭⣉⣉⣙⠛⠛⠻⠿⠟⢋⣼⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡘⣿⠿⠛⠛⠉⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠉





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠐⢦⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠈⠻⣷⣄⣰⣿⣆⠀⠉⠁⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠘⢿⣿⠟⠿⣷⡀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠉⠀⠀⠈⠛⢦⠀⠘⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡟⠋⠉⠉⠙⢿⣿⣿⢿⣿⣿⣷⡀⠀⠘⢿⣿⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⣿⡿⠀⠀⢀⣤⠀⠀⠉⠀⠀⠈⢿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⢱⡟⣴⠀⣠⣾⠋⣴⡆⠀⠀⠀⠀⣼⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⣿⢹⣿⣶⣿⣧⡞⣉⡴⠆⠀⢀⣼⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⢹⣿⢸⣿⣿⣿⣿⣿⣥⡤⠄⣰⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟⣈⣵⣿⣿⣿⠿⣛⣵⣶⣄⣼⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣢⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣡⣾⣿⣿⣿⣿⡿⠋⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⢰⣿⣿⣿⣿⡸⣿⣿⣿⠿⣋⣵⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠙⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢠⣄⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠘⠉⠀⠀⠈⠉⠛⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠎⠀⠀⡀⠀⠿⠁⠀⣾⡟⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠰⡀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠄⠒⠒⠒⠒⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⢣⠠⣄⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠈⠉⠁⠀⠶⢄⡀⠀⠀⠘⡃⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠈⠙⠒⠊⠀⠀⢀⠔⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⠀⠀⠀⠀⢳⡀⠌⠙⠢⢤⣀⣀⣀⣀⣀⡠⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⡄⠀⠀⡌⠀⢠⠀⠀⢻⠀⠀⠀⠛⠶⡀⠀⠡⠀⠠⢴⢯⠀⠀⠀⢈⡠⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠴⠆⠘⠃
⠇⠀⢰⠀⠀⠜⠢⠀⠈⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠌⠘⣧⠀⠀⠁⠄⠐⠒⠀⠀⠀⣀⠀⠀⠈⠁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠃⢀⠂⠀⠀⠈⢃⠄⠐⠂⠈⠉⠀⠀⠀⠉⠁⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠀⠀⠎⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠙⢢⠀⢰
⠀⠀⢸⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⡘⠀⠀⠀⡀⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣀⠜⠀⠈
⠀⠀⠘⡄⠈⢆⠀⠀⠀⠀⠀⠠⡖⠀⠀⡈⠁⠀⠀⠀⡱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠁⠀⠈⠳⡄⠀⠀⠀⠀⠘⢆⢠⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠰⠇⡈⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠐⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠰⡦⠑⣀⠤⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⢀⡄⠀⠀⢠⣄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀
⣤⣾⣷⣶⣶⣶⣶⣾⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣯⣶⣶⣶⣶⣾⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠛⠉⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢹⡄⠀⣀⡤⠴⠶⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡼⣣⠞⠁⠀⠀⠀⠀⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣴⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣠⠶⢋⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠚⠷⢤⡘⠓⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠛⠛⠒⠲⠾⠿⠶⢤⣤⣤⣶⠛⠁⠀⠀⠀⢠⠟⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⣰⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠉⠀⠀⠀⢰⡤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠹⡄⢠⣤⣤⡼⠇⣶⠚⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢰⠇⣠⡴⠞⠋⠉⠛⢦⢀⡴⠋⠉⠉⠛⢦⡀⠹⡄⠀⠉⠙⠛⠻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣀⡤⠟⠋⠁⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠉⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠳⣄⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠈⣿⢦⣀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠈⠳⢦⣀⠀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣀⣠⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃



⣟⣻⡦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣾⣛
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⠂⡖⠒⢆⢰⠐⣶⠂⡰⡆⢠⡖⡦⢰⠀⠀⡖⠂⠀⢰⠒⠐⢲⠂⣴⠒⡄⡴⠒⢦⢰⣠⠆⣖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⡁⣇⣀⠞⢸⠀⣿⢠⠓⠻⡰⣏⡵⢸⣀⡀⣏⣁⠀⢀⣹⠆⢸⠀⢾⠙⡄⢧⣀⡜⢸⠙⣄⣏⣉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠖⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠙⠛⠛⠛⠲⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣯⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣽⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣿⢸⠈⢹⠉⠉⣻⠛⠛⠛⡟⠛⠛⢿⠛⠛⢻⠛⠛⢻⠛⠛⢹⡏⠉⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⢾⣦⣼⣄⣀⣽⣀⣀⣠⣇⣀⣀⣼⣀⣀⣸⣀⣀⣸⣄⣀⣼⣄⣤⣧⠾⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠧⠤⢤⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣁⡠⠿⣆
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⣼⠷⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠁⠀⠀⠀⠀⠘⠛⠛⣶⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣷⠀⠀⠀⠀⣴⠟⠛⠃⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠶⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠘⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡏⠀⣼⠋⠉⠉⠉⡏⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⠟⠀⠀⢿⣤⣤⣤⣤⣿⣤⣤⣤⠾⠁
⠀⠀⠀⠀⢀⣤⠶⠶⢶⣤⣤⣭⣍⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⡴⠶⢶⣤⡀
⠀⠀⠀⠀⣟⠀⠀⠀⡼⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠛⠁⠈⢹⣧⠀⢀⡼⠛⢶⣄
⠀⠀⠀⠀⠙⢦⣄⣀⣳⡀⠀⠀⢀⣰⠟⢀⣀⠀⠀⣿⠁⠀⠀⠙⣳⣦⣀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠙⢦⣠⡾⠋⠳⣮⡀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⢛⣻⣷⠞⠋⠉⢻⡄⠹⣦⡀⢠⠞⠁⠀⠙⢷⣄⠀⠀⠀⢿⡀⠀⠀⣠⡾⠋⠀⠀⠀⠈⠻⢦⣄⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠈⢧⠀⠀⣠⠟⠀⠈⠻⣧⡀⠀⠀⠀⠀⢹⡇⠀⠀⠈⠛⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣀⣼⠷⠛⠁⠀⠀⠀⠀⠈⠻⢦⣀⣀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⡀
⠀⠀⠀⠀⠀⠀⢠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣶⣶⣶⣶⡶⠶⣶⣶⣶⣶⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⡿⠿⢰⣇⠸⠿⣿⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣇⣛⢻⡿⢛⣃⣿⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⣿⣘⣃⣸⣿⣿⣿⡇⠀⠀⣿⡴⠖⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣡⣴⣾⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣧⡴⠶⠶⠶⠶⣿⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠘⠷⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠹⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠙⠳⠶⠶⠦⠴⢿⣿⣿⣿⡿⠟



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠪⢒⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠊⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠁⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⠀⠀⠐⠒⠶⣶⣄⡀⠀⠀⠀⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠉⠻⢷⡂⠤⠒⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⢼⡇
⢀⡄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣃⢸⣦⡀⠀⠀⠀⠀⢀⡠⠛⠲⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⡈
⡟⠁⠀⠀⠘⡄⠀⠠⠄⠀⠀⠀⠀⣻⠀⠈⠳⡀⠀⢠⠔⠁⠀⠀⠀⠀⠙⢄⢀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠁
⢹⡄⠁⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢳⣤⣶⣷⣦⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠁
⠀⢹⡄⢰⣄⢤⣼⡄⠀⠀⠀⠀⠀⣸⣽⡄⠀⣀⢀⠆⡶⣄⡀⢐⡤⠀⣀⣀⣨⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠃⠀⠀⠀⠀⠀⣰⠄
⠀⠀⢻⣿⣷⡈⢿⣿⡆⠀⠀⠀⣠⡿⠻⠃⠚⠉⠉⠈⠐⠋⠻⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⠟⢋⣡⣤⣶⠄⠀⢀⣠⡴⠞⠋
⠀⠀⠀⢿⣿⣷⡈⢻⣿⡄⠈⠈⠍⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠉⠉⠣⠛⡄⠀⠀⠀⠀⠀⠘⣧⣴⣾⣿⣿⣿⡿⠷⠛⠉
⠀⠀⠀⠈⢿⣿⣷⣼⠛⡇⢀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⢸⡉⠀⠀⠀⠠⡙⣶⣤⡀⠀⠀⠀⣀⣀⡀⣠⡴⠔⠋⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡀⢢⣼⠿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⣿⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣠⡀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡱⠂⠈⠛⢿⣿⣤⣌⠻⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠚⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢆⠀⠙⠻⣿⣧⣄⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠀⢀⢂⢀
⠀⠀⠀⠀⢺⢆⡀⠀⠀⠀⠀⣀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠀⠈
⠀⠀⠀⠀⠀⠢⣍⣿⣷⣏⣍⣇⡴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠰⠖⠖⠒⠋⠉⠉⠉⣉⢹⠉⠉⠉⠀⠒⠒⠒⠒⠒⠒⠒⠀⠀⠤⠤⠤⠤⠄⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⠀⠀⠀⠘⠛⠀⠀⠀⠀⠸⣿⢸⠀⠀⢘⣿⣿⣶⣶⣦⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣬⣭⣥⣤⡦⡴⠶⠷⠖⠀⠀⠀⠀⢸⠀⠀⠘⠛⠉⠉⠉⠉⢠⡀⠟⣵⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠠⣤⣤⣬⠁⢀⣀⣀⣀⣀⠈⣷⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⢹⣿⠇⠀⠀⠀⢀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣿⣿⠋⣰⣿⣿⣿⣿⣿⡇⢸⡀⢸⠂⠀⠀⠀⠀⠀⠀⠀⣴⣿⣧⢻⣷⣄⠀⠀⠀⣾⣿⣷⡀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢠⡿⠁⢸⣿⠉⠉⠿⢿⣿⡇⠈⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⠋⣧⡟⠙⠃⠀⠀⣼⣿⢏⢿⣷⡄⠀⠀⠀⣀⣸
⠀⠀⠀⠀⠀⢀⣀⡤⠤⢾⣯⣤⣀⣀⡀⠀⢀⣠⠞⢇⠀⠘⣿⠀⠀⢀⣾⣿⣿⠀⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣀⣀⣀⣼⣿⡏⠀⠀⢻⣿⣦⣿⠿⠟⢻
⠀⢀⡤⠒⠋⠉⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠋⠁⠀⢸⠀⠀⠉⣁⣀⣈⣉⣅⣤⣤⣶⣼⣧⣤⣤⣶⣶⣶⣶⣿⣿⣿⡿⠿⠿⢿⠟⠛⠿⠔⠀⠀⠀⠹⣿⡟⠈⠀⢸
⢠⣿⣿⣷⣦⣤⣀⠀⠀⠀⢀⣠⣤⣤⣤⣴⣶⣶⣶⣿⡿⠿⢿⣿⣛⣛⡻⠯⠭⠭⢿⣽⡿⠿⠯⠉⠙⠛⠂⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⡙⠀⠀⠀⢸
⢸⡏⠉⠛⠻⢿⣿⣧⣀⣚⣛⠿⠭⠭⠽⠛⠒⠒⠓⠘⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣉⠛⣷⠀⢈⣀⣠⠤⠞
⣿⣇⡲⣦⣤⣇⡀⠀⠀⠇⠀⠀⢀⣠⣤⣤⣤⣤⣀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⠀⠊⢭⠁⢹⣏⣽⣷⣶
⠸⣮⣉⠒⠏⢷⡍⠉⠈⠀⠀⣴⠟⠋⠉⠉⠉⠙⠻⡷⣄⣧⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⡇⠀⢀⣋⣀⣤⠤⠴⠖⠒⠛⠉⠹⢦⣾⣿⣿⣰⣋⡾⠛⠛⠋⠉
⠀⠙⢿⣟⡶⢶⣿⣀⣀⣀⡾⠁⠀⡰⠚⢽⣽⡢⠀⠀⠈⠯⠤⠔⠒⠒⠛⠋⠉⣙⣻⣿⡟⢋⣉⣩⣤⣶⣶⣿⣿⠿⠿⠛⠛⠁⠈⠙⠛⠛⠋⠁
⠀⠀⠀⠙⢿⣷⣦⣭⣥⡼⠃⣄⠀⣄⠀⢈⡍⠇⣤⡴⠒⢶⣶⣒⣒⣺⣭⣭⣽⣿⣷⡶⠿⠿⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠲⢮⣭⣉⣉⡀⠠⣿⣿⣿⣷⡮⣀⣼⣿⢃⣾⣿⣿⡿⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⠞⠻⣿⣿⣿⡿⠛⠁⠉⠉
⣿⣿⡟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠀⠈⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠻⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⣀⡤⠖⢒⣶⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠘⠁⢀⠤⠚⣛⡛⢟⣟⣻⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⡄⠀⠀⠀⠁⡰⠟⢛⣿⣮⣭⣧⣤⣤⣝⡲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢰⢱⣤⣆⡴⢊⠔⢺⣿⣏⡙⣿⣿⣿⣿⣿⣿⢦⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠛⢿⡴⠁⠀⠀⢻⠀⠀⢹⣿⣿⣿⣿⣿⡇⡟⢶
⠀⠀⠀⠀⢀⣠⡤⠶⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡷⠺⠤⠈⠷⡦⠾⠆⠀⣠⣿⣿⣿⣿⣟⡏⢱⣾
⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣤⣤⠄⠀⠄⠀⠘⠻⣿⣿⣿⣿⡟⠀⣾⡟
⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⣉⢿⣿⣀⠀⢀⠀⠀⡀⠀⠈⠙⣿⣿⣷⡦⠉
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠆⠀⠀⠀⠀⠀⠀⠻⢆⣿⡿⠋⠉⠁⠉⠁⢀⠀⠀⠘⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢈⠳⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠈⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈
⠈⠳⣦⣌⡉⠙⠛⠛⠛⠛⠛⢉⡉⠤⠀⡾⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⡀⠀⠀⠀⠐⡆⠀⠀⠀⢹⡤⡤⠐⠁⠀⠀⠀⣆⡀⠀⠀⠀⢸⠤
⠀⠀⠈⠙⠒⠷⠠⠀⠠⠈⠄⠄⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠄⠀⠀⠀⢀⣧⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣦⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠐⢶⠶⠆⠀⠠⠀⠀⠀⠀⠙⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠂⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣛⣛⣛⣲⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠞⠻⢦⣤⣀⣉⣉⠉⠉⠉⠉⠉⠉⠉⣉⣉⣁⣬⠟⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⠶⣶⣤⣬⣭⣭⣉⣉⣉⣉⣉⣉⣉⣉⣩⣥⣤⣶⡾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠀⢸⡇⢸⡏⢹⡏⢹⡏⢹⡏⢹⡏⠉⡏⠉⡇⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣄⣸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⠀⡇⢀⣇⣠⣧⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟⠙⠛⠛⠻⠿⠷⠾⠷⠾⠷⠾⠿⠿⠛⠛⠛⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⢷⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⡾⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣴⣦⣤⣤⣀⣀⣀⣀⣤⣤⣤⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⣤⣤⣤⣀⣀⣤⣤⣄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣉⣉⣉⣛⣛⡋⠉⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡇⠀⠀⠀⠀⠀⠀⢀⣴⠶⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠛⠿⢿⣶⣶⣤⣤⣤⣤⣤⣴⣶⣶⠿⠟⠛⢻⡇⠀⠀⠀⠀⢀⣴⣟⡱⠋⠀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠛⠻⡿⠷⠶⣦⡀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⢰⡿⠃⠈⠹⣦⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⡀⣠⡇⠉⠛⢸⡇⠀⠀⢻⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⡇⠀⠸⣧⣀⣠⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⢿⣿⣷⣾⠟⠁⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠈⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢟⣛⡛⣟⠛⠙⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠉⣀⣿⣀⣀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠁⠙⢆⠀⠀⡖⠂⠀⡠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠼⠆⠀⠀⢣⠀⡂⣰⠊⠀⣠⣞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠔⠒⠢⡴⢀⠀⣷⠃⢀⠄⢀⠥⠒⣣⢂⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡞⣩⣃⢩⠕⠋⠉⠉⠛⠳⢇⠀⣰⠁⠚⠂⠉⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡁⠀⠁⣹⣼⠃⠀⢀⡤⠶⢦⣀⣠⠟⠁⠀⣠⠴⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠙⠄⢁⡀⢞⢡⠃⠀⢠⣟⠍⠒⠒⠋⠀⢀⡬⠚⠉⠑⠒⡭⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠴⠊⠁⡀⠈⡇⠀⠠⢾⠈⠀⠀⠀⣠⠞⠋⠀⣄⣀⣀⡠⢤⣄⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡣⠀⠠⠃⡐⢠⡇⠀⠐⢘⣦⠀⠀⠰⡇⠀⡤⠊⠁⠀⠀⡟⠦⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠇⠀⠀⠠⠃⣼⡤⠖⠚⠛⠛⠦⣀⠑⣇⣰⠁⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡤⢾⡹⠄⠀⠀⠀⠀⠀⠈⠳⠚⠧⣀⣄⠀⠀⠌⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢰⠏⢀⠆⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠙⠖⠺⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⠋⠀⠀⡆⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⡇⠀⠆⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⢢⠀⡀⠀⠀⠀⠀⡀⠀⠀⡠⠊⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡑⠄⠀⠀⠀⠀⠱⠀⠐⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠐⡠⠂⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⣎⡀⠀⠀⠌⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡤⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⡤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⢬⣭⠅⠀⠀⠀⠀⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣃⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⢀⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣛⣀⣀⠀⠀⡄⠀⣾⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢉⡀⠙⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣿⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠈⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠘⠿⠃⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣤⠤⠴⠉⠎⠃⠦⠍⠦⠤⠔⠉⠀⠐⠈⠑⢤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣺⣭⣭⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠭⠍⠭⠭⠭⠭⠭⠍⠩⠍⠹⠦⡀
⠀⠀⠀⠀⠀⠀⠀⡠⡴⠁⠀⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⡐⢠⢡⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⢈⢈⠀⠀⠀⣉⢈⠀⠀⠠⠤⠀⠈⠆
⠀⠀⠀⠀⠀⡐⢀⠇⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⡇⠀⠠⢀⣀⣀⣀⣀⣀⣀⣠⠀⠐⢅⣓⠔⠀⠰
⠀⠀⠀⢀⠴⠠⠌⠼⠿⡴⠿⠿⠿⠿⠿⠿⠤⠀⠻⠛⠛⠟⠿⠇⠠⠠⠠⠤⠤⡤⢋⡙⡌⠠⠀⠀⠀⠀⠀⠀⡤⠄
⠀⠀⢀⣁⡀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣠⡄⠀⠀⡀⣀⠀⢀⣄⡄⠀⠀⠀⠀⠀⠢⡘⢃⠜⠀⠀⠀⠀⠠⡤⠠⡇
⠀⠀⢸⣀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠐⠓⠐⡇⠐
⠀⠀⠸⢩⡀⠀⠀⠀⢀⠀⣀⣤⣄⣐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡏⠋⠙⠉⠉⠉⢉⠙⢋⣉⡛⠉⡉⠉⠙⠉⢉⣩
⠀⢀⣰⣒⣃⣀⠀⠀⢠⣾⡿⠿⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣡⣾⠿⠿⢿⣷⡌⠀⠀⠂⠈⣚⡀
⠀⠨⠀⠀⠀⢈⡇⢢⢸⣿⢀⡌⣀⢸⣿⡇⡗⠚⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⣆⣿⣏⢠⣁⡄⣿⣿⣐⠒⠲⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣻⣷⣾⣶⣿⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣿⣶⣷⣾⣟⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣆⠀⠀⠀⠀⠀⠀⠀⢸⡴⠋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠳⡇⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢠⠞⣧⠀⠀⢀⣀⡤⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⣠⠋⠀⠘⠚⠉⠉⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠈⠙⠲⢤⠞⠉⠉⠙⠣⡀⠀⠉⠳⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⡞
⣀⣀⣀⣀⣀⣀⣀⣀⣀⡈⣧⠀⠀⠀⠀⡰⣋⣞⠉⣱⣄⡀⢸⡄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⡼⠁
⠙⣄⠀⠈⠉⠉⠉⠀⠈⠉⠉⠀⠀⢠⡾⣽⠣⣼⠃⢌⣇⡜⡸⠀⢀⡤⠲⡈⠳⣄⠀⠀⠀⠀⠘⠧⠤⠤⢤⣤⣀⣀⣀
⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠒⠲⢧⡦⢴⠛⣬⣶⠁⡰⠛⢢⠰⢇⣠⠟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠈⢾⣠⣿⠏⠻⣅⣀⠼⣀⡠⠃⢱⠛⡆⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⣨⠆⠀⠀⢠⡇⠀⠀⠀⠀⠠⠁⠀⣼⠟⠁⠀⠀⠘⠷⣤⢼⠒⠒⡇⢀⠇⠀⠀⠀⠀⠀⠐⠛⠲⠤⣄⣀
⠀⢀⡠⠖⠋⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠛⠳⠿⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡨⠽⠗
⠶⣉⡀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⣀⣤⠞⠉⠀⠀⠀⠀⠀⠀⣀⣤⣤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉
⠀⠀⠉⠙⠒⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⡛⢏⣙⡦⢵⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀
⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠉⢫⠈⣇⣸⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⡏⣧⣞⡁⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⣀⣀⣀⣈⣶⡄
⠀⠀⠀⣴⣁⣤⠤⠤⠶⠒⣶⠂⠀⠀⠀⡠⢿⡀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠉⠙⠲⢤⣀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣠⠔⠋⠀⠀⠙⠓⠒⠚⠋⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠑⠢⢌⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡠⠞⠁⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡽⠃⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⢀⡴⠋⠸⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣦⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢣⠏⠀⠀⠀⣿⠀⢸⣿⠉⠉⠉⠉⠉⠉⠉⢹⣿⠀⠀⠀⠔⠈⡏⠉⠋⠐⠄⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣱⢣⡏⠀⠀⠀⠀⣿⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡆⠀⠁⠀⠁⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⣰⢣⣿⡇⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠘⡁⠀⡆⠀⠒⠀⡘
⠀⠀⠀⠀⠀⢀⠀⠄⠒⠊⠁⢸⠀⠂⠿⠼⠧⠤⠤⠤⠤⠟⠀⠀⡿⠦⠤⠤⠤⠤⠤⠤⠼⢻⠀⠀⠀⠈⠒⠳⠤⠓⠊⠀⠀⠀⠀⠂
⠀⠀⠠⢂⢉⠠⠀⠀⠀⠀⠀⢸⠒⠀⠀⠀⠀⠀⠀⠺⠶⠖⠂⠀⡇⠀⠀⠀⠀⠀⠰⠶⠶⢺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂
⠀⡔⠛⢶⣤⣤⠀⠀⠀⠀⠀⢸⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠈
⡄⠟⠛⠉⠉⠉⠁⡀⢐⠈⠤⠍⣑⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡠⢂⠩⠤⠌⣐⠠⡀⠀⡀⠉⠫
⢁⠈⠤⠀⠀⢀⠌⡔⢡⡶⠒⠲⣦⠑⡌⢧⠀⠀⠀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠊⠌⣠⠶⠒⠶⣄⠱⠐⡄
⠀⠑⠂⠀⠀⢖⢠⠀⣿⠀⠀⠀⢸⡇⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠚⠀⠀⡏⠀⠀⠀⢸⡆⣁⠐⠂⠴⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠣⡙⠶⣤⡴⠞⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠙⠦⣤⡴⠟⡠⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣬⣶⣶⣶⣮⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣶⣶⣶⣬⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣬⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠉⠉⠙⠛⠛⠻⠿⢿⣿⣿⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠉⠻⣿⣦⣄⣠⣤⣤⣴⣶⣶⣶⣾⡿⠿⠿⠿⠟⠛⠻⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⠻⣿⣯⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣽⣿⣷⣄⡀⠀⠀⠀⠙⠻⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣟⡛⠛⠋⠉⠉⠉⠙⠻⣿⣶⣤⣀⠀⠀⠀⠉⠛⠿⣿⣷⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣻⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠀⠈⠙⠻⣿⣷⣤⣀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣦⣄⣀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣷⣶⣶⣶⣶⣿⣿⠁
⠀⠀⠀⠀⠀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣦⣄⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⣿⠃
⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣶⣶⣤⣤⣤⣤⣤⣤⡾⠋
⠀⠀⠀⠀⣼⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠉⠉⠉⠉⠁
⠀⠀⠀⠀⣿⣿⡿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣦⣄⣀⣠⣾⠟⣿⣿
⠀⠀⠀⠀⠘⣿⣧⡈⠙⠻⣿⣿⣶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣿⣿⠟⠋⢠⣿⣿
⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠈⠉⠙⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠀⠀⣠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢸⡇⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⣀⣀⡀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⢸⣏⢉⣿⠀⢠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣟⣛⣿⣧⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣴⡟⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣦
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣴⠟⢩⣉⠛⣷⡀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⢻⡇⣾⠛⠛⠛⠛⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⣶⣾⣿⣶⢸⡧⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⢷⣄⡘⠛⣠⡾⠃⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣸⡇⣿⣀⣀⣀⣀⣀⣀⣀⣈⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣭⣿⣿⣭⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣧⣀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⣿⠿⣯⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⢀⣿⣶⣟⣠⣶⣾⣿⣿⣷⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣶⣿⣿⣿⣷⣦⣄⣀⣸⣇
⠀⠀⠀⠀⠀⠀⣿⡏⠉⣿⣿⡿⠋⢉⡉⠛⢿⣿⣏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⡿⠋⣉⡉⠻⣿⣿⣏⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⣿⠀⣾⣿⣿⡆⠘⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⠀⣾⣿⣿⡆⠘⣿⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠙⠻⠟⠁⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠙⠿⠟⢁⣼⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠶⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⣤⠖⣲⠀⢀⡼⠁⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⣠⠇⠀⡟⢠⠞⠀⠀⣰⢳⠖⢲⡄⢠⡖⠲⡄
⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⣤⠀⠈⠛⠦⠀⠀⠀⣠⠏⠀⢰⡷⠃⠀⢀⣼⣡⡾⠀⠸⣧⡞⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣤⣀⣀⠀⠀⢀⡴⠃⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⢀⣀⣠⣤⣤⣄⣀⣸⡤⠞⠉⢙⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⢀⡴⠋⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⣴⣯⡥⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢠⠞⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢿⡀⠀⠀⡴⠃⠀⠀⠀⠀⢀⡴⠒⠚⠋⠉⠉⠉⠉⠙⠲⣟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⠛⠚⠁⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⠏⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⢉⡽⠋⠀⠀⢸⠀⠙⠳⣄⡀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢺⡏⠀⢀⡀⠀⣼⡀⠀⠀⠀⢳⡀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⢀⣠⠞⠁⠀⠀⡇⢀⡞⠀⣸⠃⠙⣦⠀⠀⢸⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠏⠉⣿⠀⠀⠀⠘⠁⢸⠁⠀⢿⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⣀⡴⢿⣀⣠⠴⠂⠀⠀⠹⣄⠀⠀⠛⠀⠀⠀⠀⠀⣿⠀⠀⣸⠇⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠠⠞⠉⠀⠘⠋⠁⠀⠀⡴⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⣤⡼⠁⠀⠀⠀⠈⠳⣄⠀⠀⠀⠰⠋⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⢸⣯⡈⢉⣅⣨⣉⢁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢰⡿⠉⠉⢿⡆⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠁⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣶⣶⣾⣿⣿
⣿⣿⢛⢻⢛⡟⣻⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠋⠉⠙⠛⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠛⠛⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡾⠥⠤⠤⣀⡀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠏⠀⠀⠀⠀⠀⠉⠓⣄⠀⢀⡼⠁
⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡞
⢀⡴⢏⠉⠋⠉⠙⠓⠦⣄⠀⣷⣀⣀⣀⣀⣀⣤⡤⠤⠤⠶⠒⠚⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⣾⡇⠀⠑⢦⡀⠢⡀⠀⠈⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⣯⠱⡀⠀⠀⠙⢦⡈⠢⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠹⡄⠱⣄⠀⠄⣀⠙⠢⡘⢦⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠰⠐⠀⢀⡾⠁
⠀⠙⣆⠈⠣⣄⠀⠀⠀⠈⠢⡙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡴⠏
⠀⠀⠈⠛⢦⣀⠉⠒⠦⠤⠤⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠶⠴⠶⠚⠉⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠛⠉⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢀⣠⠴⠚⠋⠉⠁⢀⡠⠞⠋⣻⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⢀⣴⠋⠁⠀⠈⠁⡠⠖⠉⣠⠔⠋⠁⢀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠈⠛⠲⠶⠶⠒⠋⠁⠀⠀⠀⠀⣼⠃⠀⠀⣠⠔⠁⢀⡴⠊⠡⠀⠀⢀⢼
⠀⠀⠀⠀⣠⡞⠻⢭⣀⠀⠀⠀⠀⠉⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠦⣴⠋⠀⣀⠔⠁⠀⢀⣀⠤⠞⢁⡾
⠀⠀⢀⡾⠉⠙⠲⢤⣈⠉⠒⠤⣀⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠘⢧⣀⡉⠉⠉⠋⠉⣉⣉⣀⡤⠶⠋
⠀⠀⢸⣧⣀⠀⠀⠀⠈⠙⠲⢤⣀⠉⠒⠤⣄⡀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⢿⡈⠓⠦⢄⡀⠀⠀⠀⠈⠙⠲⢤⣀⣉⣳⠖⢻⡆
⠀⠀⠀⠈⠳⣄⠀⠀⠈⠉⠑⠒⠒⠒⠒⠚⠋⠉⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣿⣶⣶⣶⣶⣾⣯⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂⠉⡇⠀⠀⠀⣀⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⡉⠈⡄⠠⢓⡢⠿⠭⠤⠤⠤⠄⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣦⠔⠛⡔⠊⢹⠀⣀⣀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⠀⠀⠀⢸⢂⡄⢀⢱⠀⠈⢾⠀⠈⢆⡤⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⡀⠀⠀⠀⠀⠋⢚⣉⣿⡆⠀⢿⠀⠀⢸⡶⠒⣺⠃
⠀⠀⠀⠀⠀⠀⠀⠤⠄⢤⠀⠀⣿⣿⠿⣿⣿⣦⡀⠀⠀⢞⠱⠲⡼⠁⠀⠸⣄⣠⡼⠉⠛⠢⠤⠤⠤⢄⣀⣀
⠀⠀⠀⠀⠀⠠⠂⠀⢀⠠⠄⠸⣿⡿⠀⠈⢿⣿⣿⣤⣄⣄⠔⠋⠀⠀⠀⠀⠀⠚⠁⠙⢄⡀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⢠⣫⠚⣵⡶⣀⠬⠖⠒⠚⠙⠻⠿⣿⠁⠀⠀⢀⡴⠒⠒⡦⡀⠀⠀⠀⠈⡹⠒⠒⠒⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⣼⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠠⣯⡡⠧⠚⠂⠈⠢⠂⣠⠞⠁
⠀⠀⠀⠀⠀⠀⡞⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⣀⣀⣀⠤⠤⠒⠉
⠀⠀⠀⠀⠀⢀⠁⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣓⣾⠏
⠀⣠⡶⢿⣿⡿⠀⠀⠀⠀⠀⠈⠑⡦⣀⡀⠀⠀⠀⢠⠒⠉⣿⡿
⣜⡬⢴⣶⡇⠰⠀⠀⠀⠀⠀⢀⠜⡱⠁⠈⠁⢒⡶⠚⠀⠀⣿⡇
⢿⡀⠀⡽⠳⡀⠀⠐⢲⠤⠴⣫⣊⠀⠀⠀⣠⠊⠀⠀⠀⠀⣿⣿⡀⡀
⠀⠈⠉⠀⠀⠈⠉⠉⠁⠀⢴⣁⠈⠉⠁⠀⣏⣀⡀⠀⠀⠀⣞⡉⠚⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣹⠋⣏⣀⣨⠇⢠⢋⢸⠀⠺⡟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠣⠤⣋⣉⠤⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢋⣉⡉⠉⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠊⠉⠉⠉⠈⠙⠛⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⣼⣷⡄⠀⢀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠻⠟⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⣀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⣤⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠳⠶⢶⡴⠶⠶⠦⠔⠛⠃⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣴⣧⡀⠀⠀⠀⠀⠀⢀⠄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⠇⢀⡙⠲⢦⡀⠀⠈⠀⠀⠀⣀⠰⣄⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠘⠣⣀⠇⠀⠉⠛⢤⣄⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⢀⡙⢷⣄⠀⠙⣷⠀⠀⠀⠀⠈⠙⠶⣤⡀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠸⢷⠊⠉⠛⠛⠉⠛⠓⠶⢤⣄⣀⣀⠀⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⢠⠔⠊⠀⢸⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠉⠉⠓⠶⠦⣤⣉⠓⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠠⠞⠁⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠳⡄⠀⠀⠀⠤⣀⠀⠀⠀⠙⠋⠹⠿⣶⡀
⠀⠀⠀⠀⠀⠀⢀⣶⠓⠈⠀⠀⡐⠀⠀⠀⢸⠀⠀⠘⠀⠀⠀⠀⠀⠙⢧⡄⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠰⠋⠁⠀⠀⠀⠄⠀⠀⠀⠀⢸⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⣀⡀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⣠⣤⣄⣄⡀
⣉⣡⣄⣤⣄⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣡⣤⣤⣤⣤⣤⣼⣟⣀⣀⣀
⣿⣿⣿⣿⣿⠿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠀⠂⡆⢰⢰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣘⣀⣁⣃⣘⣘⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⣀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢸⠉⢉⣉⣉⣉⣈⡀⠀⠀⠀⡴⠊⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢨⡇⠀⢀⠎⠈⠢⡀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠘⣀⠤⡄⠒⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⠤⠤⠤⠤⠤⠤⡇⢠⠊⠀⠀⢱⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⡇⠣⢀⣀⣀⣀⠠⠔⠊





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

⠀⠀⠀⠀⠀⠀⠀⠀⠏⠰⠖⠲⠖⠠⠧⠰⠾⢀⠳⠢⠂⠰⠉⠶⠐⠲⠇⠶⠢⠆⠠⠧⠔⠒⠲⠲⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠤⢠⠤⠤⠄⡄⠀⠤⠤⠄⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⣴⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⠀⣄⠀⠀⢸⣿⣿⠆
⠀⠀⠀⢰⣿⣧⠀⠀⣹⣷⣦⡀⠀⠀⠀⠀⢸⣿⡏⠲⠄⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠈⣳⣿⠀⠈⠁
⠀⠀⠀⠘⣿⡟⠀⠀⣩⣿⠇⠈⠀⠀⠀⠀⠈⣿⢳⠀⢀⣤⣀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠰⣿⣯⠷⣤⣀⡀
⠀⠀⠀⠀⠿⠇⠀⠠⠏⠙⠦⠀⠀⠀⠀⠀⠘⠃⢸⣠⡿⠛⠟⠷⠶⠒⠀⠀⠀⠋⠀⠀⠚⠋⣿⡾⠟⠟⠷⠶⠖
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⢀⡽⣻⣷⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷
⠀⠀⠀⢰⡮⢼⣿⣿⠤⢤⡄⠀⠀⠀⢾⠿⣿⣿⣦⠤⣤⠀⠀⠀⣾⣿⢿⣷⣶⡶⣤⣤⠀⠀⣶⢴⣿⣷⣦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⣀⠀⠀⠀⢀⣀⣀⣀⣀⣄

⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢀⣀⣲⣾⣟⣿⣶⠀⠀⢀⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟
⠀⠀⠀⠀⠀⠀⠠⠽⣿⡆⠀⠀⠀⠀⠀⢾⣿⡇⠛⠛⠛⠛⠛⠛⠛⠀⠀⢸⡷⠤⠼⠷⠿⠿⠿⠿⠷⠦⠞⢿⡛⠉
⠀⠀⠈⠉⣽⣤⣤⣾⣿⣧⣤⡀⠀⠠⣶⢼⣿⣷⡤⣤⡤⠀⠀⠀⠀⠀⠀⣸⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡾⠿⠟⠛⠛⠛⠛⠛⠿⢷⣦⣄
⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⡀
⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⣼⡟⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢻⣷⣾⣿⣿⣄⠀⣀⣤⣶⠿⠛⣿⡄⠀⢀⣤⣶⣤⡀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢠⣿⠉⠛⠛⠛⠋⠁⠀⠀⠘⣿⣤⣿⠋⣤⡙⣿⡄⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠸⣿⡀⠀⠀⣀⡀⠀⠀⠀⠀⠈⢿⣿⠀⣿⠇⣿⡇⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠻⣷⡘⠟⠛⠛⠿⠀⠀⠀⠀⠀⠉⠀⢀⣼⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⣿⠇⠘⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⢿⣧⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⢰⣿⡁
⠀⠀⠀⠀⠀⣸⡿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣤⣴⡿⠛⣿⡄⠀⠀⠀⢀⠟⠀⠀⢀⣼⡷
⠀⠀⠀⠀⠀⠻⣷⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠘⢿⣦⠀⠀⠈⠀⠀⢀⡽⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣶⣦⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠁⠀⠀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⢀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠴⠾⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣴⣶⠿⠿⠿⠿⠿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠈⠉⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢖⠋⠁⠀⠘⢒⡲⠥⢄⠤⠠⢓⡄⠀⠀⠀⠀⠀⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⢃⠃⢠⠄⠀⠀⠀⠁⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠠⢀⡄⠤⠄⣀⣀⣀⡀⡈⢸⠀⠘⠀⠀⠀⠂⠂⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠰⠃⠈⠈⠤⠘⠀⠀⠀⠠⠀⠄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⡀⠀⠀⠀⠀⠀⠀⣀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⠠⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠄⠀⠀⠀⠀⠀⠈⣂⣀⣀⡀⠈⠀⠁⠀⣸⠤⠤⠖⠚⢄⣀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⢄⠀⡀⠀⣀⣀⣀⣀⣀⣸⠀⠀⠈⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⠊⠁⠀⠀⠀⠀⠈⠢⢤⣤⠔⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣬⣭⣬⣭⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⣤⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢈⠄⠀⠀⠀⠀⠀⠀⠀⠀⢴⡖⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⡀⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠉⠀⡅⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠠⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠦⠘⡄⠸⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠁⠀⠀⠀⠂⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⢈⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⠀⣀⣀⣀⠀⠀⠀⣀⣀⡀⠐⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⣿⣿⡇⠀⠀⣴⣿⣿⣿⣿⠀⣴⣿⣿⣿⡇⠀⠀⠀⠀⣠⣴⡇
⠀⠀⠀⠀⠀⢠⣿⣦⠀⣿⣿⣿⣛⣉⠉⠉⠉⢙⣿⣿⡏⢹⣿⣿⣯⣭⣿⣿⣿⡇⣿⣿⣷⣤⠀⣿⣿⣿⠋⠉⠀⣿⣿⣯⣄⣀⠀⠀⠀⠚⠉
⠀⠀⠀⠀⠀⠸⠋⠁⠀⠘⠛⠻⠿⣿⣿⣷⣄⠀⣿⣿⡇⠀⣿⣿⣿⣿⣿⡿⠛⠀⣿⣿⣿⠉⠀⠹⣿⣿⣷⣄⠀⠈⠛⠿⠿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣄⣠⣿⣿⣿⣿⠀⣿⣿⡇⠀⣿⣿⡇⢿⣿⣇⠀⠀⢹⣿⣿⠀⠀⠀⠈⠻⣿⣿⣷⡀⠀⠀⠀⣨⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠏⠀⣿⣿⡇⠀⣿⣿⡇⠘⣿⣿⣦⡀⠸⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠄⠈⠉⠛⠛⠛⠛⠉⠀⠀⠀⠈⠻⠇⠀⠿⠿⠟⠀⠸⣿⣿⣷⣦⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⠃⠿⢿⡿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣶
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⡿
⠀⠀⠀⠀⠏⢂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣶⣤⣤⠀⠀⠀⢀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣖⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⠃⠀⠀⠀⠁⠀⠊⢠⢀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠀⠀⠁⠀⠀⠀⠀⠀⢀⡴⢂
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠿⠟⠋⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠌⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠦⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⢟⣩⣵⣶⣿⣿⠏⢀⣴⣶⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠿⢋⣴⣿⣿⡿⠿⠿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡏⣾⣿⣿⡎⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠋⢸⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠟⠁⠀⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠁⠀⠀⢰⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠁⠀⠀⣀⣴⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠁⠀⢀⣤⣾⣿⣿⣿⡿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠋⠀⢠⣾⣿⣿⣿⣿⢟⣫⣾⣿⣿⡟⠛⠿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠋⠀⠀⠀⠘⢿⣿⠿⠋⣴⣿⣿⣿⣿⣿⠁⠀⠀⢀⣮⣭⣯⣭⣶⡇
⠀⢀⣤⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣬⣥⣀⣀⣀⣘⡛⠛⠛⠻⠿⠃
⣰⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣀⣀⣀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⡿⣫⣭⣭⣛⣛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢹⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⢿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠙⠻⠿⠮⠭⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠎⢓⡴⠀⠀⠀⠀⡄⠀⠀⠘⡏⣁⣬⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠴⢼⡆⠀⠀⢦⠚⠹⣤⡄⠘⠋⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⢀⠀⠀⠂⠀⢸⠖⢾⠁⠠⠄⠠⠀⢀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠛⢤⡤⠀⠂⠀⢀⠴⢖⣋⡙⠓⠒⢢⣄⠀⠐⢮⢉⢨⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠷⠲⡏⠀⡀⠀⣠⠓⠤⣄⢀⣩⠗⠊⢉⣬⠧⡀⠟⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⢰⠓⣦⡤⠚⢉⡤⠔⠊⠁⠀⢃⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠾⠥⠴⠞⠓⠒⠒⠒⠒⠒⠚⡚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡏⠀⠀⠀⠀⠀⠀⣀⣀⣸⠬⠗⢚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠠⡈⠉⠉⣉⡭⠉⠉⠀⠰⡤⣀⠀⠈⣋⠝⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉⠀⠀⠹⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⠀⠀⠀⠀⠀⠉⠁⠀⠀⢰⡇⢠⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢀⡠⠤⠔⠦⠤⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⢢⢤⣄⣀⣀⡴⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⠼⠀⠋⠔⡡⢊⢞⡽⠲⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠙⣅⢜⢮⡳⢄⣀⠈⠑⢁⣋⡭⢊⡴⣩⠏⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠈⠙⠶⣉⡗⣺⢭⡭⢭⢔⣾⠿⠋⠁⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠠⢂⡠⢀⠀⠀⠈⠉⢉⠉⢉⠉⢀⠀⡄⢀⠔⣠⠂⡠⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⢋⠔⣡⠎⣠⠞⡰⢋⠔⢁⠔⣡⠎⡰⢃⡔⢁⠎⡰⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠈⠁⠀⠁⠈⠀⠁⠀⠋⠘⠁⠘⠁⠈⠀⠃⠘⠐⠡⢸⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⢀⣰⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣄⣴⣿⣿⣿⣿⣿⣦⠀⣀⣤⣶⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠈⣿⣿⣿⣿⣿⡿⢋⣴⣾⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠸⣿⣿⣿⣿⡟⣡⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠻⣿⣿⡿⢰⣿⣿⣿⣿⣿⡿⢋⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣌⠛⠃⣾⣿⣿⣿⣿⡿⢡⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⠇⣾⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠿⢋⣴⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠸⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⢻⣿⣿⡟⣠⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠿⠹⣧⠀⣶⠈⠉⣉⣰⣿⡆⣿⢋⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠏⠀⠈⢻⣿⣿⣷⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠙⢿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢩⣭⣭⣭⣴⣿⣿⣿⣿⣦⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣇⠘⠛⠛⠛⢿⣿⣿⣿⣿⠟⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⡿⠿⠿⠟⠉⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣟⣻⡿⣿⠿⠿⠿⣿⡿⢿⣟⣻⢿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠶⢮⣭⣭⣭⣭⣭⣭⣭⣭⡵⠶⠛⠿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⡶⠛⠛⢶⡞⠉⠀⠈⠉⢉⣭⣭⣿⣿⡛⠉⠉⠉⣴⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣼⣷⡀⠀⠀⠹⢦⣤⣤⣤⣴⣿⣿⣿⣿⣇⣀⣀⣤⣿⡿⣿⠟⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠁⠀⠻⢶⣄⣠⣶⣽⣶⡉⠁⢻⣿⣿⣿⡟⠉⠉⠀⣨⣽⣿⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢰⣀⠀⠀⠀⠀⣩⣛⣿⣿⣇⣠⣴⠿⠿⢿⣻⣿⣶⣤⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⣙⠻⠶⣦⣤⣿⣿⣿⣿⡟⠉⠀⠀⠀⢻⣿⣿⣿⠇⠀⠉⣉⣽⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣌⣉⡙⠛⠋⣄⣀⣠⣤⠶⠟⢛⣉⣀⣤⣶⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠤⠤⠤⠤⢤⢤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⣀⣸⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠉⠉⠉⠉⠈⠹⢿⣇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠⠤⠤⠤⠤⠶⠾⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠏⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡰⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⣇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠛⡌⠐⢲⡶⠲⠂⠒⠒⢒⣾⢻⠀⠀⠀⠀⠀⠀⠀⣧⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣄⡔⠺⣾⡟⢀⣦⣀⡸⠟⡀⣸⠀⠀⠀⠀⠀⠀⠀⣥⣿⡆⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⢈⣿⡋⢁⣼⡁⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⣽⣿⡇⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠘⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⣀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠓⠲⣶⠶⣾⠟⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠃⠀⠀⢤⣧⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢙⡆⠀⠀⣞⠉⣷⠀⠀⣚⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⣀⣀⣠⣤⣬⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠈⠋⠁⣀⡀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⢸⡇⣼⣿⣿⣿⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡄⢀⠀⡤⠠⡄⠀⠀⣠⠒⢠⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠹⠉⠉⠉⠉⠉⠉⢸⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠼⠃⠀⠀⠢⠴⠃⠀⠀⠙⠶⠞⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣋⣸⡇⠀⠀⢨⣀⣵⠀⠀⠺⣤⡿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⠐⠀⠀⢠⣤⣤⣤⣤⣤⣶⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢰⡄⠀⠀⣔⠀⣆⠀⠂⢠⡁⣰⠄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⢹⠙⠛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠙⠛⠃⠀⠀⠈⠛⠋⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⣀⣈⣀⣀⣼⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠁

⣷⠛⠛⣶⢶⡶⣶⠶⠶⣾⠶⢶⠶⠶⣾⠷⠶⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⢶⡶⡶⣾⢿⣿⣿⠾⠿⠷⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠭⢤⣸⠀⠀⠀⡏⠀⡠⠚⢚⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡄⢰⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣿⣧⡾⠚⠁⠀⠒⣄⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣠⣿⠇⠀⡴⠟⠻⠿⠿⠓⠚⠛⢻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠿⢿⣿⠀⢸⣿⡆⠀⠀⠴⠶⢾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠰⣸⣷⣀⡼⠏⠀⠀⡄⠀⡀⠀⡋⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣾⡷⠉⠉⠻⣷⠃⠀⣼⣶⠏⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣏⣴⠇⠀⠀⠀⠈⠀⠀⢙⣧⣚⣀⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣏⠀⠃⠀⠀⠀⠀⠀⡸⡃⠙⠛⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡛⠀⠀⠀⡠⠂⢹⠁⠈⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡄⠀⠀⠀⡠⠃⠀⠀⠁⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣧⣄⡴⠁⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡧⣀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⠋

⠀⠀⠀⠀⢀⡀⠀⣰⢲⡀⡴⢢⠀⡠⣄⠀⢀⠔⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⢄⠀⢀⡤⡀⣠⠲⡄⡰⢲⡀⠀⣀⡀
⣰⠶⢤⡀⡯⠙⣦⠇⠀⠻⠁⠀⠛⠁⠹⣤⠋⠀⠴⠞⢉⡽⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⡀⠀⠀⠸⣍⠙⠾⠆⠈⢣⡼⠀⠘⠃⠀⠹⠃⠀⢧⡞⠨⣇⣠⠔⢶
⠈⢦⡀⠉⠛⢀⠈⠀⡀⢀⣀⠀⡀⠀⠀⢁⠀⢀⠀⠰⠿⠶⡄⣴⠚⢳⡌⠙⡃⠰⠋⠉⢙⡆⠀⢴⠚⠳⠀⠀⢀⠀⠁⡀⠀⣀⠀⡀⡀⢀⡈⠀⠘⠋⢀⡠⠊
⠀⣠⠽⠶⠀⢀⠀⢸⢡⠸⠆⠨⠀⠀⢠⠘⠡⢈⠀⠀⠀⠛⠤⣽⠀⠘⠃⠀⡇⢳⠀⢰⡏⠀⡤⠚⠓⠀⠀⠀⢸⠴⠘⡆⠀⠯⠆⠖⡁⠸⠀⠀⠀⠐⠻⠤⣀
⠘⢣⡶⠀⠀⠀⠀⡄⢠⢂⢠⠀⠨⠄⢀⠀⠠⡄⠀⠀⠀⣠⡔⢩⡆⠀⠀⠀⡇⠈⢳⠀⠙⣆⢙⣦⠄⠀⠀⠀⢦⠀⠖⠀⠲⠀⣦⠀⠐⢀⡀⠀⠀⠀⠐⢶⡊
⠰⣏⣀⣀⠀⠀⠰⠒⠼⠁⠸⠁⠘⠆⠀⠄⠀⠃⠀⠀⠀⠈⠉⣶⣇⠀⠀⠀⠇⡞⠉⠀⣠⠿⣏⣀⣀⠀⠀⠘⠘⠀⠁⠀⠀⠐⠉⠂⠀⠘⠃⠀⠀⢠⡤⢤⠕
⠀⠀⠀⡿⠀⣠⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣤⡘⢟⠉⠁⠘⠛⠃⠛⠀⠓⠖⠚⠁⠀⠀⢨⣋⡠⡆⠀⠀⣀⠀⠀⡀⠀⢠⡄⠀⡀⠀⢠⣄⠸⡆
⠀⠀⠀⠳⠚⢹⡄⢰⢧⣠⠻⡄⢸⢧⡀⡜⢳⡀⠀⡇⠙⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⡇⢀⠔⠉⢦⡴⢻⡀⡌⠱⠴⢻⡀⡶⠈⠙⠃
⠀⠀⠀⠀⠀⠀⠓⠋⠀⠀⠀⠱⠏⠀⠉⠁⠀⠉⠒⠃⠀⢀⡀⣀⣀⣀⡀⠀⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⣉⡁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⡏⣨⠊⣿⠁⠀⠀⣨⠏⠀⠆⣠⠔⠊⠉⢷⡀⠀⣠⠞⢩⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠤⠄⠂⠀⠀⠀⢓⠀⠀⡀⠀⠀⣏⣳⠋⣹⠁⠀⣰⠇⠀⠀⡄⢳⡀⠀⠀⠈⢳⡼⠁⢀⡙⠁⠀⣨⠇⠀⠀⠀⠀⠈⠈⠤⠉⠁⠠⠉
⠀⠀⠀⠀⠀⠂⠀⠀⣀⣀⣤⣤⣌⠀⠀⠈⠐⠀⡷⢋⠀⢿⠀⣰⠃⠀⠀⠀⡄⠀⢳⡀⠀⠀⠀⠠⠀⠀⣀⢀⡴⠃
⠀⠀⠀⠀⠁⠀⠀⠘⣯⣿⠶⣯⡟⠀⡀⠀⠀⢸⠇⢩⠸⠏⠰⠷⠤⢤⠀⠀⡁⠀⠀⣷⠀⠀⠘⠖⠀⢜⣡⠟⠀⠀⠀⣠⢤⣴⢲⡶⡄
⠀⠀⠀⠂⠀⢀⣀⣴⠏⠀⣀⣈⣳⣄⣀⠀⠂⠘⠶⠶⡄⠀⠀⠀⢦⡏⠀⠀⠃⠀⡴⠃⠀⠴⢀⣶⡗⠺⡁⠀⠀⠀⠀⢘⡶⠛⠛⢷⡁
⠀⠀⠀⠒⡀⠀⣧⢸⡀⠀⢫⡀⠀⣤⢬⡿⠀⠂⠀⠀⢹⠀⣀⢫⠟⠀⠀⠀⣧⠞⠁⠯⢈⡴⠗⠉⠀⠀⠹⡀⠀⢠⡖⣾⠀⢀⡤⠤⠿⠤⢤⣄
⠀⠀⠀⢠⡇⠀⣽⠶⠛⠲⣴⠃⠀⡿⠈⠱⣆⠀⠀⠀⢸⡤⢡⡏⠀⠀⠀⠰⣇⠀⠤⠁⠀⣡⢶⡀⠀⠀⠀⢻⡀⠀⣧⢻⣀⠀⢳⠀⠰⡖⢶⡏
⠀⠀⠘⠀⠀⢸⡇⠀⠀⠀⡿⠒⠚⠛⢦⣤⣿⠀⠀⠀⠘⣤⠟⠀⠀⠀⠀⠀⡉⠳⢤⣀⡼⠃⠀⢳⡀⢀⣠⡴⠏⢠⠟⠋⠉⠙⣟⣀⣰⡇⠀⠙⡆
⠀⠀⠀⡈⠀⢸⡄⢀⣠⠞⠁⠀⠀⠀⠀⡂⠙⣆⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠙⠋⠁⠀⠀⣼⠀⠀⠀⣰⠏⠉⠁⠙⢷⠶⣇
⠀⠀⠰⠆⠠⢄⠹⣏⠀⢋⡈⢁⡀⠀⢀⡇⠂⢸⠀⠀⠀⢀⣀⠤⠔⠒⠒⠒⠢⠤⣄⡀⠀⠀⠀⠀⠈⠉⠅⢈⣂⠻⣄⡤⠞⠋⣄⠀⠀⠀⢠⡄⠘⣇
⠀⠀⠠⠀⠀⡀⠓⠈⣿⠦⣄⣙⠀⠀⠈⠀⣠⠞⢀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠄⠀⠀⠀⠀⠀⠙⣦⡘⠺⠭⣤⠀⡀⠸⠈⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠉⠙⠛⠛⠋⠁⢠⠎⠁⠀⠔⠠⠶⠀⠰⠠⠄⠀⠶⠀⠆⠀⠈⠳⡄⠀⠐⠀⠐⠀⠐⠈⠀⣟⢳⡦⣤⣀⣀⣀⣠⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣰⠃⠀⠤⡄⠰⠀⠆⠀⠀⠤⠀⠀⠂⠰⠀⠀⠤⠀⠹⡄⠀⠀⠀⠀⢀⡀⢀⡉⢉⣁⢀⣀⠉⣉⢀⡀⣠⠀⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡏⢐⠆⠀⠠⣤⡆⢠⠄⣤⠀⠀⢠⣠⠄⡄⢄⢀⠠⠄⠇⠀⢘⡲⠘⠃⠘⠋⠁⠸⠈⠀⠇⠸⠼⠰⠋⠈⠇⠱⠆
⠀⠠⠀⠀⠀⠀⡹⠀⠀⠀⠀⠁⠀⠀⠀⠠⡇⠀⣴⠆⢀⣶⠠⡆⠀⡄⠀⠀⢠⢤⡀⢀⠀⣀⠀⠀⡌⠀⠸⣤⠆⢀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠰⠶⠶⠂
⠀⠙⠀⠀⠀⠀⠑⠀⠀⠀⠀⡃⠀⠀⠀⠀⣇⠘⣧⡤⡼⠿⡇⣿⡤⣿⣤⠀⠘⠋⡇⠸⠀⣿⠀⢀⠇⠀⠀⠁⠒⠘⠃
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠇⠀⠀⠀⠀⠹⡄⠀⠰⠄⠀⠀⠠⠤⠴⠄⠰⠴⠀⠠⠤⠄⠀⢠⡞⠀⢠⣴⠛⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠆⠶⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠈⠉⠉
⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠙⠦⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐
⠀⠀⢈⠁⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠒⣺⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠇⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⢧⠀⠤⠠⠤⠀⠀⠀⠀⠀⠠⠇
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡯⢠⣛⠈⠄⢹⠀⠀⢰⠒⢂⡒⠒⣀⠀⠂⢒⠀⠀⠒⠒⠐⠆⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢃⡈⡉⢐⠃⡈⠀⠀⢸⢀⣘⢛⣉⣟⣉⡀⠸⠀⠄⠐⠆⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠈⠉⠀⠀⢀⡀⢀⠀⠀⢀⡀⠀⣀⢀⡀⠀⠀⣾⣯⣠⡄⠇⢸⠀⠷⡆⠀⢸⠈⢁⠈⣁⠉⢉⡁⢀⠀⠃
⠀⠀⠀⠀⠀⠍⠤⠈⠠⠤⠈⠠⠤⠄⠀⠁⠀⠀⠀⢠⡂⣤⠄⣤⠀⢀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⢠⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠒⠒⠂⢤
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠂⠀⠒⠂⠀⠀⠀⠀⠀⠀⠞⠛⠘⠃⠳⡈⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠰⠀⡇⢸⠀⠀⣃⠀⠀⢀⡄⡈⠉⢂⠁⠁⠘⢀⠃⠀⢸
⠀⠀⠀⠀⠀⠉⠀⣍⠈⠀⠈⡅⠡⢨⠀⠍⠁⠀⠀⢰⠀⡄⣰⣯⠘⣄⠀⡇⢸⡀⠀⠀⠀⠀⠀⠀⢨⠀⡇⢸⠀⠐⠆⠀⠀⠀⢠⠠⠘⡄⠀⢠⣀⡦⢠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠈⠑⠂⠈⠀⠣⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠃⠸⠤⠾⠶⠄⠸⠏⠽⠴⠶⠤⠾⠤⠟⠦⠴⠧⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣶⡄⠀⠀⠀⠸⣿⣿⣿⣋⠀⠀⠀⠀⠹⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣦⣤⣈⠻⣿⣿⣿⣷⣦⣤⣀⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣧⠀⠀⣠⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⡍⠈⢹⣿⣿⣿⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡆⠀⣹⠟⣀⣾⣿⣿⣿⠀⠀⠤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣿⢤⣤⣾⣿⣿⣿⣿⣿⠀⣀⠀⠀⠀⠉⠙⠛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⣿⣿⣿⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⣹⣿⣿⣟⣵⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠘⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡄⠀⢿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣤⣄⣠⣀⣹⣿⣿⣿⣿⣿⣿⣿⣄⠀⠉⠛⠋⠁
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠆⠀⠀⣠⣤⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢀⣾⠿⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠡⠂⢉⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⢠⠾⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠊⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠻⣆⠀⢠⡄⠀⠀⠀⣿⣿⣿⣿⡿⠛⠉⠉⠉⠙⢿⣿⠇⣤⣤⣶⣶⣦⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢷⠏⠹⣄⠀⠀⠘⢿⣿⡏⢀⣠⣴⣶⣶⣿⣿⠏⣼⣿⣿⣿⣿⣿⣿⣷⣌⠢⡀⠢⡀
⣴⣤⣀⠀⠀⢸⣦⣄⡀⠀⠀⠘⢆⠀⠀⠀⠙⠿⢿⣿⣿⣿⠿⢛⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠂⢀
⠀⠉⠙⠛⠶⣾⠀⠈⠙⠳⢄⡀⠀⠀⠀⠀⣰⣿⣶⣶⣶⣶⣾⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡑⢀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⠽⢋⣥⣶⣶⣦⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡁⠀⡑⢄
⠀⠀⠀⠀⠀⠀⢻⡛⠛⠃⠐⠀⠀⠀⢀⣿⣿⣿⣿⣿⣠⣾⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣧⠈⠻⣿⣿⣿⣿⣿⣦⡈⠢⡀
⠀⠀⠘⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣡⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⡈⠻⣿⣿⣿⣿⣿⣷⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⣫⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠰⢁⠀⠈⠻⢿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠎⠄⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠋⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠐⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠈⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢂⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠇⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣏⠖⢾⣏⣉⣉⣍⣉⣙⣩⣋⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢦⠀⠀⠀⠀⢀⡄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⢓⡆⠀⠀⡾⠀⡎⠀⠀⠀⣴⠩⣬⢡⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠀⠀⢻⡅⠀⢰⠁⢰⠀⢀⡴⠞⠀⠀⣀⠀⡀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠔⠋⠹⡆⠈⢧⠀⢸⠄⡈⢠⠏⠀⡰⠚⠉⠉⠉⠉⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠗⠛⣶⢣⡈⡄⢹⠇⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠁⠀⠀⢿⡆⠙⠀⠀⠀⠈⠈⠉⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠠⠄⠀⢀⠄⠀⢼⣿⠀⠀⠰⠀⠀⡰⠀⠀⠀⠈⢣⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⡅⢀⠀⠀⠀⡠⠛⠉⠀⠀⠀⢀⣀⣁⣀⣐⡥⠖⣚⣃⡠⠍⠁⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠔⠋⠀⣶⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠙⠋⠉⠀⠀⠀⠉⠀⠀⠀⠀⠠⢒⣽⡟⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠘⢦⡆⡀⠀⠀⠠⢀⣾⣦⠄⠘⠀⠀⠀⠀⣀⣤⡤⠤⠀⠀⠀⠈⠉⠚⠛⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠄⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⣷⡿⠀⠀⠀⠀⠀⣼⠋⠁⠀⠁⠀⠀⣀⠀⢀⣁⢢⠛⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠆⠀⣀⠜⠛⠁⠰⠁⠀⠀⢀⣯⣈⡄⠀⢠⠁⠀⣿⠱⠞⢩⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⢀⣀⠈⡸⢀⡁⠀⢸⠷⠂⡀⠀⠀⠀⠀⣔⡾⠃⠈⠙⠲⣄⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣈⣽⣠⠞⠋⠁⠀⠂⢀⠀⠈⠀⠀⠀⠀⠸⣞⠀⠀⠀⠀⠀⢪⢣⣤⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣀⠾⠋⠀⡹⣄⡠⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⡏⠆⠀⠀⠀⠀⠀⠆⢻⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⣾⠁⠀⢠⠎⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢰⠘⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠁⠠⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢧⡞⠰⠼⠧⣀⣐⣂⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡀⢀⡸⢀⠃⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠄⠀⠀⠀⠀⠀⣀⠀⠐⢞⠀⠀⠀⢰⣽⠋⡩⢀⢸⠀⠀⠀⠀⠀⠀⠀⡆⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣠⠞⠉⠉⠙⢢⣘⡢⢀⣠⠞⠁⢠⠁⡎⢦⡄⠀⠀⠀⠀⠀⢰⠃⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⢄⠀⠀⠀⠉⠁⠉⠁⠀⣠⠊⣰⠁⠀⣎⡄⠀⠀⠀⠀⢃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡢⡀⠈⠃⠀⠀⠀⠀⠀⠀⢠⢁⠌⢹⡇⠰⠋⠸⡖⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⣀⠀⠀⠀⠀⡰⢣⠂⠀⠈⠘⠀⠀⠀⠉⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠈⠷⣦⣴⠺⡕⠁⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⢎⠁⠀⢧⡀⠀⠀⠀⠀⠀⠀⠘⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠈⠀⠀⣿⠙⠆⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠚⠀⠀⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⠖⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠉⠁⠀⠀⠀⡀⠉⠉⠛⠳⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⢰⡟⢀⡀⢀⡀⠀⠈⠛⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣴⠟⠁⠀⣤⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢷⡿⠁⠀⠀⢰⠏⢢⡀⠀⠀⢹⣇
⠀⠀⠀⠸⠭⠟⠁⠀⠀⠀⠘⣧⡀⠀⠀⠀⢀⣠⣤⡌⠁⠀⠀⠀⡿⢰⠏⣸⠟⠀⠈⣿
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⢷⣄⠀⢠⡾⢋⡿⡇⠀⠀⠀⠀⣧⣿⡼⠃⠀⠀⣸⡷⣶⠶⠶⢤⣤⣀
⠀⠀⠀⠀⠀⠀⣏⡇⠀⠀⠀⠀⠀⠙⠷⣌⡁⠘⠇⢻⡄⠀⠀⠀⣿⠟⠀⠀⢀⣴⠟⠀⠈⠙⢷⡄⠀⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡄⠀⠀⠀⠈⠛⠷⣤⣄⣀⡀⠀⠀⠀⢀⣠⣴⠟⠁⠀⣀⣤⣤⡀⢿⡄⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡧⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⠟⠛⠛⡋⠉⠀⣠⣶⣶⠿⠿⣿⣿⠸⣷⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢹⡄⠀⣤⠿⠁⢸⣿⣿⠁⠀⠀⣸⠟⠶⣿⠖⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢸⡇⠀⠀⠀⢀⣠⡿⠿⡶⠶⣾⡟⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠈⣷⣀⣤⡶⠟⠉⢀⠀⠀⠀⡀⠁⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⡏⠁⠀⠀⠀⢙⡆⠀⠀⠹⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⣀⣀⣤⣤⣤⣤⣄⣀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣀⣴⠾⠋⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠳⣄⠀⢠⣄⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⡰⠋⢀⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠘⣧⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣼⠃⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣶⡤⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣫⠝⢛⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⣏⠳⡄⢀⡞⢡⡾⢋⡴⣫⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢰⣎⢿⡿⣱⡾⣡⡾⣫⠖⣹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⡀⠹⡞⢤⣏⣰⢋⡴⣡⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⣿⣎⢱⡛⢰⢏⣼⢫⠞⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠂⣧⠀⠈⠳⢈⣓⣞⣰⢃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢸⣿⣷⣝⡷⢮⡱⢏⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣯⠈⢯⠃⠘⣆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠸⣷⡱⣾⣧⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠂⢹⢀⡀⠀⠘⣆⠘⣆⠀⢸⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⡿⣿⣿⣧⢹⣧⢻⣿⣇⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣯⠀⠉⠛⠒⣿⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣭⣭⢨⣽⣶⣿⣽⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⡸⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⢸⣷⣷⣶⣿⢎⢿⣿⣿⣿⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠇⠹⠀⠀⠀⠻⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣸⣇⣿⣿⣿⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠢⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢰⡇⠀⠀⠀⠀⠉⢳⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⡐⡇⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠻⣤⡀⠈⠳⣶⣤⣈⠻⢿⣶⣤⡀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡥⠀⠀⢀
⠀⠀⠀⠈⠙⠷⣾⣿⣿⣿⣷⣦⣉⣻⣟⠂⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣼⣷⣔⡁⠀⠀⠀⢀⡸
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣟⣋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣟⣿⠡⣓⣤⡻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢜⠁⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠
⣀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠒⠉⠁⢀⣤⠏⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢷⠀⢀⠀⠀⢀⠀⣀⣴⣿
⣿⣶⠦⠄⠀⠂⠀⠈⠀⠀⣀⡠⠴⠚⠋⠁⠀⠀⠀⠀⢠⣄⣀⣀⣀⣤⣆⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢉⣻⣿⣿⡿⠃
⠙⠻⠶⣤⣤⠤⠤⠖⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⠄
⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠒⠐⠚⡆⠀⠀⠀⠀⠀⠀⢠⣾⣿⠞⠓⠂⠐
⠀⠀⠀⠉⢁⢤⠁⠀⠀⠀⠀⠀⠀⠘⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣟⡽⠁
⠀⠀⣾⡤⠴⠐⢦⠀⠀⠀⠀⠀⠀⠀⢻⡧⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠀⡀⢸⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⣿⢳⡴⠀⠚⠇⠰⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠸⡇⢹⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⢹⣿⢀⣄⣄⣰⡶⠀⠀⠀⠀⠀⠀⢹⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⢸⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠻⣏⡭⠵⢿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⣭⣿⡇⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣀⡠⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠶⠦⠴⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠂⠀⠄⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠲⠤⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⠀⠀⠀⠀⠉⠉⠙⠒⠲⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠰⠀⠀⢀⡄⠀⠀⡖⠀⠠⢄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠶⢤⣄⣀⡈⠐⠂
⠀⠀⠀⠀⠀⠙⢆⠀⠗⠀⠀⠈⠂⠀⠀⠀⢋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠰⢢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠶⠦⣤⣄⣀
⠀⠀⠀⠀⠒⠂⠀⣀⡀⠀⠐⠒⠈⠉⠉⠁⠀⠀⠉⠒⠦⣄⣀⠀⠀⠀⠀⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⢦⣄⣀
⠀⠀⠀⢀⠄⢶⡾⠩⢀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⡀⠈⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⢀⣴⣼⣅⡿⠁⠀⠀⠈⠒⠤⣀⠈⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣄⡀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⡀⡸
⠠⠈⠋⠉⠻⠃⠀⠀⠀⠀⠀⠀⠀⠁⠒⢤⡀⠈⠑⠤⣀⠀⠀⠀⡀⠠⠄⢐⡒⠄⠈⢹⡀⠀⠀⠀⢸⢸⠀⠀⠀⠀⡇⣿
⠘⠂⠀⠐⠄⡀⠢⠀⠀⠀⠀⠀⠠⣄⠀⠀⠈⠑⠢⢄⠀⠀⠀⠀⢀⢠⠼⡖⠦⠩⣕⡚⣧⡀⠀⠀⠀⠈⠀⠀⠀⠀⡇⣿
⢳⡿⣷⡐⡀⠀⠑⠤⡈⠂⢄⠀⠀⠲⢍⡂⢀⣠⡀⠀⠀⠐⠀⣀⣠⣤⠦⠀⣞⣽⣿⠻⡘⣇⠈⠑⠲⢤⣀⠀⠀⠀⡇⣿
⠸⣿⣿⡷⣝⡦⣄⠀⠀⠁⠀⠈⠐⠄⠀⠀⠸⣿⣿⠂⠀⠀⢸⣳⣿⣯⡠⠀⣿⡿⠟⡁⡇⣿⠀⠀⠀⠀⠈⠙⠲⢤⣇⣻
⠀⠈⠉⠙⢶⣝⣪⠙⠢⣄⠀⠀⠀⠀⠢⡐⠀⠈⠉⠁⠀⠀⣾⡿⠻⣋⡀⡤⣛⡁⠁⠀⡎⢺⠀⠀⠀⠀⠀⢀⠀⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠉⠻⣄⣸⣤⡁⠀⣀⡀⠀⠈⠈⠐⠀⣀⣀⣀⡏⠉⡉⡤⠀⠟⠉⠁⠀⠀⡇⣸⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣷⣦⡀⠀⠈⠁⠛⠉⡇⢀⡀⡤⠄⠖⠚⡁⠤⠒⢉⣸⠀⠀⠉⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠈⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⣾⣿⣿⣧⠀⠀⠀⠀⠀⣿⠀⡀⠠⢔⡫⣥⣠⣴⣞⠁⣠⠟⠀⠀⠂⢄⠈⠓⢦⣀⠀⠠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⣿⣷⣤⣀⠀⠀⠉⢁⣀⠤⣾⣿⠿⣛⡭⠖⠋⠁⣀⠀⠀⠀⠀⠉⠢⣄⠈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⡀⠀⠀⠀⠀⣀⡬⠖⠊⠉⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠑⢦⡀⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠉⠁⠠⡀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠈⠳⣄⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣷⣦⣽⣿⣿⣿⣿⣯⣴⣾⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⢸⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⡄⢀⣤
⢸⣿⣿⣿⣿⣶⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣴⣫⣶⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿
⠘⢿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣧⠙⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣷⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⠿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠈⣿
⠀⠀⢀⣴⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠷⠶⠶⠶⠿⠷⠶⠶⠶⠶⠶⣶⣦⣄
⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣬⣿⣷⡀
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄
⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⠀⠀⠀⠀⢸⣿⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀
⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡟⠙⠛⠋⠀⠀⠀⠀⠈⠛⠛⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄
⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⣧⣤⣤⣤⠀⠀⠀⠀⢠⣤⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⡀
⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⠀⠀⠀⠀⢸⣿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣤⣤⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⣿⠀⠀⠀⣠⣴⠿⠟⠛⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠛⠻⢷⣦⡀⠀⠀⠀⢸⣿
⣠⣶⣿⣶⣶⣶⡿⠁⣠⣶⠶⣶⣄⠘⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡟⠁⣠⣶⢶⣦⡀⠙⣿⣶⣶⣶⣾⣿⣦
⣿⡇⠀⠀⠀⣿⡇⠰⣿⠁⠀⢈⣿⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢸⣿⠀⠀⢸⣿⠀⣹⡇⠀⠀⠀⠀⣿
⠻⠷⠶⠶⠶⠿⣷⡀⠹⢷⣶⠿⠋⢀⣾⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠾⢿⣧⠀⠻⢷⣶⠿⠃⢠⣿⠿⠶⠶⠶⠷⠿
⠀⠀⠀⠀⠀⠀⠙⢿⣦⣤⣤⣤⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣤⣤⣤⣶⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠐⠲⠤⠤⠤⠤⢤⠤⠤⠴⣶⢶⢾⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠸⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡽⠦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣾⣟⣲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠁⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠉⠉⠉⠛⣛⣿⢿⣿⠑⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣙⡎⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠠⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⠿⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠹⠀⡆⡆⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣱⢳⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡆⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠦⠴⠶⠞⠳⠻⠛⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡖⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠤⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⢰⡆⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡼⠇⠸⣤⣄⣄⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣤⣤⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣮⠉⢧⠀⠀⡎⠘⢿⣿⠉⠉⢏⠉⠉⠉⠉⢩⠉⣴⣦⡶⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢀⣡⡀⣷⠀⣸⣿⡖⠀⢈⢄⠀⠀⠀⣸⢴⡿⠈⢅⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣿⡀⠉⠻⣿⡻⣿⡇⣠⢞⣺⣧⣤⡰⠣⠋⠁⡐⠕⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣄⠀⠈⠻⣾⣿⡿⠋⠁⠀⣨⡧⠁⠀⡰⠋⣴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣟⣷⠤⣠⣿⣿⣀⡠⣤⣾⢟⣷⣀⣠⣦⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠿⠿⠶⠾⠿⠛⠛⠛⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣄⣄⣤⡄⣠⠀⡄⣠⣀⠄⣤⠀⠀⠈⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠉⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⣠⣤⣤⣤⣤⣤⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⣡⣾⣿⣿⣿⣿⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢠⡤⠀⣠⡾⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣳⣞⣋⣐⣂⣛⣛⣛⣛⣛⣛⠛⠛⠛⣛⢀⣀⣀⣛⣛⣛⢛⡛⠛⢛⡛⢛⣛⣛⢛⣛⣛⣛⣛⡛⠛⡛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠋⠁⠉⠉⠉⠉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠭⠭⠭⠭⠭⠭⠭⠭⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢺
⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣻⣟⣿⣷⡀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣺⣿⣿⣷⣿⡇⠀⠀⠀⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣽⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠉⠀⠀⠀⠀⠈⠻⣿⣿⣾⣿⠟⠉⠀⠀⠀⠀⠈⠻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠙⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⣏⡀⢀⠀⠀⠀⢀⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣄⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⣾⣿⣦⠀⠙⠿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠛⠁

⢰⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡶⠶⠶⠶⠶⠶⠶⣶⠶⠶⠶⠶⠶⠶⠶⢶
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠶⠒⠛⠛⢻⡦⠶⠛⣱⠞⠳⣄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠉⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠘⠀⠀⠙⠶⢤⣤⣤⠀⢸⠇⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⠀⠀⠀⠀⠀⢀⣠⣿⣠⠟⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠶⣿⣄⣠⡤⢦⡴⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣇⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣼⣠⡆⣸⣇⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⡿⠋⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢸⠃⠀⢸⡇⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⢸⠁⠀⢀⣴⠞⠋⠁⠘⣤⠇⠀⠀⢀⡏⠛⠶⣄⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠹⡇⠀⠀⠀⢸⡄⠀⢸⠀⣰⠏⠈⢆⠀⠀⠀⡸⠀⠀⣀⣸⠁⠀⠀⠈⢷⣸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠙⠳⢦⣄⣀⡀⠀⢀⡼⠃⠀⠀⣿⠀⠀⠀⢸⡇⠀⢸⡇⡏⠀⠀⠈⢆⣠⠞⠁⠐⠀⠀⠙⣄⣀⣀⠀⢘⣿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⡁⠀⠀⠀⢿⠀⠀⠀⠀⣧⠀⢸⡇⢷⡀⣀⣀⣼⣿⢠⢾⠀⡶⣀⡗⢻⣝⠟⠛⣽⢿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⢸⡆⠀⠀⠀⣿⠀⢸⡇⠈⠻⣄⡈⢻⡾⠛⠿⠖⠷⠿⠛⠋⠁⣀⡴⠋⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠘⣇⠀⠀⠀⢸⡄⢸⡇⠀⠀⠈⠙⠳⠦⣤⣤⣤⣤⣤⡤⠶⠛⠉⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⢻⡀⠀⠀⢸⡇⢸⡇⠀⠀⣠⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⣠⡤⣤⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠈⣧⠀⠀⢸⡇⠘⢷⣤⣴⣋⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡟⠁⠀⢈⣷⣤⣄⣀⣀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣇⠀⠀⠀⠀⣠⡾⢷⡀⠀⢷⣤⣭⣛⣮⣉⣉⣛⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣧⣤⣀⡟⠀⠀⠀⠀⠉⠉⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⢀⣤⣾⠏⠀⠈⠳⣤⣤⣤⡤⠿⠿⠿⢻⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⣨⠟⠛⠒⠲⠶⠶⠦⣤⣄⣹⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣴⠟⣱⠏⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢻⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⢸⡇⠀⣴⠋⠁⢸⠃⠀⠀⣠⡴⠚⠋⠉⢷⣄⠀⠀⠀⠀⠘⣧⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⢾⠇⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣇⡟⠳⠶⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠸⣇⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡟⠁⠀⠀⠀⠀⠈⠉⠉⠛⠛⠓⠶⠶⠦⢤⣤⡴⠞⠁⠀⠀⠈⠛⠦⣤⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⣀⣀⣀⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢠⠏⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣄⣀⣀⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠸⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡠
⠀⠀⣀⣀⣀⣀⣀⣀⣤⣭⠤⠤⠤⠶⠖⠚⠛⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠤⠀⠠⠄⠀⠀⠂
⠉⠉⠉⠉⠡⠒⠒⠒⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠛⠲⠶⣦⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠂
⠀⠐⣿⣾⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢷⡀
⠀⠀⢹⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⢻⡇
⢰⣶⣶⣶⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣧⣤⣈⡁⠀⠐⠶⠶⣾⣧⣀⣀⣀⣤⣤⣤⣤⡶⡶⠶⢶⣶⢶⡶⣛⣿⣷⣦⣀
⠘⠉⠙⠛⠛⣛⣛⣛⡛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⡈⠉⠙⠛⠿⠿⣿⠿⠿⢾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠒⠒⠒⠲⠶⠶⠆⠀⠀⠉⠛⠻⠿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠉⠋⠉⠉⠁⠀⠀⠀⠀⢈
⢠⣀⣀⣀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⢿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠘
⠀⠀⠈⠉⠁⠀⣿⠁⣐⡒⠲⠶⠤⠤⣤⣀⣀⣀⣀⣀⣀⡀⣄⡀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠙⠶⣿⠿⠃⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠙⠓⠂⠀⠀⣿⡟⠉⠉⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⢡⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡿⢤⢤⣀⣀⣀⣀⣀⣀⣀⣠⡽⡇
⠀⠀⠀⠀⠀⠀⣀⠴⠚⠙⢧⡀⠻⣤⣀⣀⠀⠀⠀⠁⢈⣀⣀⡴⠃
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠙⣆⡧⢀⣈⡉⠉⠉⠉⠉⠁⠀⣶⣛⣉⢉⣙⣦
⠀⠀⠀⢠⣶⠋⠙⢫⡳⡀⠀⠀⠘⡇⠀⠀⢩⢭⠉⢹⠀⠀⢸⡷⠤⠤⠤⠤⢾⣀
⠀⠀⠀⠇⡇⠀⣠⠤⣷⢹⠀⠀⠀⣷⠀⠀⠘⡫⠆⢸⠀⠀⢸⠀⠀⠀⠀⠀⠈⡇⠉⠓⠢⢄⡀
⠀⠀⠀⡇⢧⡠⠗⣶⣹⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⣾⠑⠒⠲⠶⠒⠊⡇⠀⠀⢀⠔⠉⡆
⠀⠀⠀⠘⢾⣤⣞⣡⡧⠏⠀⠀⠀⢸⠉⠒⠦⠤⠴⠚⠀⠀⢻⠀⠀⠀⠀⠀⠀⡇⡌⡀⡜⢰⠁⢩⣦
⠀⠀⠀⠀⠀⠈⢉⣈⣱⡦⠤⠤⠴⠚⠓⠤⣄⣀⣀⣀⡤⠔⢻⡄⣀⣀⢀⣀⣠⠏⠙⠓⠷⠞⠛⠛⠉⠑⠢⢄⡀
⠀⠀⡠⠤⢤⠴⢅⣀⡤⠟⠀⠀⠀⠀⠀⡴⠶⠶⣆⠀⠀⠀⠀⠉⠛⠛⠚⠛⠁⠀⢠⠤⠖⠢⠤⢤⡀⠀⠀⠀⠀⠁
⠀⠀⠑⠲⠦⠤⠤⠃⠀⠀⠀⡆⢉⠉⣹⡯⠭⢭⡿⠶⡉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠄⣤⡤⠤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠭⠭⠟⠁⠀⣎⠀⣀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣬⣭⣬⣭⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⡳⠀⢤⠀⡠⠄⢹⢀⠄⠀⣤⠠⡀⠠⡄⢠⡁⣤⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠽⢶⠸⠇⢦⠀⢸⠓⠄⠀⢸⢠⠇⠆⠿⢠⠇⠷⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣄⠀⠤⠤⠀⢀⢠⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⠉⠉⠁⠒⠤⢀⣀⣀⣀⡀⠀⠀⠀⡀
⠀⠀⢀⠤⠖⠒⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⢀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⡠⠤⡾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⣀⣀⠤⠔⠐⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠰⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠙⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠈⠒⢄⣀⠀⠀⠀⠀⠀⠀⠀⠘⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢻⠀⡠⠊⠀⠀⠀⠀⠀⢀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢠⡇⢧⣈⡃⠀⠀⣀⡔⠈⠀⠀⠀⠀⢀⡠⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⣄⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⢏⢘⠒⠄⣄⡀⠀⠀⠀⠀⠀⢠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢀⠀⠀⠀⠀⠀⠀⢠⠴⠴⠒⠋⠀⡀⠻⠤⠀⢀⣀⡀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠄⠤⠐⠂⠀⡀⢰⡀⢀⠉⠈⠁⠀⢀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠄⣀⡐⠂⠀⠀⢀⣼⠋⠁⠘⠉⠋⣀⡀⠠⠴⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠈⠑⠀⠁⠀⠀⢧⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢸⡇⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢀⣠⣄⡀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠀⣸⣏⣹⣇⠀⠴⠶⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣭⣭⣿⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢠⣾⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣻⣦⡀
⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⢉⣉⣭⣉⡉⠉⠉⠉⠉⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⣉⣉⣉⣉⣳⣄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣰⠟⠉⣤⠉⠻⣆⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⢹⡇⣿⠉⠉⠉⠉⠙⢷⣄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠸⠿⣿⠿⠇⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⢷⣤⣉⣤⡾⠃⠀⠀⠀⠀⠸⣧⣤⣤⣤⣤⣤⣤⣤⣼⠇⣿⣤⣤⣤⣤⣤⣤⣤⣬⣿⣆
⠀⠀⠀⠀⠀⠀⢸⡷⠶⠶⠶⠶⠶⠶⠾⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡶⠿⢷⡄
⠀⠀⠀⠀⠀⠀⢸⣷⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣿⣶⣼⣷
⠀⠀⠀⠀⠀⠀⢸⣟⣻⡇⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣼⡿⢿⣷⣾⣿⣿⢿⣿⣿⣷⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣾⣿⣿⢿⣿⣿⣷⣶⠶⢿⡄
⠀⠀⠀⠀⠀⠀⣿⣀⣴⣿⡿⠁⣠⣤⣄⠙⣿⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⡟⢁⣤⣤⣄⠙⣿⣿⣄⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⡇⠸⣿⣿⡿⠀⣿⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢹⡇⠸⣿⣿⡿⠀⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣈⣉⣠⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣈⣉⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⠛⠉⠉⠛⠛⠿⢶⣤⡀⠀⠀⠀⠀⢀⣤⡶⠿⠛⠛⠉⠉⠛⠛⠻⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣄⠀⠀⢀⣾⠇⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⣤⣤⣤⣴⡿⠋⠻⣷⣄⣾⠏⠀⠀⠹⣷⡀⠀⠀⣠⣤⣤⣤⣤⣤⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠿⠏⠀⠀⠀⠀⠹⣷⡀⣴⡿⠉⠉⠉⠉⠁⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠏⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢁⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣠⣾⠟⠁⠀⢻⣷⡾⠋⠉⠙⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⣷⡄⠸⠟⠁⠀⠀⣠⡾⠋⠀⠀⠀⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⣤⡿⠋⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⣠⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢸⣿⠀⠀⢸⡇⠀⠀⣿⡇⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣸⣿⣀⣀⣸⣇⣀⣀⣿⣇⣀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⠾⠷⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣴⠟⠋⠉⠉⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣀⣀⣿⠀⠀⣿⣀⣀⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠉⠉⠉⠀⠀⠉⠉⠉⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠿⠶⠶⣶⠀⠀⣶⠶⠶⠿⠀⠀⠀⠀⠀⣿⣷⠀⠀⢀⣀⣀⣤⣤⣴⢾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡿⠛⠛⠋⠉⠉⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣿⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠀⣿⡀⢶⡄⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⢸⣧⠈⠻⣦⣤⣤⡀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⠟⠁⠀⠀⠙⢷⣤⣀⣀⣀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣠⡀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢧⢰⢻⡇⣾⣩⠆⣶⠙⡇⢰⢠⡎⠁⢐⣩⡆⢹⠋⢷⢠⠎⢱⡄⡖⠙⡆⢾⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠃⠘⠃⠙⠒⠂⠙⠒⠃⠘⠀⠓⠒⠙⠒⠃⠘⠂⠙⠈⠓⠚⠁⠃⠀⠃⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣼⣿⣿⣷⣯⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡔⣫⠔⣛⣛⣿⣿⠛⠷⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢢⠞⢉⣡⣾⣿⣿⣿⣧⡀⢆⢸⣍⣷⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣴⣶⡿⠀⢺⣵⣶⣴⣿⣿⣿⣿⣿⣇⠉⢝⣿⣆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢉⡘⠋⠁⠀⠐⠛⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⢛⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣾⡇⠀⢀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣹⣛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢨⡻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢠⡿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⡾⠀⢼⢃⡄
⠀⠀⠀⢰⣿⣿⣾⣇⣠⣤⣾⣷⡁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣤⡿⠁⢸⡏⠚⠀⠁
⠀⢀⣠⣾⡟⠉⠉⠙⢿⣿⣿⣿⠁⠰⠸⢫⣿⣿⣿⣿⣿⣿⣿⡿⠃⡼⡟⢁⢠⣏⡀
⠀⠙⣿⣿⡅⠀⠀⢸⣿⣿⣿⣿⡆⠀⢀⠈⣿⣿⣿⣿⣿⣿⠟⠁⠐⠀⠀⢸⣿⣿⣿⣶⣿
⠀⠀⢻⣿⣯⡄⢀⣿⣿⣿⣿⣿⡇⠀⠘⣆⢸⣿⣿⣿⣿⠟⠀⢀⡤⠀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⣈⣿⣿⡇⠈⠁⠀⠀⢿⣿⡇⠀⠠⣿⡄⣿⣿⡿⠁⢀⣴⣿⢀⡼⣻⣿⣿⣧⠀⠀⣯⣿⣿⣿⡄⢤
⠀⠀⠉⡈⠻⣿⣶⡈⢆⠀⠀⢻⡇⠀⠀⢻⡇⣿⠟⠇⠀⠈⠸⠟⣾⢁⣿⣿⡿⠋⣰⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣙⣿⣷⣠⢀⠀⢸⣿⠀⠀⢸⣿⡟⠀⢀⠀⡀⠀⣼⠇⣼⡿⢤⠴⣛⣿⣷⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠈⢿⡻⢿⣄⣀⠈⠛⢠⣴⢟⣿⣿⣤⡈⠀⠴⣆⠉⠘⠡⠀⣤⣾⣿⣽⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠈⣵⡶⠿⣿⣧⣄⣀⡽⠾⣿⣿⣿⣿⣿⣶⣤⣴⣿⣷⣶⣾⠿⠋⠩⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⢿⣟⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣭⣭⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⢠⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⢣⣄⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣶⢀⣹⣿⣿⣿⣿⣿⡏⣸⡇⠻
⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢣⣿⣿⣿⣿⣿⣿⡇⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⢿⡇⠁
⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏⠊⣡⠃
⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⠒⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠼⠧⠤⠤⠤⠿⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠶⠶⠶⠶⠶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡏⣠⠤⠤⠤⠤⠤⣤⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⡞⢠⠇⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⡼⢀⡟⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢀⣀⣀⡼⠁⣾⣀⣀⣀⣀⣀⣀⣀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿
⢀⡞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⣸⠀⠀⠀⠀⠀⠀⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⠀⠀⠀⠀⠀⠀⣀⡤⣶⣒⣒⣶⢤⣀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⣀⡤⣶⣒⣒⣶⢤⣀⠀⠀⠀⠀⣿
⢸⠀⠀⠀⠀⢠⣞⡵⠋⠉⠀⠀⠉⠙⠺⣷⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠕⠋⠉⠀⠀⠉⠙⠾⣷⣄⠀⠀⣿
⢸⠀⠀⠀⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⣿
⢸⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿
⢸⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿
⠈⠛⠛⠛⠋⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠘⠲⣄⣀⠀⠀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⣀⣠⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⠉⢁⡄⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⠀⣿⣿⣦⠀⠈⣿⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢀⠟⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡿⠍⠀⠘⢿⣿⡆⠀⣿⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠹⠋⠁⠀⠀⠀⠈⠉⠁⠀⣿⡀⠀⠀⠀⢀⣿⡀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠶⠊⠛⠛⠁⠐⠚⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⠀⠀⠀⠀⠀⠀⠀⢠⣴⠶⠆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⡀⢀⠀⠀⠀⡴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⣦⣴⣶⣶⣮⠙⣿⣧⠀⣰⠀⠀⠈⠠⠀⠀⢀⢦⣼⣶⣿⣍⣀⠚⠲⣦⠶⠄⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡰⠖⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣌⡻⠷⢋⡀⠀⠀⣀⣰⣾⢺⣿⣿⣿⢿⡟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⢰⣆⡴⠋⠈
⠀⠀⠀⢀⣴⣿⣿⡟⡿⠟⠉⢿⢿⣿⠿⠇⠀⣿⠄⠀⢸⣿⣧⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠘⠃⠰⣦⢰
⠀⠀⢀⣾⣿⣿⣉⠀⡀⠀⠀⠀⠀⠀⢠⣦⢠⣟⡦⣾⢿⣿⣿⡇⣿⣿⣿⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠟⠀⠀⠀⠀⠀⠀⣀⡴⢦⣬⠈
⠀⠀⢸⣿⣿⣾⣟⣾⡷⣶⢂⠀⠀⠀⣿⣿⠀⢿⣆⣻⣾⣿⣿⣱⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⢀⣴⣿⣿⣏⣁⡠⢆⣠⣴⡆⠘⢿⣿⠋⠀⠈⠁
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣮⢀⡀⠀⣉⡟⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣰⣿⣿⣟⣿⣶⣿⣷⣿⣡⣿⡇⠀⠀⠻
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⣸⣿⣿⣿⡑⢻⣭⣿⣄⠀⠀⠀⠀⠀⠀⠠⢻⣿⣟⢿⣿⣿⡿⣿⣿⣿⣿⠿⠷⠀⠀⠀⢀⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣐⡿⢿⢿⣩⣮⢿⣶⣟⣷⡋⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡎⣿⣿⢳⣿⣿⣿⣿⣦⣄⢀⣹⣿⣿⡇
⠀⠀⢻⣿⣿⡿⣿⢿⣿⣿⣿⡿⣿⣾⣯⠁⣸⣾⣿⣿⠂⣿⣿⣿⠷⠑⠲⠏⠁⣠⣶⣿⣿⣿⠟⢠⣿⣷⣾⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⢸⡟⣹⣾⣿⣾⣿⣿⣿⣷⣛⣿⡧⠀⠀⠙⠈⣿⡵⣿⢁⣹⣤⠀⢀⠰⣤⡛⢹⣿⡟⢱⣇⠺⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⢸⣴⣿⣿⣿⣿⣿⣿⢫⣸⣿⣿⠇⠀⠀⠃⠀⠈⡷⣬⠻⣿⣿⣻⣮⡷⣿⣿⣿⣿⣿⣿⡅⣦⠘⠛⣿⣿⣿⣿⡿⢿⣾⣿⡿⠛⡀
⠀⠀⢸⣿⣿⣿⣻⣿⣿⡟⣿⣾⡹⣯⡂⠀⠀⠀⠀⠀⠈⠹⢿⣷⣾⠅⢩⡿⢦⡜⢿⢿⣿⣻⡇⢹⠈⡀⠈⠉⠁⠉⠁⠀⠉⠀⠀⠀⠁
⠀⠀⢸⣿⣿⣿⣿⢿⡀⢾⣬⢏⠐⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠈⠁⠈⠁⣼⣿⣿⣯⡇⢶⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢸⣿⣿⣿⣿⣾⡇⣼⡏⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⣿⣯⠗⠈⠀⠁
⠀⠀⠀⢿⣿⣿⣿⣿⣷⡼⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⠢⡀
⠀⠀⠀⠸⣿⣿⣿⣿⣿⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⣏⠀⠄
⠀⠀⠀⠀⠘⢿⣿⣿⣿⡎⠀⢀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢋⣼⠀⢀
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡀⠀⡤⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠔⣻⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⡄⠀⠂⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠈⠀⢙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⡃⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣟⣤⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⡆⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇⠑⣄⡃⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣷⡀⠳⢮⠄⣀⠀⠀⠀⠀⢼⠁⠀⣞⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣧⡆⣰⢩⣀⠀⠀⠀⠈⠀⠀⠈⡇⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡟⢣⡈⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣀⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣯⡄⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣇⡙⠀⠀⡀⠀⠀⠀⠀⡀⠻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⣁⣴⣤⣤⣤⣾⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⢿⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠠⣄⣀⡀⠀⢀⠀⢀⣴⢶⡚⠳⠀⢀⣀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠾⢶⣦⣽⠀⠈⠉⠙⠁⠂⠉⠁⢱⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠠⠐⢢⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠱⠀⠀⣸⢳⡖⠀⠀⠈⠠⠤⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠃⠀⠀⠀⠀⣠⠞⣁⠀⠀⠀⠀⠀⢀⠃⠀⠀⡿⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡤⢺⠁⠉⠙⠛⠁⠀⠀⢀⡎⠀⢠⠴⠃⠀⢉⠓⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢠⠀⠛⠛⠟⠀⠀⠠⣀⠄⠀⠀⣸⠃⠀⠀⠀⠰⠋⠘
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠠⢟⡧⣀⣀⣀⠰⡄⠀⠀⠀⠀⠐⣾⠶⠴⠛⠈⣳⢄⡀⡄⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⡿⠇⠀⠀⢱⣌⣹⠋⠈⠙⠄⢰⣶⣄⣀⣅⠀⢀⣠⣴⢧⠀⠀⠈⠁
⠀⠀⠀⠠⢄⠀⠀⠀⠀⢀⠀⠀⠐⠤⡄⢶⠾⠛⠛⠀⠀⠀⠈⣟⠉⠉⢽⣛⣛⣯⡅⠀⢣⠁⣠
⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢻⣋⠙⠻⠿⢿⡄⠀⠈⠒⠁⠀⠀⡀
⠀⠀⠀⠤⠴⠂⠀⠀⠀⡠⠐⢢⣄⠀⣀⠀⠀⠀⠹⣀⠀⢠⠾⣿⢽⣯⡷⠄⠀⠀⠉⡄⠀⢠⣄⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠹⠀⠈⠀⠒⠒⢂⠀⠉⡁⠈⠀⠀⠀⡳⠳⠾⠛⠋⠀⠉⠀⠈⠀⠀⠈⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠁⠀⠀⠀⠀⠀⢀⡴⠀⡠⡗⠀⠀⢁⡀⠀⡄⠀⠀⠀⠀⠀⢀⠄⠀⠀⢠⡔⠊⠀⠀⡀
⠀⠀⠀⠠⠂⠀⠀⠀⠹⠿⠄⠀⠀⠀⠀⠀⠀⠜⠀⠀⡁⠁⠀⠀⠀⣠⡴⠀⠀⠀⠐⠂⠀⠀⠀⠀⠐⠁⠀⠠⡀
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠋⠔⠉⠀⢠⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⢿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣀⡷⠾⠛⢹⡄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⢇⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠟⠻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢋⣴⣷⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡷⠀⠀⠀⠀⢾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡁⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣀⡙⠿⠿⠟⠁⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⣠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⢀⣴⣶⣶⣦⡀⠉⠀⠀⠈⠙⠛⠛⠛⠛⠁
⠀⣼⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡟⢻⣿⣿⡇
⣼⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣾⣿⣫⡄
⢿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷
⠈⠻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡟⢹⣿⣆
⠀⠀⠈⠻⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣄⣈⡛⢿⣷⣦⣀
⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠿⢿⣿⣿⣿⣿⠆⠈⢛⣯⣴⣶⣿⣿⣀⣀⣀⣀⡀
⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⢠⣿⣿⡟⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⡿⢀⣿⣿⡿⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠻⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠛⠋⠉⠁⠀⠸⣿⡿⠃⢸⣿⣿⣿⣿⡟⠿⠿⢿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣿⣿⡟⠋⠀⠀⠀⠀⠛⠋⠀⠉⠛⠛⠛⠛⠛⠛⠛⠋
⣶⣖⢲⡶⢶⣶⡶⢶⢶⡶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠿⢿⣿⣿⡟⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣤⣼⣟⣁⣀⣀⣹⣯⣴⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠟⠉⠉⠛⠉⠉⢻⣿⣷⡄⠀⠠⠴⠶⠾⠿⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⢿⣻⣿⣶⣄⠀⠀⠀⠀⣸⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⣽⣾⣿⣿⣿⣿⡟⠀⠀⠀⣴⡇⣻⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣿⣿⣿⣿⡿⣟⣯⣷⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⠟⠈⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡿⠿⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠈⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠘⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠁⠀⠀⠀⠘⣿⣿⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡤⠤⠤⢤⠄⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡼⠁⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣼⠀⠀⠀⠃⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠜⡼⢹⠀⠈⡈⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠉⠉⠉⢉⣉⣉⠀⠀⠈⠉⠉⠉⠉⠉⣉⣉⡁
⠀⠠⢄⣀⣀⠀⠀⠀⠀⠀⢸⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠤⠄⠚⠂⠂⠀⠀⠀⠀⠘⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠤⣄⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⡆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣤⠴⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠒⠚⠛⠛⠛⠛⠛⠛⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠲⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⢿
⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠫⣉⠀⠸⣄⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠀⠀⣀⠟
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠳⡄⢸⠙⠛⠒⠒⠶⠦⠴⠤⠶⠶⠖⠚⠛⡃⣠⡤⠤⠤⢤⣄⡀
⠀⠀⠀⠀⣜⣀⣤⣀⡀⠀⠀⠀⠀⠹⣼⡇⠂⠤⢤⣄⣀⣀⣀⡀⠀⠀⠀⢰⣿⠧⠤⠤⠤⠤⠴⢿
⠀⠀⡴⡿⠋⠉⠙⢦⡹⣄⠀⠀⠀⠀⢹⡇⠀⠀⠀⡤⠤⡄⠀⣿⠀⠀⠀⢸⡿⠶⠤⠤⠤⠴⠶⣏⣀
⠀⡼⢰⡇⠀⠀⢀⣈⣧⠘⡆⠀⠀⠀⠀⡇⠀⠀⠀⠷⢮⡤⠀⣿⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠈⡏⠉⠓⠦⢤⣀
⠀⣇⢸⡇⠀⢾⣁⣈⢿⡄⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠉⠀⢸⠀⠀⠀⣿⠤⣀⣀⠀⠀⢀⣀⡤⡇⠀⠀⠀⠀⠈⣹⠦⡄
⠀⢹⡀⢧⠔⠋⢩⠿⣼⢡⡏⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠉⠉⠉⠉⠁⠀⡧⠀⡀⠀⠀⡞⢁⡀⣿⡀
⠀⠀⠳⣜⡦⢴⣋⣴⣣⠞⠀⠀⠀⠀⠀⢿⠈⠙⠓⠶⠶⠶⠖⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣇⢰⠁⡄⣸⠀⡏⠀⢀⣽⡆
⠀⠀⠀⠈⠉⠉⠉⠉⠳⢤⣀⣀⣀⣀⡤⠾⠦⣄⣀⠀⠀⠀⠀⠀⠀⣀⡤⣿⡀⠀⠀⠀⠀⠀⠀⢀⡟⠛⠲⢧⣿⣤⠽⠳⠾⠋⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠤⠒⠻⠉⢹⡄⠉⠉⠀⠀⠀⠀⠀⣉⣉⣉⡛⠛⠋⠉⠀⠀⠈⠳⣭⣓⣒⣒⣒⡪⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠄
⡞⠋⠉⡛⠛⠓⢦⡴⠒⠋⠀⠀⠀⢀⣀⣀⡀⡾⣒⣂⣉⣹⡆⠀⣀⣀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡖⠉⠉⠉⢹⠉⠓⢦⡀
⠉⠒⠲⠧⠤⠤⠼⠁⠀⠀⠀⢠⡎⠁⡸⠉⢉⡷⠦⠭⠭⣾⠖⠫⡁⢀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣤⣼⡤⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣙⣛⣛⡩⠇⠀⠀⡼⠁⠀⠀⣰⠞⠁

⠀⠀⠀⢀⣤⡀⠀⠀⣀⠀⣄⢀⣶
⠀⠀⠸⡌⠸⡇⠀⠀⠛⠙⠈⠋⠸⢒⠏
⠀⠀⠀⠘⠆⠉⢀⣠⣤⣤⣄⠀⠀⢈⡽⠋
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⠀⠨⠓
⠀⠀⣼⣿⣿⣟⣿⣿⡿⠋⢹⡿
⢀⣾⣿⣟⣿⣿⣿⣟⣻⣞⣯⣶⣤⣀
⢿⣿⣿⣜⡿⣿⣿⣿⣿⡿⠉⠛⢿⣿⣷⣦⣄
⠀⣽⣻⢿⣿⣾⣽⡿⣿⠇⠀⠀⠀⠈⠙⠿⣿⣿⣶⣄⡀
⢠⣿⣿⣷⣯⣻⢿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⠇
⠘⣿⣿⣿⣿⣿⣷⣯⣟⠛
⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠹⣿⣿⣿⡟⢿⣿⣿⣿⣦⡀
⠀⠀⠀⣿⣿⣿⣿⠀⠙⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡄
⠀⠀⣰⣿⣿⣿⠇⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⢿⣿⣷⢶⣶⣶⣶⣶⡀
⠀⣰⣿⣿⣿⠏⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣏⣿⣿⣾⣿⣿⣿⣿⣧
⣰⣿⣿⣿⠏⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣠⣾⣿⣿⣾⣝⣿⣿⣿⣽⣿⣷⣿⣽⣿⣿⣿⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠻⣿⣿⠏⠀⠀⠀⠀⠀⠘⢿⣿⠟⠀⠀⠠⣿⣿⣿⣿⣿⣿⢹⣿⣿⣏⣿⣿⣾⣧⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣝⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡻⣿⣿⣿⣿⠟⠀⠀⠀⠀⢹⣿⡇⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣛⣛⣛⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣦⢤⢤⣴⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⢠⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣼⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠀⠁⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⣿⣿⠿⠿⠿⣼⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡷⢶⣦⢉⡉⡋⠉⠁⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠸⡧⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠈⠉⠓⢥⡀⠄⣪⣽⡄
⠀⠀⠀⠀⠀⠀⢸⣿⠶⠴⡶⢶⠒⣻⠂⠀⠀⠀⢀⣹⡥⡀⠀⠀⠹⡿⠿⠿⠿⢿⣶⣶⡶⢶⣤⣤⣇⡀⢸⠉⠙⠓⠒⢲⠀⠀⢱⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣀⠸⠀⠿⡂⠀⢠⣾⡿⠛⠿⣖⢄⠀⣠⣷⣄⠀⠀⠀⠀⠈⠉⠲⡄⠈⠙⣿⣿⡄⠀⠀⠀⢸⠀⠀⢸⢸⣿⣿⣇
⠀⠀⠀⠀⢀⣤⠟⢳⣯⡿⠯⢿⣄⣶⣛⣦⣼⣿⣦⣤⣤⣾⣿⣟⢋⣡⣾⡁⠀⢀⣹⣿⣿⣷⣷⣦⣶⣿⣿⠁⠀⠀⠀⢸⠀⠀⢸⣼⣿⣿⡟
⠀⠀⠀⠀⡿⢥⣀⣀⠈⠉⠉⠉⢡⣿⣤⣤⣠⡤⣼⣟⣭⢫⡉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⣽⢫⣿⡏⢸⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿⣿⣷
⠀⠀⠀⠀⡇⠀⠀⠈⠉⠉⠉⠉⢹⣿⣿⡆⡇⠀⢸⡟⣸⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⡇⠸⠀⡀⠀⠀⢸⠀⠀⢸⡟⣿⣿⣿
⠀⠀⠀⠀⡇⠀⡏⠓⠒⠒⠒⠒⠚⣿⢛⣿⠻⠛⣿⡇⣿⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠻⣿⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⣿⣿⣿
⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⣠⣾⣛⠋⣘⣃⢨⡳⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⠂⠉⠉⠉⠀⠒⣦⡀⠀⠀⠀⠀⡇⣿⣿⣿
⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⣞⣿⣿⣿⣾⣿⣿⣗⠙⡘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠛⠛⠛⠒⠚⠋⢹⡇⠀⠀⠀⠀⡇⣿⣿⣿
⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠳⠤⠤⢤⣤⠤⠴⠚⡇⠀⠀⠀⠀⡇⣿⣿⣿
⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⡇⠀⢉⠉⠉⠉⢉⣉⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡉⠛⠒⠤⠶⠶⠶⠖⠙⢙⣆⡠⠤⢤⣧⣿⣿⣿
⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⡇⠀⠘⢒⡶⠻⣟⠛⠀⠀⣿⣝⡢⢤⣄⣀⣀⣀⣀⣀⡤⣿⣝⣲⠲⠤⠤⠤⠤⠒⣎⣭⡏⠀⠀⠀⠀⠈⠉⠙⠓⠲⠦⢤⣄⣀⡀
⠀⠀⠀⠀⣧⠀⠓⠤⠤⠤⢤⡇⠀⢰⡋⠀⠀⠈⣱⠆⠀⣿⣿⡿⠋⠓⠓⠒⠒⠒⠒⣋⣿⠀⠉⠉⠛⠒⠛⠋⠉⠁⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠽
⠀⠀⠀⠀⠙⠦⣄⣀⣀⣀⢀⡇⠀⢀⠙⢦⣤⠞⢁⠀⠀⢿⣿⡇⠒⠢⢤⠖⠂⠛⢿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡇⠀⠈⠙⠋⠛⠋⠋⠀⠀⣸⠿⣇⣀⡀⢸⣶⣶⣲⠷⡳⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣦⣤⣀⣀⠴⠊⠁⠀⠀⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣷⣶⣦⣤⣤⣴⣶⡆⢹⣿⠀⠀⠈⢉⡹⣻⡉⢈⠇⢱⣿⣄⣀⠀⠀⠀⠀⠀⠀⣀⡤⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡤⠞⠉
⠀⠀⠀⢠⠶⠶⠖⠒⠒⠒⠒⠛⠉⠉⠉⠙⣿⣟⣛⣡⠴⠃⣴⣆⣢⠿⠿⣿⣏⣁⣠⣿⣽⠀⠉⠙⠛⠒⠒⠛⠋⠁⠀⣿⠉⠙⠻⠿⢿⣿⣿⣇⡤⠞⠉
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠄⠀⡄⠀⡈⠉⠛⠂⠀⠼⠈⠉⠉⠀⠘⠧⣄⣀⣀⠀⠀⢀⣀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣗⠺⢿⡶⠦⠛⠲⣎⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠸⡧⠤⠤⠶⠒⠒⠒⠒⠒⠚⠛⠋⠉⠉⢻⠀⠈⠳⠖⠚⠉⠁
⠀⠀⠀⠀⣧⡤⠤⠤⠤⠴⠶⠶⠒⠒⠒⠒⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠛⠋⠉⠁⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣦⡀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⢼⣿⡿⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠻⣿⣿⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⣿⣿⣧⠀⢠⣶⣶⣄⠀⠀⠀⠀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡇⢀⣀⠀⠈⢿⣿⣿⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠟⠋⠁⠀⠀⢻⣿⣿⣿⣿⣯⠁⠀⠀⠡⡄⠀⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠐⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⠀⣿⣿⡿⠁⠈⠉⠛⢿⣿⣷⠦⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣦⠀⢀⣠⣄⣼⣿⣿⣿⣿⣿⡆⠀⠀⠀⠈⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⠿⠿⠋⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⢀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠃⣿⣿⡇⠀⠀⠀⠀⠀⠀⠃⠀⠀⣰⣿⣿⠀⠘⣷
⠀⠀⠀⠀⠀⢰⠋⠲⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡀⠀⣿⡇
⠀⠀⠀⠀⠀⢰⣠⣶⣷⠀⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣄⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣄⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣆⠀⠀⢻⣿⣿⣿⣿⣷⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⠀⠀⠙⢿⣿⣿⣿⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠀⠀⢀⡤⠘⣿⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠹⣿⣿⣿⣿⣿⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠈⠀⠀⠈⠻⢟⣿⠄⢹⣿⣿⣄⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠹⣿⣿⣿⣿⡅⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⣁⢀⠉⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠘⢿⣿⣿⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⢀⡀⠘⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⠇⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣦⣷⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⢸⣿⣿⡿⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣏⠙⠿⣿⣿⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⣿⣿⠃⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣤⣄⣈⢃⡄⠀⠀⠈⠀⠀⠀⠀⠀⣀⣠⣤⣾⣿⣿⣿⡀⢰⣿⣿⣿⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣧⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠉⠛⠛⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡬⠅⠤⢄
⢀⣀⣠⣤⣤⣤⣤⡶⠾⠿⠟⠛⣻⣋⣉⡁⢀⡀⠀⠀⡴⠢⢀⡀⠀⠀⠲⠒⣀⣀⣀⣤⣄⣀⡀
⢙⣛⣭⣥⣤⣴⠶⠶⠾⠻⠛⠛⢛⡿⠛⠅⢸⠿⣷⣦⣯⣦⡈⠁⠀⠀⠀⡄⠘⠋⠉⠛⠛⣑⠈⠑⢆
⠈⣿⡎⠁⠀⠀⠀⠀⠀⠛⠁⠀⠈⠇⠀⠀⢸⣄⣤⣬⣝⣿⡿⠿⠿⠷⠶⠶⢷⣶⣶⣶⣤⣴⣤⣤⣭⡅
⢠⢹⣷⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⠒⠒⠢⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡀
⢈⠀⣿⡄⠀⢀⢀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠨⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠘⡄⢸⣷⠀⠀⠀⠀⠀⣛⠀⠀⠘⠃⠛⠀⠀⠀⡆⠀⠀⢀⣇⡀⠑⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⢸⣿⣾⣿⣶⣶⣦⣤⣤⣭⣄⣀⣀⣛⣀⠀⠀⠀⠳⢄⣀⠋⠈⠣⠴⠈⠆⠐⢀⡀⠀⠀⠉⠑⠶⠤⣤⣍⡉⠁⠤⠤⠷
⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠿⠿⠿⢿⣿⡇⠀⣿⣿⣶⣬⣆⣠⠧⢶⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢲⣤⣄⠀⠀⠀⡀
⠀⣆⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠛⠛⠛⠻⠿⠶⢤⡉⠋⠀⠰⣄⠀⠀⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠀⠀⠈⠀⡄
⠠⡀⠙⢱⡾⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⢸⣧⠀⢀⠰⡆⠀⣀⠀⣀⣀⣀⣤⠤⣔⣷
⠀⠀⠀⠈⢁⣦⢃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢈⣷⣃⣮⣃⣀⠀⠀⠻⠻⢞⣛⣿⣭⡵⡃
⠀⠀⠀⠀⢸⣿⠸⠅⠐⠳⠦⣤⣀⡶⠉⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⣶⣿⣶⣦⣀⣤⠐⠚⠉⠉⠛⠒⠁⠀⠁⣀⢨⣩⣭⣭⡷⠶⠛⠃
⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠀⠈⠁⠀⠀⡶⠈⡓⠶⠄⠀⠀⠀⢰⡟⠉⠉⠉⠛⢳⡹⡄⠠⣀⠀⠀⠀⠈⠛⢾⡆⣶⠈⣀⣤⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⢀⡿⠀⣾⣉⠷⡀⠀⢷⢳⠘⣶⣤⠁⡄⠀⠀⠈⠃⠸⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡁⠊⠡⡄⠀⢸⣧⠑⠀⠀⠉⠀⠀⣀⠀⠀⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣶⡤⠀⡰⣸⠁⠁⠀⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣭⣤⣾⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣺⣯⣻⣿⣫⣫⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⣤⣤⣦⣤⠄⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⡞⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⡞⠘⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⢎⡞⡇⠀⢂⠑⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠘⠒⠓⠒⠚⠓⠒⠚⠀⠀⠘⠒⠒⠒⠒⠒⠒⠒⠋
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⣀⣉⣱⣂⣢⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠉⠙⣆⠀⠈⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠿⠛⠛⠛⠻⠿⢿⣷⣤⡀⠀⠀⠀⠀⢀⣤⣾⡿⠿⠟⠛⠛⠛⠿⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⣠⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠃
⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠆
⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⣾⡿⠉⣿⣇⠀⠀⠀⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⡀⠀⠀⠀⠀⠀⠀⣾⡿
⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠠⣶⣶⣾⣿⠃⠀⢹⣿⡄⠀⣸⣿⠛⣿⣆⣠⣶⣶⣶⠀⠀⣰⣿⠏⢻⣿⡄⠀⠀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⢠⣿⡏⠀⠹⣿⣿⠋⠀⠀⠀⣴⣿⠋⠀⠀⠻⣿⣆⠀⣠⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠈⠁⠀⠀⢀⣼⡿⠃⠀⣴⣆⠀⠹⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⢿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⣿⣿⠀⠀⠘⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⢿⠟⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠸⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠈⣩⣿⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉