Pollination Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠔⡳⠀⠀⠱⠀⠀⠀⠀⠡⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⢣⠀⠀⠀⡘⠀⣀⣀⡠⠀⠀⢀⠂⠀⠠⠈⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠤⠄⡈⠀⠀⠀⠸⠆⠀⡁⠈⠑⠂⠠⠧⣠⡛⢢⣾⠛⠛⠋⠻⠛⢻⣻⣯⡎⠀⠀⠙⣼⣟⡛⠛⠛⠛⠛⠟⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠂⠈⠗⠂⢦⠘⠂⠀⠀⠀⠀⢀⡿⣶⢻⠁⠉⠈⠻⠶⣶⣶⠿⠟⠿⠛⠃⠀⠀⠀⠛⠻⠻⠿⣶⡶⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⣀⠃⡰⠐⠄⠀⠀⠀⠀⢸⡷⢁⠄⠀⠀⠂⠀⠰⢈⠟⠛⠒⠶⢴⡃⠀⠀⢸⢦⠴⢶⡓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣄⠀⢀⠀⠀⠀⠀⠀⠄⠠⡀⠠⠀⠀⡀⠀⣸⠗⠀⠀⠁⠀⠀⠁⠀⠀⡇⠀⢀⡠⠜⣣⠀⢀⡂⠀⠀⠀⠉⠑⢦
⠀⠀⠀⠀⢀⣀⣀⣤⡀⢀⠀⣤⣌⠋⠊⡿⠣⡄⠀⠉⠀⠘⠀⠀⠉⠑⡄⠈⠹⡿⢤⠀⠀⠄⠀⠀⢀⢢⠛⠀⠀⢈⠇⠘⢿⣇⣿⠟⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⣠⣦⣭⣭⣽⣷⣞⣷⡟⢻⠟⠈⠀⠀⣄⠀⠡⠀⠇⠀⢆⠀⠐⠌⠀⠀⠈⠑⠐⢟⢠⡚⡈⠈⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⣭⣍⣙⠻⠏⠀⠈⠿⠃⠀⠀⠀⠀⡀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠑⣔⢂⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⢻⡿⠛⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠡⠘⡄⢀⠳⣦⠀⢀⢀⣀⣀⣠⣤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠄⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠳⡀⣥⠀⢉⠄⠀⠆⠁⢄⠉⡇⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠁⠀⠀⡀⠀⠓⠀⠀⢀⠈⠧⠘⡌⠻⡊⠄⠑⠆⠀⠸⠁⠀⠀⠈⠘⠇
⠀⠀⠀⠀⠀⠀⠲⠒⠶⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠑⠀⠂⢀⠀⠂⢤⠀⡅⠠⠡⠀⣠⡔⠂⠀⠚⢃⠀⣾⡷⡄⠁⠀⠀⠀⡀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠠⠀⠀⠀⠀⠂⠓⠀⠀⠀⢀⣀⠤⠀⠂⠉⠉⠀⢀⠸⡁⡇⢰⢦⡄⠰⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢳⠀⠀⡀⠉⠐⠀⠤⡀⠀⠀⠀⠶⠆⡀⠄⠠⠀⠀⠂⠠⠀⠀⠀⠈⢇⠀⠀⠐⢤⡀⠀⠀⠀⠀⠀⡇⠠⠀⡤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠙⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠐⠐⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⡀⠀⠘⡂⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⠀⠀⠀⠀⢀⣠⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠁⠄⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠋⡛⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡀⠀⠄⠋⠲⠅⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⣇⠎⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠎⠰⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⣟⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠂⠀⠀⠀⠀⠐⠟⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠉⠉⠉⠙⣦⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⡆⠀⠀⠀⡠⠀⠀⠀⢀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⢀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⢠⡤⣀⠀⠀⠰⣄⠀⣠⣾⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠘⣇⠀⠀⠀⠈⠑⠂⠀⠙⣷⡿⢿⣿⡿⢀⣠⠠⠴⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠐⠀⠀⣀⠀⠘⣿⣷⣾⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣠⠂⠀⠉⠐⠾⣿⣿⣿⡟⠁⡀
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠈⡀⠀⢀⡤⢶⣶⣾⣿⣷⣉⠀⠐⠓
⠀⠀⠀⠀⠀⠀⠈⢳⠆⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠻⣰⣟⢠⣟⣻⣿⣿⣇⠙⠛⣆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⢦⠀⣸⠟⠉⣾⣟⠺⢿⣿⡟⠀⠀⣿⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠲⠆⣐⠦⠀⠀⠀⠄⠃⠀⠀⢹⣧⣴⣿⣿⠇⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⡌⢻⣿⡿⠋⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠰⢇⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠑⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⡆⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠸⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠌⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⢀⣀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠒⠀⡀⠀⠀⠀⠀⠀⢀⠈⡈⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⢻⠀⠀⠀⠑⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⣠⡄⠈⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⠀⡇⠀⠀⠘⠧⠀⠀⠄⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⢀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⢰⠁⠀⠀⠀⡀⠳⣄⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠁⠀⠀⠀⠀⢀⣄⠀⠀⡆⣾⠈⡌⠀⠀⡰⠃⠀⠈⠱⣄⠀⠈⠢⣆⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⣿⡄⠀⢸⡇⣠⠃⠀⠐⠁⠀⠀⠀⠀⠈⢷⡈⢄⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠘⣷⠀⣼⠀⡏⠀⣴⡷⠃⠀⠀⠀⠀⠀⠈⣷⠼⣷⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠈⠄⢀⠸⣧⡏⢠⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠘⢇⠹⣆⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⢠⠄⠘⣧⡉⢀⢸⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠠⡇⠈⠨⣿⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⡀⡏⢢⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢠⡿⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠀⠄⢹⣏⣋⡟⡿⢛⣉⣛⣏⣽⢛⣙⠋⣿⠋⠛⢉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣛⣻⣿⣟⣻⣟⣛⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢦⡀⢀⠏⠀⠀⢃⠀⠀⡞⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⢀⠊⠀⠀⠀⠱⡞⠀⠀⠀⠈⡄⣸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⡄⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠁⡏⠀⠀⠸⠀⠀⠀⠀⢀⡤⠖⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠄⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣠⣲⠟⣻⣀⣤⣄⠀⢀⠔⠉⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠓⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢀⣴⢛⣭⠵⠛⠉⠉⢀⣽⠔⠁⠀⢀⡞⠁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠈⠳⡀⠀⠀⢸⡀⡠⠒⢠⣾⣿⣿⣿⣯⣥⣤⣶⠶⠞⡟⠁⢀⠀⣠⢋⣤⠞⣩⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠹⡄⠀⠀⠉⣿⡆⢸⣿⣿⣧⣿⣿⣃⢼⣿⢇⡀⠀⠰⠃⣼⡵⠋⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⣆⠠⠚⣿⢏⠈⠙⣻⠟⠻⢿⣿⢛⣥⣻⣷⠀⢁⡾⠋⠀⢀⡞⢀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⣀⣀⡀⠈⠻⢦⡀⠀⢀⣀⣬⣧⡔⣛⣱⣶⠶⠚⢷⣿⣽⡿⣼⣴⠟⠀⠀⣀⡾⠞⠉⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠑⠂⠻⢦⣀⡿⣿⣷⣞⠻⢿⣿⣻⠷⢾⢻⣿⡾⣿⢁⢀⣤⠾⠉⠀⣠⣴⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⣛⣶⡶⠶⠶⠶⠶⣶⣿⣦⠼⣭⣿⡓⣮⣾⠛⢻⢟⡆⠹⣾⢇⣼⠟⠃⣀⣴⡾⠟⠋⢩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠉⠀⠀⠀⠒⠊⠉⢁⣀⣽⣍⢿⣫⣥⣦⡟⡡⢶⡃⡩⠼⡿⢨⣾⣿⣴⠿⠿⡟⠁⢄⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⣀⣠⣤⣶⣶⠿⠛⣫⣿⣿⣆⣶⣻⣶⣦⣽⢛⣿⣡⣋⣵⣿⠿⠋⠀⠀⡼⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠛⠋⠉⠉⠀⠀⣠⡴⠛⠛⠻⣿⣧⣬⣥⣿⣭⣤⡞⠋⠉⠀⣸⠋⠀⢀⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠴⠚⠋⠹⣤⡴⠶⡈⠀⠀⠀⠀⢀⣠⡞⠀⠀⣠⣾⣥⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠀⠒⠋⠀⠘⣷⣾⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠰⣃⠾⠋⡴⡦⠀⠲⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⣤⡄⢦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠯⣸⣲⠁⡀⠀⠀⠠⠄⠐⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒⢀⠀⠀⠀⠀⢀⠁⡰⡬⠀⡬⠃⣘⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠄⠀⠈⠁⠀⠰⢀⠒⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠠⠤⠋⠁⠢⡂⠀⠀⠀⠀⠐⠚⠣⠚⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡀⡈⢁⠀⠃
⠀⠀⠀⠀⠀⠀⢰⠆⠀⠠⠔⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⣎⠀⠀⡆⠀⠀⠀⠀⠀⠀⠈⠠⠄⠠⣀⠈
⠀⠀⠀⠀⠀⠀⡞⠁⠉⠀⠉⠁⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢣⣱⣧⡈⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠀⠆⠀⠄⡀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢧⣞⠖⠀⠀⠀⠀⠀⠠⣬⢤⡄⣞⡄⠀⠑⠀⠀⠀⠜⣈⡒⠁⡀⠀⠀⠀⠀⡀⡑⠀⠀⠀⠀⠔⠀⠢⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠠⣀⠀⠀⠶⠃⠀⠀⠀⠀⠀⠀⠙⠾⡇⣻⢵⠔⠂⠀⠐⠄⡂⠓⣀⠁⠀⠀⠀⠀⠂⠀⠄⠐⠂⡈⠀⠀⠂⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠁⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢸⡡⠈
⠀⠀⠀⠀⠀⠀⡀⠈⣦⡀⠀⠀⠀⠀⠀⠄⠈⠆⢸⠀⠀⠀⠄⠀⢃⠔⠀⢀⣃⠀⠰⡀⢿⡀⢠⠈⠑⠿⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⣠
⠀⠀⠀⠀⠀⠀⠉⠃⠙⠃⢐⡀⠀⠤⣢⠀⠄⠙⠄⠈⢄⠁⠀⠨⠄⣄⠐⠈⠁⠀⣀⠍⣄⡁⣠⠓⠄⠀⢀⡄⠒⠃⠆⠰⠒⠋⠿⠂⠂⠆⢁⠋⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⣿⢾⡒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠐⠒⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⢱⢀⠤⠒⠒⠀⢄⠀⠀⠀⠀⠀⠔⢆⠀⠀⠀⣀⠤⡄
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠱⡀⠀⠀⡌⢀⢀⡃⡠⠊⠀⠀⠇
⠀⠀⠀⠄⠂⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡇⠀⢩⡟⠒⠠⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢱⠀⡼⠀⠀⠀⠀⠀⡈
⠀⠘⠀⠀⠀⠀⠀⠀⠠⠤⠖⠒⣽⣟⡾⢖⡁⠀⠀⠀⢀⡠⠂⠀⠀⠀⠈⣴⡁⠀⠀⠖⣮⡗⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⡃⢸⢄⡃⠀⠃⢀⡀⠴⠓⠒⠂⠁⠐⠄⠀⡀⠉⢥⣁⠲⠉⡑⡟⠂⠀⠀⠁⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠀⢙⠇⠀⡁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠸⡆⡀⠉⢣⡤⢉⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠠⡀⠀⣀⠠⠇⠀⠀⠘⠀⠀⠈⠳⢄⣀⣀⢀⠀⠀⠀⣀⣰⠡⠀⠀⠻⡀⠀⢫⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⡍⠉⠉⠉⡩⡒⠅⠈⠀⠀⠀⠈⡗⣻⠀⠀⠀⠀⠀⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠓⠦⣀⢀⡀⠤⠄⠒⠁⠀⣠⡫⠊⠀⠀⠀⠀⠀⠀⠀⢶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠄⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⢀⢂⠀⢀⡀⠄⠈⠁⢠⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠎⠀⡀⠎⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠸⠀⠉
⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢱⡀⠀⠀⠀⠀⣠⠔⢙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢦⠀⠀⠈⠃⠀⠀⣠⠞⠁⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢄⠈⠉⠒⠂⢌⡣⡀⠀⡁⠀⣰⠃⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⢀⣀⣙⣮⡱⠆⢰⠇⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠠⢄⠀⠈⠇⣼⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⠁⠀⠀⠀⠑⠒⠺⣇⣠⠔⠋⠀⣠
⠀⠀⠀⠀⠀⠀⢐⠲⢄⡀⠀⠀⠞⠁⠁⡰⠋⠀⠙⢆⠀⠀⣘⠀⠀⡰⠊⢡
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠉⠲⣄⢦⡀⠀⢇⠁⠀⠀⢸⠆⢰⡟⠀⡼⠁⢀⠆⠀⠀⠀⣀⡀⠀⠎⣳
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⢆⡉⠀⠀⠙⠒⠒⠁⠀⢸⠡⡔⠇⣠⠎⠀⠀⢸⠋⠁⢨⠛⣯⣉⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⢸⡈⠢⡀⢀⡤⠒⠒⠲⣇⠀⣿⠚⠁⠀⠀⠀⠘⣄⠴⢁⠜⡠⢷
⠀⠀⠀⠀⢀⣤⣤⡄⠠⠤⠄⠀⠀⠜⢶⣄⠀⠀⢠⠛⠄⠈⠁⢿⠀⠀⠀⠀⠀⠀⠈⠲⠧⠴⠱⠋
⠀⠀⠀⠀⠀⠑⠲⠤⣄⣀⣀⣀⣀⣠⡤⠞⠓⢄⠸⠀⣏⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠻⣴⠃⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⢎⢱⠊⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⡠⢿⠙⡍⢏⢣⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⣶⠀⠀⠀⠀⠀⢀⣤⡔⢢
⠀⠀⠀⠀⠀⢰⡁⠀⢣⠘⣈⠿⢤⠄⠦⢄⠀⠀⠀⠀⠀⠈⢧⠀⠉⠀⠀⠀⠀⢀⣽⠦⠷⣮⣀⡀
⠀⠀⠀⠀⠀⠀⠙⣲⠜⢛⡩⢀⣄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⣇⠰⠀⠀⠀⠀⢈⠀⠸⢀⠃⠸⢫⠳⠖⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠎⠀⠀⡎⡀⠄⠀⢓⠀⢴⠁⠀⠀⠀⠀⠀⠀⢩⡄⡄⠀⠀⠀⡜⠣⣤⣬⣀⣴⣃⡀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⢢⣀⠀⠱⣄⠀⣠⠆⠀⢘⠀⡴⠤⣀⡀⠀⠀⠀⢸⡇⠀⠀⠀⢧⡀⠀⠀⡞⢁⠀⠈⠆⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⣠⡄⠤⠊⠀⠈⢆⠀⠈⠑⢢⡀⢸⡇⠀⠀⠀⢠⡇⠀⠀⠳⣀⣤⠴⠃⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠚⠉⣆⠀⠀⠀⠀⠀⠑⠦⢀⣀⠙⢼⡇⠀⢀⠔⢻⠣⣀⡀⣤⡀⠀⠀⢀⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⠀⠀⠀⠈⠑⠻⡇⣰⠃⠀⢸⠀⠀⠀⡆⠙⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠀⡰⢻⠁⠀⠀⠀⠀⠀⣴⠃⠀⠀⡌⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠟⠲⢄⠀⠀⠀⠀⡇⠀⡜⠀⡦⠀⠀⠀⠀⠀⠀⣿⠀⢀⠞⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠙⢦⡀⠀⡇⡜⠀⢀⠃⠀⠀⠀⠀⠀⠀⣯⠔⠁⢠⡀⠀⠀⡇⠀⠀⠀⣀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠱⡄⢸⠆⠀⡼⠀⠀⣖⢤⡀⠀⠀⠁⠀⠀⠈⠱⡀⢀⠃⠀⣠⠞⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⢡⡜⠀⡜⠀⠀⠀⠘⢆⡈⢳⣐⡇⠀⠀⢃⠀⢣⢸⠀⡰⠁⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⣿⠎⠀⠀⠀⠀⠀⠀⠉⠒⢼⡇⠀⠀⠘⣄⠀⣟⠰⠁⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢢⣿⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢻⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠄⠀⠀⠀⠀⠀⠀⠀⠘⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠗⠀⠀⠀⣴⣿⣿⣦⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⠀⠘⠿⠀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⣤⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣤⣾⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⣛⠻⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⣠⣾⣿⡿⢛⡛⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⡛⣣⣿⣿⣿⣇⢸⣿⡟⢩⣍⢻⣿⡇⢰⣿⣿⣿⣧⣙⣋⣼⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⣀⠀⠹⣿⣿⣿⣿⡿⠿⣿⢸⣿⣿⣎⢡⣾⣿⡇⣼⡿⢿⣿⣿⣿⣿⠏⠀⣀⣀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣦⠹⣿⣿⣏⠸⠷⣸⠘⣿⣿⡏⢸⣿⣿⠇⣏⠺⠗⣹⣿⣿⠏⣴⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⡙⢿⣿⣷⡸⣿⣇⢻⣿⡇⢸⣿⡿⣸⣿⡇⣾⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣧⠹⡿⠆⠻⠃⠘⠟⠱⢿⡟⣸⣿⢟⣴⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣦⡙⣡⡰⣿⣿⣯⣸⣿⣿⠆⣀⢋⣴⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⡇⢿⣿⣾⣿⣿⣿⣿⣿⣾⠟⣸⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣮⣍⣙⣛⣛⣋⣩⣵⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁




⣿⣿⠿⠿⡿⠻⠿⢿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣂⣥⣤⣉⡒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣷⣤⣿⣶⣆⢠⡀⠻⣿⣶⣶⠆⢀⡄⣴⣿⣽⣿⣿⣟⠀⢀⢀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⢿⣿⣿⣿⡩⣅⠸⡿⢊⡴⣤⣦⡁⢾⠇⣡⠌⣿⣿⣿⣞⣿⣿⢯⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠚⠛⠿⠿⠷⠎⠳⠀⣸⣏⠻⣿⣇⠀⡞⠱⠞⠻⠻⠛⠛⠛⠉⠈⠀⢆⡀
⠀⠀⠀⡀⠀⣠⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⡇⢀⣼⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠲⡦⠅⠂⢄
⠀⠀⠐⠀⠀⡘⣧⣕⡠⠀⠀⠀⢀⠀⠠⠄⠀⠀⠸⣿⣾⣿⣿⣿⡇⠀⠂⠠⠄⠀⣀⠀⠀⠀⠄⣊⣶⣄⣠⣰⡌
⠀⠀⡄⠀⢸⣿⣯⣿⣿⣶⣦⡄⠀⠠⡴⣓⢤⣦⠤⢿⠏⠿⣿⡿⠤⣰⡦⠘⢦⡄⡀⢀⣠⣶⣾⣿⣿⣿⣿⠟⠃⠆
⠀⠀⢄⠀⠼⣿⣛⣿⣿⡿⢟⣁⣀⠪⣵⢿⠇⡼⢶⣥⣴⣶⣾⣯⡴⢧⠘⣿⡦⠑⣀⣬⣙⠉⢿⣻⣿⣿⡤⠀⡀
⠀⠀⠀⠙⠂⠈⠛⢋⣥⣶⠿⠛⠉⠑⠢⠉⣐⠃⣼⣁⣠⣶⣶⣿⣅⠀⣃⠉⠀⠀⠉⠛⠿⣿⣦⡈⠉⠁⣠⠊
⠀⠀⠀⠀⠀⠀⠀⡌⠉⠁⠀⠀⠀⠀⠀⠀⡟⣴⢹⣥⣤⣴⣾⣿⡍⣤⢻⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⡠⠏⡄⣿⡀⢧⣀⣬⣿⡦⠰⣷⠀⠹⢄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡃⢟⣮⡌⠻⢿⢟⣡⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡈⠛⠷⠞⠛⠋⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⡠⠚⢰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂⠀⠀⢲⡄⠀⠀⠀⠀⠀⣤⠄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢸⡟⠛⠛⠛⠋⢰⡏⢰⠇⣰⢂⠀⣠⡄
⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⢹⠀⠀⠀⢰⠇⡼⢣⡾⢱⡆⢀⣿⢀⡿⢸⢳⡟⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣿⠈⠀⠸⡷⠊⠀⢸⡇⣼⢁⡟⠘⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠿⠀⠈⣷⣀⡀⠀⠀⠀⠁⠘⠇⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠀⠀⠠⠟⣸⡤⠖⠚⠛⠛⠛⠶⢼⢃⡶⢰⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣯⠁⡀⡆⢸⡆⢰⡆⢀⡿⠃⠛⠛⠁⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⣴⠃⢸⡆⣿⠸⣇⠇⣿⠀⣾⠁⣾⠃⣼⢠⡆⢀⣤⢀⣀
⠀⠀⠀⠀⠀⠀⢠⡆⠁⠲⣄⠀⠘⣇⣿⠀⣼⠀⢿⠘⣇⠰⠏⢸⡇⣾⡃⣼⠃⣼⠋⣹⢻⡏⢰⡇
⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠈⢷⡄⡏⢿⡄⠙⠂⠘⠇⠉⠀⠀⠀⠀⠈⠁⠙⠺⠃⣼⠃⣼⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠘⠓
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠸⢿⣦⡀⠀⠀⠉⠒⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⠀⠀⠈⠉⠻⣶⣄⠀⠀⠀⠀⠁⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢸⣦⣶⣤⠞⠉⠙⠃⠀⠀⠐⠀⠺⢿⣷⣄⠤⠒⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⣿⢻⣷⣤⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢐⣦⣄⠀⠀⠀⠀⠀⠀⢶⣶⣤⣿⣮⣿⣿⣿⣦⡀⠀⠀⡆⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠀⠀⠀⢀⡀⣀⠀⢉⠤⠈⠁⠈⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠘⠀⡀⠀⠀⠄⠨⣿⣨⠶⠆⠂⠀⠀⠀⠀⢸⣿⣦⣅⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠘⢿⠀⡄⠀⢀⡄⠁⠰⣞⣏⡻⠀⠀⠀⡾⠻⠝⢿⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠘⣷⠀⣤⠁⣀⠀⠀⢺⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠐⠆⠀⠀⠰⠏⠀⠀⠄⣸⣆⠀⠘⠏⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀⠈⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠰⣿⣏⠈⠙⠲⣦⢄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠷⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⢀⣀⡀⡿
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠐⢠⣤⡴⠂⠀⠀⣿⠁⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠃⠀⠋⠀⠀⠰⡾⠏
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⡗⢚⠉⢋⡡⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠰⠞⠂
⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣀⣀⣠⣴⣶⣾⣿⣶⣶⡶⠄⠀⠀⠀⣠⠀⠀⠀⡠⠉
⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣄⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣦⣄⣀⠀⢀⣤⣄⠀⠀⠉⠛⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠋⠉⠀⢠⣿⣿⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣧⣀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠁⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡀⠀⠀⠀⣩⣿⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠴⠾⠟⠋⠀⠀⠀⠘⣧⠀⠀⠀⢨⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣼⣿⣿⡄⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠘⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢻⣿⣿⣿⣿⣸⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢸⠏⠹⡇⢸⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡜⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⡉⢄⠀⢷⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⠻⣿
⠀⣶⠀⠀⠀⠀⠀⠻⣼⢦⠘⡇⠀⠒⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⣠⣿⣿⣿⣿⣿⣿⣿⡁⠁⠀⠀⢸⣿⣇⠈⠉⢛⣫⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿
⠀⠘⣧⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⠀⠘⣿⣿⣆⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿
⠀⠀⠹⣷⣦⣀⠀⠀⠀⠀⠈⢻⣿⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠋⠉⠀⠉⢻⣿⣿⣿⣿⡆⠀⢿⣿⣿⡆⠀⠈⢿⣿⣿⣿⣿⣿⣧⠀⠀⢸⣿
⠀⠀⠀⠹⣿⣿⠁⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠱⢦⣀⣠⣤⠀⠀⠈⠛⠿⣿⣿⣇⡜⡘⣿⣿⣿⡄⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿
⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⣄⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⠀⠀⠩⠿⢿⣶⣶⡇⠀⠀⠀⠙⢿⡼⣷⢿⣿⣿⡷⠀⠀⠘⣿⣿⣿⣿⡿⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣧⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠈⣿⣹⣤⣿⠿⡥⠃⠀⠀⠸⣿⣿⣿⡇⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣤⣤⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣈⠻⣷⣦⣤⣴⣿⣿⠟⠁⡆⠀⠀⠀⠀⣰⣿⣿⣿⡇⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⠀⠀⠄⠀⠀⠀⠀⢸⣿⣿⣿⣧⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣼⣷⣼⣿⣿⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⣿⡇⠀⢰⣾⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣼⣿⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣰⣦⡀⠀⠀⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⡴⠛⠿⣿⣿⣿⣿⣿
⠀⢠⣿⣿⣿⣦⠀⠀⠀⠀⠀⠲⣌⠻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠈⢻⣿⣿
⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠹⢶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡠⡄
⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⡠⡜⢄⠉⣇⣀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⡠⠚⠢⢠⠀⠀⠀⠀⠀⠀⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢍⠳⢘⡌⠢⡨⠊⠀⠀⠰⠝⠊⢀⠀⠀⠀⠊⠈⢃⡀⠤⠆⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⡏⡭⡢⡀⠙⠢⠅⢀⡴⢊⠁⠀⠰⠇⠀⠈⠀⠀⠀⠀⣠⡄⠀⠀⢀⠀⠀⠀⠰⡹⠁⠹⠂
⠀⠀⠀⡖⠢⡀⠘⢄⡚⡀⠀⢀⠔⠉⠀⠣⠐⠀⠀⠀⠀⠀⠐⠂⠀⠄⠻⢀⡠⠐⠁⠀⠀⠀⠛⠃⢀
⠀⠀⠀⠘⢄⠑⠄⡄⠀⠀⠘⠀⠀⠀⠀⠀⣠⡾⢑⢄⠀⠈⠐⠁⠀⠐⠂⠁⠀⠎⠐⠀⠀⠀⠀⠀⠃⠁
⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⠀⠀⣰⢯⣲⠃⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⠞⢛⣼⠃⡐⠀⢀⠀⡰⡡⢀⠀⠀⠀⠀⠛⠀⠀⠈⠀⠀⠀⠐
⠀⠀⠂⠀⠀⠀⠀⠠⡒⠁⠀⠀⠀⠉⢤⡾⠋⢉⠔⠀⠀⠈⢄⣔⢲⠇⠀⠂⠂⠢⡀⢀⠾⠆⠀⠞⢂⠄
⠀⠀⠀⠀⡀⢄⡀⠀⠈⠈⠁⠀⠀⢀⠀⠀⠀⠁⠀⢀⢤⡀⠀⠉⢻⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠁⠀⠀⢀
⠀⠀⡄⠊⡤⠊⠑⡀⠀⠀⠀⠀⠒⠀⠆⠀⠀⠀⠰⡟⠋⡰⠀⠀⠈⢇⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠈⢎⠀⠀⠅⠅⠀⠀⠀⠀⠀⠆⠐⠄⠀⠀⠀⣵⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⡁
⠀⠀⠀⣊⡇⠀⠀⠀⠀⢀⠊⠀⠉⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠊⠉⠉⠀⠀⢠⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣀⠀⠀⣈⠀⠀⠀⠀⠂⠀⠀⠠⠒⢀⠀⠀⠒⠀⠀⠠⡀⠀⠀⠀⡞⠂⠂
⠀⠀⠀⠀⠀⢶⣀⠀⢀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠐⠀⠀⠐⢄⣀⣶⣠⡔⠁⠀⠀⠀⠁⠀⠘
⠀⠀⠀⠀⠄⠄⠌⠍⡒⠀⠀⠀⠀⢀⠴⣗⢄⠀⠀⠀⠀⠀⠀⠀⠌⠍⢿⡇⠀⡃⠀⠀⠀⣀⣀⡀
⠀⠀⢠⢆⠀⢊⠈⠌⠀⠀⠀⠀⣰⡁⠀⠈⡪⠇⠀⠀⠄⠀⠀⠀⡂⠀⢺⣇⣀⡁⠀⠸⠛⠃⠉⢁
⠠⠀⠀⠀⠁⠆⠆⠀⠀⠀⠀⠀⠀⠀⢠⢊⠀⠀⠀⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢆⠄⠀⠘⠃⠀⠀⠂
⠀⠀⠄⠆⠶⠲⠀⠀⠀⢀⠀⠀⠀⠀⠈⠈⠀⠀⠘⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⢀⣜⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⠔⣠⣤⠊⣠⠀⠀⣨⡕⢶⣤⠤⣤⠣⠁⢨⣄⡀⢀⣀⣀⣀⣀⡄⢀⣀
⠀⠀⠀⠀⠈⢢⡉⠠⠈⠻⣄⠀⠙⢆⠀⠐⡄⠈⠉⠓⠀⠀⠀⠈⢰⢧⠀⠈⠀⠐⠈⠒⠀⡀⠀⠈⠁⠉⢸
⠀⠀⠀⠀⠀⠂⢀⣀⠈⠉⠀⠀⠁⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⠀⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠸⢶⡦
⠀⠀⠀⠀⠀⠀⢸⠐⠀⢀⡄⢃⠀⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠁⠀⢀⡀⠀⠰⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠬⠥⠴⠤⠤⠴⠧⠤⠴⠾⠄⠀⣶⣾⡄⠀⠀⠤⠔⠒⡲⢀⠾⣆⠀⠀⠙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠅⠀⠀⠀⠔⠉⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡈⡂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣍⠁⠨⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡑⠈⠉⠢⡀
⠀⠀⠀⠀⠀⠠⠔⠒⠉⠉⠉⠉⠁⠐⠠⢌⡀⠀⠀⠘⠦⡀
⠀⠀⠀⠀⠐⠤⣄⢀⠀⢀⣀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠑⠠⠤⣤⣄⣀⣀⡀⠒⠦⠁⠀⠈⠂⢀⠹⣧⣾⢷⣾⣷⣤⣤⣄⡀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⣿⣷⣤⡶⢶⣄⣀⣘⠢⣴⣀⣀⣿⣿⣿⣿⣿⡍⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠿⣇⣤⣿⣿⣿⣿⣿⡛⡿⠿⠿⣰⣿⣿⣷⣸⣿⠟⠉⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢿⣿⣆⠀⢻⣿⣿⣿⣿⣿⣿⣿⡘⢶⣶⣿⡿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⠀⠈⢿⣿⣷⣴⣿⣿⣿⠿⣷⣾⠛⠿⢻⡟⡟⢡⡈⢿⣯⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠺⣷⣦⣤⠀⠙⢿⣟⣵⣿⠏⠀⣾⣿⠀⠀⠈⠃⠁⠈⢷⡄⠀⠉⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠈⠻⣿⣿⡿⣷⣿⡿⠁⢀⣴⡟⠃⠀⠀⠀⠀⠀⠀⠀⠹⣦⠔⠆⠀⠀⢀⠔⠀⠀⣀⣴⣶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣦⣴⣩⣿⣿⡏⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠁⠀⠀⠀⠉⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠛⣿⣿⠏⣿⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣿⡿⠊⣡⢂⠀⡀⠀⡠⠔⠊⠈⠁⠀⠀⠉⠐⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⠀⠁⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠿⠇⠸⢧⣾⣪⠄⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠹⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⢠⠔⠀⠀⠀⠀⠀⢻⣾⡇⠔⠊⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣻⣿⡍⠃⠀⠀⢀⠈⠀⣰⣿⣿⠿⠿⠿⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⠃⡠⠀⠀⣈⣴⣾⣿⣏⠙⠓⠂⠀⠠⠀⠀⠀⠉⠐⠒⠄⠀⠡⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣝⣿⣿⣿⠟⠿⢿⣮⠃⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⡀⠈⠁⡾⢫⢯⠏⠸⣿⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠐⠀⠀⠀⠀⠯⠉⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠛⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⢄⠀⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰⣎⣷⠀⠀⠀⠀⠀⠒⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠈⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡧⠊⠀⠀⠀⠀⠀⠻⡅

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣁⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣵⣾⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⢿⣻⣿⣿⣿⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠋⣀⡼⣿⣹⣿⣿⡆⠀⠈⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⣧⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⢿⣿⣿⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡝⣯⡇⠈⢻⣿⣿⣿⣿⣿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣼⣷⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣱⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⣳⣦⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣄⣀⣤⣶⠟⠃⠀⢿⣿⣿⣿⢻⠻⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⣿⣿⣿⣇⣷⢹⣿⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡀⠀⠀⠀⠀⣿⠿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⢹⣿⣦⢠⣤⢀⡀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⢠⠦⣠⣶⣦⣤⣤⣤⣵⣦⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣏⣾⣿⣿⣶⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⢠⣀⣴⣿⣿⣿⡿⢉⠀⠀⠀⠰⣦⣤⣄⣀⠀⠀⠉⢩⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣧⣶⣴⣸⣿⣿⣿⣿⣶⣶⣿⣿⣿⡿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠛⠇⠀⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠
⡄⠀⠀⠀⠀⠀⠀⠀⠉⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣼⣿⣿⣿⣿⣿⣿⡇⣹⡁⢀⣴⡀
⣿⣶⣄⣠⣾⣿⣿⣿⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⠉⠿⣿⣏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣯⣷⣿⣷⣿⣿⣦⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠤⠴⠶⠦⠤⠤⣀⡀
⠀⠀⠀⠀⠀⢀⡄⢀⡤⠖⠋⠉⠀⢀⡠⠴⠒⠚⠛⠛⠛⠒⠀⠉⠛⢦⣄
⠀⠀⣀⢶⡒⠈⡷⠉⠀⢀⠀⠀⠈⠁⠀⠀⣀⣠⠤⠴⠒⠒⠀⢀⣀⣠⠽⢚⡥⣰⠃
⠀⠀⠉⢢⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⡤⠶⠊⠉⠠⠒⣩⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣤⣤⡤⢤⣤⣀
⠀⠀⣰⠃⠄⠀⠀⠀⠀⠐⠂⠤⠤⠤⠤⠤⠤⠐⠒⠉⠀⠀⠀⠀⣠⡴⠞⠁⡌⣇⠀⠀⠀⠀⢀⣀⡠⠔⣉⠤⠒⠉⠀⠀⠀⠀⠀⠀⢉⣲⣄⣀⡴⠋⡙⠛⢶⡄
⠀⢰⠃⡜⠀⢠⠂⠀⠀⠀⠀⡀⢀⣀⣀⣀⣀⣀⣤⣤⠤⠶⠚⠋⠁⠀⠀⠀⢱⣹⠀⠀⣠⠞⠩⠎⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⢿⣀⡠⠀⠹⡄
⠀⡟⢠⡆⠀⡇⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣼⠃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣆⢷⡠⠔⠀⡇
⠀⡇⢸⡇⠀⢀⠄⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⠆⠀⡇⢰⢻⠸⡀⠀⠀⠀⠀⠀⢈⣉⣉⠉⠑⠒⠤⣄⡀⠀⠀⠀⠀⣠⠟⡾⠇⠀⣸⠃
⠀⣧⠀⠇⣠⠋⣠⣤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⡇⢸⠸⢀⠓⢦⣄⣦⠤⣄⣀⠀⠈⠙⠲⢤⡀⠀⠉⠓⠶⠶⠾⣫⠀⡷⠴⠚⠁
⠀⢻⡀⠀⡏⣾⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⠀⠀⣸⠁⠘⣇⣸⠰⠀⠀⣤⠀⠀⠉⠙⢦⡀⠀⢀⠙⣆⠐⠀⠀⠀⠊⠁⡔⡇
⠀⠘⣷⠀⠀⠙⢮⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡼⣰⠃⠀⠀⠈⢿⠀⡄⠀⠈⠀⠀⠀⠀⠀⠃⢸⡍⢱⡈⠀⠀⠀⢀⠄⡼⢡⡇
⠀⠀⠸⣧⡀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⢞⡵⠃⠀⠀⠀⠀⢸⡘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠈⢬⠼⠁⠀⠀⠂⣡⠞⢁⣾⠁
⠀⠀⠀⠈⠳⣄⡙⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⢉⡴⠋⠀⠀⠀⠀⠀⠀⠀⢷⣄⣀⡤⠎⠀⠀⠀⠀⠀⠀⢠⠀⠀⠐⠒⠉⠀⣠⣿⠋
⠀⠀⠀⠀⠀⠈⠙⠓⠺⠷⠦⢄⣀⡀⠀⠀⠀⠀⢀⣀⣀⡤⠖⠋⠀⠰⠿⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠂⠤⠤⠖⣋⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⡄⠈⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠙⠒⠤⣄⡀⠀⠀⣀⣠⣷⣤⠤⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠓⠤⠍⠓⢤⡀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣦⣀⣀⠀⠀⠀⠀⠀⢀⡨⢆⣀⢎⡀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠰⡄⠀⠀⠀⠀⢡⠈⠧⠀⠀⠀⠀⠹⣿⣿⣿⡿⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠇⠀⠀⠀⠀⠀⡆⠣⢄⡀⠀⠀⠀⠀⠙⠛⠁⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠛⠃⠀⠀⠀⠀⠀⠀⢡⠀⠀⠉⠙⠒⠶⡶⠜⣦⠤⠴⠚⠉⢈⠀⠀⠀⠀⠀⠀⠸⣄⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⠊⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠳⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⡞⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⠲⡄⠀⠀⢀⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢠⠇⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠦⠤⠿⠗⢒⠋⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢑⣠⠀⡀⠀⣀⣠⣼⢰⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⠞⠉⢂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠾⢦⢰⣴⡉⡿⠾⠛⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠃⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⠤⣤⣄⣀⣤⡤⠤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣄⡤⡀⠀⣏⠋⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢮⠀⢀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠤⠜⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠈⠰⠩⠽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⣄⣼⡿⣷⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣶⡏⢟⡇⠻⢿⠿⣇⠊⢳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠁⠋⡿⡿⠿⢶⢷⡌⢀⣼⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠶⠿⡏⠂⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠙⣻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⡿⠂⠁⠀⠀⢠⡀⣀⢂⠀⠀⠀⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣬⡙⢋⠇
⠀⠀⠀⠀⠀⣠⣶⡿⠿⢫⠙⠿⠶⠒⢂⠐⠛⣄⠻⠿⠻⠁⠀⠀⠠⣆⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡂⢦⢢⣦⣼⡇
⠀⠀⠀⢀⣾⣷⣮⡀⣠⣀⡄⣀⠀⣰⣺⣠⣀⢿⠋⠀⠀⠡⠀⠀⠀⠈⠝⠀⠀⣿⡛⠶⣤⠀⠀⠀⣼⣿⣶⣿⣿⡿
⠀⠀⢀⣾⣿⣿⡟⠁⠈⣛⣾⡿⠒⠺⣿⣿⣉⠀⠀⠀⢀⡴⡆⠇⢠⠀⠀⠀⠀⠈⠛⠂⠈⠁⠀⢸⡿⢿⠿⢿⡿⠁
⠀⠀⢸⣿⣿⣟⠂⠀⣼⢿⡿⠁⠀⢠⣿⣿⡇⠀⠀⢀⠊⢠⠇⠀⠠⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⢹
⠀⠀⢸⣾⣿⡏⠀⠀⢻⣸⣄⣼⠯⠛⢱⣶⣬⠀⠀⠈⠀⠁⠀⠀⠄⠈⠒⠦⠄⠀⡀⠀⠀⠀⠀⠀⠒⠃⡠⠂
⠀⠀⠘⣿⡜⡿⠁⠀⠸⣷⡜⣿⡷⠀⢘⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠁
⠀⠀⠀⢿⡷⣘⣴⣦⢀⠀⣤⣿⠃⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠘⠬⢀⡀⣀⢀⡀⠤⠄⠐⠊
⠀⠀⠀⠘⣿⡹⣿⣷⢀⢸⣿⣇⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠇
⠀⠀⠀⢀⠈⢀⠘⣿⣷⡍⢻⣶⣿⡉⠑⠚⠁⠀⠀⢀⣠⠤⠖⠊⠁
⠀⠀⠈⣾⣶⣿⡇⣾⣿⣽⣿⣿⡿⠇
⠀⠀⠀⠙⠝⠟⠿⣿⣦⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⡀⠈⡂⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠂⠀⠀⠂⠖⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢤⠄⠛⠈⠐⢂⣀⣼⠯⣼⡀⠀⠌⠁⠀⣸⠆⠐⠴⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⢧⠄⣤⠀⠐⠎⠀⠀⠳⠀⠈⡁⠀⢀⡴⠔⠀⠈⠐⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣍⠀⠀⠛⠀⠀⢰⠂⢂⠩⡀⠀⠠⠀⠀⠰⠉⠂⢀⢓⠀⠀⠀⠀⠀⡁⠀⠀⠐⠘⠳⠦⠄⢀⠔⡀⠀⣠⠀⠀⢀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠰⠄⢊⠀⠂⠀⡇⠂⠁⣶⣀⠀⠠⠀⠀⠀⢠⠀⡀⠀⠐⠒⢦⣀⠀⠀⢀⡀⠀⢀⣀⡀⠼⢇⣀⡀⣈⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡏⣠⣄⠈⠀⠀⣰⣾⠉⠀⠐⠠⡄⠦⠀⠀⠀⡠⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⢸⡆⠈⡁⠁⠈⡠⠊⠁⠈⠑⠀⠀⢀⢁⡀⠋⠈⠩⠁⠀⠀⠥⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠈⠂⠀⠀⠀⠅⡆⠀⠀⠀⠥⠀⠀⠄⠄⠀⠀⢤⡀⠠⠀⠀⠀⠀⠁⠀⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠒⠶⠦⣠⢀⠀⣡⡈⠀⠀⠀⢀⠀⣀⠀⠃⢀⠀⠀⣰⣀⠀⢀⡀⠙⠆⠀⠀⠀⠀⠧⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠆⠆⠈⠋⣃⠉⠀⡀⢰⡟⠀⠁⠀⢀⠍⡀⠊⠁⠀⠀⠚⠄⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠠⣗⠀⠀⠀⠀⠀⢭⡀⠰⠛⠸⠇⠀⠀⠀⠉⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⢠⢠⡖⠡⣄⠠⠀⠙⡠⠀⠀⠈⠪⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀
⠀⠀⠀⠀⠀⡄⠐⢶⠀⠱⠆⢸⠂⠀⠀⠉⢈⡁⠂⣴⠆⠀⠀⠐⠲⡈⠀⠐⡊⠄⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠀⠀⠤⣁⣀⣀⣀⠀⠀⠀⠀⢧⡀⠈⠫⠁⠀⠀⠀⠀⠀⠀⠕⠀⠀⠀⠀⠀⠀⠀⢀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠂⠀⠉⠙⠛⡦⠴⠖⠒⠋⠀⠀⠀⢠⠀⠀⠠⠐⠀⠀⠂⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠠⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠂⡀⢉⠴⠡⠄⠀⡠⠀⠑⠄⠀⡀⠀⠈⠀⠀⠤⠂⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠄⠀⠀⠀⡤⠀⢀⡀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⣤⠿⠀⠄⠀⡁⢀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠁⠀⠈⡄⠁⠀⠄⢦⡰⠀⠙⠂⠉⠀⠴⢠⡀⣀⠀⠚⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣈⠀⢢⡀⠀⠀⡀⣘⡄⠀⠀⠀⠀⠀⢆⡇⠀⡀⠀⡀⠸⠋⠶⠆⠀⠈⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠒⡐⠋⡉⠉⠐⠉⠑⢳⣦⣴⣤⣚⡉⠀⠀⢈⡁⢆⠀⠀⠀⡅⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠈⠋⠔⡲⠦⠄⢸⣇⢧⠙⡇⠐⠀⠉⠀⡈⡗⢀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠂⠀⠀⠀⠀⠇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣼⣀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⣄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠻⣦⡀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⣤⠾⠛⠉⠉⠈⠉⠙⢷⣄
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠈⢿⡄⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠻⠟⠀⠙⢿⡄⠀⢸⡇⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢸⡇⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠷⠿⠷⣤⣀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠉⢳⣤⣴⡶⠶⠺⣿⣷⣤⣾⣋⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣀⡀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢀⣿⣿⣿⡏⠉⢻⣿⣿⡟⠛⢿⣿⣛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠋⠀⠁⠀⠀⠀⠀⣸⣿⣿⠃⠀⢸⣿⣿⣿⠇⠀⣾⣿⣿⡇⠀⢸⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⢠⣿⣿⣿⡟⠀⢀⣿⣿⣿⠇⠀⣾⣿⣿⠃⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠒⠛⠻⣿⠃⠀⣠⣿⣿⣿⡟⠀⠀⣼⣿⣿⡿⠀⢰⣿⣿⡟⠀⢸⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⣿⣿⣿⠟⠀⠀⣼⣿⣿⡿⠁⢀⣿⣿⣿⠃⢀⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡃⠀⣠⣾⣿⣿⡿⠁⢀⣾⣿⣿⠃⢠⣾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣟⣀⣠⣿⣿⣿⡷⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⢰⣦⠀⡟⢦⣠⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠑⣤⡭⠧⣧⡚⠁⠀⢹⠁⠹⢄
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⡀⠀⠀⠀⠲⣦⣄⡀⢇⠀⢰⠍⠀⠀⠀⠙⢆⠀⠀⠀⠀⢨⡦⡴⢤⣀⣀⢀⣀⠤⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡍⠓⠦⣀⠀⠈⢇⠈⢻⣄⣸⣆⠀⠀⠀⠀⠈⠀⣄⣆⣠⠋⠀⠀⠀⠋⠘⢿⣇⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡀⣾⣧⡴⠚⠿⣿⣿⡿⠿⣄⣖⠙⠢⣄⠀⠉⠛⢿⣦⡀⣠⠖⠛⠛⠻⣿⠓⠒⠲⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠋⠁⠀⠀⡿⠁⠀⣠⠿⣯⠄⠀⠘⠫⠿⢶⢤⣿⢿⣇⠀⣠⣄⣠⣾⣥⠴⠚⠋⠉⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠛⢷⡀⠀⠀⠇⠀⠞⠁⠀⡼⠷⢖⣰⣋⠙⢻⡀⠁⠀⠈⣾⠃⠀⠈⠛⠖⣤⣴⡊⠉⣻⠟⠉
⠀⠀⠀⠀⠀⢀⣠⣤⠒⣾⠀⠀⠀⠀⠀⠁⠐⢓⡀⠀⣀⡤⠾⢧⠀⣜⠉⠉⠉⢢⠱⣄⠀⢀⡎⠀⠠⠄⠀⠈⠉⠛⣇⠴⠁
⠀⠀⠀⠀⠀⠈⠉⢉⣲⣿⣄⣀⡠⠲⡤⣥⣚⣛⣉⠵⠿⠀⠀⣰⠋⣹⣤⠶⣦⣸⣶⠿⣶⣿⣦⠀⠀⣀⣠⣤⣤⣴⣧⠤⣀⡀
⠀⠀⠀⢀⣤⣴⣞⣁⠬⠿⠛⠛⢣⡄⡠⠋⠁⠀⢀⠀⠀⢀⡾⠁⠀⠙⢦⣴⠄⠌⠃⠲⣶⣾⠻⡏⠉⠁⠀⠀⠹⣿⣏⣀⣀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠦⠔⠋⠉⠓⠋⠀⠀⠀⠀⠀⠙⠶⢦⣖⡆⠄⣅⣸⡧⠀⢀⣀⠀⠀⠀⣽⣿⣿⣋⠉⠉⠉⠷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠾⠿⢤⡀⠀⢘⡇⠀⠀⣿⣿⣯⠛⠻⣕⠒⠊⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠧⠴⣾⣿⣿⣷⡀⠀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠌⢿⡌⠙⠒⠒⠾⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻

⠀⠀⠀⠀⠀⢘⡔⢁⠀⠀⡠⠃⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⣶⣾⣛⠀⠈⠢
⠀⠀⠀⠀⢀⡈⠀⡜⢀⠴⠡⣚⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠒⠂⠄⠐⠖⠋⠀⠘⣿⠋
⠀⠀⠀⢠⣼⣧⡄⠀⠀⠀⠉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠰⠋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢰⠏⠉⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏
⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⡗
⣶⣤⣾⠂⠀⠒⡄
⠉⢻⡿⠃
⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠑⠦⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠤⣉⠊⡆
⣀⣴⣄⣠⠔⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⣁
⠀⣽⣿⡏⠁⠐⠄⠀⠀⡠⠊⠠⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⢀⣷⣶⡾⠆
⠴⠋⠀⠀⠀⢀⡁⢀⣌⠀⢐⠀⠀⠠⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⣿⠟
⠀⠀⠀⠀⡠⠜⢻⣿⡇⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠦⠤⢤⣠⣶⡿⠷⢤⡷⠴⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡋⣁⡀⠀⢀⠀⠀⢻⣦⣾⣧⡀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠶⠶⣒⣒⠛⢛⣋⡉⠭⢨⣟⢲⣿⡟⣿⡞⠋⠙⣷⠼⣿⣿⠟⣿⣦⠟⠉⠛⠛⠒⠶⠶⠶⠴⠖⢤⣄
⠀⠀⠀⠀⢀⡤⠒⡡⠊⠉⢑⠀⠠⡔⠀⠈⠁⠀⠛⠉⢀⣤⡾⠉⠾⣿⡿⣿⣶⣾⣿⣿⣷⠈⠿⣿⣿⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⢀⣠⣴⠞⢉⡞⣰⣇⠈⣿⣧⣙⢿⡿⣿⣿⡋⠀⠀⠘⡇
⠀⠀⠀⠀⠁⠀⠄⠀⠀⣀⣀⣀⣀⣠⠴⠺⢿⡿⠃⢠⣾⠅⢿⣿⣶⡍⠛⠿⣿⡞⠲⡏⠀⠀⣾⣿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡹⢿⣿⣄⠈⠣⠴⠛⢿⣦⠘⣿⣿⣏⣀⣀⣼⣷⠚⠉⣀⠞⠙⠛⢭⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣶⣡⡀⠘⢿⣿⡀⠀⠀⢀⣼⡿⠷⢟⣿⢟⣟⠟⡼⣿⡷⠊⠁⠀⠀⠀⠀⠙⢿⣧
⠀⠀⠀⠀⢀⣠⠿⡭⠭⣯⡈⢿⣿⣷⡀⠙⢿⣦⠀⠘⣿⣀⡰⠋⢡⣾⣧⣾⣠⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠋⠁⠀⠀⣬⣿⣿⡌⠻⣿⣷⡀⠘⣿⣿⡶⠋⢘⢷⣴⠟⠁⠽⠁⣿⠻⣟⡒⢢⣄⡀⠀⠀⠀⠀⠐⠛
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡿⣿⣄⠙⣿⣿⣦⣘⡿⠅⠀⠉⠛⢳⣄⡔⠰⣺⠇⠀⠈⠻⣿⣿⣍
⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣷⣌⢿⣷⣌⣿⣿⣿⠀⠀⠀⢀⡔⢣⠋⠀⢠⡏⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠃⠉⠉⠉⣠⡏⠀⠠⠖⠉⢀⠄⠁⠶⡞⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡇⠀⠀⠤⠐⠁⠊⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠈⣀⠖⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠦⣠⠾⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠈⠙⢏⠛⠃⢤⠀⠀⠉⠉⠳⣄⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣶⡟
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⠳⠀⢄⣠⣄⡈⢦⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⢺⠝⣧
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢦⣀⣃⠀⠉⠋⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⣿⠞⠋⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⣀⠀⣨⠟⠒⢀⣀⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠘⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠿⠗⠒⠛⠉⠀⠈⠲⢝⢢⡀⠀⡀⠀⠀⣀⠀⡼⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠳⡑⡾⠁⠀⠀⠈⢏⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠂⠛⠐⠒⠢⢄⣀⠀⠀⠙⣜⡄⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠘⣞⡄⠐⡜⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡏
⠀⠀⢀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠤⠤⣄⡀⠀⢀⠀⠀⠀⢳⡀⠘⢂⡔⠓⠂⠀⠀⠀⠀⠠⠶⠊⠁⠀⣷
⠀⠀⠈⠑⠤⣄⣤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢤⡀⢳⠀⣄⢹⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠉⠓⠦⣌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡇⢰⠸⠀⠀⣠⠚⠁⠀⡀⡠⠊⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠏⢲⣄⣀⠠⣄⡰⠖⠛⠁⠈⠛⢦⡀⡆⢰⠃⠀⢀⢀⠟⠁⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⡤⠧⢤⣿⠀⠀⠈⠿⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠈⠑⠚⠛⠒⠦⣄⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠓⢦⡦⣾⠤⠖⠛⠛⠛⠲⣄⠀⣀⣀⣀⡈⢳⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠋⠉⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⠃⠀⠀⢀⡀⠀⠀⠀⣼⢰⡖⣪⡅⠪⣽⢃⠀⢀⡤⠀⠀⠀⣤⣟
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⣆⠀⣀⡇⠉⠓⣤⡾⢻⣌⠳⢭⣠⠞⠉⢧⠞⠁⠀⠀⠀⠀⠈⠉⠑⡄
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣨⠟⠋⠀⠀⣼⠋⠀⠀⠉⠳⣄⠟⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠤⠐⠒⠠⡏⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⡏⠀⠀⣠⠞⠒⣒⢦⡄⠀⣠⡶⠶⠋
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠹⣦⡀⠀⠀⣀⣉⠤⠞⠁⣠⠎⠹⣄⠀⢠⠏⠉⠳⣄
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣄⣀⡠⠞⢋⠟⠉⠀⠀⠀⣀⡾⠁⠀⠀⠀⠉⠉⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⢤⣄⠀⠀⠀⠀⠰⢟⣁⢀⣠⢞⠟⠒⠒⠉⢩⠑⢀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⣤⣀⣀⣀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠉⣉⡩⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠴⠶⠚⠉⠂⠈⠙⠓⠛⠛⠲⠶⠴⠖⠚⠁

⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣀⢤⡀⢰⠁⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⣀⡀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢂⣂⠴⠚⠁
⠀⠀⢧⠀⠈⢦⣧⢠⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣹⣶⣿⠤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣯⠠⠈
⠀⠀⠀⠙⠲⢄⣳⡍⢇⣀⠀⠀⠀⠀⡤⣊⡵⢆⠜⣷⠶⣿⠦⡱⢮⣑⢤⠀⠀⠀⠀⢾⣿⢀⡍⡔⣇⣦⡀
⠀⠀⠀⢠⣾⣇⡮⠇⠘⠟⠀⠀⠀⠈⠉⠛⠚⠁⠀⢘⡿⠍⠀⠈⠓⠛⠉⠁⠀⠀⠀⠠⠂⠈⡀⠸⡙⢟⠇
⠀⠀⠀⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠨⠁⠂⠄⠀⣰⣆⠀⠠⠐⠈⡅⠀⠀⠤⣄⣀⡀⣠⠶⣤⢀⣀⣀⠤⠤⡀⢀⠤⠤⠄⣀⢠⣶⣄⢀⠀⠤⠤⣄
⠀⠀⠹⠛⠓⢿⠷⠾⡿⠚⠛⠏⠀⠀⠀⠀⠀⠀⠀⣽⠒⣿⠀⠀⡀⠄⠀⠀⠈⠒⠶⡒⣨⢿⠿⢿⢭⡐⡲⠖⠊
⠀⠀⠀⠀⠀⠈⢽⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠃
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠢⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠉⠳⣄⢰⣄⡠⠞⠁⠀⠀⠀⠀⠀⢀⣀⣀⢠⢢⢀⣀⣀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⡱⡎⠀⣀⣀⣀
⠀⠀⠈⠓⠒⠂⣡⣈⠒⠒⠚⠁⠀⠀⠀⠀⣏⠀⢀⣨⠞⠉⠀⠀⡷⠀⠀⠀⠀⠘⠤⣄⢈⣁⡷⢞⣉⠀⣤⠔⠁
⠀⠀⠀⠀⠀⠘⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢫⡝⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣯⣵⠀⠉
⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠐⠲⣕⣦⡔⣩⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠤⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⡔⠉
⠀⠀⠀⠓⢒⣾⣿⣿⣶⡒⠚⠀⠀⠀⠀⠀⠀⣀⠴⣞⣙⣳⠤⡀⠀⠀⠀⠀⠀⠀⠂⠉⣩⣤⡼⣦⣬⣉⠁⠂
⠀⠀⠀⠚⠁⠐⣟⡿⠀⠉⠂⠀⠀⠀⠀⢀⠜⠁⡠⢧⠀⡼⣄⠈⢢⡀⠀⠀⠀⠀⠲⠟⠋⠐⣛⡛⠈⠛⠷⠂
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠃⠉⠀⠀⠉⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢀⠉⢉⠱⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣠⣆⢴⣏⣀⣀⣠⣨⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡾⢿⠻⠿⠃⠁⠝⠉⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠛⠻⠟⠁⠀⠀⠀⠀⠑⢐⠀⠀⠀⢀⡈⠳⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⣆⠦⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⠒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡗⣤⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣾⢿⣿⡁⠬⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠈⠲⣶⡀⠀⠀⠀⠀⠀⠀⢺⣤⠋⠀⠀⢀⢻⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡇⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣦⡝⠁⠀⠀⠀⠸⠘⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡇⠀⠀⠀⠀⠀⠢⢹⡄⠀⠀⢀⡤⠃⠀⠀⠀⠀⠀⢀⣾⡄⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠁⠀⠀⠀⠀⠀⠀⠻⢷⡀⠀⠉⠀⠀⢀⠀⠀⠀⠀⣠⠟⠛⢾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠠⠖⠛⣳⠀⡤⠀⠀⠀⡀⡤⠔⣻⠟⠰⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⣤⠶⠉⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢄⣀⠀⠀⠀⠀⢀⣀⣤⣾⠃⠀⠠⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠉⠛⠛⠛⠋⢻⣿⣏⠀⠀⠗⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⣿⣾⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠁⡄⠀⠀⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⠿⠉⠛⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠏⠁⠀⠀⠀⢸⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀⣼⣧⢸⡆⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⡀⢸⣿⠘⣇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢻⣿⡀⣿⠀⠀⠀⠀⠀⠀⢸⡇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢩⠂⠀⠀⠀⠀⠘⢻⡇⣿⠀⠀⠀⠀⠀⠀⢸⠃⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠸⡇⠿⠀⠀⠀⠀⠃⠀⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⢿⠟⢻⠿⡿⠟⣿⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠉⠉⠉⠉⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⠢⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⡠⠴⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠙⣄⢣⠀⢸⠀⡏⠀⠀⡰⣡⠔⠁⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢌⢇⠘⠀⠀⢀⣾⠞⠁⣀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡈⠓⠄⢀⠼⠚⠓⠒⠲⡟⠁⠠⠊⢀⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡏⠀⢛⢀⠘⠃⢸⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⢒⣒⠭⠛⠧⡀⠘⠚⠀⢀⡼⢍⠑⠒⠤⣄⣀⣀⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠁⢀⠤⠀⠀⢨⣷⠒⠒⠁⠀⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠴⠁⡰⠁⢀⣿⣿⠀⢰⠀⠳⡀⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⠻⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡿⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⡸⢰⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣀⠤⠒⠉⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⠳⢄⡀⢀⡰⠁⠸⡇⢸⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⡠⠊⢁⡠⠖⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡇⠀⠣⡀⠀⢀⡠⠴⠊⠁⠀⣠⠊⢀⠴⠋⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠑⢄⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠁⠀⠀⠀⢀⠜⢁⡔⠁⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠣⡀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⡠⠃⠴⠋⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠈⠢⣄⠀⠳⡄⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢀⠜⠁⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡈⠁⠀⠈⠢⡀⠀⠀⠀⠘⡌⡄⠀⠀⠀⢠⠎⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠈⢦⡀⠀⠀⢃⢱⠀⠀⢠⠃⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⠈⠢⣀⠸⡈⡆⢠⠇⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢌⡓⢧⠱⣎⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⣤⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⢀⣾⣄⣀⡀⠀⠀⢀⣀⣀⣀⣠⣿⣧⠀⠀⠀⠀⠠⠾⣿⠧
⠀⠀⠀⠘⢿⣿⣿⣏⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣦⣄⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⣤⡄⠀⠀⣺⣿⠆
⠀⠀⠀⠀⠘⠟⠉⠙⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣇
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠠⠿⠟⠛⠻⣿⣿⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⠋⠉⠁⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠘⠻⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡶⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢠⣿⣦⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠰⣶⣶⣾⣿⣿⣿⣶⣶⡤⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣾⣿⠃⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠐⠛⠿⢿⣿⣿⣿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃
⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⣧⡀
⠀⠹⢿⡏⠀⠀⠀⠨⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠶⣾⣿⣿⣿⡿⠃⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⡀⣠⣾⣿⣷⠀⠀⠀⠀⠀⢸⣿⠿⣿⣇⠀⠀⠰⣶⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠾⠿⢿
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⡿⠉⠁⠀⠀⠀⠀⠀⠀⠰⠿⠿⠛⠛⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀
⠀⠀⠀⠀⢸⣿⣿⣦⣠⣤⣤⡄⠀⠀⠀⣤⣤⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣦⣶⣶⣶⠆
⢀⣤⣴⣶⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠈⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢀
⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠛⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⢲⣶⣿⣤⡀
⠀⠀⠀⠀⣿⣿⣿⠿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⣠⡄⠀⠀⠀⣀⡀⠀⠀⠀⢸⣿⣿⣿⠿⠿⣿⣿⡀⠀⠸⠛⢿⠁
⠀⠀⠀⠀⡿⠋⠁⠀⠀⠀⠈⠀⢀⣴⡀⠀⠀⠀⠀⣠⣿⣿⣿⣧⡀⠀⠘⠟⠃⠀⠀⠀⠸⡿⠋⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣾⣿⣧⣀⡀⠀⠈⠉⠙⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣆
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⣿⣷⣶⡶⠀⠀⠼⣿⠇
⠀⠀⠀⠀⠰⣾⣿⡶⠄⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣠⣦⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠛⠉⠀⠈⠙⠇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡷⠆⠀⠀⠀⢀⣿⠟⠛⠻⠿⠀⠀⣠⣤⣿⣦⣀⡀
⠀⠀⠀⠀⢀⣰⣆⡀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠿⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠿⠿⠇⠀⠀⠀⢈⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⡼⠁
⠀⠀⢀⠴⠒⠛⠛⠒⠲⠤⣄⡀⠀⠀⠀⠀⢀⡼⠟⠉⠉⠻⢧⡀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠛⠛⠒⠦⡀
⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠦⣄⣠⠏⠀⠀⠀⠀⠀⠀⠹⣄⣠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣤⣤⣤⣤⣤⣤⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣽⠟⠛⠛⠻⣯⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋
⠀⠀⠀⠀⠙⠒⠦⠤⠤⠤⣴⡶⠶⠛⠋⠉⢠⣿⣶⣶⣶⣶⣿⡄⠉⠙⠛⠶⢶⣤⠤⠤⠤⠴⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⣠⠋⠉⠉⠉⠉⠉⠉⠛⣄⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⣴⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣦⡀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠖⠋⠈⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⠃⠙⠲⠤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⣟⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣾⠟⠁⠀⠀⣠⣿⢃⣾⠃⠀⣾⠇⠀⣠⡿⣧⣼⡿⠛⠁⠀⠀⠀⠀⠀⠀⢠⡾⠃⢀⡜⠁⠀⠀⢠⣿⣧⣃⣤⢾⡟⠀⢀⡆
⠛⠁⠀⢀⡴⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⣠⡾⠛⠻⠟⠁⠀⠀⢿⣤⡾⠋⠀⠀⢻⣀⣀⣴⠖⠀⠀⠀⠀⢀⡿⢁⡴⠋⠀⠀⢀⡴⣿⣏⡟⠉⠀⣾⠁⢠⠚⠷⣴
⣀⣀⡴⠞⠀⠀⠀⠀⠀⠀⠸⣿⡀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣾⡷⠋⠀⠀⢀⡴⠋⠀⠻⠛⠀⠀⠀⠿⠖⠁⠀⠀⠸
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⡤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡄
⠀⠀⠀⢠⡾⠛⣦⠀⢀⣠⣾⠆⠀⠀⠀⠀⠀⣴⡶⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⢀⣿⣿⣰⣿⡶⠿⣿⡏⠀⢀⡄⠀⢠⣾⠋⢠⣾⠇⠀⠀⠀⠀⠀⠀⣠⡟⠁⢀⡼⠁⢀⠄⠀⠀⠀⢴⡆⠀⠀⢀⡀⠀⢀⣴⢿⡆⢠⡀⠀⠀⠀⣠⣿⣿⠁
⠀⣴⣿⣿⢋⣿⠋⠀⣸⣿⠀⢀⣾⡇⢠⣿⣃⣴⠿⠃⠀⠀⠀⠀⠀⢀⣾⡿⠁⣰⠟⠀⣠⢷⣠⡤⠊⣠⠏⠀⠀⠀⣼⠃⣠⣞⡡⠋⠀⢸⠃⠀⠀⣰⣿⡿⠁
⡾⠋⢿⣇⡼⠃⠀⠀⣿⡇⢠⣾⠉⠓⢾⡿⠋⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣡⡞⠁⢠⢾⣏⡠⠀⠀⢠⠏⠀⠀⣠⠎⠻⣴⣿⠋⠀⠀⣠⡟⠀⠀⢠⣿⡿⠁
⠁⠀⠀⠉⠀⠀⠀⠀⠻⢷⠿⠁⠀⠀⠸⣇⣀⣀⣤⡴⠂⠀⠀⢀⣿⣿⠟⠃⢀⡴⠋⠈⠉⠀⠀⠀⣏⠀⢀⡼⠁⠀⠀⢾⣿⣀⣠⣾⠏⠀⠀⢠⣿⡿⠁⠀⠀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢸⣿⣟⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠿⠶⠋⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⣼⡿⠁⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⣠⠟⠀⠀⡠⣄⠀⠀⡀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀
⡆⠀⢸⡆⠀⠀⠀⠀⠀⢀⣾⣿⢃⡾⠋⠀⣠⣶⡇⠏⣠⣾⠏⠀⣴⠂⢠⣾⣿⣿⠋⠀⠀⡀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⢠⣿⢻⡆⠀⣠⣿⠃⢀⡀⠀⣠⡿⠋
⠀⠀⣸⠇⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⢀⣴⣿⣏⡟⠋⣹⡟⠀⡴⣿⣤⣿⡿⠋⠁⠀⣠⠎⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⣼⡿⣿⣧⣾⣿⠃⠀⣸⡇⢰⣿⣡⣾
⠀⣴⠏⠀⠀⠀⠀⠶⣾⣿⡏⠀⢀⣴⠏⠸⠿⠟⠀⠀⢿⣧⠞⠁⠀⠹⣿⣄⣀⣤⡾⠃⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠛⢹⡏⠀⣰⡟⠙⣿⠟⠋⠁
⡾⠋⠀⠀⠀⠀⠀⠀⣿⣿⣥⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⣠⣿⠛⢿⠟⠀⠀⣿⡇⣴⡿⠁⠀⢿⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠙⠻⠛
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⣠⡖⢶⡄⠀⢀⣴⡷⠀⠀⠀⠀⠀⣠⣾⠟⣶⡀⢠⡏⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⢠⣿⡇⣼⣧⣶⢿⣿⠃⠀⣀⠀⠀⣴⡟⠁⣴⡿⠀⢸⡇⠀⠀⣠⣾⠟⠀⠀⠀⣠⠖⠀⣸⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀
⠁⣶⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⣰⣿⡿⢻⣿⠉⠀⣾⡏⠀⢠⣿⠀⢰⣿⣠⡾⠛⠀⠀⠀⠳⠶⠿⠋⠁⠀⠀⢠⣾⠏⢀⡼⠁⣠⠈⠀⡠⢀⡟⠁⠀⢀⡖⠀⣰⢏
⢠⠇⠀⢠⣿⡿⠃⠀⠀⠀⢠⣾⠟⣿⢃⣾⠃⠀⢰⣿⠃⢠⡿⠉⠳⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢏⣴⠋⢀⣴⠋⡙⠋⢀⡞⠀⠀⣠⢾⣇⣼⡿⠋
⠏⠀⢀⣾⣿⠃⠀⠀⢀⣴⡟⠁⠀⠉⠛⠁⠀⠀⠈⢿⣴⠟⠁⠀⠀⠹⣇⣀⣠⣴⠖⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠁⣴⠋⠘⠛⠀⠀⡼⠀⢀⡴⠁⠀⢸⣿⠀⣀
⠀⠀⣸⣿⠃⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢁⣠⠟⠁⠀⠀⠀⠀⠀⠿⡶⠋⠀⠀⠀⠈⠛⠛⠋
⠀⠀⣿⡏⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛⠁
⠀⠀⠻⢧⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⣠⣾⠟⠁⢠⣤⣄⠀⠀⣠⣶⠄⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⢷⠀⠀⠀⢀⡀
⢀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⣠⣾⡟⠁⠀⢠⣿⣧⣿⠶⢻⣿⠃⠀⢠⡄⢀⣔⢋⣼⠃⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⣠⠏⠀⠀⢠⡏⡃⠀⠀⣠⡟

⠀⠀⢀⠀⢀⠀⠀⣀⠀⠀⠀⢠⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⡀⠀⠀⠀⡄
⠀⠀⠀⢀⠄⠀⡀⠈⠀⠠⠀⠁⢁⠰⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⣾⣷⡖⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣭⠀⠀⠀⠀⠀⠢⣤⣥⡤⠂
⠀⠉⠠⠀⠀⠀⠀⠀⠁⠀⠤⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠈⣻⣿⣾⠟⠁⢠⡀⠀⠂⠐⠆
⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠠⣤⢿⡤⠄⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠚⠀⠠⠟⠋⠛⢇⠀⠙⠛⠀⠠
⠀⠀⠈⠀⣄⠀⠀⠁⠀⣣⢬⡇⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠞⠙⠇⠀⠀⠀⠀⠀⣀⣀⣠⠃⢧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠠⣤⠞⠘⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠀⠀⠉⠲⡔⠀⠀⣠⠊⠀⠀⠴⠆⢠⡀⠀⠀⠀⠀⠄⠀⠄
⠀⠀⢨⣃⣤⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠠⠈⠀⠀⢸⣥⠖⠦⣸⡀⠀⠀⣤⣤⣾⣧⣤⡤
⠀⠀⢈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣰⢇⠀⠀⠐⠐⠀⠐⠀⠀⠀⠈⠀⠀⠀⠈⠡⠀⠀⠀⣹⣿⣿⡏
⠀⠀⠈⠀⠄⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣤⣤⣾⣿⣏⣤⣤⣄⡄⠀⠀⢶⣶⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠋⠁⠈⠓⠀⠀⠈⣇
⠀⠀⠀⠐⠀⢀⡾⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢻⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠠⣄⠀⠋⠀⠐⠦⡤⠀⠀⠀⠀⠈⠛⠻⣦⣯⣤⠔⠂
⠀⠀⠲⢶⠶⢋⡴⠟⣻⣶⣦⠶⠂⠀⠀⠀⠀⠀⠱⡄⠀⠀⢸⣿⡿⠿⣿⣷⠀⠀⢀⣀⣼⣧⣀⡀⠈⠁⠀⠀⢠⡀⠀⠀⢤⣦⡤⠀⢀⡿⠁⢷⡀
⠀⠀⡀⠈⢶⡿⢁⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠛⠁⠀⠀⠈⠙⠂⠀⠀⢹⣿⢿⡏⠀⠀⠖⠉⠀⠐⠇⠀⠀⠘⠉⠃⠀⠈⠀⠀⠀⠉
⠀⠘⠋⠀⢨⢶⠿⠿⣿⣿⡀⠀⠀⠀⠀⠀⠐⠒⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠊⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⠂⢀⣀⡰⠛⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠄⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⢀⡞⢧⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠙⡆⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠂
⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⠠⣤⠤⠶⠞⢀⠈⠳⠦⠤⣤⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠸⠛⠉⠛⠇⠠⠀⠀⠀⢀⡀⠀⠀⠀⡀⢀⠀⢀⡄
⠀⠲⣶⣶⣿⣿⣷⣶⠖⠀⠀⠄⠀⠈⠳⡄⠘⣿⣿⠂⡴⠊⠀⠀⣤⠀⠀⠰⣶⣶⡿⠧⢀⡄⠀⠀⠀⣀⣴⣆⣀⠀⠀⠁⠀⠀⠀⠀⣀⡤⠞⠙⠤⢀⡀
⠀⠀⠈⣿⣿⣿⣿⠁⠀⠂⠀⠀⠐⠂⠀⡇⠀⣁⣉⠀⢧⠀⠐⣾⣿⡶⠂⠀⠈⣹⣮⣶⡏⠀⡀⠀⠀⢙⣿⣿⡁⠀⠀⠀⠀⠀⠐⠀⠈⢲⠀⠀⢰⠋
⠀⠀⠸⠛⠁⠈⠛⠇⠀⠀⠂⠀⠃⠀⠸⠗⠉⠀⠈⠙⠻⠀⠀⠋⠉⠓⠀⠀⠀⠉⠀⠈⠛⠀⠀⠀⠀⠈⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠟⠊⠙⠺⠄

⠀⣀⡜⣆⣀⠀⠀⠀⠀⠀⢠⠧⠀⠀⠀⠀⠀⠀⠀⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣰⠄⠀⠀⠀⠀⠀⠀⢠⡆
⠙⣤⠁⠡⡜⠁⠀⠀⠈⠳⠀⠀⣩⠋⠀⠀⠀⠉⢛⡽⡻⠋⠀⠀⠀⠀⢩⠰⠆⠅⠁⠀⠀⠀⠑⠀⠀⡈⠉⠀⠀⠀⠘⢻⡭⠶⠉⠁⠀⠀⠈⠻⡭⠀⠈
⠀⠷⠊⠑⠇⠀⠀⠀⠀⠸⠊⠁⠺⠀⠀⠀⠀⠀⠋⠀⠘⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠊⠀⠘⠀⠀⠀⠀⠀⠛⠁⠙⠂⠀⠀⠀⠀⠘⠃⠈⠁

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⢀⡴⢦⡀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠠⢢
⠀⢖⢣⢗⠆⠀⠀⠀⠀⠛⣟⠙⡴⠂⠀⠀⠀⠒⠀⠀⠀⠒⠀⠀⠀⠘⣭⠁⠈⣭⠃⠀⠀⠀⠒⠆⠉⠲⠂⠀⠀⠀⠐⠖⠈⠐⠛⠂⠀⠀⠘⢭⠁⠀⢩
⠀⠘⠁⠑⠀⠀⠀⠀⠀⠸⠃⠛⠆⠀⠀⠀⠀⠀⠶⠀⠸⠀⠀⠀⠀⠀⠻⠖⠲⠟⠀⠀⠀⠀⠀⠟⠈⠳⠀⠀⠀⠀⠀⠴⠃⠸⠇⠀⠀⠀⠀⠠⠕⠒⠭

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢀⠄⡄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢠⡄
⠐⢖⣚⣓⠖⠀⠀⠀⠀⢶⣾⣿⣶⠆⠀⠀⠀⢈⠉⠀⠈⡡⠀⠀⠀⠠⣄⠁⠀⠒⠂⠀⠀⠀⠠⣤⠻⡤⠀⠀⠀⠀⠰⣖⠋⢓⡶⠀⠀⠀⠰⢦⠈⠀⠒
⠀⠘⠛⠛⠀⠀⠀⠀⠀⠰⠿⠻⠧⠀⠀⠀⠀⠀⠡⠤⠄⠃⠀⠀⠀⠀⢀⠤⠀⢣⠀⠀⠀⠀⠀⠛⠛⢃⠀⠀⠀⠀⠀⠺⠖⠾⠆⠀⠀⠀⠀⢠⠔⠀⢷

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢠⣄⠊⠂⣤⠄⠀⠀⠠⡆⠀⠈⠀⡦⠀⠀⠀⢤⠐⠁⠓⣠⠀⠀⠀⢰⣟⠃⠘⢻⡆⠀⠀⠀⢤⡀⠃⢤⠄⠀⠀⠀⠤⠀⠀⣀⠠⠄⠀⠀⠠⣤⠘⠑⢤
⠀⣸⠴⢮⡅⠀⠀⠀⠀⢰⡀⠀⣀⠀⠀⠀⠀⠀⣇⠤⣘⡅⠀⠀⠀⠘⢿⣤⣤⡿⠃⠀⠀⠀⠀⡤⠀⢦⠀⠀⠀⠀⠀⡁⢲⣿⡗⠀⠀⠀⠀⢨⡤⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⣀⡀⡀⠀⠀⠀⠀⣀⡠⠧⣀⡀⠀⠀⠀⣀⠴⠋⠢⢀⠀⠀⠀⢀⣀⣰⣀⠀⠀⠀⠀⢀⡠⠞⠀⠳⢆⠀⠀⠀⣀⠠⠇⠤⢤⠀⠀⠀⠀⠚⠁⠁⠙
⠀⠠⠛⢏⠀⠀⠀⠀⠀⠈⡧⢠⡍⠀⠀⠀⠀⠀⢆⣀⣰⠃⠀⠀⠀⠀⢹⣿⣷⡄⠀⠀⠀⠀⢹⠀⣀⠐⡏⠀⠀⠀⠈⠓⣠⠐⡆⠀⠀⠀⠘⢆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉

⣀⠤⠎⠣⠤⡀⠀⠀⠀⣀⣰⢧⣀⡀⠀⠀⠀⢀⣀⣾⣄⣀⠀⠀⠀⠀⠤⠎⠱⠤⠀⠀⠀⠀⣀⠀⡗⢀⡀⠀⠀⠀⣀⠠⠏⠡⢀⡀⠀⠀⠀⡀⢠⢇⣀
⠘⡆⠀⠀⡖⠁⠀⠀⠀⠙⣆⡀⣞⠁⠀⠀⠀⠈⣿⣥⣿⠋⠀⠀⠀⠈⡢⠀⠀⢔⠁⠀⠀⠀⠉⣃⠀⣍⠁⠀⠀⠀⠉⣷⢀⡀⡞⠁⠀⠀⠀⠙⢊⡺⡍
⠀⠓⠉⠑⠂⠀⠀⠀⠀⠘⠉⠈⠉⠀⠀⠀⠀⠀⠋⠁⠉⠀⠀⠀⠀⠀⠙⠋⠉⠊⠀⠀⠀⠀⠀⠉⠀⠙⠀⠀⠀⠀⠀⠛⠉⠙⠃⠀⠀⠀⠀⠘⠉⠀⠉

⠀⠀⡀⣀⠀⠀⠀⠀⠀⠐⠀⡀⠐⠀⠀⠀⠀⠀⢀⠆⢀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡰⢳⣀
⠀⠨⠀⠈⡄⠀⠀⠀⢠⠀⣻⢿⠃⡠⠀⠀⠀⠑⠄⠀⠀⠌⠀⠀⠀⠈⢫⠀⢈⡝⠁⠀⠀⠀⠘⣿⣿⡿⠃⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⠈⢣⠰⠷⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣋⢈⣠⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣭⣭⢡⡆⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣾⡇⠀⠀⠀⠀⠀⣀⣼⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⣰⣋⠸⣿⣿⣿⣿⣿⢿⣿⣿⠁⠀⠀⠀⠀⠀⠰⣿⢻⣿⣿⣿⣿⡿⣽⣿⣿⡉⠿⠿⠉⢻⣿⡇
⠀⠀⠀⠀⠀⠉⣿⠿⡏⠻⠿⢿⣿⠛⠁⣿⡆⠀⠀⠀⠀⠷⣄⠹⣆⢹⣿⢻⣵⣿⠟⢿⣿⠀⠀⠀⠀⠀⠻⠁
⠀⠀⠀⠀⡇⠀⣽⡄⢣⠀⠀⠀⠀⠉⠀⠘⠀⠀⠁⠀⡀⢠⠘⣶⡿⠿⠿⠋⠀⠟⠛⠘⣯⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⣈⠉⠁⠀⠈⢻⡀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⢀⣿⣧⣆⠀⠀⠀⠀⠀⠀⠘⠂
⠀⣤⣿⣾⡏⢛⠀⠘⢷⠀⠙⣆⢠⠀⠀⠀⠀⣼⣿⠀⠀⢀⣾⣷⡇⢹⣿⠀⢠⣾⠀⠀⣰⣄
⠀⠻⣿⣿⡿⣿⣆⠀⠀⢳⡄⢻⣿⣷⣷⡆⢸⡿⣿⣤⠀⠺⠿⢿⣿⣈⣤⣟⠀⠀⣄⢀⠁⠉⠀⢡⣄⣀⢀⠀⠀⠀⡀
⠀⠀⠈⢿⣷⡈⠛⣦⠀⢸⣷⣎⣿⡻⣿⡇⠾⢳⣿⢃⡤⠠⣠⠄⢹⣿⡏⠟⣷⠀⢻⣿⡄⡀⠰⠈⢹⣿⣟⠃⠀⠐
⠀⢠⠀⠀⠻⣿⡖⠨⣻⣮⡙⣿⣿⣧⣿⣇⡠⢻⡿⠟⠀⠈⠁⠀⠘⣿⣧⡀⢸⣧⣤⣟⠠⠄⣀⣼⡀⠛⢛⣧⠀⠀⢀
⣤⣧⣤⠤⠄⠈⠙⠿⣿⣿⡷⠚⢿⣿⣿⡯⠙⢟⠇⣴⢿⣄⢀⠤⢺⠿⢿⣇⣿⣿⣿⣿⣾⣏⡿⠟⠁⢸⡏⠐⡆⢀⣼
⠈⠉⠉⠒⠒⠦⠄⠀⠈⠻⣿⣦⠀⠙⣿⠁⢁⡸⣿⠋⢀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠁⠹⣿⣷⣶⡇⠸⣗⡆⠈⢉⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡉⠊⢿⣧⡀⠟⢻⣅⣤⣾⣿⣯⡀⠠⣤⣤⣤⣤⣤⣨⣿⣿⡆⠑⠹⣿⠋⡁⠀⢩⡅⢰⡏⢻
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣷⢀⣤⣤⠰⢿⣿⣄⣿⠀⠙⠛⠛⠛⠿⢿⣿⣿⣿⣀⢶⣸⣿⣿⠀⠈⡆⠈⠁⠂
⡿⣦⠘⣶⣶⡄⠀⠘⣷⠀⠘⠟⠻⣿⡏⣡⣼⣧⣴⣿⢻⣧⢠⡄⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣯⣽⣫⠀⠀⠈
⠀⣿⣤⡆⠙⢤⣀⠀⣸⡃⠀⠀⠀⢠⣿⣿⡟⠋⠙⢿⣿⠀⠼⣿⠶⣄⠀⠀⠀⢀⣾⣷⣿⣆⡿⣿⣿⣿⣿⣶⣦⣄⡀
⣤⣿⣿⣿⠿⣄⢈⠛⠻⣿⣳⣄⠀⠀⠈⠃⠀⠐⠒⠚⠛⠶⣇⣽⣿⣿⣗⡎⠙⣶⣿⣿⣿⡏⠁⠘⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣬⣿⣷⣄⡀⠉⠉⠀⠀⠀⢸⣀⣠⣎⡀⠀⡞⢿⢿⣿⣿⣿⠇⣆⠹⣿⣿⡿⠁⠈⣆⠀⠹⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣤⣬⣿⣿⣦⣴⣤⣴⣄⢀⣹⣍⣉⠁⠈⢠⣜⣿⡿⠟⣯⢠⣿⣆⣹⣿⣁⣀⣀⣸⣠⣴⣦⣽⣽⣿⣿
⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⠀⠈⣟⣑⢀⣤⡟⢹⣿⣿⣿⣿⣿⣿⣿⣷⡟⠏⠉⠡⠿⠿⣿
⣶⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾
⣿⣿⣤⣤⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠋⠀⠀⠀⢀⣴⣶⣄⠀⣀⣀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣷⣦⣄⠀⠀⠙⠛⠋⠁⣠⣴⣾⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣦⣤⣄⡀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢀⣠⣤⣴⣦⣤⣄
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⡿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⣿⣿⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⣀⣀⣹⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡟⠋⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠙⢻⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠐
⠀⠀⠀⠀⢀⣀⣀⠌⠀⠀⣀⣀⡀⠉⠙⠛⠿⣿⣿⣿⣟⡁⢄⠀⣾⣷⠀⠀⠀⠀⠀⠀⣾⣷⠀⡠⢊⣻⣿⣿⣿⠿⠟⠋⠉⢀⣀⣀⠀⠀⠡⣀⣀⡀
⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠂⢸⣿⡷⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⢸⣿⡇⠔⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠘⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀
⠀⠲⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠖
⠀⠀⠀⠙⠻⣿⣿⣿⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⢀⣠⣾⣷⣄⡀⠀⠀⠀⠀⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⠀⣠⣴⣿⣿⠟⠻⣿⣿⣦⣄⠀⠀⠀⠀⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⢀⣴⣾⣿⠿⠋⠀⠀⠀⠀⠙⠿⣿⣷⣦⡀⠀⠘⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢏⣠⣾⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣄⡸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢻⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠁
⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣆⡀⠀⠂⠀⣠⠀⠀⠀⠀⠀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀
⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠂⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠽⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠿
⠀⠀⠀⢰⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠈⠁⠀⠀⠀⣴⣀⡀⠀⠀⠀⠀⠀⠀⠀⢺⢿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿
⡀⠀⠀⠀⠠⠀⠀⠀⢹⡿⣿⡁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⢻⡿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⣶⠀⠀⠀⢴⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⢴⡦⠀⠀⠠⣼⣷⠄
⠀⠀⠀⠤⣽⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠃⠀⠀⠀⢀⠀⠀⠀⠰⣾⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠃
⠃⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠟⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐
⢀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠠⣦⠄⠀⠀⢸⣿⡷⠄⠀⠀⠀⢀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⢠⡦⠀⠀⠀⣻⣿⡶
⠿⡗⠀⠀⠀⠟⠻⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠃⠀⠀⠀⠸⢿⠂⠀⠀⠨⠟⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡦
⠀⠿⠆⠀⠀⠀⠀⠂⠀⠀⠛⠙⠂⠀⢴⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠀⠠⣼⣧⠄
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⡀
⡦⠀⠀⠀⠀⠈⠛⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⢲⣿⠄⠀⠀⠀⠀⠘⠃⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠹⠏⠀⠀⠀⣶
⠁⠀⠀⢀⣠⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⢀⣤⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠘⠻⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⠄⠀⠀⠀⠀⠀⠀⠚⠻⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⠀⠀⢀⣄⠀⠀⠀⢀⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠙⠀⠀⢠⣄⠀⠀⠀⢠⣄⡀
⠀⠀⠀⠀⢰⣀⡀⠀⠐⠀⠀⠀⠀⠈⠉⠀⠀⠀⠹⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⡿⠿⠄
⡦⠀⠀⠈⠝⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠈⠟⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢠⣴⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢤⣴⣄
⣴⡄⠀⠀⠐⣾⣷⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠚⠛⠏⠀⠀⠀⢠⣴⡀⠀⠀⠰⣿⣗⠀⠀⠀⠀⠀⠀⠘⠻⠁⠀⠀⠛⠻⠇
⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀
⣀⣶⣄⣀⣀⣀⣀⣀⣀⣈⣿⣿⣄⣀⣀⣄⣀⣀⣀⣀⣀⣀⣈⣀⣀⣠⣦⣀⣀⣀⣀⣀⣀⣀⣈⣿⣯⣀⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄⣀⠀⠀⢠⡅⠐⠀⠉⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠀⠀⠀⠈⠑⢤⠀⠀⠠⢊⠀⠀⠀⠀⠀⠀⠑⢄⢀⡠⣛⡆⢀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⡢⡀⠱⡀⠁⠀⠀⠀⠀⠀⠀⢀⢔⣫⣵⠊⢁⢁⠅⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠁⠀⠀⠀⠀⡀⢔⡬⠒⠉⢁⠸⠀⠈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡥⠚⠁⠀⠀⠀⢐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠈⢆⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢆⠆
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠨⢁⠊
⠀⠀⢀⠄⣒⠃⣿⣶⣤⠄⡪⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⠶⠁⠀⠀⠀⠐
⢔⣪⣿⣛⣽⡿⢞⣩⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⡀⢈⠕⠉
⠀⠈⠉⠻⣵⠚⠅⠀⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢑⠠⠂⠁
⠀⠀⠀⠀⢱⠆⣆⠠⠊⠁
⠀⠀⠀⠠⠌⠊
⠀⠀⠀⠀⠀⢠⠀⠀⡠⠠⡀⡠⡢⠀⠀⡰⠂⠀⢀⢄⠀⠀⡀⠀⢀⠐⢀⠀⠀⡀⡀⡀⢀⢀⢀⢀⠀⢀⠀⢄

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⡄⠀⢄⠋⠉⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠈⠀⠀⢉⣩⠇⠀⢘⣈⠉⠀⠀⠈⢁⡂⠄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣂⠉⠀⠀⠀⠈⢭
⠀⠀⠀⣀⠀⠀⠀⠀⠑⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠔⠁⠀⠀⣠⣄⠀⣣⠏⠀⠀⠀⠡⠤⠀⠀⠀⠈⠉⠀⠈⠂⢄⢀⢄⠀⡠⠊⠁⠀⠀⠂⠀⠀⠀⠠⠍
⠀⠀⠐⠄⠀⠐⠀⠀⢁⠁⡄⡅⠀⠀⠀⠀⠀⠀⢀⢈⠑⡀⠀⠀⠀⠀⠬⠁⢠⡌⠀⠀⠀⠀⠀⠰⡒⠀⠀⠀⠀⠀⠀⠀⠀⣿⠞⡿⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃
⠀⠀⢰⠠⠄⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠡⡤⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠑⠂⠀⠔⠒⠒⠀⠀⠀⢺⣶⡗⠀⠀⠀⠀⠀⠠⠀⠐
⠀⠀⠆⢁⠄⠀⠐⠀⡀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡄⠁⠀⠀⡸⣟⠁⠀⠀⠈⠐
⠀⠀⠁⡈⠁⠀⠁⠀⠀⣰⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠍⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⠀⠠⠂⠀⠃⠀⠐⠀⠀⠄⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢁⢠⣤⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢦⣄⡀⠀⠀⠀⠀⠀⣠⢞⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠋⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⣿⠛⣤⡀⠀⠀⢰⢿⡾⢏⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠼⡇⠀⠀⣤⢶⡦⠀⠀⠀⠀⠀⢸⡞⣿⠀⠉⣴⣦⣠⡟⡟⢀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠰⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⡀⠀⢀⡽⠁⠀⠀⠀⠀⠀⠀⣏⢸⡇⠀⠸⠁⢹⡟⢁⣤⣠⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⣀⠊⠀⠀⠀⠀⠀⠀⠀⠀⣏⣼⣇⠀⠀⣸⠏⢙⣆⠉⠛⢿⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢀⣻⡗⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⡄⢺⣧⣸⣏⡟⠠⠠⣠⣾⡿⡟⢿⡟⠀⠠⠀⠀⠀⠀⠀⠀⠰⣶⠎⠀⡀
⠀⠀⠀⠀⠀⠀⠹⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡌⣿⢺⡯⣾⠤⢢⡤⠶⠛⢻⣄⢹⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢤⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢼⡇⢟⣿⣏⠐⠇⡠⠋⡠⠴⠶⠾⠉⠁⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠁⠀⠀⠳⢯⣷⠋⢙⣦⡤⠀⠀⠴⠍⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠺⡙⡆
⠀⠀⢠⡤⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡛⢯⡳⢤⡄
⠀⠀⢸⡧⢼⠅⠛⢱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⣄⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢧⡙⠀⢁⢸⡇
⠀⠀⠀⢱⠂⢘⠒⠄⠸⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠚⢨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠛⣯⢈⣿⠑⠀⠀⠀⠀⠀⣠⠞⠻⢇⢠⡍⠁⠈⣾⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⡠⣪⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠉⠁⠀⢀⢀⣤⣴⡛⠃⠀⣀⠀⠀⠼⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠈⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⢾⡭⠗⠉⢀⣷⡀⠀⠉⠀⠀⡶⣀⡈
⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⣀⡌⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡴⠋⠛⢷⡀⠀⠠⠲⠻⢷⠀⠀⣾⡟⠀⠀⠀⠈⠉⠀⠠⠄⡀⠀⠂⢠⠇
⠀⣠⠔⠈⠉⢤⠀⠀⠈⠉⠒⣷⡛⣇⠀⠀⠀⠈⠀⠈⠀⠠⠀⠀⠀⠀⡀⠀⠰⠄⠀⢻⠀⡀⠚⠀⠃⠀⠀⠻⢿⣤⠀⠀⠀⠀⣀⣀⣤⣅⡥⣤⣿⡀
⠀⠳⣀⠀⠀⠈⠀⠀⠀⠀⠐⢿⣷⣿⡀⠀⠀⠁⡠⠀⠀⠀⠀⠀⠰⠀⠀⠘⠧⠀⠀⠈⠇⠁⠀⠀⠀⠀⡔⣰⡋⠀⠀⠐⠀⠀⣀⠠⡔⠚⣁⣹⠋⠉
⠀⠀⠈⠑⢂⠀⠀⠀⠀⠐⠀⠈⠉⠻⡌⠀⠀⠀⠀⠀⢀⠈⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⣠⠀⠁⠀⠀⠀⠉⠒⢙⡤⠀⠀⠈⠉⠁⠀⠹⣦⡞⠁
⠀⠀⠀⠀⠀⠁⡏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠆⠀⠒⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡴⣿⠄⠀⠀⠀⠀⠀⠀⠈⡓⠀⠀⠰⠀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠠⠤⠤⠍⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣠⣤⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠛⠛⠛⠛⠻⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⠛⠛⠛⠛⠻⠷⣶⣄⡀
⠀⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣄
⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣾⣄
⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣇⣶⣶⡀
⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣿⣿⣷⣿⣯⣥⠄
⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡾⠽⢿⣿⣿⣥⠄
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄⠀⣀⣹⣶⣦⣿⣿⣿⣟⡥
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣐⣾⡞⠁⢹⣿⣿⣿⣯⢾⠏
⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣩⠴⢿⣾⠞⣯⢻⣸⣧⣯⣤⠄
⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⢤⣰⣿⢻⣀⣰⣿⣋⠙⣿⣿⢿⣿⡿⠆
⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⢁⣏⣓⣿⣿⣿⣿⠛⢾⡿⠴⣿⠋⣩⠽⣇
⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠳⢾⣍⡿⠛⢿⣽⣿⣌⣿⡛⠙⣧⣾⣷⣤⠈
⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣤⣴⡷⢋⣹⣯⡤⠿⢶⠤⣿⡙⠛⣿⢧⢞⣙⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣯⡏⣸⣿⡁⡞⢽⠳⡍⢳⣸⡄⢸⡝⢦⢸⣟⣉⠉⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⠻⣿⣴⠻⣄⡙⣷⣮⠷⢛⡫⠋⡇⢸⠀⢨⢿⡁⣠⣾⡅⣩⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⡏⠙⠒⡾⠻⣄⠈⠫⣭⣭⣟⣋⡤⣾⣴⠋⡰⠋⢀⣿⢁⣀⢻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⡞⢆⢀⡄⣈⠉⢳⣙⣤⣹⣇⠀⢻⡓⠲⠾⠶⠤⠴⠚⢁⡼⠋⢀⣤⠿⣿⠈⣉⣠⣽⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠶⣷⣿⣸⣇⣿⢶⣋⣉⠤⢬⡟⠓⣤⣉⣓⣲⣶⡦⠴⠒⠛⢒⣫⢿⣯⣅⠘⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡀⠒⠶⢿⣿⣿⡛⠛⢉⢩⣿⡿⠂⢲⠞⢳⠤⠽⠓⢤⣤⣤⣔⣋⣁⣀⣁⣈⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣉⠛⣹⠿⣿⠗⣺⣿⢻⡇⠀⠉⠀⣀⣠⠴⣾⡉⠉⠗⣨⠏⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⣰⠃⢈⡵⢿⣨⡷⠛⢛⣯⠤⠶⠛⠁⠉⠳⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡾⠋⠀⠘⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠑⢆⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⠎⠀⠀⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠝⠂⡎⠀⢑⠀⠐⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠒⠊⢠⠤⠴⠃⠀⠀⢀⡀⠐⠃⢀⠔⠁⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠚⢄⣀⡰⠀⠀⠀⣀⠠⠤⢀⣐⡦⣎⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⢧⠈⢦⣀⣀⡤⠶⣁
⠀⠀⠀⠀⡰⠋⠀⠁⠀⠈⠑⡄⠀⢰⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢐⡝⢦⠈⣦⠀⠀⠀⠀⢣
⠀⠀⠀⠀⢇⠀⠀⠄⠀⠁⠀⠼⠀⢸⣀⠔⠒⠂⠀⠀⠀⠈⠒⠤⠤⠖⠋⠀⠈⠱⢴⠢⠤⠤⠤⠊
⠀⠀⠀⠀⢘⣄⠀⠀⠠⠀⠀⢠⠟⢹⠃⣀⣀⣀⣀⠀⠀⠀⠀⠀⠸⡀⠀⠀⡠⠃
⠀⠀⠀⡔⠉⠈⠓⢄⣀⣀⡔⠁⢠⠟⠩⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠑⠂⠊⠁
⠀⠀⠀⢣⠀⠀⠀⠀⢀⡞⠀⣰⡏⢀⠀⠀⠀⡀⠀⠠⠉⡄
⠀⠀⠀⠀⠑⠒⠬⠔⢾⣠⡞⠑⠘⢆⡀⠀⠀⠀⠀⠐⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢧⠀⠀⠀⠈⠙⡖⠓⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⣀⣠⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⣸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⠀⠰⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢡⡃
⠀⠀⠀⠀⠰⣿⡏⢛⣿⠏⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠀⡐⠀⠀⠀⠀⢼⠁
⠀⠀⠀⠀⠀⠿⠟⠿⢿⠀⠀⠀⠀⠀⡺⠀⢀⠘⠀⠀⢠⡆⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠠⠀⠈⠐⠀⠀⠀⠀⠀⠸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠏⠀⠀⠈⠁⠀⠀⣼⠗⠀⠀⠀⠀⠀⡸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢧
⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢀⡀⠄⡀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠉⠀⠀⠀⠀⠀⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡘⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠂⠀⠠⡀⠀⠀⠀⠀⢰⣳⠄⠀⠀⠘⣧⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⣆⠄⠀⠐⠃⠀⠀⠀⠀⠀⡄⠁⠁⠠⠀⠀⠈⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⣤⠀⠀⠀⢠⠇⠀⠀⠀⠘⠁
⠀⠀⠀⠓⠞⠂⠀⠀⠀⠀⠀⠀⠄⠄⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⠀⠀⠀⠀⣤⠀⠐⠀⠘⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⡀⣤⠄⠀⠀⠀⠀⠚⠄⠈⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠉
⠀⠀⣠⡄⠀⠁⡀⠰⠆⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⣠⣆⠀⠀⠀⠀⢀⡄⠀⠀⠂⠀⠀⠀⠀⠘⠡⡀⢠⠀⢀⡀
⠀⠶⠈⠘⠳⠆⠀⢴⢄⢰⠆⠀⠀⠀⠠⠀⡆⢀⠀⠀⠀⠐⠛⡟⠉⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠴⠀⠀⠈⡆⡀⠂⠁
⠀⠀⢤⠑⢂⠀⡁⠀⣝⢁⠰⠆⠀⠈⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠑⠆⣠⠁⠀⣀
⠀⠀⠀⠀⠐⠆⠡⡀⠡⠀⠦⠀⠀⠀⠉⠉⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣄⣠⠏⠁⠀⠀⠖⡀⠀⠠⡁⠄⠂⠉
⠀⠀⣘⠃⠛⠐⠖⠀⡀⠴⠆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠢⣘⠀⠀⠀⠀⡸
⠀⠀⠈⠀⣤⠁⠀⠀⠈⠂⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡄⠀⠀⠀⠀⣘⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠠⠁⠀⠀⠀⢹⣋⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⢀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⣿⠛⣻⣇⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠾⠀⠀⠀⠁⠀⠀⠀⠄⢯⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢿⡞⠋⠁⠀⠀⠉⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⢀⣀⠀⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣩⠶⡀⠰⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠆⠀⠀⠀⠀⡄⠀⠂⠀⠀⠀⠀⠀⡴⠀⠈⠐⣀⣧⢞⠁⢠⠀⠀⢀⠠⠀⠀⠄⠚⢢⡄⠊⠉⠹⡄
⠀⡲⠐⠄⡀⠀⢀⣼⣗⠇⠈⠀⠀⠈⠀⠀⢧⠀⢀⢸⠏⠜⢈⣶⡋⠈⠓⠀⠀⣠⠞⠀⠀⠀⡁⠀⠀⢠⢃⠄
⠀⠸⡂⠬⣟⣴⡯⠦⠯⠋⠀⠀⠀⠀⠀⠂⠈⠿⣿⣴⣮⠜⠉⠜⢁⠠⠀⠀⠀⠘⢄⡢⣀⠢⠁⣀⣀⡜⠁
⠀⠀⠄⠀⡐⡿⠗⠀⠀⠤⠀⠀⠀⠀⠀⢀⡴⠚⢹⠋⠟⣛⣿⢣⡀⠀⠀⠀⠀⠀⠀⣉⡻⠛⢻⠛⠓⡀
⠀⠀⠀⠈⠁⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠜⠀⠀⠀⠈⡆⠀⠉
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠐⠆⠠⠀⠀⠀⡄⠀⠀⠀⠀⡠⡁⠡⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈⠁⠐⠂⢃⠰⠆⢠⠂⠋⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡁⠀⠎⡀⠠⠆⠀⣀⠀⠀⠀⠀⠀⠄⡀⠄⠀⠈⠄⠀⠃
⠀⠀⠀⠀⠀⠁⢀⢀⠀⠀⠀⠀⠀⠈⠁⢦⡀⠓⠸⡀⠤⠔⠁⠀⠉⣁⠀⢀⠀⠀⠀⠀⠋⠀⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢠⠀⠙⢶⠀⠁⠂⡴⠒⢋⠀⠀⣀⠠⠀⠀⠀⢀⡠⠠⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⡀⠁⠀⡀⠀⠀⡀⠀⠀⢁⠠⠄
⠀⠀⠀⠀⠀⠐⠿⠄⠀⡀⠀⠀⠀⠂⠀⠀⠈⠀⠈⠀⠒⠀⠈⠁⠀⠀⠁⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠁⠀⠐⠲⠀⢈⣊⣉⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠐⠀⠀⠁⢀⠄⠀⠀⠀⠀⠀⠃⠀⠀⠉⠃⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠀⠀⠀⠀⡏⡀⡀⠀⠀⠄⠃
⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠀⢀⡀⠀⢤⠆
⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠘⢅⠢⠌⠻⡖⠀⡦⠮⡀
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⡀⠈⠂⠀⠀⠈⠑⠢⡌⠉⠐⢲⠮⡶⣄
⠀⠀⠀⠀⠀⠈⠀⠁⢐⡄⠀⠄⠀⠀⠀⠀⠐⠃⠀⠑⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢣⠀⠀⠄⢆⠈⠊⢁⠠⣄
⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡀⣀⠹⡄⠀⠀⠙⠋
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠆⠀⢠⡀⠈⢀⠀⠀⠀⠀⢀⡀
⠀⡴⢉⣌⠱⣄⣀⣀⣀⣀⣀⣰⣉⣦⣄⣀⣀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⣀⠀⢄⠘⠂⠐⠂⣢⡅⠱⡀
⠀⢳⣌⠛⢿⡇⢰⢦⢹⡇⣴⣸⠀⡇⢠⢦⢸⠃⣴⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠒⠃
⠀⢯⡙⠛⣠⡇⢘⢊⣸⣃⡇⢸⣀⣇⣸⣸⢸⣆⣙⡁⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠉⠉⠁⣇⣸⠉⠀⠉⠀⠀⠉⠈⠁⠈⠉⢧⣙⣡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⠔⠒

⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡄⠀⠀⣸⡐⠀⠀⠤⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠘⠀⠀⠀⠈⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⠂⡀
⡀⠀⠀⠠⠃⠓⠀⠀⠀⠀⠀⣄⠀⠀⡄⠐⠀⠀⠰⠠
⠀⠀⠀⠀⡄⠀⠀⡄⠀⠐⠄⢠⠄⠀⠀⡀⠀⠀⠠⠀⠀⠴
⠈⠀⠀⠀⠁⢠⠚⠀⢀⠀⠀⠀⠀⡆⠀⠁⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⢀
⠈⠀⠀⠀⠀⠘⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣶⣶⣀⣀⣀⣀⣀⣀⣴⡶⣦⣄⠢⠀⠀⠀⠀⠘
⣤⣄⣀⣀⣠⠿⠶⠒⠒⠊⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠘⠛⠷⢶⣴⣶⣾⠗⠲⢷⣤⣀
⠀⠉⠉⠉⠑⠒⠶⠶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠛⠶⣶⣄⣀⡉⠹⣷⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⣿⡿⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⡀⣀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢀⡀⣠⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⢠⣿⡿⠦⠀⠀⠈⠀⠀⠀⠀⠸⠃⠀⠀⠀⢀⠀⠀⠀⢠⣿⡿⠦⠀⠀⠈⠀⠀⠀⠀⠸⠇⠀⠀⠀⢀
⠀⠀⠀⠁⠀⠀⠀⠀⢤⣦⠄⠀⠀⠀⠀⢘⣶⣿⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⢤⣦⠄⠀⠀⠀⠀⢘⣶⣿⡄
⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠀⠀⠈⠉⠏⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⠀⠀⠈⠉⠋
⠀⠈⠛⠂⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠚⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣤⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣾⣤⡀⠀⠀⠀⠉
⠀⠀⣀⣷⣶⠁⠀⠀⠀⠚⠛⠇⠀⠀⡀⠀⠀⠀⠴⠀⠀⠀⣠⣷⣶⠁⠀⠀⠀⠚⠛⠇⠀⠀⡀⠀⠀⠀⠴
⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠹⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⡷⠀⠀⢀⣀⠀⠀⠐⢾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⠀⠀⢀⣀⠀⠀⠐⢾⣿⡟
⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠀⠁⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠀⠁
⠀⢀⡀⣀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢀⡀⣠⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⢠⣿⡿⠦⠀⠀⠈⠀⠀⠀⠀⠸⠃⠀⠀⠀⢀⠀⠀⠀⢠⣿⡿⠦⠀⠀⠈⠀⠀⠀⠀⠸⠇⠀⠀⠀⢀
⠀⠀⠀⠁⠀⠀⠀⠀⢤⣦⠄⠀⠀⠀⠀⢘⣶⣿⡄⠀⠀⠀⠀⠃⠀⠀⠀⠀⢤⣦⠄⠀⠀⠀⠀⢘⣶⣿⡄
⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⠀⠀⠈⠉⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⠀⠀⠈⠉⠋
⠀⠈⠛⠂⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣾⣤⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣾⣤⡀⠀⠀⠀⠉
⠀⠀⣀⣷⣶⠁⠀⠀⠀⠚⠛⠇⠀⠀⡀⠀⠀⠀⠴⠀⠀⠀⣀⣷⣶⠁⠀⠀⠀⠚⠛⠇⠀⠀⡀⠀⠀⠀⠴
⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠹⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⡷⠀⠀⠀⣀⠀⠀⠐⢾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⠀⠀⠀⣀⠀⠀⠐⢾⣿⡟
⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠀⠁⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢆⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠱⡈⢾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠑⡄⢻⡀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⣄⠀⠑⠄⠹⡘⣇⠀⢀⡷⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢤⣄⠢⡱⣽⣆⠸⣇⣀⣠⣄⢨⠇⢀⣀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣬⣿⣿⣷⣏⡉⠻⢿⣿⣶⡁
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣶⣶⣆⡀⠀⢈⣿⣿⣿⣿⣿⣦⡀⠹⣿⠇
⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠉⢉⣀⣨⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⠺⠿⠿⠛⠲⠦⡄
⠀⠀⠀⠀⠀⠀⠀⣠⣠⡴⠞⠛⢩⣿⠁⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣽⡷⣦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⢠⣿⣿⣦⠀⠀⠀⠀⠉⠿⣿⣿⣿⠿⠋⠻⣿⡲⢍⣻⠻⠏⠍⡙⠻⠟⢛⢒⠢⡀
⠀⠀⣀⡤⠚⠙⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠈⣿⣿⣦⠀⠀⠘⠀⠀⢈⠁⠀⠀⠉⠉⢁⠀⠀⢨⠟
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⣿⣿⣿⣿⣷⣶⣤⣠⣽⡆⠻⣿⠇⠀⠀⠀⠂⠙⢶⡦⣤⣀⡠⠨⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠀⠙⢿⣿⣿⣿⣿⡿⠋⣿⠇⢸⡿⠀⠀⠀⠐⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠲⠼⠿⠛⠉⢀⣼⡟⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⠟⠁⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢤⣄⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⣏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢦⡘⢶⡿⢈⣷⣫⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣿⣿⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⣾⣆⠃⠋
⠀⠀⠀⢠⣴⣶⣶⣶⣾⣶⣦⣸⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠙⠶⠚⠀⠀⠀⠀⠀⠀⠀⣀⠛⠶⠟⠀⠀⠀⠀⠀⠀⢲⣤⡀⠀⣥⣭⣿⡆⠺⠟⠁
⠀⠀⠀⢼⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣄⠘⠻⢋⢻⣷⣶⠆
⠀⠀⠀⢾⣿⣸⣿⣿⣿⣿⣃⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⢰⣿⣿⣿⠟
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠙⢿⡿⡾⠿⠛⠁
⠀⠀⢰⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠓⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢿⣿⣿⣆⠀⠘⢀⣐⣒⢢⣄⡀
⠀⠀⠀⠙⠺⣬⣿⣿⣿⠟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣾⡟⢿⣿⣠⣴⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⣦⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣭⣿⡟⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡿⣏⡿⣿⣿⣿⣒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⣿⠃⣴⠀⠀⠀⢀⣴⣤⣄⠀⠀⠀⠀⠀⠘⣿⣿⠋⠀⡜⢿⣿⠟
⠀⠀⠀⠀⠠⣤⡀⠀⢀⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠓⠀⢸⡿⠀⠀⠀⠹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⡀⠈⠁
⠀⠀⠀⠀⠀⢿⣿⣷⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣾⠁⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠻⠿⢧⠄⠀⠀⠀⣾⣤⠀⠁⠀⠀⠀⠀⢀⣿⣿⠿⠃⢸⣿⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡄
⠀⠀⠀⠀⠀⢤⣤⣶⡚⣠⣶⠀⣠⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠈⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⣾⣿⣿⣿
⠀⠀⠀⢴⣦⡈⢻⣿⣿⡟⠁⠈⠁⢠⡜⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⣿⣿⣿⡿⠀⠀⠀⢠⣼
⠀⠀⠀⠸⣿⣿⡄⠈⠛⢿⠟⠃⢤⣜⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡟⣿⣿⣿⣿⠇⢠⢀⣴⠿⡟
⠀⠀⠀⠈⢻⣿⣿⡏⢀⣰⣾⣆⡰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠈⣿⣿⣿⣿⠟⢀⣼⣿⡿⠞
⠀⠀⠀⣀⣼⣿⣿⣷⡀⠈⠉⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⢄⠹⣌⠛⢃⣴⣤⣤⣤
⠀⠀⠀⠉⠻⢿⣿⣿⣇⠀⢀⣴⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠂⠉⠁⠈⢉⣥⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠠⠼⠿⠂⢸⣿⣿⣿⣿⡿⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠻⠛⠀⠠⠀⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠿⠿⠟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣄⠀⠀⣠⡶⠆⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⡉⠉⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠈⠀⠘⢿⡇

⠀⠀⢼⡿⠄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡿⠃
⢀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀
⠻⠂⠀⠀⠀⠀⣲⣿⡥⠀⠀⠀⠀⠀⠀⢰⡦⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠐⢿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠁⠀⠀⠀⣄⣠⠀⠀⠐⠀⠠⣴⣄⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠐⢻⠟⠂⠀⠀⠀⠐⠛⠃⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠠⣶
⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢿⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠀⠀⠀⠀⠀⠀⠘⠗⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟
⠀⢠⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⡧⠀⠀⠀⠀⠀⣺⣷⡥⠀⠀⠀⠀⢀⣠⡄
⣶⡇⠀⠀⠀⠀⠀⠀⠄⢠⣷⣇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠄⠀⠀⠘⠻⠋
⠛⠉⠀⠀⠀⠀⠀⠃⠀⠉⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠆⠀⠀⠀⠀⣽⣯⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠋
⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣄⠄⠀⠀⠀⠀⠀⠀⢀
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠜⡿⠏⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢀⢀⠀⠐⠂⠀⠁⠀⢀⣄⠀⠀⠀⠀⠀⠚⠟⠃⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⢠⣀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢠⠏
⠀⠀⠀⣀⡤⠤⠤⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣹⡶⠒⠒⢶⣏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⣤⣀
⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⡀⠀⢀⡞⠁⠀⠀⠀⠀⠈⢳⡀⠀⢀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢾⡀⠀⢀⣀⣀⡀⠀⢀⡷⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⢛⣿⣁⣀⣀⣈⣻⡛⠶⢦⣤⣀⣀⠀⠀⠀⠀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⡽⠛⠋⠉⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠉⠙⠛⢯⡉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢀⡞⣀⣀⣀⣀⣀⣀⣀⣀⣳⡀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⢀⡴⢿⣿⣿⣿⡿⡿⠿⢿⣿⣿⣿⡿⢦⡀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠘⣇⣀⣀⣀⣀⣀⣀⣀⣀⣸⠃⠀⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠿⠿⠿⠿⠿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣹⣿⡟⠉⠀⠀⠀⠀⠀⣄⣠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠿⠛⠁⠀⠀⠀⠀⣹⣿⡟⠉⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠿⠛⠁
⠉⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠾⣿⣿⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠠⣤⣤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡼⢿⣿⠁⠀⠀⠀⢠⣴⣦⡄⠀⠀⠀⠀⠠⣤⣤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡼⢿⣿⠁⠀⠀⠀⢠⣴⣦⡄
⠀⠀⠴⠿⣿⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⠛⠁⠀⠀⠀⠀⠴⠿⣿⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⠛⠁
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠂⠀⠀⠀⠀⣤⣼⣧⣤⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠂⠀⠀⠀⠀⣤⣼⣧⣄⠀⠀⠀⠀⢠⣤
⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠻⠿⠁⠀⠀⠀⠀⠀⡿⣿⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠻⠿⠁⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠘⣿⣿⠆⠀⠀⠀⠀⢠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠆⠀⠀⠀⠀⢠⣴⣦⡀
⣴⣦⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠰⠟⠻⠁⠀⠀⠀⠀⣤⣼⣇⡀⠀⠀⠀⢠⣴⣦⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠰⠟⠻⠁⠀⠀⠀⠀⣤⣼⣇⡀
⠛⠏⠀⠀⠀⠀⠀⠀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⠋⠁⠀⠀⠀⠚⠛⠏⠀⠀⠀⠀⠀⠀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⠋⠁
⠀⠀⠀⡀⠀⠀⠀⠰⠿⣿⠷⠆⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⠷⠆⠀⠀⠀⠀⣤
⠀⢤⣾⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⠂⠀⠀⠀⢠⣤⣶⠀⠀⠀⠀⢤⣾⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⠂⠀⠀⠀⢠⣤⣶
⠀⠀⠿⠛⠓⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠰⠿⣿⠃⠀⠀⠀⠀⠿⠛⠓⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠘⠿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠁⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠁⠀⠀⠀⢀⣄
⣀⣴⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⢿⣿⡃⠀⠀⠀⠠⣤⣦⣀⠀⠀⠀⢀⣀⣴⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣿⣿⡃⠀⠀⠀⠀⣤⣦⣀
⣹⣿⡟⠉⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠿⠛⠁⠀⠀⠀⠀⣽⣿⡟⠋⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠿⠛⠁
⠉⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠾⣿⣿⠀⠀⠀⠀⣀⣠⡄
⠀⠀⠠⣤⣴⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡼⢿⣿⠁⠀⠀⠀⢠⣴⣦⡄⠀⠀⠀⠀⠠⣤⣴⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡼⢿⣿⠁⠀⠀⠀⢠⣴⣦⡄
⠀⠀⠴⠿⣿⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⠛⠁⠀⠀⠀⠀⠴⠿⣿⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠂⠀⠀⠀⠀⣠⣴⣷⣄⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠂⠀⠀⠀⠀⣠⣴⣧⣀⠀⠀⠀⠀⢠⣠
⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠿⠁⠀⠀⠀⠀⠀⡿⣿⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠿⠁⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠘⣿⣿⠆⠀⠀⠀⠀⢠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠆⠀⠀⠀⠀⢠⣴⣦⡀
⣶⣦⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠰⠟⠻⠁⠀⠀⠀⠀⣤⣼⣇⡀⠀⠀⠀⢰⣶⣦⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠰⠟⠻⠁⠀⠀⠀⠀⣤⣼⣇⡀
⠛⠏⠀⠀⠀⠀⠀⠀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⠛⠁⠀⠀⠀⠚⠛⠏⠀⠀⠀⠀⠀⠀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠿⡿⠷⠆⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠿⡿⠷⠆⠀⠀⠀⠀⣤
⠀⢤⣾⣷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⠂⠀⠀⠀⢠⣤⣶⠀⠀⠀⠀⢤⣾⣷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⠂⠀⠀⠀⢠⣤⣶
⠀⠀⠿⠛⠓⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠋⠁⠉⠀⠀⠀⠀⠰⠿⣿⠃⠀⠀⠀⠀⠿⠛⠓⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠐⠿⣿⠓
⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠁⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⢀⣄
⣀⣴⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣿⣿⡃⠀⠀⠀⠠⣤⣦⣀⠀⠀⠀⢀⣀⣴⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣿⣿⡃⠀⠀⠀⠠⣤⣦⣀

⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠎⠀⠴⣾⣿⣿⡇⠈⠃⠉⠛⠂⠀⠀⠂⠀⠀⠀⠰⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠤⠒⠚⣸⣿⣿⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠈⡇⠀⠀⢀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡿⠋⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼
⠀⣀⠔⠂⠀⠦⢄⠀⠀⠀⠀⠀⢀⣠⠤⠄⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠠⡀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⡄⢀⣾⡟
⠴⠁⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠈⠙⢂⣀⣀⣀⡀⢀⡠⠐⠒⠦⢄⠀⠀⠀⠑⠇⡀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣤⣾⡿⠋
⠆⠤⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢡⠀⠀⡀⠀⠐⢄⣀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⢤⣶⣶⣼⣷⣷⣤⣾⣿⣿⣿⠖⠈
⠀⠀⠀⠀⠠⠀⠀⠐⠠⠀⠄⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⢳⡎⠀⠁⠈⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠉⠉⠹⠛⢛⣟⣿⣿⣿⣷⣶⣖
⣦⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠎⢳⠀⠀⠀⠀⣠⠤⠀⠠⠤⢺⣿⣿⠘⠻⠟⠿
⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠊⠁⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣆⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠄⠀⠀⠀⠀⠀⠀⡘⠁
⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠹⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣻⣷⡀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣤⡄
⠀⠀⠀⠈⠀⣦⢄⡀⣀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣤⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠐
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠤⠱⠶⣦⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⣿⣿⡇⠀⣾⡇⠀⢀⠔⠀⡠⠊⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠢⣀⣀⣀⠀⠉⠙⢿⣿⣿⣇⢰⣿⣷⣾⣿⡵⠄⠀⠀⠀⠀⠀⠀⠀⡚⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠘⠛⠛⠛⢻⣿⣾⣿⡿⢿⡅⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠂⠸⡄⠀⠀⡼⠀⠀⣠⡄
⠀⣠⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠁⠈⠁
⠀⠠⢀⣸⣆⠀⠀⠀⠀⠀⢉⡂⠀⡀⠀⠀⠀⠀⠀⠀⠠⠶⠒⣈⡽⠟⠉⠉⠻⣧⠀⠉⠀⠀⠀⠶⠤⢄⠀⢀⠌⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣠⠂
⠀⠀⠀⠀⠹⠞⠀⢀⠂⠀⠀⠀⠀⠀⠀⠐⠢⠤⠤⠴⢒⢀⠝⠉⠡⠚⠐⠆⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠂⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢠⠀⠀⠀⠀⠀⠀⣠⣄⡀⢸⠀⠀⠀⠀⠀⢀
⠀⣀⠀⠀⠀⠀⠀⠀⠐⠆⢀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠋⠉⠉⠻⢟⢿⣇⣠⡀⡀⠀⠀⠀⠀⠐
⠊⠁⠀⠀⠀⢀⠀⠀⢀⠈⠈⠲⠤⢶⡀⠀⣀⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡄⠀⠀⢀⠀⢠⠀⠀⢀⣴
⠀⠀⠀⠀⡤⣈⣀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⢳⣇⠀⢸⣧⣤⣤⣶⡿⠛
⣀⠀⠀⠀⡎⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠹⣆⣧⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⠿⠿⠛⠂
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡄⠀⡌⠀⠀⠀⢀⣴⣾⡥⠂⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢿⣍⠀⠀⠀⠐⠊
⠀⠀⠀⣀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⠀⠀⠀⠤⣄⡀⠀⠀⠀⣹⣿⣿⣄⣄⡆⠀⣴⣾⣿⠯⢀⡄⠀⠂⠐⠀⠀⠲⠀⠠⠁⠈⠀⠈⠳⣍⡀⠒⠒
⠒⠠⢀⠀⠀⠀⠁⠀⠀⠢⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠙⢿⣿⡏⠃⢠⣿⣿⣯⠖⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠉⠐
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣷⣶⡅⣤⠛⠲⣹⣿⣣⠄⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠆⠀⠀⠀⠐⠚⠋⠉⠁⠘⠞⠛⠙⠋⢻⡿⢿⠅⣀⣶⠋⣵⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠀⠀⠀⠀⠀⠀⢴⡄⠀⠀⠠
⠀⠀⠀⠀⠉⠀⠀⠂⠀⠀⠽⡗⠀⠀⠐⠀⠀⢀⣀⠀⠀⠀⠲⠆⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⣀⠀⠀⢰⡄⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⣷⠇⠀⠠⠀⠀⡀⠀⢠⠀⠀⠀⠀⣤⣀
⠀⠀⠂⠀⠀⠉⠀⠀⠀⠀⠀⢠⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠁
⠄⠀⠀⠰⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠃⠀⠂⠀⠀⠀⠀⠀⠀⢺⣷⠀⠀⠀⣠⡄⠀⠀⢀⡀⠀⠀⠸⠗⠀⠀⠀⠂⠀⠀⠀⠐
⠀⣤⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⢰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⠃⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠂⠀⠀⠸⠇⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠐
⢰⠄⠀⠀⠂⠀⠀⢀⠀⠀⣰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⠀⠀⠠⠄⠀⠁⠀⠀⠀⠀⠐⠷⠀⠀⠀⠀⠂⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠿⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⢠⡄
⢠⠄⠀⠁⠀⠀⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢷⡧⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠄⠀⠀⠀⠀⠀⢰⣴⡄
⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠉⠀⠀⠀⡄⠀⠀⠀⠶⠀⠀⠀⢀⡀⠀⠀⠀⠂⠀⠀⠀⠈
⢀⠀⠀⠈⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⣠⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⣰⣦⠄⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠃⠀⠀⠆⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠆⠀⠀⠛⠀⠀⠀⠰⠀⠀⠀⠀⠆
⠀⠘⠿⠅⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⡀⠀⠀⠂⠀⠀⠛⠀⠀⠀⠀⠀⠐
⠀⠈⠀⠀⠀⠘⠃⠀⠀⠀⠋⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠙⠃⠀⠀⡀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠂⠀⠄⠀⠀⠰⠆
⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣠⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⡀⠀⠰⠆⠀⠀⢀⡀
⠙⠃⠀⠠⠀⠀⠁⠀⠀⠀⠛⠃⠀⠀⠠⡄⠀⠀⠀⣠⡤⠀⠀⠀⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣠⡤⠤⣤⡀⣀⡀⣶⣤⣤⣄
⠀⠀⠀⠀⠀⢠⡞⢸⡟⠀⣿⠁⢸⡏⠐⢻⣿⣿⣿⣿⣿⣿⣴⣦⡀
⠀⠀⠀⠀⢰⣾⡇⢸⣧⠀⣿⡀⠸⡇⠘⣿⣿⣿⣿⣿⣿⣯⣿⣿⡿
⠀⠀⠀⠀⠀⠈⠻⠀⢿⡗⣩⡥⢤⣻⠄⢨⠟⠳⢿⣿⢿⣿⠃⠈
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠈⠳⡀⠀⠙⠀⠹⡗⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⡀
⠀⠀⠀⠀⢀⡠⠶⠋⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠔⠂⠀⠁⠀⠀⠀⠀⠀⣴⣿⣿⣯⡿⡷⠄⡀⡐⠒⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⣤⣿⣿⣿⣷⣿⣿⣻⣿⠀⢠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⢿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣾⣿⠁⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠐⠚⡿⣿⡿⠁⠹⡟⠋⠀⣿⠈⠛⣽⢿⡿⠟⠋⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠔⠁⠀⠀⠀⠁⢈⡇⠀⠀⠈⠃⠐⠁⠀⠀⣠⣾⣿⣶⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⣿⣿⣿⣿⡿⣇⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣠⡾⠃⠀⣬⣤⣤⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⣾⣿⣟⣿⣿⣟⢼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠘⢿⣭⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼⣿⡋⠀⢸⣼⡧⠊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣽⢿⣿⠻⣿⣿⢏⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⣍⡛⠛⣋⣭⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣴⣧⣌⠉⠛⠛⠛⣩⡌⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡿⠁⢮⣙⠛⠶⠶⢟⡯⢳⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣝⡛⠓⣛⡋⠁⠘⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⠏⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡁⢰⠠⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠀⢀⡀⠀⠀⠀⠀⠀⠠⡐⢄⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠐⡁⡱⠀⠀⡇⠀⠀⠀⠀⠀⠈⠐⢸⢔⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⣀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⡠⢠⠀⠠⠀⠀⠀⠠⢚⡠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⠀⠀⠀⠠⠈⠢⠀⢀⠀⡇⠀⠔⠂⢰⡠⠠⠀⠐⠁⠀⠀⢀⠀⠀⢓⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠐⢄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠂⢇⡂⢄⠀⠀⠀⡀⢀⠄⠐⠁⠘⠀⠀⠀⢠⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠠⠀⡄⠀⠀⠀⡠⠈⢠⠤⠀⢣⢸⠀⠀⢀⡔⠑⠄⠡⠀⢣⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠑⣥⠀⠀⡐⠀⠰⠀⠑⠐⠊⢾⠀⣠⠊⠀⠀⠀⠀⠀⠀⡄⠀⡘⠀⠠⢂⠍⠀⠀⠀⠀⠠⠉
⠀⠀⠀⠀⠀⠀⠨⠔⣐⠒⠠⢀⣀⠀⠀⠀⠈⡄⠰⠀⢀⠄⠀⠀⠀⠀⢸⡔⠁⠀⠀⢀⠄⡄⠀⠀⠁⢠⠁⠔⡠⠂⡠⠢⡄⠀⡠⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠘⠼⢴⣙⠈⡐⠀⠀⠀⠀⠸⡀⡠⠂⠀⠄⡀⢀⠀⠀⠀⠀⠈⢀⠢⢂⣀⠀⠀⠀⣌⠈⣐⢠⣾⣦⡀⣇⠔⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢⢠⠐⢦⠐⢅⠂⠄⡀⢣⠀⠀⠀⠑⢈⣄⡄⠀⡇⠀⠀⡡⠂⠂⠒⠁⠀⣸⠇⡐⡃⣠⠀⣁⠘⠿⢆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢁⠀⠀⠳⡀⠑⠠⡈⠐⣆⠀⠀⠐⠥⠊⠈⢢⡇⢀⠞⠀⠀⠀⠀⠀⢀⡿⠐⢀⡀⠀⠒⡠⠃⠀⣨⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠐⢄⠱⡀⠀⠈⠀⠈⡄⠀⠀⠀⠀⠀⠀⢣⠊⠀⠀⠀⠀⠀⠀⠈⡏⠀⠠⠈⡄⡰⠁⠀⠐⠙⠙⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢱⡀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠑⢸⠁⠀⠀⠄⠴⡀⠒⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⣁⠀⠈⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣙⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣦⠤⣄⣀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⢀⠀⠀⠀⣀⠊⠀⠠⠀⠙⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢀⡀⠀⡿⠉⠑⣶⠟⠀⠀⠀⠀⠀⣅⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠀⠀⠀⠁⠈⣾⠇⠀⠀⠀⠀⠀⠢⠐⠀⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢀⡀⢀⠂⠀⠀⢠⡟⣇⡀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠐⠀⠀⠀⠠⣧⡄⠀⣺⣵⣷⠆⠀⠀⢀⢁⠎⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠑⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠙⢯⠁⠀⠀⠘⣿⡏⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠺⠟⠯⡀⠀⠀⠈⠓⣄⣀⠀⠹⠧⢂⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠓⡄⢸⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠜⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠉⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠤⠄⠀⠤⠀⠀⢀⡀⠀⢀⡀⢠⡔⠋⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠠⡀⡘⠁⠀⠼⣇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠙⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠁⢀⠀⠠⠋⠉⠦⠄⠀⠀⠀⠀⠀⢇⠀⠀⣀⢀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢲⣾⣿⣿⡟⠀⠈⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡟⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠉⠀⠀⢀⠀⠀⠀⠀⢀⣰⡿⠁⢻⡏⠈⠉⢄⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠚⠁⢁⠀⠀⠀⠐⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⣀
⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⣀⣤⣶⣿⣟⢿⣻⣿⣿⣿⣿⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⡏⠁⠀⠙⢻⠿⡿⣿⣿⣿⣷⡒⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣞⣙⠙⢷⡄⠀⡠⠣⢀⠀⠿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⣄⣀⣀⡤⢤⣤⡞⠀⠈⣿⡿⣄⠘⢇⠰⠁⣶⣾⣷⣶⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠻⠃⠉⠀⠀⠀⠀⢹⣟⣃⠀⠀⠈⢻⣽⣣⢾⣿⣿⣿⣿⣿⣿⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⣰⠉⡇⠐⣆⠀⠀⡀⠤⠀⡀⠿⡽⣦⣀⠀⠘⠪⠀⠀⣸⠿⠟⠋⠁⢠⣾⠋
⠀⠀⠀⠀⠀⠀⣾⡿⡀⢣⠈⠹⡄⠀⠀⠐⠀⠀⣄⡈⠋⠀⠀⠀⠀⠀⠰⣿⡄⠀⠀⢠⠞⠁
⠀⠀⠀⠀⢀⡾⢿⣿⡱⡀⢂⠀⢘⠢⠀⠀⡀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠉
⠀⠀⠀⠀⣸⠷⢡⢻⣿⣽⢄⠀⡈⠀⠙⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⡀⠀⠙⠑⢿⣷⣦⣈⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠁
⠀⠀⠀⠀⢿⣿⣦⣴⣶⣷⡽⠿⠛⠛⠃