Letters Emojis & Symbols

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⣼⣷⡀⠀⠀⠀⣿⣿⢻⣿⡇⠀⢀⣾⣿⡿⢿⣿⠆⠀⣿⣿⣿⣿⣦⠀⠀⣿⣿⠿⠿⠟⠀⢸⣷⡿⠿⠿⠃
⠀⠀⠀⠀⣼⣯⣼⣷⡀⠀⠀⣿⣿⣿⣯⡀⠀⢸⣿⡏⠀⠀⠀⠀⠀⣿⣿⠀⢹⣿⡇⠀⣿⣿⣶⣶⠀⠀⢸⣿⣷⣲⡄
⠀⠀⢀⣾⣿⡟⠹⣿⣷⡀⠀⣿⣿⣨⣿⣿⠀⠸⣿⣷⣦⣶⡷⠀⠀⣿⣿⣶⣿⡿⠃⠀⣿⣿⣤⣤⣤⠀⢸⣿⡏
⠀⠀⠈⠉⠉⠀⠀⠉⠉⠁⠀⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠀⠈⠉⠁
⠀⠀⢀⣴⣶⣶⣶⣤⠀⢰⣶⡦⠀⠀⣶⣶⠀⢰⣶⣶⣶⣶⣶⠀⢰⣶⣲⣲⣲⣖⠀⢰⣶⡆⢀⣶⡖⠀⢰⣲⡆
⠀⠀⣾⣿⠟⠉⠙⠟⠁⢸⣿⣷⣤⣤⣿⣿⠀⠈⠉⣿⣿⠉⠁⠀⠈⠉⢹⣿⡏⠉⠀⢸⣿⣷⣿⠿⠁⠀⢸⣯⡇
⠀⠀⣿⣿⣄⣀⣻⣷⡆⢸⣿⣿⠛⠻⣿⣿⠀⢀⣀⣿⣿⣀⡀⠀⢀⣄⣼⣿⡇⠀⠀⢸⣿⡟⢿⣦⡀⠀⢸⣿⣧⣀⣀⡀
⠀⠀⠈⠻⠿⠿⠿⠋⠀⠸⠿⠿⠀⠀⠿⠿⠀⠸⠿⠿⠿⠿⠷⠀⠙⠿⠿⠋⠀⠀⠀⠸⠿⠇⠘⠿⠇⠀⠸⠿⠿⠿⠿⠇
⠀⠀⣀⣀⡀⠀⠀⣀⣀⠀⢀⣀⡀⠀⢀⣀⡀⠀⠀⢀⣀⣀⡀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⣀⡀
⠀⠀⣿⣿⣷⣀⣼⣿⣿⡄⢸⣿⣿⡄⢸⣿⣧⠀⣴⣿⡿⢿⣿⡆⠀⢸⣿⡿⣿⣦⠀⣰⣟⣿⣿⣿⣆⠀⢸⣿⡟⣿⣷
⠀⠀⣿⣿⣿⣿⡿⣿⣿⡇⢸⣿⣿⣿⣾⣿⣿⠀⣿⣏⠀⠀⣿⣿⠀⢸⣿⣷⣿⡟⠀⣿⣿⠀⣠⣿⣿⠀⢸⣿⣿⣿⠏
⠀⠀⣿⣿⠀⠉⠀⣿⣿⡇⢸⣿⡇⠹⣿⣿⡿⠀⢻⣿⣶⣾⣿⠇⠀⢸⣿⡏⠁⠀⠀⠹⣾⣷⣿⣿⡏⠀⢸⣿⡿⣿⣷
⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠈⠉⠁⠀⠈⠉⠁⠀⠀⠉⠛⠋⠁⠀⠀⠈⠙⠁⠀⠀⠀⠀⠈⠉⠉⠙⠁⠀⠘⠛⠁⠙⠙
⠀⠀⠀⠀⠀⣠⣶⣶⣤⠀⢰⢶⡶⣶⢶⣶⡆⠀⣶⡆⠀⠀⣶⣶⠀⢰⣶⣦⠀⣴⣶⡆⠀⢰⣶⣆⠀⠀⠀⢀⣶⣶
⠀⠀⠀⠀⠐⣿⣿⣉⠁⠀⠈⠉⢻⣿⡏⠉⠁⠀⣿⣧⠀⢀⣿⡟⠀⠀⣿⣿⣀⣿⣿⠀⠀⠈⢿⣿⡄⢀⠀⣼⣽⠇
⠀⠀⠀⠀⣀⠈⠙⣿⣧⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⣄⣼⣿⡇⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠘⣿⣷⣯⣷⣿⡟
⠀⠀⠀⠘⠿⣿⣿⡿⠋⠀⠀⠀⢸⣿⡇⠀⠀⠀⠘⠿⣿⠿⠋⠀⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠹⠟⠁⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⣀⣀⠀⣀⢀⡀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣾⡿⠃⠀⢻⣿⣆⣿⡿⠁⠀⠛⠛⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡀⠀⠀⠀⢻⣿⡿⠁⠀⠀⠀⣰⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⢿⣷⡄⠀⠀⢸⣿⡇⠀⠀⠀⣾⣿⣿⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠹⠿⠿⠿⠀⠀⠀⣿⣿⣿⣿⣾⠟⠀⠀⣾⣿⠛⠗⠘⠛⠀⠀⠛⠃⢀⣿⣿⣿⡿⢀⣤⠶
⢶⡄⠀⠙⠿⠿⠛⠷⠂⠀⠀⠀⣀⡀⠀⠀⠀⢿⡟⢸⣿⡟⠀⠀⠀⠈⠛⠀⠀⠀⢀⣤⡴⠶⣤⠈⠙⠛⠉⠀⠘⣿⣾
⣾⠏⠀⠀⠀⠀⣠⡴⢦⡀⠀⠀⢹⡇⣴⠟⠀⠀⠀⠀⠉⠀⠀⢀⣶⡄⠀⠀⠀⢰⣿⣿⣧⣤⣿⡇⠀⠀⠀⡀⠀⠈⢿
⠁⢠⣤⡄⠀⠘⢿⣷⣾⡗⠀⠀⢸⣿⠋⠀⠀⢰⣿⠿⣷⡄⢀⣾⣿⣧⣼⣿⠇⠈⢿⣿⣿⠿⠛⠁⠀⠀⠹⣿⣆⠀⠈
⢠⣿⣻⣷⠀⠀⠈⢻⣯⡀⠀⠀⠸⠟⠀⢰⣶⣄⣻⡄⠈⠀⣾⡟⣿⡿⣻⣿⠀⠀⠘⠃⠀⠀⣀⣠⣴⡄⠀⠘⣿⣆
⣾⡿⠿⣿⣇⠀⠀⠀⠙⠁⠠⣴⡆⠀⠀⠀⠙⠻⠟⠁⠀⠀⠀⠀⠉⠀⠿⠿⠀⠀⠀⠀⠀⢻⠟⢿⣏⠀⠀⠶⠿⠋
⠛⠁⠀⠛⠋⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⢀⣶⡄⠀⣤⣤⡀⢰⣶⠀⠀⠀⢠⣦⠀⠀⠀⠈⢿⣇⠀⠀⠀⢀⡀
⣦⡀⠀⠀⠀⠀⣴⡿⠃⣀⠀⠀⢻⣷⡀⠀⢀⣴⣿⠟⠁⠀⢸⣿⢿⣜⣿⡀⠀⠀⣾⡟⣠⣾⡦⠀⠘⠋⠀⠀⣰⣿⠗
⣽⣿⠀⠀⣠⣾⠿⣷⣾⡿⠃⠀⠀⠁⠀⠐⢿⣿⣁⠀⠀⠀⢸⣿⡆⢻⣿⡇⠀⣸⣿⣿⠟⠉⠀⣀⣤⠶⣤⠀⢻⣿⣄
⠟⠁⠀⠀⠙⠁⣴⡿⠋⠀⠀⢀⣤⣀⡀⠀⠀⠙⠋⠀⠀⠀⠈⠛⠁⠀⠉⠁⠀⠈⠛⠁⠀⠀⠀⠹⣿⣶⣿⠇⠀⠙⠻
⠀⢠⣤⠀⠀⠀⠈⠀⠀⠀⢀⣾⣟⠛⠃⠀⣀⣠⣀⡀⠀⠀⢠⣾⡧⠀⠀⠀⠀⢠⣶⣦⣄⠀⠀⠀⢻⣿⡉
⣷⣌⣿⡆⠀⢀⣤⡀⠀⠀⣾⣟⡉⠀⠀⣼⣿⣀⣼⣿⠆⠀⢸⣿⡄⠀⢸⣷⠀⠈⢿⣯⣿⣿⣶⡄⠀⠛⠃⠀⣤⡀⢹
⡏⠻⣿⣷⠀⠈⢻⣷⡄⠀⠉⠙⠛⠀⠸⣿⣿⣿⡿⠋⠀⠀⠀⠙⠿⣿⡿⠋⠀⠀⠘⣿⣇⠈⠋⠀⠀⠰⣶⣄⣿⡇⠈
⠿⠀⠘⠛⠀⠀⢀⣿⣿⠀⠀⢀⣀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠘⠋⠀⢰⣶⠒⣦⠈⠛⢿⣧
⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠘⣿⣿⣷⣶⣤⠀⠀⢰⣿⣡⣶⠆⠀⢠⣿⡿⠛⠻⣿⠆⠀⠀⣼⣿⣿⣟⠀⠀⠈⠛⠃
⠂⠀⠀⠀⠐⢿⣦⡀⠀⠠⣶⣶⣾⣿⣷⡍⠉⠀⠀⣾⣿⣿⡁⠀⠀⠸⣿⣦⣼⡶⠀⠀⠀⢠⣿⣧⣤⡟⠀⠀⢀⣤⣾
⡄⠀⠺⣿⣄⠀⠹⣷⡀⠀⠈⠙⠿⣿⣭⠁⠀⠀⠠⢿⠃⢻⣧⠀⠀⠀⠈⠙⠋⠀⣠⣶⡦⡄⠀⠈⠁⢀⣤⠀⠹⠋⠻
⣿⠆⠀⠙⢿⣶⣶⡿⠁⢀⣤⡀⠀⠈⠁⠀⠀⣶⡄⠀⠀⠀⠈⣀⣀⣀⣠⠀⠀⣴⣿⣿⣦⠏⠀⢠⣦⡈⣿⣷⡀
⣄⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠻⠂⠀⠀⢰⣶⣼⣿⣶⣤⣄⠀⠙⠋⣽⡟⠀⠺⠏⣸⡇⠀⠀⠀⠀⠹⣿⣟⠙⣿⡆
⡟⢀⣤⡀⠀⠀⠠⣾⠟⠙⠃⠀⠀⠀⠀⠀⠀⠈⠹⣷⡉⠁⠀⢀⣼⡟⣀⡀⠀⠀⠉⠁⣤⡄⠀⠀⠀⠘⢿⠆⠈⠀⢀
⣶⡿⠋⢁⣠⣤⣀⠀⠀⠀⣠⣾⠿⢿⠂⠀⠀⠀⠀⠙⠁⠀⠀⠸⠿⠟⠛⠃⠀⠀⠀⠀⢿⣧⠀⠀⢠⣦⣤⡀⠀⢀⣾
⠁⠀⢠⡏⠈⣿⣿⡆⠀⠀⣿⡏⠀⢀⠀⠀⠀⣿⡇⣠⣤⢀⣄⡀⠀⠀⢀⣠⣴⣾⡄⠀⠸⣿⡆⠀⣾⣿⣀⣽⡄⠈⠻

⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⢀⡠⠒⢄⠀⠀⠀⢄⡤⠒⠒⢤⣠⠄⠀⠀⣠⠀⠐⢦⣄⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢀⠤⠤⢄⡀
⠀⢸⠀⠈⢻⣧⠀⠀⠀⠀⠀⢸⡟⣦⡜⠀⠀⢰⡟⠀⠀⠀⠈⠉⠀⠀⠀⣿⠀⠀⠀⢹⡆⠀⠀⣿⣀⡀⣄⠀⠀⠀⣿⠀⠀⠈
⠀⠘⣿⠗⢠⣿⣧⠀⠀⠀⠀⢸⡧⠋⢹⡆⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣸⡇⠀⠀⣿⠀⠀⠁⠀⠀⠀⣾⠒⠲⠄
⠀⠀⠈⠀⣼⠘⣿⡆⠀⠀⠀⠘⠇⠀⠘⠁⠀⠀⠛⠳⠤⠤⠔⠀⠂⠀⠀⠿⠆⠤⠞⠋⠀⠀⠀⠟⠀⠠⠴⠀⠀⠀⠿⠄
⠀⠀⠀⢰⠇⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀
⠀⠀⠀⡾⠶⠒⠒⢻⣧⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⡆⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⢀⡇⠀⠀⣏⠀⠀⠀⠀⠀⠀⡿
⠀⠀⣸⠃⠀⠀⠀⠈⣿⣆⠀⠀⠻⣄⠀⢈⡇⠀⠀⣟⠰⠛⠚⡇⠀⠀⠀⡇⠀⠀⠀⠀⢀⠇⠀⠀⣿⠀⠑⡄⠀⠀⠀⣄⠀⠈⡀
⠀⣰⣯⠀⠀⠀⠀⠀⢸⣹⣆⡀⠀⠰⠛⠀⠁⠀⠠⠿⠀⠀⠀⠳⠀⠀⠀⠴⠀⠀⠘⠇⠁⠀⠀⠀⠿⠀⠀⠙⠀⠀⠀⠃⠐⠒⠁
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⡄⠀⠀⠀⠒⢲⡀⠀⠀⠀⠀⠀⣿⡁⠐⢺⣟⠀⠀⠀⢀⠔⠁⠀⠈⠑⢦⡁⠀⠀⢹⡿⠀⠉⣷⠀⠀⣴⠋⠀⠀⠀⠙⢦⡀
⠀⠘⠁⠀⠀⠀⠀⠘⣾⡀⠀⠀⠀⠀⣿⢷⡀⢸⡇⠀⠀⠀⢺⠀⠀⠀⠀⠀⠘⡷⠀⠀⢸⣷⠲⠤⠛⠀⢸⣯⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⡄⠀⢀⠀⠀⠘⠧⠀⠀⠀⠀⣿⠀⠻⣼⣷⠀⠀⠀⠹⡄⠀⠀⠀⠀⣸⠃⠀⠀⢸⣇⠀⠀⡠⠀⠀⠻⢄⠀⠀⢀⣀⡾⠁
⠀⠐⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠈⠉⠀⠀⠀⠀⠀⠑⠒⠀⠈⠀⠀⠀⠀⠉⠉⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠈⠉
⠀⢠⣤⡤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⠀⠀⠀⠀⠠⢤⣄⠀⠀⠀⢤⡄⠀⠀⢤⡄⠀⠀⠀⢠⡤
⠀⠀⣿⡇⠀⢸⣿⠆⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠈⢉⣴⠋⠁⡀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⢸⡃⠀⠀⠘⣷⡀⠀⠀⡜
⠀⠀⣿⡧⢤⡞⠋⠀⠀⠀⠀⠀⠀⠀⠳⢗⣆⠀⠀⠀⠀⣿⡃⠀⣞⠿⠤⡀⠀⠀⣸⡇⠀⠀⠀⠀⣸⡇⠀⠀⠀⠹⣧⠀⡰
⠀⠀⣿⡇⠀⠙⣂⡄⠀⣤⠀⠀⢀⡀⠀⠀⣹⠀⠀⠀⠀⢻⣇⠀⠈⠉⢀⡄⠀⠀⢹⣧⡀⠀⠀⠀⢻⡇⠀⠀⠀⠀⢿⡦⠁
⠀⠐⠓⠃⠀⠀⠈⠙⠒⠛⠀⠀⠘⠙⠒⠒⠋⠀⠀⠀⠀⠀⠉⠛⠒⠒⠋⠀⠀⠀⠀⠉⠛⠛⠋⠀⠛⠋⠀⠀⠀⠀⠀⠁
⠀⠀⣠⣀⣀⣀⣠⣄⢀⣀⠀⢠⡄⢠⠀⠀⢤⡤⡄⠀⠀⠀⣠⣤⠀⠀⠀⠀⠤⣄⠀⠀⠀⠀⢤⢀⠀⠀⣄⠀⠠⣤⣀⣀⣀⣤⡄
⠀⠈⠃⢉⡤⠀⠁⠀⡽⠁⠀⠀⣧⣝⠀⠀⠀⠹⣷⣄⠀⢀⡈⠀⠀⠀⠀⢸⠇⢸⣷⠀⠀⠀⢸⣿⠀⠀⠀⠀⠄⠀⠀⢀⣾⠟
⠀⠀⠀⣾⠃⠀⠀⣴⡇⠀⠀⠀⢸⣯⠀⠀⠀⠀⠙⢿⢢⡏⠀⠀⠀⠀⠀⠁⠀⢸⣻⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣞⠏
⠀⠀⢸⣿⡄⠀⠀⣿⡇⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⣠⢫⣵⣄⠀⠀⠀⠀⠀⠀⠈⢿⣇⡀⢀⣼⣿⠀⠀⠀⠀⠀⢀⣭⠂
⠀⠀⠀⢻⣧⣄⠀⢹⣷⣄⣀⣀⣼⣿⠀⠀⢠⡤⢰⣃⠀⠙⣿⣦⡀⠀⠀⣀⡀⠀⠀⠉⠉⠉⢸⢿⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⠉⠁⠉⠉⠁⠀⠀⠘⠛⠃⠀⠀⠘⠒⠛⠀⠀⠛⠃⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠐⠖⠓⠛⠛⠲⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⠀⠆⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⡉⢻⡟⣙
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⠿⢻⣄⢹⠿⠿⠿⠿⠿⠿⠿⠿⠷⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠾⠦⠴⠷⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠁


⠀⠀⠀⠎⢥⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠄⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠐



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠂⢲⣶⣦⡵⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⡿⣴⠟⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⣈⣛⣛⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢈⡧⣜⢻⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠛⢁⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⡀
⠀⠀⠠⠆⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡆⠐⠁
⠀⢀⠀⡀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢀⠀⢀⠀⡀⢀⠀⣠⠀⡀⠀⠀⡀⠀⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⢁⡌⣠⣈⣠⢁⣜⣠⣤⣄⢡⣌⣤⣎⣤⣱⣿⣆⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿
⣿⣿⡟⠛⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣒⠢⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⢉⡇⡷⠀⢀⡀⠀⡰⢩⢤⡙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⠇⣠⠟⢿⠀⡇⠰⠬⠵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡼⠋⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠊⠉⠙⢅⠀⠀⠔⠛⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠈⠙⠲⣄⠀⢸⠀⠀⠀⠀⠉⢀⣿⠀⠋⠀⠀⢠⠇⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠑⣼⠳⢄⣀⣀⡤⠞⠀⠓⠦⠤⣶⠋⢀⡤⠚⠉⠁⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⣀⣂⠀⢠⡾⠃⢀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢹⡖⠁⠀⠀⠀⠈⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⠟⠀⠀⠀⠑⠠⠤⠤⠤⠴⠚⠁⠀⠘⣯⣐⣀⣀⣂⡤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡋⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠁⠀⠀⠀⠀⠀⢠⡾⡇⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⣿⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⣀⣤⡀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⣸⣥⣀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢳⡀
⠀⠀⠀⠀⠰⠏⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣄⠁
⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⠶⠶⠶⠶⠶⠶⠶⠶⣶⠀⠀⠀⠀⠐⡄⠀⠈⣇⠀⡇
⠀⠀⠀⢠⣞⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠔⢠⠉⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠙⠿⣦⣀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠈⠒⠊⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣶⣶⠾⠿⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡀⠠⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡁⠀⡀⢰⡀⠀⢢⣌⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⡄⠀⠚⠛⠒⠴⣯⡜⠂⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⢛⠀⠐⠁⠀⠀⠈⠛⢦⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⢠⠄⢠⡀⠰⠋⢀⡌⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠁⠀⠄⠀⠈⠀⠀⠑⣆⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠘⠀⠀⠀⡀⠀⠀⠈⣿⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⡸⠀⠀⠀⠀⠠⠀⠀⠀⡅⠰⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠁⢀⠀⠀⠇⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢆⠆⠀⠀⠠⠀⠀⠀⠰⢌⣄⡀⢈⠀⢸⠎⠀⣰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠨⡀⣀⡀⠀⠀⠀⠀⠖⠒⠀⢀⣈⢙⣧⣸⡀⠋⠄⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⣀⠀⠀⠀⠀⠀⢂⡀⠀⠐⠈⠀⡠⠀⠘⢙⢷⣅⠀⠠⠎
⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠊⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠁⢸⠉⠓⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠈⠀⠀⠁⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢃⢸⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢄⡀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠔⠈⠀⠀⠀⠀⠂

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⢻⡀⠀⢸⡇⢸⠆⢠⡆⠀⠘⠀⣼⠁⢲⡆⠀⣏⡌⠃⠀⣾⣉⠛⢠⡞⠁⠘⠇⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⣄⠀⠀⢰⠀⠀⢀⠀⢰⠍⢀⠀⡀
⠀⠀⠀⡀⡂⠂⣷⡀⠘⣇⣠⡆⠈⣇⣀⣤⠀⣿⡀⠸⠇⢀⣏⢁⡤⠀⣿⡙⠀⠘⠧⠀⣰⠇⠀⠀⢸⢰⡀⢸⠀⠸⠀⢧⣀⠐⠇⢸⡀⢻⣈⠀⢸⠀⢉⣐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠙⠃
⠀⠀⠀⠀⢀⡄⠀⡄⠀⢀⡄⠀⢀⡀⠀⢀⠀⣀⠄⠀⣀⠀⠀⠀⣠⡀⠀⣤⡄⠀⣄⠀⣠⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⢀⠀⠀⠀⣀
⠀⠀⠀⠀⢸⠦⠀⡇⠀⢸⠀⠀⢸⡇⠀⣿⢾⡁⠀⠀⡇⠀⠀⠀⠉⢧⡀⢹⡇⠀⠉⢣⣼⠀⠀⠀⠐⠠⡀⠀⠂⢠⠀⢸⣠⠂⠀⣥⠀⠴⠒⡔⢢⠀⠰⠲⡆
⠀⠀⠀⠀⠘⠆⠀⠳⠀⠸⠆⠙⠘⠁⠄⠷⠀⠸⠦⠀⠓⠠⠏⠐⠆⠈⠀⠸⠇⠀⠄⠀⠻⠀⠀⠀⠀⠄⠃⠈⠀⢸⠄⠸⠌⠦⠀⠛⠀⠣⠀⠇⠺⠀⠐⠔⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⡴⠀⠲⣄⠀⠰⠀⡄⢀⡄⠀⢠⡀⠀⡆⠀⡆⠀⢄⠐⠆⠀⠀⡖⠲⠀⡔⠀⠰⠂⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⢀⢀⡀⠀⡀⠀⣄
⠀⠀⠀⠀⢃⠀⢀⠟⠀⢾⠈⠁⠘⡇⠀⢰⠇⠀⡁⠸⡅⠀⡀⠙⡆⠀⠀⡇⠀⠀⢇⠀⣠⠀⠀⠀⠄⢨⡅⢸⠀⣳⠀⡃⢨⠀⢸⠉⠁⡐⣍⠀⣎⠀⣆⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠰⠥⠀⠀⠉⠀⠉⠀⠉⠀⠀⠀⠀⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠀⢸⡉⠁⠀⠉⢩⡄⠈⠁⠀⠉⠁⠀⠉⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢥⠀⠊⠀⠀⢧⢀⠿⣀⠎⠀⠈⢶⠀⠀⠈⢣⡠⠃⠐⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⢀⡄⢤⠠⠀⢠⡤⠀⢠⠀⡄⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠈⠋⠀⠟⠀⠠⡄⠀⢷⡄⠀⠀⣇⠀⠀⢼⣀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠟⠈⠏⠀⡄⢣⡀⠈⡟⠀⢰⣇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⡄⢱⠀⠀⠀⡇⠀⠀⠀⠈⡇⠀⠀⠀⣼⠀⠀⠀⠀⡇⠀⠀⠠⣍⠀⠀⢠⡎⡀⠀⠀⠉⠹⠁⠀⠘⢤⡇⠀⠀⡄⢸⠀⠀⢀⠈⡇
⠀⠀⠀⠀⠀⠀⠰⡇⠐⠀⠀⠀⣇⠀⠀⠀⣮⣤⠀⠀⣀⡹⠀⠀⠐⢺⡗⠀⠀⣀⡸⠃⠀⠸⣀⡗⠀⠀⢠⠇⠀⠀⢰⣈⡗⠀⢀⣩⠞⠀⠀⠸⠀⠃

⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠄⣷⠀⠀⡇⠀⠀⣠⠀⠀⠀⠀⠀⠀⢠⣰⠆⠀⠀⠠⠂⢈⣀⠢⠀⠠⣾⠲⠄⠀⣆⡆⢠⠆⠀⠀⠀⣴⡦⠀⢲⡄
⠀⠀⠀⠀⠀⢸⠀⠀⣀⠀⢀⡀⠀⣀⠁⠀⢀⡁⠀⠉⣿⠙⠀⠴⠶⠀⢰⡈⢳⣼⡁⠀⡇⢰⣡⡟⣰⠃⢀⢨⣿⠄⠀⠈⡡⠃⣰⣲⠀⠀⠉⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠘⠦⠀⠉⠀⠸⠁⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠙⠤⢉⣉⠕⠁⠈⠙⠋⠀⠀⠈⠁⠀⠈⠉⠀⠀⠀⠀⠀⠼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⠀⠀⠀⠀⢰⡔⠀⠀⠀⠀⠀⢠⡎⠁⢦⠀⠀⠀⠀⢠⠀⠀⠈⢟⢄⠀⠀⠀⢀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠨⣾⠀⠀⣔⡟
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠾⣦⠀⠀⢀⠅⠀⠤⠀⠀⠀⠘⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣪⠋⠀⠀⠢⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⡉⠀⠀⠀⠀⠰⠄⠀⠀⢀⡄⠀⢴⠋⠀⠀⠆⢠⠜⠀⡄
⠀⠀⠀⠀⠀⠈⣟⠂⠀⠀⣾⡅⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⢀⣙⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠶⢀⣏⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢤⠀⠀⢈⡁⠀⠀⠆⠀⠨⡌⠀⠀⠀⠰⠀⣸⡇⠀⠀⣀⠀⠚
⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠈⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠒⠋⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⡰⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⡀⠀⠀⠀⣤⠔⠀⠀⠀⠀⠀⠀⠀⢠⠤
⠀⠀⠀⠀⠀⠁⢨⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⢀⣇⠀⠈⠁⠀⠀⣾⠆⠀⠀⠀⠀⠀⠀⠀⠐⡊
⠀⠀⠀⠀⠀⠀⡴⠆⠀⠀⠀⠀⡀⠀⠀⠀⢀⡃⠀⠀⠀⢀⠀⠰⣷⠀⠀⠀⠀⠰⣷⠀⠀⠀⠀⠀⠀⠀⡀⡨⠂⠁
⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠥⠄⠀⠀⠀⠀⠈⠹⠆⠀⠀⠀⠀⠘⠶⠄⠀⠀⠀⠀⠈⠕⠊
⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⣦⠉⠀⠀⠀⠀⠀⠀⠉⠀⠟⠀⠀⠀⠀⠀⠀⢿⣇⠂⠀⠀⠀⠀⠀⠲⢠⡿⠀⠀⠀⠀⠂⠀⢠
⠀⠀⠀⠀⠀⢰⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣊⠀⠀⠀⠀⠀⢀⡀⠙⢷⡄⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠈⢡⣄⠀⠀⠀⠀⠀⠀⢃⡐⠎⠀⠀⠀⠀⠀⠈⠀⠀⠘⠃⠀⠀⠐⠃⠰⠟⠀⠀⠀⠀⠀⠀⠨⣿⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⡄⠸⠁⠀⠀⠀⠀⢤⠌⠀⠀⠀⠀⠀⠀⠀⢠⠄⠉⣓⡀⠀⠀⠀⠀⠀⠒⠀⣘⢝⠁⠀⠀⢠⠄⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠆⠀⠀⠀⠀⠀⠀⠀⣅⡌⠀⠀⠀⠀⠀⡰⢯
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⢩⣅⠀⠀⠀⠀⠀⠒⣠⡟⠀⠀⠀⠀⣠⣼⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⣠⣤⣤⣄⡀⠀⣤⣤⣤⣄⡀⠀⠀⢀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣼⣿⣧⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⣾⣿⠟⠛⠻⠇⠀⣿⡿⠿⢿⣿⡄⠀⢸⣿⠿⠿⠛⠀⠀⢸⣿⠿⠿⠟⠁
⠀⠀⠀⠀⣰⣿⣯⣿⣧⠀⠀⣿⣿⣿⢿⣿⠀⠀⣿⣇⠀⠀⠀⠀⠀⣿⡇⠀⢈⣿⡇⠀⢺⣿⣿⣿⠂⠀⠀⢸⣿⣿⣿⠆
⠀⠀⠀⢰⣿⡿⠿⠿⣿⡆⠀⣿⣷⣶⣾⣿⠀⠀⠙⣿⣷⣶⣿⡇⠀⣿⣷⣶⣿⠏⠀⠀⣾⣿⣶⣶⣶⠀⠀⢸⣿
⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠈⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠈⠉

⠀⠀⠀⠀⢀⣴⣶⣶⣦⡀⠀⢠⣶⠀⠀⠀⣴⡆⠀⢰⣶⠀⠀⢰⣦⠀⣠⣶⠀⠀⢠⣶⠀⠀⠀⠀⠀⢰⣶⡀⠀⠀⢠⣶⡄
⠀⠀⠀⢠⣿⠟⢉⣉⣉⠀⠀⢸⣿⣤⣤⣤⣿⡇⠀⢸⣿⠀⠀⢸⣿⣾⡿⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⣷⡀⢀⣿⣿⡇
⠀⠀⠀⠸⣿⣄⠸⢿⣿⡇⠀⢸⣿⠿⠿⠿⣿⡇⠀⢸⣿⠀⠀⢸⣿⢿⣷⡄⠀⠀⢸⣿⡀⡀⢀⠀⠀⢸⣿⢿⣷⣾⡿⣿⡇
⠀⠀⠀⠀⠙⢿⣿⣿⠟⠁⠀⠸⡿⠀⠀⠀⢿⠇⠀⢸⡟⠀⠀⢸⡟⠈⠻⡿⠀⠀⠸⣿⣿⣿⣿⠃⠀⠸⡟⠈⠻⠟⠀⣿⠃

⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⢸⣿⣦⡀⢸⣿⠀⠀⠀⣰⣿⡿⠿⣿⣷⡄⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⣴⣿⣿⣿⣿⣦⡀⠀⠀⢸⣿⣿⣿⣧
⠀⠀⠀⢸⣿⢿⣷⣬⣿⠀⠀⠀⣿⡏⠀⠀⠀⣻⡇⠀⠀⠀⣿⣷⣶⣿⠃⠀⠀⢸⣿⠃⠀⣀⡈⣿⡇⠀⠀⢸⣿⣦⣾⡿
⠀⠀⠀⢸⣿⠀⠹⣿⣿⠀⠀⠀⢿⣷⣤⣤⣴⣿⠃⠀⠀⠀⣿⡟⠛⠋⠀⠀⠀⠘⣿⣷⣤⣿⣿⣿⠁⠀⠀⢸⣿⠻⣿⣷⡀
⠀⠀⠀⠘⠋⠀⠀⠈⠋⠀⠀⠀⠀⠙⠛⠛⠛⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠀⠀⠀⠘⠟⠀⠘⠿

⠀⠀⠀⠀⣠⣤⣶⣤⡀⠀⢠⣤⣤⣤⣤⣤⠀⢠⣄⠀⠀⠀⣤⡄⢀⣤⡀⠀⢀⣤⠀⢀⣄⠀⠀⠀⣠⡀⠀⣠⣤⣤⣤⣤⡀
⠀⠀⠀⠀⣿⣿⣛⣿⠇⠀⠘⠛⢻⣿⠛⠛⠀⢹⣿⡆⠀⣼⡿⠀⠈⢿⣿⣴⣿⠏⠀⠸⣿⣧⣀⣼⡿⠁⠀⠿⠿⢿⣿⡟⠁
⠀⠀⠀⢀⣙⠿⠿⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⢻⣿⣴⣿⠁⠀⠀⢠⣿⣿⣿⡀⠀⠀⠘⢿⣿⡟⠁⠀⠀⢀⣴⣿⠏
⠀⠀⠀⠘⢿⣿⣿⣿⠃⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⢿⣿⠃⠀⠀⢰⣿⠏⠘⢿⣿⠀⠀⠀⢸⣿⠀⠀⠀⢠⣾⣿⣶⣶⣶⠄
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠈⠋⠀⠀⠀⠈⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠄⠒⠒⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⣀⠁⠂⢄⠈⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠐⠀⡐⠁⣴⣤⣀⣈⣻⠀⣖⣀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢰⣅⠈⢀⡤⠂⠈⠙⢷⡄⠈⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢇⠀⠀⠀⠀⠀⣉⠄⠙⡞⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⠄⠁⠀⠀⣳⠂⠰⢄⠐⠁⠀⠴⠁⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡵⠀⠀⢐⠁⠀⠃⠀⠀⠈⢣⣀⢀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⡀⠀⠀⠀⢹⠇⠀⠀⠀⠈⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢰⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠠⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠐⢀⠎⠀⠀⠀⠀⢰⠀⠀⠀⡈⠀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠸⠀⡁⠀⢠⠃⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠠⡆⡀⠁⠀⠀⠀⠀⠀⠀⢠⡑⠄⠀⠂⠀⠀⣌⠎⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠱⠁⠄⠀⠀⠈⠀⠀⢀⡨⠉⠉⠓⠰⣶⡀⢟⢀⠔⠛⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠃⠒⠒⠀⠈⢀⡀⠀⠁⢀⡠⠜⠓⠒⢚⣿⢾⡈⠀⠁⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠤⠄⠀⠀⠤⠀⠀⠤⠤⠀⠁⠀⠀⠒⠁⠀⢠⠾⣽⣧⡀⠈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠁⠀⡏⠀⠨⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠈⢃⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡀⠀⠀⠀⢢⡀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠂⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⡤⠄⠀⠀⠀⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⡀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠈⠁⠀⠀⠀⠀⣰⣶⠈⠀⠰⣿⠔⠀⠀⠀⠀⠀⠀⠀⠀⣴⢀⣀⠺⠿⡴⠂⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡠⠆⠀⠀⠲⠄⠀⠂⠆⠈⠁⢀⡤⠤⠀⢀⡼⢠⡦⠀⠀⠀⠀⠀⠈⠻⠯⠀⠀⢶⠁⠀⠀⠀⠀⠹⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⡗⠘⠿⠇⠠⠐⠛⠀⡖⠀⡎⠀⠀⠠⠭⠔⠋⠀⠀⠀⠀⠀⣀⠀⠀⠒⠀⠀⠀⠱⡄⠀⠀⠀⠀⣇⡸⠇
⠀⠀⠀⢰⡆⠀⣀⣀⠀⠀⠀⠀⢀⠀⠁⢰⠒⠀⠀⢸⠀⠀⠰⡀⠡⢀⠀⠐⠀⠀⢀⠀⠀⢀⡀⠀⠙⠓⠶⠶⠚⠁⠀⠰⡚⠂⢀⡆⣰⠋
⠀⠀⠀⢸⠀⠈⣵⡄⠀⠀⠴⣄⠀⠀⢢⣀⡠⠀⠀⠛⢄⠀⠀⠀⠄⠀⠀⠀⠀⣠⠞⠒⠢⠜⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠈⠀⣩⠜⠁⠀⠀⠀⠀⠀⠾
⠀⠀⠀⠈⠣⠘⠂⠀⠀⠘⠿⠈⠀⠀⠀⠈⡖⠒⠀⠀⠀⣇⠀⠀⠒⠖⠲⠒⠊⠁⠀⢰⡆⠖⠃⠀⠀⢠⣦⡄⣄⠀⠀⠀⢠⠞⠁⠀⠀⢊⣭⠀⠀⠀⡐⢢
⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⢩⣀⠀⣰⠴⠆⠙⠀⠀⠀⢠⠏⠠⠞⠱⠆⠀⠀⠀⠀⠀⢀⠀⢢⣿⣣⡀⠈⠉⢀⡿⠀⠳⣄⠎⠀⠀⠀⠀⠪⠫⠀⠀⢘⠟
⠀⠀⠀⠀⠀⠂⡀⢀⡠⠔⠀⠀⠉⢀⣀⣀⣀⣠⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⡈⠃⠀⢀⡞⠋⡆⠀⠈⠀⠀⣤⡄⡑⠒⠎⠀⠘⣠⣀⣠⠞
⠀⢀⡀⣀⠜⠙⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⠆⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⣀⡀⠄⠑⠲⣷⠀⠀⠀⡀⠀⠀⢀⠈⠀⠄⠀⡇
⠀⠀⠉⠁⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠈⣄⢾⡗⢀⢠⣦⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠀⢷⠀⠀⠀⠀⠑⣦⠞⣥⡄⡀⣨⣙⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⣀⡀⠀⠂⠀⠀⠀⠙⠋⢸⠀⠀⢀⠄⠇⠀⠀⠶⠄⠀⡆⠀⠘⡆⠀⠀⠀⠠⠀⠐⠺⠁⠐⠬⠅⠀⡆⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢅⡀⠀⠈⠄⠀⠤⠀⠀⡸⠳⠆⢄⠺⠷⠀⢄⠿⢆⠀⡇⠀⠞⠁⠀⠀⠀⠀⠐⠒⠒⠂⠀⠁⣠⠾⠷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢸⠈⠢⠀⠀⠀⡟⠀⠐⠀⠉⣀⣀⣀⡩⠕⠂⡇⠀⠀⠀⠀⠈⠛⠓⠒⠖⠀⠄⢀⠞⠉⠢⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠈⠀⠀⢠⡇⠈⠓⢲⡄⡏⠉⠉⢡⡖⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠶⠃⠀⠀⠀⣀⡼⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠃⠀⠀⠀⠒⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢾⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣯⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣿⣿⡿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⣼⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣟⠛⣷⠀⠀⠄⠁⠀⠈⠀⠀⡀⠂⠀⠀⠀⠀⠀⠔⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣼⣻⣿⡋⠄⠀⠀⠠⢀⠠⢀⠀⠄⡁⠂⠈⠀⠀⢀⠀⠐⠊⠁⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠂⠐⠈⣉⣉⠛⠉⢁⠀⠀⠨⠕⠢⠀⠤⠔⠠⠄⠤⠆⠉⠒⠁⠀⠀⠀⣰⢶⠀⠀⠐⠀⠈⠑⠂⠤⢀⡀⣤⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠁⠀⠈⠻⢞⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢷⡻⡧⣬⣤⣧⠌⣁⠂⢄⠨⢘⣿⡔⠟⡽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⡋⣰⣤⣀⣶⣿⣿⠴⠀⠉⠀⠀⣏⣻⣧⣤⣙⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⠃⠐⣰⢃⣯⣠⣼⠛⠁⠀⠀⠀⠀⠀⢰⡯⣷⡄⠍⡁⠸⠅
⠀⠀⠀⠀⣠⠀⠀⠀⠠⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣴⠛⠓⣘⠛⣿⣡⣬⡿⠋⠀⠀⠀⠀⠀⠀⣠⠀⠀⠛⡳⢷⡆⠆
⠀⠀⠀⠀⠘⡀⠀⠀⠐⣚⠃⠀⢀⠀⠀⠀⠀⠀⠀⣀⣠⣶⡿⠿⡡⢠⣨⡁⣾⣷⣶⠏⠀⠀⠀⠠⠄⡐⠲⡌⢿⣧⠀⠀⣯⡈⡇
⠀⠀⠀⠀⠀⠈⣦⠀⠥⠏⠀⢀⡪⠁⡔⠊⠛⣛⠛⣻⢻⡓⠄⢲⣓⣾⡿⠷⠋⠉⠁⠀⠀⢀⠐⠁⠀⠀⠠⠗⢈⣾⠀⠀⠶⠁⠁
⠀⠀⠀⠀⠀⠀⠈⢔⣻⡁⠀⠰⠁⣾⠂⠀⠀⠿⢷⢶⡾⣡⣼⣾⣏⠒⡀⠀⠀⠐⠀⠀⠀⠀⠈⠐⠀⢨⠔⠀⠺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠰⠀⣷⢀⡀⠀⠀⢀⠈⣿⣿⢟⠛⡉⣴⣧⣤⣀⡐⢀⠀⠀⠀⠀⠀⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠉⠁⠀⠀⣰⣿⠁⠴⠇⢙⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣰⡟⠀⡁⠀⣈⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠖⠓⠛⠦⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⣿⠤⢚⠦⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠄⠐⢶⣖⣴⣌⣷⡀⠈⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣑⢂⠠⢈⣿⡀⠀⠀⠀⠀⠀⣀⣤⣾⣸⡽⣧⡀⠀⢨⡿⡿⢿⣿⡟⠀⠆⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⡎⣴⢧⣺⢿⣦⣤⣤⡴⠿⠋⠁⣡⣿⣧⢸⡇⠀⠈⠀⠀⠀⢹⣿⠶⠀⢠⣿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠒⠲⠶⣤⣀⠻⣿⣶⣌⡿⣶⣿⡿⣥⢀⣀⢰⣟⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⡈⣬⡟⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣦⣴⣴⣶⣧⣡⠀⣉⡛⢮⡝⠻⢿⣿⣿⣷⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⢀⣠⠠⡴⣿⣤⡔⣷⣿⣥⣤⠼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡼⣿⠟⠁⠀⠈⠙⠻⣿⣿⠆⠈⡓⢦⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⡟⢻⣿⣿⡾⣿⠻⣿⣤⠶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠻⡀⠀⠀⠀⠀⠀⠈⠛⢧⣲⣍⡂⢈⠑⠦⢤⣀⣀⣀⣀⣄⣠⣤⡴⢘⣛⣤⣤⣰⢶⣋⣿⠟⠙⠷⣦⣤⣴⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⢳⣄⡀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣧⣀⣤⣤⣄⣨⠿⣿⣡⣿⢔⡠⠿⣿⢟⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣿⢻⡶⢤⣀⡀⠀⠀⠀⠀⣀⠉⠛⠿⠿⣷⣿⣽⣶⣷⣾⡶⠀⠀⠈⠿⣟⡁⠀⠀⠀⠆⠀⠓⢄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠷⣾⣿⣿⣿⣿⣿⣷⣿⠿⠿⠿⢿⣶⣄⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣍⣾⢽⣿⣿⣛⠿⡿⠿⢻⣯⣡⣾⣟⣼⣭⡶⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⣿⣹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣹⡟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡹⣿⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣩⣿⣿⡟⠛⣩⠉⣹⢫⡮⢹⣿⣿⣿⣿⢷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⣿⣿⣿⣷⡝⢎⣹⣶⣿⣿⣿⣿⣟⣻⠠⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣮⣿⣿⣿⣟⣭⡉⣶⠏⠉⣻⡿⣿⣽⣿⡶⣚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸⣿⣿⣿⣹⣫⣿⣸⡕⢎⣶⣿⣴⣿⣿⣿⣿⣥⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡿⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣮⣿⣯⣾⢿⣿⣿⣿⣷⣤⣴⣟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣻⣿⣿⣿⣿⣿⣥⣷⣾⣿⣿⣿⣿⣿⣿⡟⠿⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⡿⣿⣿⣿⣿⢹⣿⣿⣿⣏⣾⣿⣿⡿⠵⠁⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾⣴⣾⣗⣽⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠷⢿⢿⡿⠿⠛⠿⠿⠦⢿⢿⣿⡟⠭⠿⢿⠷⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⠘⠈⠃⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠒⠂⢄⠀⠀⡍⠂⣈⠀⠐⠁⠀⠐⣆⠀⡀⠤⠐⠂⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠓⠀⣋⣀⣈⣀⣈⣈⣀⣈⣁⠈⠂⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣗⠐⢉⣃⢀⣠⠂⣸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣰⠁⠀⠼⠿⠿⠿⠿⠿⠿⠿⠦⠈⢳⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠠⠏⠓⠲⠸⠸⠄⠢⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⡟⠠⢉⡅⠂⡀⣀⢄⠴⣡⠂⢀⡆⠸⡆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠰⠆⠒⠒⠐⠂⠲⠒⠂⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠃⠀⠤⠌⠁⠁⠀⠊⠀⠀⠠⠢⠉⠀⠙⠒⠒⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⡦⢎⣡⢰⢹⢼⠙⡶⣂⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠛⠻⠘⠀⠸⠉⠠⣂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠠⠄⠰⡄⠤⠂⣿⠀⡀⠀⠀⠀⢀⣔⠄⠀⡀⠀⡤
⠀⠀⠀⠀⠀⠀⣀⠠⠦⠄⠀⠀⠀⠙⠉⠆⠨⡍⠁⡰⢀⠈⡏⠐⢄⠀⠀⠀⠀⠀⠀⢸⡇⠈⠩⠭⣭⣥⠀⠃⡤⠤⠃⠊⣉⡉⢩⣀⠀⣈⢀⣀⠂⡀
⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠉⠀⢨⠤⡊⡡⡄⢘⢑⠯⠀⡇⠀⢠⠀⠀⠀⠀⠀⠀⠘⡇⠈⠉⠑⡚⢻⠀⢠⡇⢀⡙⠙⠙⠧⠟⠪⠜⠓⠙⠚⠖⠁
⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠰⠒⠃⡈⠁⠘⢈⠃⡐⠃⠒⢁⠀⠀⠀⠀⠀⠀⠀⢒⣀⣀⡀⠠⣸⡄⠃⠈⡁⠀⠰⠦⠀⠀⠂⠐⠆
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢩⠁⢀⡔⢻⠀⠰⠶⠀⠈⠁⡛⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⠈⠀⠺⠀⠀⠀⡇⢠⢶⡤⢂⡐⢶⠓⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⢸⠀⢾⠗⠺⡔⠻⣋⠴⢊⣉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡠⠘⠀⠀⠀⣅⡠⠥⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠒⠂⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⣀⡀⠀⠠⠀⣄⢄⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⠦⠀⠤⡅⡴⠣⡖⠓⢞⠈⢢⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⣶⠀⠂⢠⢀⡄⣴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠄⠀⠉⠃⠂⠁⠀⠀⠈⠂⠣⠂⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡏⠀⠃⠘⣾⢁⣟⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢀⠂⢁⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⠀⣙⠉⠁⠀⡀⢀⠉⣡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠐⢸⠀⣿⢸⣹⠆⣇⡾⢸⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢠⠀⠀⡁⠌⠉⠀⠐⡂⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠄⢸⠀⠷⠤⠅⠀⠘⠃⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠑⠄⣀⠀⡀⠠⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⡀⢰⣛⡆⠶⢳⡄⣇⡼⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⢸⡋⣳⠰⣿⡇⡏⢧⢸⡏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠹⢀⡠⣤⠤⠤⠤⢢⡀⠶⠀⠀⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢠⠁⠈⠉⠁⠀⠈⠁⠁⠈⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠦⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢰⣴⣶⣤⣀⣀⣤⣀⣀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠀⠀⠀⠘⣿⠀⢀⣀⣀⡈⢻⣿⠀⢿⣿⡆⠀⣌⣉⡳⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⢰⠟⠀⢻⣿⡿⠋⣠⡟⠁⢀⣿⣿⠀⣀⠀⠀⠈⠉⢦⣄⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇⠙⠁⠀⠻⣿⢠⣾⣿⣿⣿⣿⠋⢸⣷⣤⣀⡀⠈⠐⡀⠈⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⢀⣿⠁⢾⣿⣿⣦⠀⠈⠛⢿⣧⠁⠙⡆⠀⠹⣿⣿⣿⡷⠂⠩⠄⠈⠉⢳⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠛⠋⠛⠃⠀⢸⣿⣤⣶⡄⠈⠁⢀⣶⠀⢸⣿⠃⠀⠁⠀⠀⣿⣿⣿⣷⣤⣤⠀⠀⠀⠈⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠁⠀⠀⠘⠢⡀⠀⠀⠀⠘⠛⠻⠋⢵⣦⣠⣾⣿⣷⣌⠁⠀⡆⠀⠀⠀⠛⠁⠙⠛⠛⠉⢀⠀⠺⢗⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣠⡄⠀⠀⢀⣤⡤⠴⠏⠉⠙⠛⠉⠙⠳⢦⣴⣶⣤⠄⠀⠀⡀⢀⡀⢀⣠⣶⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠀⠀⠸⠿⠁⢠⣾⣿⣶⡀⠀⡇⠀⢠⣿⡟⠋⠀⠀⠀⢀⠋⠈⣿⣿⡿⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⢿⠀⠀⠀⣤⠀⠸⣿⡟⠿⠿⠾⢻⡆⠈⣩⣥⡀⠘⠃⢀⣤⠀⠸⣿⣿⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⡄⠀⠻⣷⠖⠀⠀⢸⡇⠀⠘⢿⣿⡄⠈⠻⣿⠀⠀⣿⣿⠃⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣍⣹⠇⠀⠀⠀⠴⠁⠀⠀⠀⢸⣿⣄⡀⠀⠀⣀⡴⠚⠃⠀⠰⢂⣿⡇⠀⠀⢨⡗⢤⠀⠀⢤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠛⠻⣷⡔⢀⠀⣾⠀⠒⠀⠀⢸⣿⡿⠿⠛⠛⢿⡄⢠⠀⠀⢰⣿⡿⠀⠀⠀⠀⢱⣤⠴⠛⢳⡾⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢸⡏⠀⠈⠀⠟⠀⠀⠀⣠⣿⡟⠁⠀⠀⣀⡄⠀⢀⣴⣠⡞⠁⠀⠀⠀⢠⡄⠿⠁⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠇⡜⠀⠀⠀⢰⣶⣿⣿⢿⣇⠀⣠⡾⠟⠁⢀⡾⢻⡟⠀⠀⠀⠀⢁⡘⠇⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠈⢷⣷⡄⠀⠐⣿⣿⣿⢏⡼⠃⢸⣿⣷⣄⠀⠙⡇⢸⡧⠀⠀⠀⠀⠀⠀⠛⣶⣤⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣿⣿⠉⠀⠀⠈⣿⣧⠂⠠⠐⠊⠉⠁⠛⠂⠀⠈⡌⠳⠆⣤⡄⢀⠀⣤⣤⣿⣿⠀⢀⣀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢶⡀⠙⠿⡧⣠⠄⣤⠀⠈⢉⢵⣶⣶⣤⣤⠀⠀⠀⠀⣤⡿⠀⣤⣵⣶⣿⣿⡿⠋⠉⠉⠀⠀⣿⣿⣿⡶⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠸⣿⣤⡀⠀⠀⡀⣿⠀⠀⢠⠀⠹⣿⣿⣿⠀⠀⠀⠰⠀⠀⣀⣀⠉⢿⣿⡁⠰⣿⣿⡆⢀⡖⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠈⢄⠀⠙⣅⠀⠀⠀⠀⠀⢻⣿⣿⠗⠀⠀⠀⠐⣿⡿⢿⣧⠘⠿⠷⠀⠘⠋⢠⡎⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡼⠀⠀⠀⠑⢄⠿⠑⢤⡀⠀⠀⢈⢿⣥⡶⠒⠀⠀⢴⠏⢀⠀⠛⠀⠂⠀⠀⠀⣤⡈⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡾⠆⠀⠋⠀⠀⣴⣾⣿⠁⠀⢈⣃⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠊⠀⠱⢆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⠀⠶⠀⠀⠀⣀⣀⠀⠀⠀⠀⠻⣿⠛⣿⠃⠀⢼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢰⣿⠙⢮⣯⠐⣆⡰⢶⠶⠛⠛⠁⠀⠀⠀⠀⢈⣤⡿⠃⠀⠀⠀⠀⢴⡏⠀⠘⠇⠀⡄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠛⣤⠍⠁⠀⠀⢀⣆⠀⠀⣀⡀⠀⠈⠻⣇⠀⢠⣾⡆⠀⠘⠁⠀⣀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⡀⠀⠀⠀⠒⢦⠀⠀⢸⡟⠀⣼⣿⣿⠀⣤⣾⠟⡠⣿⣀⠀⠀⠀⠀⢠⡉⠀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢛⡃⠀⡼⢃⣴⣧⠈⠉⠄⣴⣆⡀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢀⡀⠀⠀⠐⣤⣤⠀⠀⠀⠓⡈⠉⠳⠄⣶⣶⡯⠈⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠈⠉⠀⠀⠀⠈⠁⢠⣦⡀⠀⠱⠆⠀⢸⠟⢫⣴⣿⠟⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⡇⣿⣶⡖⠀⠀⢴⣤⣦⣠⡄⠀⢘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟⣯⠀⠈⣿⡇⠀⠀⣴⠃⠀⠉⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⢹⠄⠀⣯⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⡿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠻⠂⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⡀⠀⠐⠃⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⡻⠃⠀⠠⠄⠀⠀⠀⢀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠛⠛⠉⠁⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠁⢀⠀⠐⠠⠶⠖⠐⠛⠂⠒⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⢠⡘⠷⣄⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠐⠀⠀⡠⠀⠀⠄⡶⠄⠷⠒⠀⠶⠂⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⡑⠷⣦⡄⠀⠄⢀⢀⣀⣀⣀⣀⣀⣨⡆
⠀⠀⠀⠀⠡⠀⠀⠀⣀⢀⠀⢀⣀⡀⣷⠦⠤⢀⣀⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣀⡀⠀⠀⠀⠈⠉⠉⠉⠀⠉⠙⡄
⠀⠀⠀⠀⣄⠐⠈⠀⢀⣀⣀⢼⣶⣷⣿⣶⣄⢀⡉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣶⣤⣀⠀⠀⠀⡀⠀⠀⠀⠉⠉⠉⢓
⠀⠀⠀⠀⠀⠠⠖⠒⠋⠉⣡⣈⠀⢈⣀⣻⣯⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠿⣮⣝⣓⣀⣀⣈⣁⠀⠀⠀⠐⠀⠈⡀
⠀⠀⠀⠀⠀⠀⡠⢤⢖⡙⠀⠀⠀⠿⠤⠀⠸⣿⠷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⣈⣍⣃⣀⣈⣉⣉⠀⠀⠀⠠⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠐⠐⠂⠀⠈⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣧⡙⠛⣿⣄⣉⠉⠁⠀⠒⣊⠁
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠠⠈⢈⣉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡤⠄⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⣦⢀⡶
⠀⠀⠀⠀⠀⡀⢀⠀⢸⡇⠀⠀⡘⠇⠐⠥⢠⡟⠀⠀⠀⠀⠉⠼⠶⠂
⠀⠀⠀⠀⠀⠙⣊⢃⢸⣧⡀⠀⠀⠀⣠⡄⢸⣇⠀⢨⡅⢀⡤⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠘⠋⠀⠀⢿⣆⠈⣷⣀⣿⠀⠸⣇⠀⢸⡇⢿⡂⠀⣿⠀⠸⣠⡶⠆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣿⠁⠉⠉⠀⠙⠂⠀⠁⠈⠁⠀⠸⡧⠀⢿⡁⠀⠀⠀⢀⡶
⠀⠀⠀⠀⠀⠠⠤⠶⠀⠀⠀⠴⠋⠀⠀⠀⠀⠦⠞⠣⠄⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢢⡉⢤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠻⠀⣀⡀⠀⣦⠀⢀⡀⠀⠀⠀⠰⡀⠀⢠⠠⠀⠀⠀⣾⠀⣠⠄⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⢹⡆⣼⠦⢤⠀⣷⠀⢠⡇⠻⣦⣠⡾⠀⣿⢰⡇
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⡇⠳⠀⠘⠃⠻⠂⢸⡅⠀⠈⠃⠳⠄⢻⣸⣧
⠀⠀⠀⠀⠀⣤⠍⣁⠀⠀⠀⠀⣼⠃⠠⢀⣀⠀⣠⠄⣀⠀⠀⠀⠀⣀⠐⡀⠈⢧⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⠶⠞⠁⠀⡶⡍⠁⠀⢱⠇⠙⠃⠀⠀⠀⢫⡌⠳⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⢠⣿⡆⠀⣿⡀⠀⣿⣿⡇⣧⡀
⠀⠀⠀⠀⠀⠀⣼⡏⢸⡀⢹⣧⠀⣿⣿⣧⢸⡷⠄
⠀⠀⠀⠀⠀⠈⡏⠀⣼⣧⠈⣿⡄⣿⣿⣿⠈⢿⣷⣄⠀⣤⣤⣶⣤⣄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡆⠹⣿⣿⣿⣿⣀⠠⣙⠻⠀⣿⡟⣻⣴⣦⣧
⠀⠀⠀⠀⠀⠀⡇⠀⠀⣸⣿⡄⢹⣿⣿⣿⡇⠀⠀⠀⠀⣿⢼⡽⣜⣃⠙⢀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⢻⣿⣿⣻⣶⣶⣶⣿⣿⣾⡆⣿⣭⣾⣻⣽⡟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⣼⣿⣿⣿⢿⠿⠿⠛⠋⠷⣿⢿⣿⣿⣿⣿⣿⠄⠐⢠⣀⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠻⣿⣿⣿⠟⠋⠁⣀⠠⠄⠀⣢⣴⣿⣾⣿⣏⠙⢿⣮⡓⢄⡻⣭⣑⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢽⡀⠀⣽⣿⣁⣤⠠⠊⠁⢀⣶⣿⣿⣿⡿⠏⡿⠿⣀⣠⡌⡿⣦⡉⠺⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠿⠏⣿⣟⢻⡀⠀⠀⠀⠹⠳⣦⡀⠀⠀⠀⡏⢸⡇⠀⠘⢿⣦⡈⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠈⣿⡄⣇⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠓⠘⠃⠀⠀⠈⢿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⣀⣴⣿⣧⣽⠀⠀⠀⠀⠀⠁⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⢀⡀⠐⠀⠐⠀⣤⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀
⠀⠀⠀⢠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣀⠀⠀⠘⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠛⣝⠷⢚⣳⡀
⠀⠀⠀⠖⠓⠀⠀⠀⠀⠀⠀⠃⠀⠀⠓⠡⢿⣧⡀⢀⠀⣰⠿⠿⠾⡟⠁⠀⠄⠀⠀⠀⠀⠋⠿⡿⠁
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⢶⠲⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠙⠀⠀⠀⠀⢸⠍⢠⠀⠀⠄⠀⠀⠸⡟⠘⡛⣷⠖
⠀⠀⠀⠠⠄⠈⠁⠀⠀⠀⠈⠐⠀⠆⠁⠰⠀⠀⠈⠁⠘⢦⣄⣿⠀⠀⠀⠶⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⢠⠀⠀⠀⠀⠐⠿⠋
⠀⠀⡀⠀⠀⠀⠚⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⢀⢠⠆⠐⠀⠀⡀
⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣼⡛⡷⣦⣀⠴⠂
⠀⠈⢀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠀⠀⣿⣷⣷⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⣼⣥⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⣄⠀⠀⠀⡀⠀⡠⠇
⠀⠂⠀⠀⠈⠳⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠾⠷⡄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⠀⠀⠐⠀⠀⠐
⠀⠀⠀⠀⡄⠁⠀⠀⠀⢀⠀⠀⠐⢀⣹⣿⣿⣏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡀⢀⠀⡆
⠀⠀⠀⠀⠁⠀⠀⠀⠀⢬⡙⡆⠀⠀⡉⠻⠏⠁⠀⠀⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⢀⠀⢲⢃⠘
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠁⠀⠀⠁⠀⠀⠤⠀⠀⠀⠀⠉⣿⣿⣿⠿⢀⠈⠀⠈⠆⠀⠘⠀⢀
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⣤⠐⠀⠀⢠⡶⠂⠀⠀⠀⠀⠀⠀⢀⣐⠂⠀⠀⠀⠐⠀⢀⠁⣰⡽
⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⣠⠔⢚⠟⠁⠀⠀⠀⢠⣀⣤⠂⠀⠀⠃⠀⠀⠀⠀⠆⠐⠂⠀⠈⠀⢠⠞⠃
⠀⠀⠀⠀⢀⡞⠀⠀⠀⣴⣋⠤⠚⠁⠀⠀⠀⠀⠀⠘⡿⠿⠄⢀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢀⡎⢀⣠⣴⡴⠿⠓⠒⠒⠲⢤⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⢀⠂⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⢀⢂⡴⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⢀⠀⢸⣿⠀⠀⠀⡠⢡⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣼⠟⠀⣿⡇⠀⠀⠈⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠻⡀⠀⣿⡅⠊⠀⡄⢸⡟⠀⣴⡟⠇⠀⠀⠀⣨⠀⠀⠀⣀⠻⣧
⠀⠀⣀⠄⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⣿⡄⠀⣾⠇⣾⡇⢰⡿⠀⠀⠀⠀⢠⣿⠀⠈⡀⢹⡆⢹⡇
⢀⡞⠁⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⢹⣇⢀⣿⢀⣿⠁⢾⡇⠀⠀⡄⠀⠈⠧⢸⠂⠀⢼⠇⢸⡇⠀⠀⠀⠀⢀⡤⠄
⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠜⠘⠚⣿⠃⠘⣧⠀⡰⠀⠀⠀⠀⠀⠂⠀⠀⢀⠜⠁⠀⠀⣠⠞⠁
⡇⠀⠀⠀⠀⣠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⡠
⢣⠀⠀⢀⡾⠁⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠂⠀⢹⡗⠄⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠈⢆⠀⣼⠃⠀⠀⠆⢀⡴⠃⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣈⠄⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⢱⣿⠀⠀⠌⠀⢸⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⢸⡟⠀⡘⠁⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⣿⠃⡔⠁⠀⠀⠀⠀⢰⡟
⠀⡆⢸⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠠⡄⢰⣿⠀⠀⣠⠀⢀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢠⠤⡀⢀
⠀⠁⠸⣿⠀⠀⠀⠀⣀⣄⢀⡤⢄⣤⠀⣠⡆⣰⡇⠀⣿⠁⠀⣾⠃⢸⡟⠀⣼⡏⢠⣿⠀⢀⣿⠀⠀⠀⠀⠀⠀⠙⠂⠘
⠀⠀⠀⣿⡄⠘⣶⣰⣿⠄⣾⠇⢸⡟⢀⣿⠀⣿⠁⢠⣿⠀⢸⣿⠀⢾⡇⠀⢿⠁⢸⡏⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢹⡇⠠⣿⠘⣧⡠⠻⡤⠙⢧⠂⠛⠈⠹⣄⠊⣿⠀⠜⠻⠈⢸⡷⠀⠈⠂⠀⠓⠌⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠃⠀⢀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢿⡂⢀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⢃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⠿⠛⠛⠛⠛⠛⠛⠳⢶⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⣄⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣶⣶⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⣷
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⣛⣛⣛⣛⡳⢶⣶⣶⣶⣷⣷⣄⣠⣤⢴⠄
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠟⢁⣴⠾⢻⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡿⣇⣠⡞⠁⠀⢀⣁⣽⣿⣿⣿⠆⢹⡿⣿⣿⣿⣿⣿⣿⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠿⠇⠸⠿⠦⠥⡀⠀⠘⠿⣿⣿⡿⠋⠀⡿⢁⣽⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⣤⣿⣧⣼⣿⡟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠿⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⣦⣤⣄⠀⠀⢀⣤⣀⢠⠖⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢹⣇⢹⣷⡴⠁⠈⣿⠏⠀⢹⡇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸⡟⠈⣿⡇⠀⠀⣿⡇⠀⢸⡇⠀⠀⢀⡤⠄⠀⡟⡐⢀⣴⠂⢼⣡⣠⡿⠁⠀⣰⡶⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣿⡇⠀⠀⣿⡇⠀⢸⡇⠀⠀⣿⣇⠂⠀⡹⠓⣿⠃⠀⠈⢡⡿⠁⠠⢺⡿⠁⡰⣿⠇
⠀⠀⠀⠀⠀⠀⣠⡶⠛⢳⡀⠀⢰⡖⢆⠀⠀⣿⡇⠀⠀⢹⡇⠀⢸⡇⠀⠀⢻⣧⣠⠔⠁⠸⣏⡠⠊⠀⠸⡧⠔⠀⢿⡥⠊⣼⠏⠀⠀⢀⡷
⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⡇⠀⢻⣇⢸⠀⠀⣿⡇⠀⠀⠉⠁⠀⠀⠻⠦⠴⠃⠀⠠⠤⠤⣤⣤⣴⣆⣀⣠⡤⠂⠀⠀⢀⣼⠯⠤⠤⠶⠟⠁
⠀⠀⠀⠀⠀⢸⣿⠈⠷⠞⠁⠀⠸⣿⡸⠀⠀⠀⠀⢀⣀⡀⢠⣾⠀⠀⠰⠆⠀⢰⡏⡁⠀⠀⣸⡟⠉⠉⠀⢠⠊⣀⣤⠞⠁
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⣾⠁⣇⢼⣿⠀⠀⣶⡆⠀⢹⣯⠀⠀⢀⣿⠁⠀⣠⠀⣈⠉⢉⠁⠀⠀⢀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠈⣿⣆⠐⠙⣷⡘⠷⣟⢸⣿⠀⠀⣿⠀⠀⠌⢿⣇⠀⢼⡇⠀⢀⣿⠁⣸⠆⢸⡇⠀⣴⠏⢠⣿⠁⢸⣇⠆⠀⢦⡀
⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⢸⣇⠀⢸⠈⣿⣀⠜⣿⣆⠌⣀⠼⣿⡄⢺⡇⣠⢾⡇⠀⡿⠀⣾⠁⢸⡿⠀⣼⡇⠀⠸⣿⡀⢀⡾
⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⣿⣧⠀⠈⣿⡀⡔⠀⠀⠀⠀⢈⠽⠊⠁⠀⣿⡇⠈⠉⠀⠈⠀⠈⠃⠀⢿⠔⠻⠷⠊⠻⠤⢊⡀⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⠀⠀⠀⡏⢿⠇⠀⠈⠋⠁⠀⠀⠀⡴⠁⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⠀⠀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠾⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣦⠀⠀⠀⠀⣴⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠛⠋⠀⠀⠀⠀⠛⠛⠿⢷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠒⠒⠒⠤⣄⠀⠀⢀⡠⠔⠒⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠈⢷⣠⠏⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣀⠀⠀⡟⠀⠀⠀⠀⣠⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠛⠀⢀⣿⠀⠀⠀⠀⠈⠁⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⢀⡾⠈⠳⣄⣀⡀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠶⣤⣤⡤⠾⠋⠀⠀⠀⠀⠉⣹⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢠⠀⠀⠀⠀⠀⠀⠀⢀⡜⢁⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠳⠤⣀⣀⡠⠤⠚⠁⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣀⣠⣤⡴⠶⠶⢦⣤⣄⣀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⢀⣤⠿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⣀⣀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⠙⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠓⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠶⠲⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⣀⣤⣴⣾⣿⣿⣿⠿⠛⠉⠀⣿⠀⠀⠀⠀⢿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡇
⠛⠛⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢉⣡⠟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠛⠻⠷⣤⣍⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣶⣶⣶⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠻⠻⠿⠿⠿⣿
⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣀⣀⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⡀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠉⠑⣦⡀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠈⠒⢠⡿⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠠⠆⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⣶⡄⠈⠉⠁⠀⠈⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡾⢋⣀⣀⣀⠀⠀⢲⣾⣧⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⠔⠀⠀⠀⠀⠀⠀⠐⠠⣀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢋⣴⣾⣿⣿⣿⣿⣆⠀⠹⣿⣶⡀⢀⣤⣤⣀⡀⠀⠀⠴⠞⢣⣹⣿⣿⣿⣷⣶⣶⣤⣀⠀⠁⠀⢢⣘⡄
⠀⠀⠀⠀⡁⢈⡁⣀⠀⠀⡰⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣷⣄⠈⠛⠛⠛⠃⠌⠉⠙⢷⣷⡜⢣⢃⡾⠛⣿⣿⣿⡿⣿⠿⡿⠷⣤⡠⠌⡩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⣼⣾⡛⢾⠙⣿⣿⣿⣿⣿⠟⣿⠏⠙⣿⣾⣿⣿⣿⢿⣷⡀⠸⣿⡤⢣⡟⠀⠀⣿⣏⡇⠀⠀⠀⠀⠀⠈⣷⠘
⠀⠀⠀⠀⠀⠀⢠⢀⣼⠏⠙⠛⡄⠀⠘⠉⠀⠁⠀⠀⠋⠀⠠⣾⢿⡿⣉⣁⢻⡿⠀⣰⣟⣵⣟⣿⠀⢼⣿⣟⠁⠀⠀⠀⠀⠀⡠⡌
⠀⠀⠀⠀⠀⣴⢃⣾⣿⣤⠄⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠐⡏⢠⣿⣭⣿⡿⠀⢠⡿⣿⡿⣹⠟⢿⣿⣿⣏⠀⠀⠀⠀⠀⣼⠷
⠀⠀⠀⠀⢰⡧⣾⣏⣼⣿⣷⣾⣶⣥⡀⠀⠀⠠⠀⡀⠀⠠⠞⠀⠂⢹⣰⠎⠀⢀⣼⣻⡿⣓⡙⠀⢠⣙⣻⠿⢷⣆⣀⣀⣀⣿⠘⢄
⠀⠀⠀⢀⣧⣼⠻⡟⠉⠛⠣⠀⠉⠙⣿⡆⠀⠀⠀⠁⠀⠀⠀⢀⡤⠈⠁⠀⣰⡿⠿⢡⣾⣿⡗⠀⠀⠀⠀⠃⠨⣍⠛⠉⢸⣿⠀⠀⠑⡄
⠀⠀⠀⢸⠿⡿⠼⣿⣷⣤⣬⣂⣄⣼⣿⠟⣤⠠⣄⠀⠀⡠⠄⠈⠀⠀⢀⣴⢟⡤⢀⣾⡏⠛⢿⣦⡀⠂⠀⡀⠀⠀⠀⣰⡗⣿⢸⠀⠠⣈⠲⣄
⠀⠀⠀⡇⣠⠀⠀⠀⠙⠛⠛⠿⠟⠛⣡⣾⣏⣦⣈⠳⠈⠀⢀⣤⣴⠶⢋⡴⢋⡴⢋⠉⠀⠀⠀⠉⠻⠄⠀⣤⣤⣤⠾⡿⠇⠿⣠⠀⠀⠀⠀⠈⠣
⠀⠀⠀⣷⠹⠆⠀⠀⠀⠀⠀⢀⠀⣾⠟⢿⣿⡿⠋⠄⠀⣰⣿⠋⢀⣴⠟⣀⣼⣷⣶⡆⠀⠀⠢⡀⠀⠀⠀⠀⠘⠀⠀⠀⢠⠀⣿⡆⠀⠀⠈⠀⠀⠇
⠀⠀⠀⣿⣴⣿⣷⣶⣦⣴⣶⡟⢴⣿⣦⡴⠂⠤⠀⠀⣠⣿⣣⠾⠋⣹⣿⢿⣿⡿⣿⡷⣄⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣿⣿⣷⡄⠀⠀⠂⢸
⠀⠀⠀⣿⢿⣿⣿⣿⣿⡿⣳⣾⣷⠟⠉⠀⢀⡤⢄⣼⠟⠋⢉⣶⠶⠞⠁⠀⠉⠀⣨⣓⡝⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⢹⡄⠸⣿⠿⠟⣿⣄⣀⡼
⠀⠀⠀⢻⡄⠉⠛⠿⠿⠾⢛⡉⠀⠀⣀⡖⣋⠴⢎⣤⣀⡀⠊⠀⠀⠀⠁⠀⠀⠀⣼⣿⠇⢢⣤⡀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠇⠀⢿⣿⣷⡿⢿⣿⠁
⠀⠀⠀⠀⢳⡀⠀⠀⠀⠁⢀⣴⡶⠞⢫⠞⠁⣤⠜⠁⠀⠀⠐⠀⠀⢀⠀⠀⠀⠰⣿⣇⠀⠘⢫⢳⡄⢀⠀⠀⠈⠀⢀⡀⠘⣧⠀⠘⣿⣿⡤⠈⢻⣇
⠀⠀⠀⠀⠀⢻⣦⣤⣤⣴⣾⡏⠀⢠⡇⢠⡷⢴⡀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⢸⣿⣿⣿⢆⠀⠀⢠⠀⠀⠀⠀⠀⠈⠁⠀⠈⡄⠀⣿⠋⡷⣄⠘⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⢧⠀⢿⡄⣿⣷⣟⡟⡆⢠⡀⠐⣆⣠⢤⡄⡌⢻⡏⣿⣾⣿⠹⢿⣷⡄⠀⠀⠆⠀⠀⢀⠀⢀⣤⡇⠀⣿⠀⣴⣀⠀⢻⡅
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⢸⠀⠘⣧⣈⣿⣿⡇⣸⢸⣇⣢⣭⣽⣦⡙⠞⣄⠙⣿⠃⠹⣦⣈⣻⣷⡄⠀⠀⣱⡦⣌⠀⠠⢟⡅⠀⣿⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠛⠢⠀⠙⢧⠙⢯⠸⣿⡌⢻⡟⢿⣯⡻⣿⡄⠘⠀⠘⣧⡄⠹⣈⠛⢿⡇⠀⠀⠉⠘⠿⣋⠀⢈⠃⠀⠻⢀⢠⡛⠀⢸⡇
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⢼⠀⢀⠀⠈⢷⡐⢶⢻⣇⠸⣿⢳⣟⣷⣞⣿⣇⠤⠀⠉⢻⣤⣇⣀⡾⠁⠀⠀⠀⠀⠀⢀⢀⡏⠀⢠⣶⠃⢸⡇⠀⠘⡇
⠀⠀⠀⠀⠀⠀⣿⡿⣯⠁⠙⣦⢀⡀⢁⠀⠈⣧⠈⠉⢿⡀⠻⣦⣌⣭⠁⠈⣿⡄⠀⣀⡤⢬⣽⠏⠁⢀⣼⣿⣶⣄⠀⠀⠸⠃⠀⣾⡁⠀⢸⡇⠀⠰⡇
⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⠀⠈⢧⡁⠄⠀⠀⠈⠳⡀⠠⠿⣶⣻⣿⣿⣷⣾⣿⣿⠋⠁⠀⠀⢹⢷⡄⣸⣿⣉⣾⣿⠧⠀⣾⠀⠀⡟⠃⠀⢸⠅⠀⣺⠇
⠀⠀⠀⠀⠀⠀⢹⡃⠀⠀⠀⠒⠀⠻⣦⡠⠀⠀⠀⠈⠁⠒⠲⠲⠤⢬⣤⡭⠶⠒⠲⡄⠀⠀⠈⢈⣿⡿⡯⢵⣾⣳⣄⣦⠉⠀⢸⠁⠀⠀⣸⠆⠰⣿⠁
⠀⠀⠀⠀⠀⠀⢸⣇⣈⢁⣀⣀⣀⡀⠈⠻⣦⣙⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⠺⢿⣧⣾⣿⣿⣿⣿⡏⠀⢀⡟⠀⠂⣰⠋⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⢿⡀⠉⠉⠉⠀⠈⠛⠶⣤⣀⠀⠀⠐⠄⡀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠹⣿⣿⣿⡿⠛⠀⠀⡸⠁⠀⢀⣧⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣴⣒⠛⠟⠉⠓⠀⣀⠼⠁⠐⠀⢸⢹⠀⠀⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠰⢄⠀⠀⠀⠄⠈⢉⠀⢀⠀⠠⡄⠘⠗⠀⠀⡸⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⠀⠀⠀⠁⠀⠤⢀⣀⠀⢀⠀⣀⠀⠰⢀⡀⠟⠁⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⡀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠑⠈⡙⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣶⣦⣀⡀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠉⢀⠈⠈⠁⠈⡉⠈⡉⠉⠁⠈⠉⠀⠙⠛⠋⠀⠀⠀⠀⠉⠙⠛⠛⠲⠶⣿⣿⣤⣤⣤⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠁⠉⠉⠉⠉⠀⠉⠉⠈⠉⠈⠁⠉⠉⠀⠉⠉⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⢰⣿⠿⠛⠛⠛⢛⣿⡿
⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠠⡀⠀⠠⡧⢀⡤⢄⠠⣄⢤
⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⣼⠁⠀⠀⠀⠀⢸⠄⢌⠛⠆⠀⠀⡇⠸⡄⠸⠀⡏
⠀⠀⠀⠀⠀⠀⣠⣿⣟⣀⣀⣀⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢄⠸⡏⣿⣿⣿⣷⡄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡕⠻⠋⠉⠛⣋⣴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣠⠀⠄⠈⢢⡈⢻⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣋⠁⠀⠁⠂⢀⡆⢀⠎⡀⠘⠉⠙⠑⡖⠲⠆⠤⢤⠤⢤⣤⡤⢤⠤⢤⠴⣏⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠁⠐⣀⡡⠄⠈⢾⠀⠡⠀⠀⠀⠰⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠒⢀⣀⣸⠖⠁⠀⠈⢇⠃⠀⠀⢠⠃⠀⠀⠺⠀⡄⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠀⠀⢀⣸⡀⢀⠀⡆⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠄⠀⡞⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢒⣫⠵⠚⡇⢈⣤⣇⣀⣀⣂⣀⣁⣀⣬⣠⡤⠞⢻⣄⠙⢳⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡜⠁⠀⡜⠱⠃⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠰⢐⡇⠈⠦⣈⡼⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣰⠀⠀⡼⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠇⣀⠞⠀⠀⠘⣅⣀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠀⢠⠇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢡⡶⠋⠀⠀⠀⠰⢂⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⢠⠟⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡶⠋⠀⠀⠀⠀⣴⣦⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⣰⠇⠀⣀⠀⢸⡆⡀⠀⡀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⣀⢼⠀⠛⢸⡇⢸⠀⣟⠈⢈⠅⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠈⠁⠀⠈⠁⠁⠀⠉⠀⠈⠀⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⡴⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠤⠀⠀⠀⢀⣏⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢾⠆
⠀⠀⠀⠀⠀⠀⣂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⣀⠀⠀⠙⠒⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠋⠙⠛⠳⢦⣄⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⣠⡾⠁⢀⡴⠞⠋⠉⠙⢻⡟⠺⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⡤⢀⠀⠘⠀⠀⠀⢸⡿⠁⠀⠀⣼⠿⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠙⢿⣧⠤⠀⠁⠀⠀⢸⡇⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⢡⣾⡇⠀⠀⠀⣿⣇⠀⢠⣿⡟⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⣾⡏⠀⠀⠀⢀⣿⣿⠷⠾⠏⠀⠀⠀⠀⠀⠈⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣾⡏⠀⠀⠀⢰⣿⠣⣈⠀⢤⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢈⢷⣄⠀⠀⠀⠀⠀⠀⣠⣾⣿⠛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢠⣿⠇⠀⠀⠀⠀⢸⡏⢰⡷⣯⠘⠀⠀⠀⠀⠀⣀⢀⡀⣼⣤⣢⣤⣠⣦⡆⣴⣿⣦⣤⣴⣶⣶⣿⡿⣿⠿⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣣⣶⠀⠀⠀⣠⣴⡾⣿⣁⠀⠀⠀⠀⠀⢠⣵⠟⠛⠛⠻⢿⡇⢩⣿⣿⣿⠛⠟⠋⠉⠉⠁⠄⠀⠈⠁⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣦⠀⣰⣿⡼⠂⠁⠀⠀⠀⠀⢀⣴⠿⣿⠿⠟⠛⠛⠛⠛⠙⠛⠉⠀⠀⠀⠀⠀⠀⣀⢀⣀⣨⣶⣿⣧⣾⣷
⠀⠀⠀⠀⠀⢠⠀⠀⣠⣶⣿⣿⣿⣿⣯⡻⢄⡿⢁⡸⠧⢴⠄⠀⠀⢠⣿⣿⣟⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⠶⠄⢀⡀
⠀⠀⠀⠀⠀⠉⢀⣼⣿⣿⣿⣿⣿⣿⣿⣷⡾⢯⡘⠃⠀⠀⠀⠀⠀⢨⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣴⠿⠿⢿⠿⠻⣿⣿⣿⡿⣟⣉⣁⡐⣶⡶⣶⡆
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣭⣿⣿⡙⠛⠁⢠⣗⠫⠽⠖⠀⠀⠀⢺⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠙⢛⣿⣿⣿⣯⠿⣯⠳⡄
⠀⠀⠤⠀⠀⣾⣿⣿⣿⣿⡟⣋⣭⠏⣡⣶⣾⠄⣩⠜⠂⠀⠀⠀⠀⠘⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠃⠀⠙⠛⠻⠷⠋
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣟⡙⢻⣿⡆⠙⠉⢱⠎⣿⣼⡦⠄⠀⢀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⣠⠦⣄⡀⠀⠀⢹⡆⠀⠀⠀⠄
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣧⣤⡙⠋⢷⣿⡷⣷⣿⢈⣀⢀⣼⣿⠋⠀⠄⢀⣦⠔⠂⠀⠀⠀⢀⣼⠁⢀⣤⣤⡾⠛⠀⠀⠘⣀⠀⢸⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⣯⣴⠿⠛⠉⠉⠙⣿⠳⠷⠀⣴⡟⠁⠀⠀⠀⠀⢠⣾⣿⣴⣿⣿⣍⠁⠀⠀⠀⠀⠘⢿⣼⠃
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⡟⢻⣧⣼⣶⡟⠁⠀⢀⡀⠀⠀⠈⠓⠓⢾⡟⠁⠀⠀⠀⠀⠀⢳⣿⣿⣿⡟⠠⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⡄
⠀⠀⠀⠀⢹⣿⣿⣿⣍⣽⣿⡿⣿⠫⠘⣷⠀⠀⢸⠇⠀⠀⠀⠀⠀⢈⡇⠰⣀⣠⡀⠀⠀⡈⢿⣿⣿⣇⠀⢠⡅⠀⠀⠀⠐⠀⠀⣿
⠀⠀⠀⠀⠈⣿⡟⣿⣿⢿⢏⡝⠀⣴⠾⡏⠁⠀⢻⠀⠀⠀⠀⠀⠀⠾⠁⠀⠈⠁⠈⠉⠀⠀⠙⣗⣿⣿⡄⠘⠷⢎⢀⡀⠀⣸⣶⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣴⣾⡏⣾⠁⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣿⣿⢷⣦⡹⢯⣿⣻⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣾⣿⡇⣿⠀⠀⠧⠀⡆⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⠀⠀⢷⠻⠀⠀⠙⠛⠟⠛⠛⠛⠻⣿⡄
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣯⡏⢰⢠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⣶⣼⡧⡴⠞⢠⣼⣾⣷⣄⠀⠀⣤⣤⣴⣶⣦⣴⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣹⣿⣧⡟⣼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠉⠉⠁⠀⡀⠚⡟⠁⠉⠛⡇⠈⠉⠉⢿⡥⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠴⠀⠹⣿⣷⣿⣿⣷⣿⣾⡙⢷⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⢠⡶⠿⠀⢠⣿⠶⢡⣄⠀⢰⣄⠀⢶⣾⠟⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣟⣻⡿⠆⠀⠀⠀⠀⠀⢀⠤⠤⣾⠇⠃⠀⠀⠀⣤⣷⡀⠀⢀⣠⡀⢸⣧⡈⣿⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⠀⠀⢀⠟⠀⠀⠀⠀⢠⡿⠏⠀⠈⠀⠙⠁⠸⣇⠉⠉⠉⣹⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣧⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⡻⠁⠢⠀⠀⠀⠀⠀⠀⠈⠂⠀⢠⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣯⣿⡤⣿⣦⣀⡀⠀⠀⠀⠀⠠⡌⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣠⣞⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⡄⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣤⣤⣤⡤⠲⡎⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣗⣻⣣⡀⠣⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢠⡾⣻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣏⣌⢀⡛⡉⠓⠀⢀⡄⠀⠀⠀⢰⣶⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣧⡐⢦⠀⡄⠀⢀⣠⣶⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣾⣯⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⣦⡴⣛⣛⡛⠛⢿⣿⣤⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠻⣿⠞⢛⠎⠁⡀⠈⢻⣿⡯⢉⠉⢻⣾⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢻⠠⢠⢽⣄⢀⡄⠛⣺⣿⣟⣶⣼⢿⢻⡏⠛⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⣠⢷⣾⣄⣺⣶⠋⠋⠉⠀⠉⠛⢻⠾⣾⣥⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⣋⣊⡇⡷⠗⢺⣾⣿⣋⡱⡷⣄⣁⢀⣈⠿⣿⠁⠩⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⠯⠭⠙⣇⠆⠉⡁⢺⣇⣵⢬⣯⡄⠁⣾⠀⠃⠀⢰⡿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠀⠄⢑⠹⣄⠀⢀⠾⠍⠭⣶⣿⡷⠿⣿⢹⣿⡼⣼⠀⠘⠋⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢻⣏⡛⣆⠐⣆⢠⠗⠛⡛⠾⡀⠀⠀⠈⣿⢃⣰⠇⠤⠦⣤⡤⠖⠀⠐⢀⣿
⠀⠀⠀⠀⠀⠀⢠⡿⠟⠉⢛⠛⣧⡞⠪⢴⣀⣂⣷⢤⣴⣾⣶⣿⡯⠑⠂⡐⢢⣦⠁⠉⠁⣈⣿⡆
⠀⠀⠀⠀⠀⢠⡟⠙⣤⠭⠤⣾⡿⣿⡜⠌⣢⣴⣽⣼⠇⠈⠻⣿⣿⡮⣄⠄⡾⣯⣠⣄⠴⣿⣻⣇
⠀⠀⠀⠀⢠⡟⠁⢉⣣⣿⣷⡿⡷⢾⡉⠛⠁⠀⠸⣧⡀⠀⠀⢨⣟⠻⠜⡾⣷⠖⡋⣙⠙⢻⣉⢻⣷⡀
⠀⠀⠀⠀⣾⠁⠀⠺⣼⠋⡀⢙⠙⣯⣷⣄⠀⠢⡞⣩⠟⢷⠦⣾⣋⡑⢄⣷⣼⣄⣾⣿⣷⣼⠁⣸⣿⠇
⠀⠀⠀⠰⣯⡀⠀⣖⣻⣦⣁⢈⣠⡟⢻⣿⣿⣶⣾⣽⠴⢿⣷⠊⠁⠉⢿⣿⠀⠀⠉⣠⢨⣧⠉⢙⣹⡆
⠀⠀⠀⠰⣿⡭⢵⡛⣳⢿⣽⡟⠳⣞⣿⠉⣶⡆⣹⡿⡉⠂⡽⣜⣓⣠⠟⠉⠑⠲⢾⠀⣻⣠⠀⡀⣟⣹⠆
⠀⠀⠀⣸⡏⠄⠛⢹⣫⡖⢎⡗⠈⠙⣼⢙⣶⠟⠛⠾⠾⠛⠛⠙⢯⡇⠐⠠⠐⠀⣼⡦⠧⣌⠀⢰⠭⢽⡇
⠀⠀⠀⢹⣧⡘⢢⠞⠛⠓⠶⡾⣦⡀⡿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢠⣏⣼⠗⣠⣿⠟⢠⣼⡇
⠀⠀⠀⠀⠉⠛⠻⣦⣀⡀⢀⡽⣯⣁⣠⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣤⢤⣿⣟⣠⣭⡆⣽⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠙⠛⠉⠛⠉

⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣻⣿⣻

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


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠁⠈⠀⠈⠉⠁⠀⠉⠀⠁⠀⠈⠁⠀⠁⠀⠈⠉⠀⠁⠁⠈⠁⠀⠈⠉⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠾⢉⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡁⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣦⣄⢀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⢀⣀⣀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣄⣷⣶⣿⣾⣾⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⣼⣿⣿⣿⣿⠿⣿⠛⢿⠋⠙⠲⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⠟⠋⠉⢀⡇⡀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⢀⣀⣁⡀⠀⠀⠀⡀⢀⣀⡠⠀⠄⣰⠃⣠⠞⠓⡀⢀⣿⣷⣿⡿⢁⡤⠀⣰⡏⠁
⠀⠀⠀⠀⠀⠜⠉⡀⠶⠦⡼⣁⠉⠉⠉⠉⠉⣿⣭⡟⢀⡾⠀⡉⢠⣧⠤⠀⠑⣾⣿⡟⠁⣰⣿⠁⢰⡏
⠀⠀⠀⠀⠀⠀⡼⠀⡈⠀⠀⠉⠀⠀⠀⠀⠀⢹⡟⠀⣾⡇⠀⡇⠀⠓⠠⣤⣾⣷⠟⠀⢞⣹⡏⠀⣌⠁
⠀⠀⠀⠀⠰⡀⠀⠀⠵⠚⢀⠾⠀⠀⠀⠀⢀⡾⠀⣼⣿⣧⠀⡃⠀⠀⠀⠉⣿⡏⢠⡁⠈⣽⠀⢸⡅
⠀⠀⠀⠀⠀⠈⠙⠛⠒⠉⠀⠀⠀⠀⠀⢠⣾⠁⣰⡿⣿⣿⠀⢀⠀⠀⢠⣼⡿⢠⣿⣧⣼⣿⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣼⡏⢰⣿⡟⣸⣿⡇⢸⣶⣼⣿⣿⠇⣾⣿⣿⣿⡿⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣶⣿⣿⠀⣾⣿⣿⣿⣿⣷⠘⣿⣿⣿⡏⢰⣿⣿⣿⣿⣿⢸⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣶⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⠀⣾⣿⣿⣿⣿⣯⢸⣿⣿⣿⣿⣿⣷⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣭⣾⣿⣿⣿⣿⣿⢁⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠇⣸⣿⣿⣿⣿⣿⣏⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠏⣰⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⠟⢛⣙⣛⠛⠿⢷⣠⡀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣏⠰⣿⣏⢹⣿⣿⣦⡉⢿⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⡿⣰⠀⣿⣿⣿⣿⣿⣿⠿⠛⠁⠸⢿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣷⠈⣧
⠀⠀⠀⠀⠀⣻⣿⣿⢛⡛⣿⡿⢃⣼⡿⣹⢿⣿⣿⣿⣿⣿⣧⣡⣾⣿⣿⣿⣿⠏⢰⠾⠂⣴⣶⣦⣤⣉⠛⠻⢿⣿⣿⣿⣿⣿⡿⠃⣰⡟
⠀⠀⠀⠀⠀⢽⣿⣿⣘⠿⢋⣵⣿⣿⣱⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣭⣭⣭⣤⣾⣿⠁
⠀⠀⠀⠀⠀⢺⣿⣿⠟⢿⡿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠋
⠀⠀⠀⠀⠀⢸⣿⣿⣛⡿⣳⣿⣿⠿⣯⢽⣿⣿⣿⣿⣿⠟⠿⠉⠉⠁⠀⠁⠈⠉⠉⠉⠉⠀⠈⠁⠉⠉⠉⠙⠋⠋⠉⠉⠋⠉
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣷⣿⣰⣿⣿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣼⣯⣽⣿⡯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠹⣿⣿⣿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣀⣄⡀⢠⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣬⡛⣶⣂⠈⣵⣾⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠈⡻⣿⣿⣾⣥⣾⣿⣿⣿⣿⡟⡟⣿⣿⣿⡇⣠⠂⠀⠀⠀⠀⠀⠸⠋⣽⣶⡄
⠀⠀⠀⠀⠀⠀⠀⡀⣠⣴⣶⣿⣿⣧⡘⠀⠙⡿⣿⣿⣿⣿⣿⠯⠡⢾⣷⠸⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⢮⣻⣿⣶⣦⣄
⠀⠀⠀⠀⠀⢠⠂⣼⣿⣿⣿⣿⣿⣿⣿⣦⡄⢹⣿⣽⣿⣿⣏⣿⡄⠸⡴⢌⣽⣽⣿⡇⡀⠀⠀⠀⠄⠀⠀⠀⠈⢿⣿⣿⣿⢸⡄
⠀⠀⠀⠀⠀⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣿⣿⣻⣿⡿⣶⣷⣸⣽⣾⣿⡟⠈⢻⡍⠀⠀⠀⠀⠀⠀⠀⡄⣡⠻⢯⣿⠀⣳
⠀⠀⠀⠀⢸⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠛⢷⡿⠿⠿⠿⠿⠋⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠂⣼⠟⢰⡏
⠀⠀⠀⠀⠈⢿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣰⣦⣦⡈⠀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣼⣿⡿⣋⣿⣯⢇⡾⠁
⠀⠀⠀⠀⠀⠀⠓⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣌⡿⠋⠀⠈⠉⠉⠛⠛⠻⢿⣷⣶⣀⣌⣤⣭⣿⠿⠿⣻⣫⣾⣿⠏⠄⢸⠃
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⡇⠀⠀⠉⡠⢀⠠⠖⢢⣼⣿⣿⣿⣿⠟⠛⠛⠛⠿⠋⠉⠋⢿⣏⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠀⠀⠀⠙⠟⠋⠆⠀⠀⢹⣷⣀⠀⢏⠈⣄⣨⣴⣿⠟⠋⠀⣠⣞⣆⠀⠀⠀⠀⠀⠀⡘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢹⣦⡀⠀⠀⠘⠄⠀⠈⠻⣿⣷⣾⣶⣿⠿⠋⠁⢀⡰⠚⠙⠿⠛⠀⠀⠀⠀⠀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⢤⠀⡄⢀⣿⣿⣷⡀⠀⠀⠀⢀⡀⠀⠈⠛⠛⠋⠁⠐⣂⡀⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿
⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⢹⠉⢋⡀⣀⠀⠀⠀⠈⠐⠀⠄⠠⠶⠶⠖⠈⠀⠀⠀⠀⠀⠀⠀⢠⣠⣾⡏⢏⡷
⠀⠀⠀⠀⠈⠉⠀⠰⠀⠀⠀⣿⠀⠀⠉⢻⣦⡀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⣄⡴⠀⣿⡿⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⣏⠀⠀⢰⣿⠟⠛⠓⠻⣤⣀⣤⣄⡀⣠⣶⣢⡾⠟⠳⣿⣞⡿⠁⠸⠙⠿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠼⠂⠀⢈⣇⣀⢈⣶⣤⣿⣭⠿⣿⣿⣿⠿⡛⢂⡠⠿⢷⣿⡇⠀⠀⠀⠀⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⢏⠀⠀⠀⠀⠀⠀⠈⠙⢻⣯⣿⣉⣻⠞⠁⠉⢿⠋⢠⣸⠟⢷⣶⣺⢹⡆⠀⠀⣆⡀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟⡻⠉⠁⠠⠠⢌⣤⡸⢁⢀⣾⠻⠻⣿⠇⠀⢰⡃⠀⠀⠀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠀⠀⢠⡄⢾⣿⣷⣷⡞⠓⣴⣣⢼⣿⡁⠀⢠⡉⠓⣾⢿⠂⠀⠎⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣠⣆⣤⣾⡻⢿⣿⡦⣴⠟⠁⣠⣠⣿⡶⠺⡇⠀⠄⠀⠀⠈⠀⠀⠀⠀⣾⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣿⠟⠉⠉⡉⢍⣇⠹⣷⡎⠀⢀⣿⠿⠛⠻⢿⡷⠦⠀⣴⠀⠀⠀⠀⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢉⣄⣴⣿⡷⠿⣧⣼⣿⠁⣠⣾⡅⢠⣾⣿⣿⣿⢣⣾⡿⣃⠀⠀⠀⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠿⢻⣿⣿⠟⢻⡿⠟⢽⣆⡀⠉⢷⡀⣿⣿⣿⡿⠛⡛⡕⠁⠀⠈⠀⣶⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣄⣈⣋⣀⣀⠁⢀⣴⣿⠿⠟⠀⣹⣧⣿⡿⠉⣀⠒⢩⠷⠀⠀⠀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢋⣤⣾⣿⡁⢲⣿⣿⡿⠃⠀⣀⠮⠱⡐⣶⣾⣷⡀⡀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠙⠛⠛⠉⠀⠀⠈⠀⣠⣾⡿⠛⠉⠉⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢐⣿⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⠛⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠁⠀⢀⣾⣿⠏⠀⠀⣀⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⢠⣿⣿⠏⢀⣴⣿⠿⣿⡇⢀⣶⣿⡿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⡄⢠⣿⣿⠏⣰⣿⣿⢣⣾⡿⢣⣿⣿⠋⣠⡾⠁⣠⣄
⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⢿⣷⡄⠀⠀⠀⠀⠀⣿⣿⠏⢰⣿⣿⠃⠘⠿⠇⣿⣿⡧⠾⠋⠀⢀⣿⡿
⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁⣠⣿⣿⢃⣴⣶⣦⡀⠀⣿⣿⡀⠘⣿⣿⣄⣀⣤⠞⠻⣿⣄⠀⢀⣠⣾⠟⠁
⠀⠀⠀⣼⣿⣿⡿⠁⢠⣾⣿⡟⠁⣼⣿⡅⣸⠇⠀⠈⠉⠁⠀⠈⠉⠉⠉⠀⠀⠀⠈⠉⠛⠋⠉⠀⠀⣀⣀⡀
⠀⠀⣸⣿⣿⡿⠁⠀⠸⣿⡏⠀⠀⠘⢿⣿⣿⣤⣤⠀⢀⣤⣶⣿⣿⣦⠀⢀⣴⣾⣿⠿⣆⣾⣿⠆⢀⣿⣿⡟⡴⢿⣿⠇⣴⢟⣿⣷
⠀⢀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣹⣿⡟⢀⣾⣿⡟⠁⣼⠏⢀⣾⣿⠟⠁⢰⣿⣿⠏⠀⣼⣿⣿⡟⣱⣿⢏⡾⢁⣾⣿⠃
⠀⠸⣿⣿⡏⠀⠀⠀⣸⣷⠀⠀⣠⣾⡿⣱⣿⡿⠁⢸⣿⣿⡴⠞⠋⢀⣾⣿⡏⠀⣠⣿⣿⠏⠀⣼⣿⣿⠏⢰⣿⣿⡟⢀⣾⣿⠃
⠀⠀⢿⣿⣇⠀⠀⣠⣿⡿⠐⠿⠿⠛⠀⣿⣿⣁⣴⠟⣿⣧⣀⣠⡴⠛⢿⣿⣷⡾⢻⣿⣯⣴⠞⣿⣿⠏⠀⣿⣿⡟⠀⣾⣿⠃
⠀⠀⠀⠙⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠈⠉⢉⣥⡀⠀⠉⠉⠁⠀⠀⠈⠉⠁⠀⠀⠉⠉⠀⠀⢀⣉⣀⣤⣬⣽⣶⣾⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⣦⣤⣄⣀⣀⣀⣀⣤⣤⣤⣶⣶⣾⣿⣿⣿⡿⠿⠛⠛⠉⢻⣿⠁⠈⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠈⠿⣷⣤⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⡀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠋⠉⠉⠉⠹⣿⣿⡷⢠⡾⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣁⣠⣤⡀⠀⠀⣀⣰⣿⣿⢧⣿⠁⢀⡞⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⣠⡾⠿⠿⣿⡿⠀⠀⠙⠛⠋⠁⣾⡏⢀⡾⠁⠀⢿⠿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⡀⠀⠞⠁⠀⠀⠀⠉⠁⠀⢀⣴⡞⠀⢠⣿⣣⠞⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⢀⡇⠀⠀⠀⠀⠀⣀⠀⡀⠀⣾⣿⣦⣀⣼⣿⠋⢀⣀⠀⢸⣷⡀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⡼⢁⣠⡀⢤⢨⠁⠓⠁⠁⠀⠙⠿⣿⠛⢻⣿⠀⠈⣿⠀⠀⣿⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⡼⠃⠀⠃⠀⠀⠀⠀⠀⣀⣀⣴⡦⠀⣿⡇⢸⣿⠀⠐⣿⡄⣸⣿⣧⣴⣶⣶⣦
⠀⠀⠀⠀⠀⠀⢀⣴⡾⠁⠀⣿⣿⡾⠁⠀⠀⣠⣤⡄⠐⣿⡼⣿⡟⢸⡇⠀⣿⡇⠈⢿⣷⡄⠙⠛⢁⣿⣿⠉⠙⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣧⣀⣠⣿⡿⠀⠀⢀⣾⠏⢀⣥⠀⣿⠃⣿⡇⢸⣷⡄⠻⠿⠂⠀⠀⠀⠀⢠⠟⣿⡇⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛⣉⣿⣇⡀⣀⣼⣿⠀⢸⣿⠀⣿⡇⠙⠗⠀⠈⠀⢀⢠⡀⢐⠂⠀⢠⡟⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠛⢧⠘⣿⣦⠏⠛⠋⠀⠁⠀⠀⠀⠀⠡⠌⠘⠋⢈⡄⠀⣼⠀⢨⣭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠘⡇⠈⠁⠀⠀⠀⠀⠀⠀⢠⣾⣇⣀⣀⣤⡶⠋⡠⠀⡇⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⣿⠀⣤⣾⣿⡿⠿⠀⠀⠸⢿⣿⠿⠟⢁⣠⠞⠀⠀⠓⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣤⠇⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣷⣶⣤⡶⠶⠚⠋⠁

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

⠀⠀⠐⢄⠀⠀⠀⠀⡠⠐⠀⠀⠉⡀⠀⢤⠐⠤⡀
⠀⠀⠒⠚⠠⡀⡠⠀⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠐⠒⠒⠂⢤⢀
⠀⠀⠀⠀⡠⠃⢓⠀⠀⠀⠀⠛⠻⠛⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣠⠀⠒⠀⡀⠂⠀⣄⡀⠀⠀⠀⠀⢀⠔⠨⡤⠈⡄⡄⢠⡆⠇⡀⣈⠢⡀
⠀⠀⠀⡎⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣤⠘⠀⠀⠀⡃⠀⡔⠁⠈⢆⠀⢀⡇⠀⡔⠁⠈⢂⠀⠀⢀⠲⢄⠀⠃⠀⠰⠘⠚⡙⠀⠳⢁⡤⠓⡀
⠀⠀⠀⢳⡀⠀⠑⢄⠀⠀⠀⠀⡠⣿⣿⣿⠏⠀⠀⠀⠀⠃⠌⠀⣶⢴⠈⢆⠀⠀⡔⠀⢸⠀⠀⠂⠀⠂⠀⣤⠛⠢⣀⢀⠧⠰⢇⣠⠔⡅⣠⢀⢠
⠀⠀⠀⠀⠉⠓⠶⠤⠤⠾⢿⠟⠁⠀⠀⠀⠀⠀⠀⡠⠊⠰⠢⠤⢀⡈⠀⠈⡦⠼⠀⠈⣈⡀⠤⠼⠀⣀⠀⠠⠟⠀⢨⠁⠀⠀⠀⢁⣀⣘⣋⣛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠢⠤⣀⣀⠀⠠⠊⠀⠀⡆⠀⡖⣀⠈⠉⠚⠀⠘⠉⢁⣀⠀⠀⢸⠀⠀⠀⡟⡫⠉⠙⠀⠀⠀⠀⠀⠀⠐⣤⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠉⠁⠀⠀⠀⡥⠀⣉⣊⣀⡀⡅⠀⡄⠀⠘⠑⠀⠀⡄⠀⢂⠀⣋⣱⠤⠔⠇⠀⠀⠠⠲⠤⠬⢈⣀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠄⠁⣈⡀⡐⠀⠀⠀⠀⠀⠀⢰⡒⠀⠀⠁⢠⠉⠉⠉⠉⠉⠉⠁⠀⠘⠁⢰⠉⣳⠀⢠⠀⢀⠁⠀⢦⠂⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡄⠀⠁⠀⠀⠀⢀⠆⠤⣘⣀⠀⠀⠀⢸⠀⠀⠰⢀⣀⠴⠀⠀⠀⡦⠤⠍⠭⠄⢸⠀⠖⠀⠤⠬⠄⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠥⠔⠊⠢⡀⠠⡆⠀⡤⠄⠈⠉⢱⠀⠈⠖⢲⡍⣡⠀⢀⡵⢠⠘⢄⠀⣯⠵⠀⠈⠀⠀⠀⡰⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠉⠀⡴⠒⠀⢠⠁⣀⡘⢄⠫⠁⠀⢀⠂⠀⠀⢁⠘⠙⠃⡣⣊⠀⠸⠀⡠⣕⢧⡀⢀⠂⠀⡀⢀⡁⠕⣚⣄⣀⡶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠑⠂⠀⡎⠀⣇⠝⠈⢢⠀⡠⠁⠀⠀⠀⠀⠣⣀⠞⠀⠏⢲⠀⡀⠤⠜⠀⡸⠃⠀⠀⠘⣁⠴⢊⠜⡙⡉⢋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⠴⠅⠀⠀⠀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠠⠇⠠⠐⠈⠀⠀⠀⠀⠀⠈⠐⠡⠴⠥⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣒⣍⣫⣍⣫⣝⣩⣝⣩⣒⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣎⣭⣉⣬⣉⣌⣩⣌⣡⣌⣡⣍⣡⣍⣥⣉⣭⣱⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣤⣉⣤⣉⣤⣩⣬⠥⠬⠇⠸⠥⠬⣥⣍⣤⣉⣤⣉⣤⣹⣄
⠀⠀⠀⠀⠀⠀⢀⣞⡴⣌⡴⣭⣴⡭⠚⠁⠀⠀⠀⡀⠀⠀⠀⠀⠈⠓⢭⣤⣭⢦⣡⢦⣳⡀
⠀⠀⠀⠀⠀⢀⡾⣮⡴⣬⡶⣬⠊⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠑⣥⢦⣥⢦⣵⢷⡀
⠀⠀⠀⠀⠀⣼⡴⢦⡴⣤⣶⠁⠀⠀⠀⠀⠀⠀⣾⠟⣿⡄⠀⠀⠀⠀⠀⠀⠈⣶⣤⢦⡴⢦⣧
⠀⠀⠀⠀⠀⣧⡴⢦⠶⢦⡇⠀⠀⠀⠀⠀⠀⣸⡿⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⢸⡴⠶⡴⢦⣼
⠀⠀⠀⠀⠀⣷⠞⢦⠞⢶⡁⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⢈⡶⠳⡴⠳⣾
⠀⠀⠀⠀⠀⡷⠞⠷⠞⠶⡇⠀⠀⠀⠀⠀⣾⡿⠿⠛⠛⠛⢿⣇⠀⠀⠀⠀⠀⢸⠶⠳⠾⠳⢾
⠀⠀⠀⠀⠀⢱⠞⠳⠞⠷⢻⡀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⢀⡟⠶⠳⠞⠳⡎
⠀⠀⠀⠀⠀⠈⢟⠳⢛⠳⢛⠿⣄⠀⠿⠿⠿⠆⠀⠀⠀⠀⠰⠿⠿⠿⠀⣠⠿⡛⠞⡛⠞⡻⠁
⠀⠀⠀⠀⠀⠀⠈⢷⣋⠳⣋⠻⣛⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⣛⠟⣙⠞⣙⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⣋⠛⣉⠛⣙⠛⣙⢒⡒⢦⡴⢒⡒⣋⠛⣋⠛⣉⠛⣙⣻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣉⠛⣉⢛⣙⢋⡙⢋⡙⢋⡙⣋⡛⣉⠛⣉⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠯⣍⣋⣝⣋⣝⣫⣙⣩⠽⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠠⢀⠈⢀⠀⠀⠀⠀⠉⠠⢀⠆⠈⠁⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⡆⠹⣄⠀⠀⠀⠀⠀⠀⠩⠄⠐⠘⠓⠀⠀⠂⡉⠀⠀⠀⢁⠀⡀⠀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠌⠀⠀⣀⠀⠘⠀⠀⠀⠀⠀⠂⡑
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠐⢄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡀⠀⠂⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠛⠀⠀⠀⠀⠒⠅⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⣀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠆⠄⡀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠢⠄⢌⣰⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⣠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡅⠤⠀⠋
⠀⠀⠀⠀⠀⠀⢀⠓⠘⠀⠡⠂⠁⠀⠀⠀⠰⠁⠠⣤⠄⠄⡶⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠸⠀⠘⠐⠁⠀⠈⠀⢤⠀⠀⠀⠀⠀⠀⠠⠄⠀⢠⠀⠀⠍⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠈⠀⠀⠀⢀⠀⠹⠇⠀⠀⠀⠈⠙⠠⣘⢀⠀⠐⠀⠂⢐⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠐⠀⢀⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⢆⣃⢔⡂⠡⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⡠⠀⠁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣄⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡈⠀⠀⠀⡄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠁⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠳⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠌⠀⠀⠀⠐⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⣀⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠊⡠⠀⠀⠀⠀⠀⠀⠀⠢⢄⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠖⢀⡐⠣⠤⠀⠀⠀⠀⠤⠤⠤⠄⠶⠀⠀⠄

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣶⣶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣸⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⢀⣀⣀⡉⠀⢹⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢠⣾⣿⣿⣿⣿⣷⡄⠙⢿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠟⣾⣿⣦⡀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣶⣄⡀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠈⢿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⠀⠈⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⣠⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠷⠶⠶⠾⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠦⠴⣄⠀⠀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⠀⠀⣀⠀⢀⠉⢤⣴⣦⠀⣼⣶⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣷⣾⣿⣿⣿⣿⣿⠁⢋⣭⣙⣧⣀⠀⡿⠋⠀⣹⠿⢿⡿⠛⢋⠁⣾⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⠯⣏⠀⢈⣽⡇⢀⣴⡇⠈⠀⠀⠀⠈⡃⠁⠶⢆⠈⠲⡀⠃⣰⠏⠀⠻⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢛⢀⣀⣠⣵⡿⠟⣡⡞⠁⠀⠀⣤⣤⣶⣶⠀⠀⠀⠰⣄⠀⠀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⢀⡄⣀⣨⣤⣿⣿⣿⣿⡿⣸⡶⡿⠧⠀⠀⠠⠿⢿⣿⣿⣆⡀⠀⡠⠋⢸⣇⢀⣀⠜⠚⠋⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢠⡐⠤⢉⣿⣿⡿⠿⢿⡏⡙⠁⠀⣤⣴⣆⠀⠀⠀⠀⠹⠟⠁⠀⠀⡤⠤⠀⠁⣁⡉⠀⠀⣤⠿⠀⠘⠁
⠀⠀⠀⠀⠀⠈⣁⡠⣿⣿⣿⣷⣿⡆⢷⡅⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⣀⣴⠺⣁⣴⣶⡄⢩⡀⠃⠀⠘⢀⡠⡆⠛
⠀⠀⠀⠀⠀⢈⣉⠀⠙⣿⢿⠿⠏⠐⡾⢿⣤⣤⣤⠖⠀⠀⣀⠀⠀⠀⠀⠻⣼⣧⡈⠛⡟⢣⡼⣩⣋⠁⠀⣈⠁⡄⣠
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣯⠧⣀⢴⣌⣿⡎⢿⡇⠻⠀⠀⣴⣿⡆⠀⠀⠀⠀⢿⠛⢍⣼⣷⣯⣧⠘⠙⡇⣤⣫⠀⢠⡝
⠀⠀⠀⠀⠀⠀⠀⢿⡙⠻⣇⡈⢻⣿⢯⣿⡾⣜⠃⠀⠀⢹⣿⣿⡀⠀⠀⠀⠘⢃⠈⢻⡿⠋⢿⣜⠁⠠⢨⣭⠠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⠈⣙⢄⡙⣿⣫⣄⡏⢠⣆⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢠⡌⢡⠇⢸⣛⠀⠚⣮⡀⣠⢰⠇
⠀⠀⠀⠀⠀⠀⠠⣶⣌⣳⢤⣼⣟⣑⣼⡟⠎⢠⡌⠁⣀⣀⢀⠠⣤⣄⠀⠀⠀⠀⠸⠁⡟⢀⣋⠙⣀⣴⣽⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠚⣡⣟⢹⣅⢘⡙⠀⣾⣷⠴⡿⠋⠀⣿⣿⣿⡇⠀⠀⠀⠀⢨⣿⠁⠀⡀⢊⣿⣿⣿⣯⣷
⠀⠀⠀⠀⣠⣤⡞⠻⣾⡶⠉⣟⣤⣿⡟⠁⣸⣅⡘⢫⣦⠀⠘⢻⢿⣿⣿⣆⠀⠀⠀⠈⢻⠆⠃⢤⡆⢴⣿⣿⠛⠉⣀⡀
⠀⠀⢠⠞⠁⠈⣡⣠⣿⣷⣋⡟⢻⣤⠀⢀⠻⠟⡗⢸⣯⡁⢠⣤⣄⡿⣿⠿⠄⠀⠀⠀⠀⠀⠑⠒⢤⠈⣟⠁⢲⣿⠋
⠀⠀⠳⠀⠀⣰⣿⣿⣿⣿⡬⢗⠛⠁⢀⡀⠐⠃⡘⢇⠙⠠⡴⠤⠀⢻⣿⠯⢿⣄⠀⠀⠀⠈⠿⠂⡢⣹⠻⠅⠋⣿⣀
⠀⠀⢼⡁⠀⠻⣿⣿⣿⡟⠉⠢⠟⠻⣏⠰⡿⢂⡑⠬⣦⠀⣶⡀⢃⢜⣿⡿⢋⠽⣢⡀⠀⠀⠀⠐⠿⠆⡤⠀⢀⡿⠛⠃
⠀⠀⠘⣇⠀⠀⠙⢛⡧⠀⣴⣶⣆⠀⢹⡐⠚⠋⠀⠀⡇⢷⠜⠀⠚⠛⠚⠿⠡⠌⠀⠆⠀⠀⣠⣀⣀⣀⡤⠴⠞
⠀⠀⠀⠘⠓⠒⣧⣸⡇⠀⠻⠿⣏⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠈⠈⠛⢢⣤⣄⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣷⣿⣿⣿⣼⣯⡟⣻⠶⣄⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣶⣄⣀⣀⣠⣾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⢾⣻⣿⣿⣿⣾⣾⡏⠁⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⡀⠀⠀⠀⠀⠀⢄⠠⠄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣀⣀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⡿⣿⣿⣷⣦⣤⣴⣶⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠿⣇⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⡿⣿⣿⡾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠙⠿⣶⣼⣿⣧⡀⠈⠟⠿⣿⣿⣿⣿⠿⢃⡾⠚⠟⠉⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠷⠶⠤⠶⠏⠁⠀⠈⠀⠠⠀⠈⠀⠀⠀⠀⠉⠀⣀⣿⣿⣿⣿⢏⣴⣶⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣠⠀⣤⣄⣀⣤⣤⣤⣤⣴⣾⣿⣿⣿⣏⢸⣯⣙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣾⣿⣿⣿⣿⣏⢸⣿⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣦⡙⠟⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠰⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢠⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢨⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣺⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢉⣿⣿⡿⠯⠁⠀⠉⠻⣿⣿⣷⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢽⣿⣿⣿⣿⡧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣱⣿⣿⠏⠀⠀⠊⠀⠀⠀⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣘⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⣼⣿⣿⠋⠀⠀⠀⠀⠀⠀⢀⡙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢀⣤⢞⣵⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣿⣿⣿⣿⣿⣷⣦⣤⣴⣶⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣀⣠⣴⣾⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⢀⣠⣴⣾⣿⡿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠟⠛⠉⠀⠀⣴⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⡏⢻⡆⢠⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠸⣿⠀⢠⡀⠀⢿⡄⠹⣾⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⣾⠋⠒⠀⠈⠀⠘⣄⣼⡇⠀⠸⣟⠢⠈⠻⠛⣿⡇⠀⠈⠷⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠹⠛⠛⠖⠀⠀⠀⠀⠀⠀⠉⠀⣀⣠⣤⣤⣀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣿⣿⣿⣿⡿⠋⠈⠁⠈⢷⣄⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⢽⣿⡿⠟⠁⡄⠀⢠⡆⢠⠊⣩⣷⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⢀⣤⡶⠀⡤⠀⣾⣿⠈⡆⠈⠀⢷⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠤⡊⢹⠟⣠⠃⠀⣺⣿⣿⣤⣷⠀⢦⢸⡄⢹⡄
⠀⠀⠀⠀⢀⡀⠀⠀⢚⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⢠⣾⠟⠀⡷⣹⣿⣿⣿⣿⡄⢸⣸⡇⢸⡇
⠀⠀⠀⠀⠈⠁⣴⠋⠛⢻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢸⡟⠳⠈⠀⠉⠜⠻⣦⠀⢤⣿⣿⣿⠿⣿⡇⠈⠁⠟⢸⡇
⠀⠀⠀⠀⢐⣦⠀⠀⠀⠀⣿⣯⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣄⠀⢠⠄⣼⣿⢀⣾⡿⣽⣿⠀⣿⡇⠀⠀⠈⠁
⠀⠀⠀⠀⠹⣷⠀⠀⠀⢠⣿⣿⣿⣿⣷⡄⢀⠀⢢⣀⡀⡠⠤⠀⠀⠀⠀⠀⠀⠀⠈⠳⡙⠀⠀⢀⢉⣰⣾⣿⡟⣿⡇⠀⠛
⠀⠀⠀⠀⠀⢿⠀⠀⠀⣼⣿⣿⡿⠛⠃⠘⢋⡷⠀⠀⠀⠀⠀⠀⠀⣴⠖⠀⢠⠀⠀⠀⠀⠀⠀⠈⠉⠟⢻⣾⣼⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⣿⡦⠼⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠋⢰⠁⠀⠈⠀⠀⡀⠀⠀⠐⢲⠚⡿⠗⢫⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⣼⣿⣿⢿⡿⠿⠿⣠⣀⣀⣴⣾⡿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⡧⠀⠈⢳⣄⠘⠇⠛⠙⠛⣡⡿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⠀⠀⠀⠻⠁⠄⠸⡷⠶⠟⣳⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣳⣶⢞⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⢀⠀⣻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡟⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡉⢁⢀⣀⣠⡄⠀⢴⣼⣿⠟⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⢒⡾⣿⣿⠆⣴⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⡄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣬⣽⣿⣿⣶⣯⣴⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠉⠀⠀⠈⢢⡀⠀⠀⠀⢀⠀⠀⠀⠀⣧⠀⠀⢀⣰⣷⣿⣿⣿⣧⣼⣿⣿⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠰⡄⠀⠀⠹⣷⣄⢳⣄⡀⠀⠀⠈⣿⣶⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⢿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢻⡀⠀⢀⣚⣿⣷⡟⢷⣿⡆⢾⣿⣿⠞⣿⣿⣻⣿⣿⣏⣄⠀⠀⠠⠀⠘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣇⠀⠀⢻⣶⣿⠉⣿⠟⢷⠈⣿⡇⢸⣿⡏⣸⣿⣿⡟⠻⢿⣿⣿⠀⣤⡀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⣿⡯⠀⢹⠀⣿⣿⣿⡗⠞⠉⢻⣿⣿⠿⢷⣦⡐⠻⣿⠄⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠉⠁⠀⢸⠀⢻⣿⡟⠀⠀⠰⣼⠟⠁⠀⠀⠈⠿⣿⣷⠀⡀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠿⠁⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠈⠛⠀⠋

⠀⠀⠀⠀⣠⠆⢀⠀⠀⠀⠀⣶⠛⠉⢑⡀⠀⠀⠀⣠⠖⠢⠆⠀⠀⠰⡖⠂⠀⠀⠀⠀⠀⢠⠖⠒⠒
⠀⠀⠀⠠⠇⠀⠐⡄⠀⠀⠀⢓⣀⣄⠞⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⢘⣠⡄
⠀⠀⠀⡴⠉⠉⠉⣸⠀⠀⠀⣛⡀⠀⣠⠇⠀⠀⠨⣄⣀⣠⠀⠀⠀⠀⠇⢀⣠⠟⠀⠀⠀⢘⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠉⠀⡀⠀⠀⠀⢀⡈⠉⠉
⠀⠀⠀⢠⠖⠋⠁⠀⠀⢠⡞⠉⠐⠃⠀⠀⢰⠇⠀⠀⢁⠀⠀⠀⢸⠁⠀⠀⠀⣿⠀⠀⠀⢰⡇⠀⡸⠂
⠀⠀⠀⢈⡴⠄⠀⠀⠀⠞⠀⠠⢠⠀⠀⠀⢨⠖⠒⠒⣾⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠈⡵⠚⠁
⠀⠀⠀⠨⠆⠀⠀⠀⠀⠀⠤⠤⠞⠀⠀⠀⠀⠷⠀⠀⠟⠀⠀⠀⠼⠀⠀⠐⠦⠏⠀⠀⠀⠀⠧⠀⠸⠇
⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⠤⠤⡀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡼⠀⢠⠞⢰⠀⠀⠀⢸⠋⠂⠀⡆⠀⠀⠸⡇⠀⠀⢰⠀⠀⠀⢼⠀⢀⡆
⠀⠀⠀⠀⠇⠀⢀⡀⠀⠀⢣⠀⠉⠀⢰⠃⠀⠀⠸⠂⠀⢡⡇⠀⠀⠀⠃⠀⢀⡟⠀⠀⠀⠀⠞⠉
⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠃
⠀⠀⠀⢀⡖⠒⠢⡀⠀⠀⠀⡴⠃⠒⡄⠀⠀⠀⡞⠉⠁⠃⠀⠀⠲⠒⠲⡋⠒⠀⠀⠀⣲⠀⠀⢰
⠀⠀⠀⠾⠀⠀⠀⢱⠀⠀⠀⠇⠀⣀⠗⠀⠀⠀⠘⠤⠄⢀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢃⠀⠀⢘⡄
⠀⠀⠀⠈⢀⣀⡥⣫⠀⠀⠀⡟⠁⠁⣤⠀⠀⠀⢀⣀⣀⡼⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠘⣀⣀⡾⠁
⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢠⠀⠀⠀⢀⣀⡀⢀
⠀⠀⠀⢸⠁⠀⠀⡟⠀⠀⠀⡿⠀⠀⠀⣾⠀⠀⠀⠱⢠⠖⠋⠀⠀⢱⠀⢀⡼⠀⠀⠈⠋⠁⠉⡼
⠀⠀⠀⠈⢢⠀⣰⠇⠀⠀⠀⢳⡀⣠⣀⡾⠀⠀⠀⣰⠋⠄⠀⠀⠀⠈⢀⡞⠁⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠳⠃⠀⠀⠀⠀⠀⠞⠁⠚⠀⠀⠀⠘⠁⠀⠀⠃⠀⠀⠀⠸⠇⠀⠀⠀⠀⠢⠿⠶⠚⠃
⠀⠀⠀⠀⣠⠤⢄⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⣠⠄⡄⡀⠀⠀⠀⠴⠒⠄⡀⠀⠀⠀⠀⡴⠂
⠀⠀⠀⢰⠃⠀⠈⡄⠀⠀⠀⠚⠁⡇⠀⠀⠀⠈⠁⠀⣠⠇⠀⠀⠀⠀⣀⣀⡟⠀⠀⠀⢸⣁⠰⣀
⠀⠀⠀⠀⠂⣀⣰⠇⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣀⣼⣁⡄⠀⠀⠀⣀⣀⣀⡇⠀⠀⠀⠈⢈⡾⠉
⠀⠀⠀⠀⠀⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⢸⠉⠉⠃⠀⠀⠀⠀⡖⠒⠃⠀⠀⠀⠑⠒⣢⠇⠀⠀⢠⡟⠉⢰⠀⠀⠀⠀⡞⠉⠁⣀
⠀⠀⠀⠀⠘⠁⢠⡀⠀⠀⢠⡞⠉⠁⣢⠀⠀⠀⠀⢰⠏⠀⠀⠀⢠⠗⠒⠈⡀⠀⠀⠀⠃⣀⣀⡏
⠀⠀⠀⠀⠦⠶⠞⠀⠀⠀⠀⠙⠖⠶⠃⠀⠀⠀⠀⠚⠀⠀⠀⠀⠘⠤⠤⠾⠁⠀⠀⠀⠠⠤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠒⠂⠈⠉⠉⠉⠉⠉⠉⠉⠒⠒⠢⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣉⣉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠒⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⡇⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⡜
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠊⠀⠀⠀⡴⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⡠⠊
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠙⢆
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠱⡀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⢱
⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠊⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡇⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠐⠒⠈⠉
⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠀⠀⠀⠀⠀⠀⢀⣿⡀⠃⠀⠀⠀⢠⣄⣸⡇
⠀⠀⠀⠀⠀⡐⠁⠆⠀⠀⠀⢹⡆⠀⠀⠀⠁⠀⢸⡿⠈⠁⠀⢀⣴⠛⣁⣻⣽⣷⣶⡄⢠
⠀⠀⠀⠈⠀⢻⠿⠿⠶⢦⣄⣀⠀⠀⠐⠀⠀⠀⢸⡆⠀⠀⣰⡟⣡⠞⠋⠉⠉⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣢⡀⠀⠀⠀⣿⠇⠀⣸⠏⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⣽⡇⠀⠀⣿⡀⢰⣿⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⠃⢸⡟⣤⠀⣠⡿⠓⠊⠀⠀⠀⠀⠈⠀⣦⣀⠀⠀⠀⠀⠀⢀⣴⡶⢂
⠀⠀⠀⠀⠀⠀⢠⠀⢠⣿⣿⠀⠀⣾⣿⣿⣿⠟⠉⠀⠀⣀⣀⣀⣤⣴⣦⢧⣿⣷⣄⣤⣴⣶⣿⡿⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣿⢇⣃⠀⠀⣹⣾⣿⡟⠀⠀⢀⣴⣿⣛⣛⣛⣿⣫⡿⠿⠛⠉⠉⠁⠀⠀⢀⣸⣿⣠⣄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⣆⣾⣿⣿⡋⠁⠀⢀⣿⣿⣿⠛⠛⠉⠉⠁⠀⠀⠀⣀⣠⣤⣴⣾⣿⣿⣿⡿⣷⣦⠀⡀
⠀⠀⠀⢠⠀⢠⣶⣿⣿⣿⣿⣟⣿⣿⣿⡖⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⢀⣴⠿⠟⠛⠻⠽⣿⣿⣭⣅⣙⡿⠿
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠟⢹⣿⣷⣾⠄⠀⢘⣿⣿⣿⡿⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⡏⡿⠛⠿⢿⣿⠆
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣏⣿⣿⣿⠦⠀⢈⣿⡟⣿⢀⠀⠀⠀⢠⡏⠀⠀⢀⣀⡀⠀⢹⣿
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣾⠟⠋⢰⣥⠦⠤⠀⢀⣾⠀⣠⣴⡿⠉⠛⢦⡘⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⠟⠛⠛⢿⣿⠒⣼⣿⠃⠀⠀⢠⣿⣿⣿⡿⠎⠁⠀⠀⠀⢿⡿⠀⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣻⣿⣷⡟⡁⠀⠀⠀⠀⠉⠙⣿⣅⠠⡀⠀⠈⢻⣿⣿⠋⣠⡄⠀⠀⠀⢨⣷
⠀⠀⠀⢹⣿⣿⣿⣿⣿⡏⣠⡿⠀⣸⠄⠀⠀⠀⠠⠏⠈⠙⠋⠒⠀⠈⢻⡿⣅⠘⣖⣀⣠⣶⣿⡟
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣾⠃⡏⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠻⣷⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣀⢻⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢇⠀⠀⠉⠉⠘⠛⢻⣿⡀
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣶⣾⣀⠁⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⣀⣾⠇⠈⢳⡄⠀⠀⠀⠐⢞⣿⡇
⠀⠀⠀⠀⣤⠹⣿⣿⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⢈⣵⠂⠀⠀⠱⡀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠐⠒⠈⠋⠀⠀⠀⢸⡿⠀⠀⠀⠀⡏⠀⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢳⠀⠀⠀⠀⠀⠆⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣯⣾⣧⡄⠀⠀⠀⠀⣠⡟⠀⠘⠆⠀⠀⠀⢀⣰⣼⡿⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣷⣤⡄⠀⣰⡟⠀⠀⠀⠀⠁⠀⠀⢁⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣭⣵⣿⣿⠀⠀⠀⠀⠀⢠⢄⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣧⣿⣿⣄⡀⢀⡀⠀⣠⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⣿⣵⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⢔⠀⡀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣶⣠⢉⣠⣴⣤⣔⣷⣦⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠙⣿⣿⠟⠉⠻⣿⣽⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠀⠀⠀⠀⠴⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢀⣴⣾⣿⣆⣤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢤⡶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢀⠀⠀⠀⠠⠄⠈⢻⣿⣿⣿⣷⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠖⠀⠀⠀⠐⠀⢀⣀⡀⠛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⢂⠀⠂⠡⠀⣰⣿⣿⣿⣶⣌⢻⣿⣿
⠀⠀⠀⠀⠀⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢲⣾⡿⠋⠋⠀⠀⠉⠉⠉⠻⣿⣿⣿⣿⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠂⠀⡾⣿⣧⠄⠂⠀⡀⠄⡉⠤⠀⠈⠙⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠶⣾⣽⡶⣆⣴⠿⠠⠀⠐⠀⠀⠀⠀⠀⠂⡄⠀⠀⠙⠻⣿⣿
⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣆⣀⡒⣚⡭⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠻
⠀⠉⠺⢷⣀⠐⠂⠦⡤⢀⢀⠀⠀⣀⠀⢀⣠⣤⣾⡾⠛⠛⢛⠿⠉⠙⠁
⠀⠀⠀⠀⠉⠙⠛⠚⠅⠦⠖⠖⠀⣠⠤⠀⡀⠊⠊⠀⡠⠖⠁⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⣋⡴⢚⣭⠀⡠⠀⠠⠄⠀⠔⠁
⠀⠀⠀⠀⠀⠀⣀⣴⣞⣯⠟⠋⠉⢠⣎⣑⡸⠁⠀⡖⠊⣧
⡀⠀⠀⣠⣴⣾⠿⠛⠉⠀⠀⠀⢀⣾⣹⣿⠂⠀⠀⠙⣯⠜⣇
⣿⣶⣬⣍⠉⠀⠀⠀⠀⠀⠀⠀⢸⣷⡼⠃⠀⠀⠀⠀⠘⠛⠿⠿⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿
⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⠿⠿⠿⠿⠿⠿⠿⣷⣶⣶⣶⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣿⠿⠿⠿⢿⣶⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄
⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⣠⣴⣶⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣶⣤⣀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⢀⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣦⡀⠀⠀⠀⠀⢻⣷
⠀⠀⢠⣿⠏⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠈⣿
⠀⢠⣿⠏⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⢸
⢀⣿⡏⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⣾
⣾⡟⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠿⠿⠛⠛⠛⠛⠛⠻⠿⢷⣶⣤⣀⠀⠀⠀⠀⢀⣠⣾⡿⠃⠀⠀⠀⠀⣸⣿
⣿⡇⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⣴⡿⠃
⣿⣇⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⢸⣿⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠁
⠈⣿⣆⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡟⠋⠉
⠀⠸⣿⡄⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⡀⠀⠀⠀⠀⠀⠻⣿⣆
⠀⠀⠹⣿⣄⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣶⣄⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠙⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⢀⣀⣤⣬⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠹⣿⡄
⠀⢠⣿⠏⠀⠀⠀⠀⢀⣴⡿⠛⠉⠉⠉⠉⠙⠻⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠹⣿⡄
⠀⣾⡟⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡉⠛⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⢻⣧
⢠⣿⠃⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠈⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠸⣿⡄
⢸⣿⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠙⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⣿⡇
⠈⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇
⠀⣿⣇⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣤⣤⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⣿⡇
⠀⢸⣿⡀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⢠⣿⠇
⠀⠀⢿⣧⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⣼⡿
⠀⠀⠈⣿⣧⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠈⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠋⠀⠀⠀⠀⠀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡿⠟⠁⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⣷⣶⣶⡾⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⢀⣠⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⢿⣶⣶⣶⣶⣶⣾⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠤⠤⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢠⢿⡄⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠚⠋⠉⠉⠉⠉⠓⢦⡞⠛⠛⠛⠛⠒⢶⡄
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢀⡟⠀⢿⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣸⠁⠀⠘⡇⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠻⠤⠤⠴⠇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣠⠴⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⣺
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠛⠛⠛⠻⡆⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠳⠦⠤⠤⠤⠤⠤⠦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤⠴⠤⠤⠤⠤⠴⠟⠀⠀⠀⠀⠀⠈⠛⠶⠤⢤⡤⠤⠖⠋⠙⠶⠤⠴⠤⠤⠶⠋
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠶⠶⠒⠶⠶⠶⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠶⠶⠒⠲⠒⠶⠶⢤⣄⡀
⠀⠀⠀⠀⣠⠞⠉⠉⠉⠉⠉⠙⡆⠀⠀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢸⡀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⣆⠀⣀⡤⠖⠛⠉⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠙⠛⢋⡉⠉⠈⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠸⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢠⡞⠉⠉⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡁
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠚⠛⠛⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⡤⠴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠋⠋⠉⠉⠉⠉⠻⡆⠀⢠⠞⠛⠓⠶⣤⣤⣤⣤⠾⠃
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢨⡇⠹⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠘⠲⠶⠶⠶⠶⠶⠶⠖⠃⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠋⠀⠀⠀⠈⠉⠛⠛⠒⠲⠶⠶⠶⠶⠒⠛⠋⠁

⠀⠀⠀⠀⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⢰⡶⠀⠀⠀⠀⠀⡠⢶⡆⠀⠀⠀⣠⡶⣆
⠀⠀⠀⠀⢿⣯⣷⣄⠀⠀⠀⢁⡈⠒⠀⠴⠄⠰⣇⡈⠀⠀⠘⢧⠀⠰⣶⣶⡜⠉⡼⠃⠀⠀⡰⢀⢀⡻⠆
⠀⠀⠀⠀⢸⡛⡿⣿⣆⠀⢀⠈⠓⠂⠀⠀⠀⠀⠛⠁⠀⠀⠀⠰⣿⣴⡿⡍⠃⣩⠞⠀⡀⡘⢓⣄⣏⢻⣦
⠀⠀⠀⠀⠈⠳⠅⢈⣻⠏⣻⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡀⣌⣛⣷⣾⣿⡿⢀⣿
⠀⠀⠀⠀⠀⠀⢠⣮⣿⠿⠛⢿⣷⣶⣦⣀⡀⠀⠀⠀⠈⢹⠋⠉⠀⠀⡒⠀⠙⣦⣴⣿⣿⣿⠻⣮⠁⠋⠁
⠀⠀⠀⠀⠀⠀⠟⠛⠁⠐⠦⢄⣩⡿⣿⣼⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠜⢿⣦⣉⣉⣭⠆
⠀⠀⠀⠀⠀⢀⠀⠀⠦⡘⠀⠀⠀⠀⢰⡤⠤⡀⠀⠐⠒⠚⠒⠒⠀⠀⣠⢤⣤⠀⣉⡉⠉⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠲⡶⠂⠀⢀⣴⣿⡇⠈⢿⣄⠚⠶⢄⠀⠀⠠⢀⡠⠶⠒⣸⡏⠀⣿⣿⡄⠀⠀⠀⢀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣼⣧⡀⠀⢿⣦⠁⠈⢃⢀⣶⣌⠀⢀⣼⡷⠀⠀⣿⢻⣿⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⡿⠿⠃⠀⢐⡦⠀⠀⠘⠙⡿⠀⠀⠀⢰⠆⠀⢘⡇⢻⣿⣇⠀⠀⠆⡀
⠀⠀⠀⠀⠀⠿⣦⣄⠀⢌⢉⠀⠀⠀⢂⠀⠀⢻⣴⡣⠀⠈⠀⠀⣠⣜⠋⠀⠀⣽⡇⣾⣿⡏⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠙⠟⠃⠈⠸⣄⣀⠀⠊⠀⠀⡼⠇⠀⠀⠀⠀⠀⠐⠿⡀⠀⢀⣾⡥⠛⠉⠀⠀⠀⠙⠛⠂
⠀⠀⠀⠀⠀⢴⣷⣤⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⢠⣾⣦⣀⠀⠀⠈⠂⢀⣄⣀⠀⠀⠀⠀⠀⢀⣤⣶⡄
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣆⠀⠀⣀⣤⣶⣾⣷⠀⠀⠀⠀⣈⣋⣙⠛⢲⣄⠀⢹⡞⣷⢿⣦⡀⢀⣴⣟⣾⣿⡆
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠋⠀⠘⠶⡌⣻⣿⣿⣿⣿⣿⣷⣿⡁
⠀⠀⠀⠀⠀⢹⣿⣿⣿⢿⡟⣿⣿⣿⣿⠉⠀⣀⠀⠀⠈⠂⠂⠀⠐⠀⠀⠀⠀⠸⣷⣽⣿⡃⠛⠘⣿⣷⣿⠅
⠀⠀⠀⠀⠀⠀⠙⠋⠁⠈⠀⠻⣿⡿⠋⠀⠀⡿⢴⣦⣀⠀⠀⠀⢀⣀⢠⣤⠀⠈⠙⠛⠛⠀⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⣄⠀⠀⢠⣄⠀⢸⡟⣻⣷⡶⣶⣬⣿⣿⡭⠃⠀⣾⣤⣄⠈⠃⠀⠈
⠀⠀⠀⠀⠀⠀⢀⡸⣷⠛⠋⠉⠀⢰⣿⣿⣆⠀⠉⠙⠃⠹⠃⠹⠿⠿⠃⣠⣴⣿⢟⣻⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠠⠰⠋⠀⢀⣀⠀⠀⠀⠸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢀⣀⣸⡿⢛⣵⣸⡏⠀⢈⠀⠀⠐⠩⣿⡆
⠀⠀⠀⠀⠀⢀⣀⢶⣿⡽⠃⠀⠀⠠⣮⡙⣿⣿⣿⣶⠀⠀⠀⣴⣿⢛⡱⣾⢻⡯⡿⠁⠰⠁⠀⠀⠐⣀⣹⡇
⠀⠀⠀⠀⠀⠸⣿⠟⠋⠀⠀⠀⢀⣴⣿⣿⣿⣼⢿⣿⠀⠀⢸⡟⣡⣾⣷⡟⠿⠟⢃⡀⠀⠀⠀⠀⠈⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣴⣶⣿⣿⡎⠝⢆⠈⠈⠁⠀⢀⠀⣉⣉⣁⠀⠐⠒⠹⣿⣅⡒⣦⢤⣄⣀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢲⣶⣿⣿⣿⣿⢿⣿⣿⣆⠀⢀⡤⢐⣲⣤⡞⠛⠛⠉⣠⣶⣿⡉⢻⠟⠟⣛⣢⣩⣵⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⣿⣽⠿⠛⢠⣾⡿⠟⠁⠈⠁⠀⠀⠀⠳⣶⣶⣶⡶⠏⠙⠛⠛⠛⠙⠛⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⢟⠛⠛⠛⠲⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⢟⣿⣿⣿⣷⠴⢶⠶⠎⠛⣦⡈⠊⢻⣿⣷⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⢟⣵⣿⡟⠋⠁⠀⠀⠈⣇⠀⠀⠹⣷⣄⠀⢻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⢁⣾⡿⠋⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠹⣿⡆⢸⣿⣿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢁⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⣷⢸⣿⣿⣇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⣿⣿⣿⣿⠃⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⣿⣿⣿⣾⣿⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣮⣿⣿⡀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣰⠏⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣷⣾⣿⣿⣿⣿⣷⣤⣽⣭⡧⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣿⣿⡿⢿⠿⠿⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⡶⠶⠾⢯⣭⣷⣲⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠀⠀⠀⢴⠶⣄⠀⠉⠛⠷⣦⣝⠲⢄⠀⠀⠀⠀⢀⣿⠟⣛⡙⠻⣯⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⣁⣠⣄⣀⣙⡿⠀⠀⢰⡿⠀⠀⠀⠀⠈⢿⣿⡆⠀⠀⠀⠀⣼⡇⠀⠉⢹⣦⣬⣷⣤⣕⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠉⢁⡈⠙⠛⠋⠉⠀⠀⣠⠾⠦⣤⣤⡀⠀⠀⠀⠙⢷⣄⡀⠘⠛⢿⠛⠦⠴⠾⠛⣩⡇⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⢰⡏⡴⠟⠉⣻⣧⠀⠀⠀⢠⡞⠁⢀⣤⣌⠙⢻⡄⠀⠀⠀⠸⡏⠙⠦⣄⣀⣀⣀⣠⣤⡶⠋⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⣈⡿⢥⣤⠗⡦⢾⣀⣤⠯⣌⡋⠀⣸⠇⠀⢀⣤⠤⢧⣀⢴⡲⢌⣩⠭⢥⣁
⠀⢀⣤⣤⣄⠀⠀⣿⡇⠀⢸⣿⣛⡿⣷⣼⣯⡷⣭⣶⠟⣿⣿⡞⠋⠀⠰⣏⣛⡛⠿⣶⣎⣹⣶⡿⣿⣳⣸⣆⣤
⠶⣾⠁⠈⠉⢷⠀⣿⡇⠀⠈⠉⠉⠙⢮⢻⣿⣷⡛⣿⣮⣳⡀⠀⠀⡤⠀⠀⣰⠋⠱⣌⢿⣿⢃⡞⠋⠁⠀⠉⠁
⠀⡹⢦⠆⠀⢸⣬⣯⣧⠀⠀⠀⠀⠀⢸⣸⣿⠿⣿⣎⠻⣷⣝⢦⡀⣙⣿⢿⠃⢀⡀⢹⢸⣿⢸
⠀⠀⠀⠀⠀⠸⣿⣽⣿⠀⠀⠀⠀⠀⢸⢼⣿⢀⣝⢿⣷⡜⢿⣷⡝⢯⣀⠘⠧⣼⠇⢨⢸⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⠻⣦⣀⡀⢸⢸⣿⢸⡏⠳⣟⢿⣦⡙⣿⣶⣽⢿⠀⠀⠀⢸⢸⣿⢸⡄
⠀⠀⠀⠀⠀⠀⠀⢾⣏⠙⢦⣈⠉⢀⡞⣸⣿⣌⢧⠀⠘⣮⢻⣿⣤⠻⣿⣿⢧⡀⢀⡟⣼⣿⣜⣧
⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠈⠻⢧⡀⢳⠹⣿⢏⡏⠀⠀⢸⣜⡛⠿⣷⣌⢻⣷⣿⢆⣷⢹⣿⢻⠏
⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠘⢻⢨⣿⢺⡇⢰⠛⢷⡄⠉⠳⣝⢿⣦⡙⢿⣦⡉⢸⣿⢹⠆
⠀⠀⠀⠀⢀⣿⠉⢀⣀⣠⡴⠶⠚⠛⢻⠈⣿⢸⣧⣄⡀⠈⣿⠻⣿⠈⢢⡙⣿⣦⡹⣿⣾⣿⢼
⠀⠀⠀⠀⠙⠈⠛⠛⢛⡟⠀⣄⠀⠀⢸⢰⣿⣸⡇⠈⠙⠳⢾⣆⠀⠀⠀⠙⢮⡻⣿⣌⢻⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠟⢀⡴⢫⣾⣿⣧⡳⣄⡀⠀⠀⠉⠳⣦⡀⠀⠈⠳⣝⢿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣭⣭⡾⠿⢿⣨⡟⠻⢾⣯⣿⣻⠀⠀⣀⡙⢦⡀⠀⠈⠳⣝⠿⠿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠳⣽⠞⠙⠓⠒⠛⣉⡀⣀⣛⡿⠈⠳⣄⠀⠀⠈⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⣹⡏⠉⠛⢯⣄⠀⠀⠹⡆⢀⡾⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠦⣴⣦⡀⠀⣼⠃⢀⠻⣿⣿⣿⣄⠀⠙⣷⣄⠀⢻⠈⠳⠖⢠⣿⠼
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢁⣤⣄⠀⠈⠳⣴⡇⠀⣹⣿⡟⣻⣽⣍⠀⠀⣿⣿⡗⢾⣦⣤⢶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣜⣁⣼⠃⠀⠀⠘⣷⠀⠻⠃⠙⣇⠘⠟⢀⣰⠇⠈⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠯⠁⠀⠀⠀⠀⣿⣷⣄⠀⠀⠈⠓⠚⠋⠁⢀⣤⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢦⣤⣤⣤⣤⠾⢛⠁⠈
⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠁
⠀⠀⠀⠀⢀⣀⡀⠀⠀⣴⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⣸⡇⠀⠀⣀⣀⠀⢤⣼⣧⡤⠀⢀⣀⣀⡀
⠀⠀⠀⢰⡋⢸⡏⠀⠀⣿⠚⢲⡄⠀⢰⡏⠈⠁⠀⡏⠁⣹⡇⠀⢰⣧⠼⠀⠀⢸⡇⠀⢠⡏⠀⣿
⠀⠀⠀⠈⠛⠋⠃⠀⠀⠙⠳⠚⠁⠀⠈⠓⠶⠂⠀⠙⠚⠙⠃⠀⠈⠳⠚⠀⠀⠘⠃⠀⠀⠙⠚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠋
⠀⠀⠀⢰⡆⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⣶⠀⡀⠀⢠⡆
⠀⠀⠀⠘⣧⣤⡀⠀⠀⢠⡅⠀⠀⢘⠃⠀⠀⣯⡞⠁⠀⢸⡇⠀⠀⠐⣿⠛⣶⠖⣦⠀⠀⢸⠞⢳⡄
⠀⠀⠀⠀⣯⠀⣿⠀⠀⢸⣇⠀⠀⢸⡇⠀⠠⡏⢷⠀⠀⠸⣧⡄⠀⠀⢿⠀⠿⠀⠿⠀⠀⢸⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⣀⣄⡀⠀⠀⣀⣀⠀⠀⠀⣠⣄⡀⠀⠀⣤⢀⠀⠀⠀⣠⣄⠀⠀⢀⣿⡀⠀⠀⡀⢀⡀
⠀⠀⠀⢸⡏⠈⣷⠀⠀⣿⠈⣷⠀⢸⡇⢸⡇⠀⠀⣿⠉⠓⠀⠀⠳⣌⠀⠀⠉⡏⠁⠀⢸⠁⢸⠃
⠀⠀⠀⠈⠛⠞⠃⠀⠀⣿⠋⠁⠀⠈⠛⢻⡇⡀⠀⠛⠀⠀⠀⠀⠲⠞⠁⠀⠀⠛⠆⠀⠘⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢸⠟⠁

⠀⠀⠀⠀⣷⠀⣸⠀⠀⢸⠀⣠⡀⢸⠇⠀⠀⠙⣶⠋⠀⠀⣼⠁⣸⠀⠀⠈⣩⠟
⠀⠀⠀⠀⠘⣦⠏⠀⠀⠘⠶⠃⠳⠏⠀⠀⠠⠞⠙⠆⠀⠀⠙⠚⣿⠀⠀⠚⠷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁

⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⣀
⠀⠀⠀⠀⣠⣾⣿⣿⣿⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣰⣿⣿⣿⡿⠿⢿⣿⣿⣷⣄⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠿⢿⣿⣷⣄
⠀⠀⠀⢰⣿⣿⣿⣿⠃⣄⠹⣿⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⣧⢰⣿⡦⢸⣿⣿⣿⡆⠀⠀⢰⣿⣿⣿⡟⢡⣴⣾⣦⣿⣿⣿⡆
⠀⠀⠀⣸⣿⣿⣿⡏⠸⠿⠆⠹⢿⣿⣿⡷⠀⠀⣿⣿⣿⣿⣿⢀⣥⣄⠻⣿⣿⣿⡇⠀⠀⢾⣿⣿⣿⡁⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠸⣿⣿⡿⢠⣿⣿⣷⡀⣿⣿⣿⠇⠀⠀⠸⣿⣿⣿⣿⠘⠿⠛⣠⣿⣿⣿⠇⠀⠀⠸⣿⣿⣿⣧⣈⠛⢋⣡⣿⣿⣿⠇
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣿⡿⠋⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠟⠛⠉⠀⢀⣀⣠⣤⣀⡀⠀⠉⠛⠛⠿⠛⠛⠉⠀⠀⢀⣀⣠⣤⣀⣀⠉⠛⠛⠿⠟⠛⠉⠀⠀⠀⢀⣀⣠⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣯⠀⣴⣤⡉⢻⣿⣿⣷⠀⠀⠀⠀⣰⣿⣿⣿⡉⣤⣤⣤⣿⣿⣿⣷⡀⠀⠀⠀⣰⣿⣿⣿⣏⢉⣤⣤⣼⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⣿⣿⣿⠈⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⡇⠛⣛⣛⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣟⠈⣛⣋⣻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠿⠿⢋⣼⣿⣿⣿⠃⠀⠀⠀⢿⣿⣿⣿⠇⠿⠿⠿⣿⣿⣿⣿⠇⠀⠀⠀⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣶⣶⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⢿⣿⣿⣷⣶⣶⣶⣿⣿⣿⠏⠀⠀⠀⠀⠈⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⡿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣷⣶⣤⡀
⠀⠀⠀⠀⣴⣿⣿⣿⠿⠟⠛⢿⣿⣿⣦⠀⠀⠀⠀⢠⣾⣿⡟⢿⣿⣿⡟⣿⣿⣷⡄⠀⠀⠀⣴⣿⣿⣿⡛⠛⠛⣿⣿⣿⣦
⠀⠀⠀⣸⣿⣿⡿⢁⣶⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⣿⣿⣿⡇⢼⣿⣿⠇⢾⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣇
⠀⠀⠀⢸⣿⣿⣇⢸⣿⣥⣤⠀⣿⣿⣿⡟⠀⠀⠸⣿⣿⣿⡇⢠⣤⣤⡄⣼⣿⣿⣿⠁⠀⢹⣿⣿⣿⣿⣿⠄⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠘⣿⣿⣿⣦⣙⠛⢛⣠⣿⣿⣿⠇⠀⠀⠀⢻⣿⣿⣇⣼⣿⣿⣇⣿⣿⣿⡟⠀⠀⠘⣿⣿⣿⣿⣋⣀⣉⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠁⢀⣠⣤⣤⣦⣤⣄⡀⠀⠉⠙⠛⠛⠉⠁⠀⢀⣀⣤⣤⣤⣤⣤⡈⠉⠛⠛⠋⠉⠁⠀⠀⠀⣠⣤⣴⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣴⣿⣿⡿⣿⣿⣿⢿⣿⣷⡄⠀⠀⠀⠀⠀⣴⣿⣿⡿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣶⣶⣦⢠⣶⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⠀⣿⠟⣡⣾⣿⣿⣿⡄⠀⠀⠀⣼⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⠀⣤⡘⢿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣏⠻⠿⠟⣸⣿⣿⣿⣿⠁⠀⠀⠀⢻⣿⣿⣿⡀⣿⣿⣄⠙⣿⣿⣿⠃⠀⠀⠀⢻⣿⣿⣿⡇⠸⠿⠟⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣶⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⣄
⠀⠀⠀⠀⣠⣾⡿⣿⣿⣿⣿⡿⣿⣿⣆⠀⠀⠀⠀⢀⣶⣿⡿⢿⣿⣿⣿⢿⣿⣦⡀⠀⠀⠀⣠⣿⣿⣿⡿⠿⠿⢿⣿⣷⣆
⠀⠀⠀⢰⣿⣿⠁⠙⣿⣿⡟⠀⢻⣿⣿⡆⠀⠀⠀⣾⣿⣿⡇⣈⠻⣿⣿⢸⣿⣿⣷⠀⠀⢰⣿⣿⣿⢋⣴⣾⣶⣄⢻⣿⣿⡆
⠀⠀⠀⢸⣿⣿⢠⣧⠘⡿⢡⣿⠘⣿⣿⡿⠀⠀⢸⣿⣿⣿⡇⣿⣧⡈⠿⢸⣿⣿⣿⠀⠀⢾⣿⣿⡇⢸⣿⣿⣿⡟⢸⣿⣿⣿
⠀⠀⠀⠸⣿⡿⢸⣿⣷⣀⣾⣿⡇⣿⣿⠇⠀⠀⠀⢿⣿⣿⡇⣻⣿⣿⣄⢸⣿⣿⡿⠀⠀⠸⣿⣿⣷⡈⠻⠿⠛⣠⣿⣿⣿⠇
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠙⢿⣿⣿⣷⣶⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠉

⠀⣠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡔⠀⠀⠀⠀⢠⠆⠀⡖⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⡀⠀⠀⠀⠀⢀⡤⠂
⠐⣿⠀⠀⣆⡄⠀⢸⠃⠀⣠⠀⠀⢣⠀⠀⠀⠠⢽⡀⠀⣯⢶⣶⠀⠀⣦⣾⡇⠀⠀⡞⠀⢰⣿⣒⢾⡏⠀⠀⣦⣄⣀
⠘⣿⠀⠀⠉⠀⠀⣼⠀⠀⣿⡆⠀⢸⠀⠀⠀⠠⢽⡇⠀⠉⠘⣿⠀⠀⠁⣸⡇⠀⠀⡇⠀⠘⠀⠈⠈⢧⣀⡀⠈⠉⠛
⢺⣿⠀⠀⠦⠼⠿⣟⠀⠀⣿⠃⠀⢸⠀⠀⠀⢀⣸⡇⠀⠀⣠⣟⠀⠀⠀⠶⠷⠀⠀⡧⠀⢠⠀⣀⣀⣠⠟⢶⣤⣦
⢘⣿⠀⠀⠀⠀⠀⣿⢄⠀⠀⠀⢠⣞⠀⠀⠀⠀⠈⡇⠀⠀⣘⣯⠀⠀⣇⣒⡒⠀⠀⡗⠀⠈⠛⠁⢠⣿⣄⠀⠙⠋⢀
⢨⣿⣽⠋⠀⠀⠀⠘⠳⠭⣴⡞⠁⠿⠧⠤⠴⣀⣼⣽⣶⠀⢀⣿⣗⠖⠁⣬⣟⣡⡰⣯⣍⣉⣒⣶⠛⠛⠬⣕⣀⣴⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣤⣼⣷⠦⠀⠐⠃⡜⠓⠖⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠄⢨⡀⠟⠆⠈⠐⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠠⡀⠂⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢬⡅
⠀⠀⠀⠀⠀⠀⡃⠂⠁⠐⠟⠀⠀⠀⠐⢦⠀⠈⠂⠀⢀⠀⠀⠀⡄⠀⢄⡰⣄⠉⠲⡘⠀⣠⠁
⠀⠀⠀⠀⠀⠀⢓⣠⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⣄⠀⢳⣄⠀⠰⡀⢀⢳⣮⢠⠈⠄⢀⠔
⠀⠀⠀⠀⠀⠈⠀⠀⠈⡀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠘⡁⣄⠩⠃⠀⡘⢶⢦⡽⠇⠀⠅⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠃⠀⠀⠀⠐⢦⡄⠀⠀⠀⠀⠈⠀⡍⠣⠀⠠⡀⠓⢂⣐⠒⣀⣠⠶⠂
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⠂⠀⠄⠀⠀⠀⠱⠋⠤⠀⠀⠀⠢⡂⡂⠀⠰⢀⣈⠈⡉
⠀⠀⠀⠀⠀⠀⢁⠐⠠⠄⢀⠀⠀⠠⠄⠀⢀⠀⠀⠁⠄⠀⠀⠀⠈⢠⡁⠁⠉⠀⠉⠈⠋⠙⠓⠂
⠀⠀⠀⠀⠀⠠⠀⠁⡀⢀⠀⠀⠁⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⢀⢀⠌⠀⠀⠀⡈⠈⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⢠⠈⠁⠈⡄⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⢀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠃⠈
⠀⠀⠀⠀⣀⠁⠈⠀⠄⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠐⠀⢀⠀⠒⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀
⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠤⠐
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠘⢅⠁⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠁⠀⠀⠡⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢀⡀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢱⡀⠀⠁⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⡀

⠀⠀⠀⣠⣶⣶⡀⠀⠀⠀⣤⣶⣤⠀⠀⠀⢀⣤⣤⠀⠀⢀⡄⢲⣄⠀⠀⣤⢰⣶⡄⠀⣠⡶⣦⡀⠀⠀⠀⣴⣿⣷⡄⠀⠀⠀⣾⣿⣷
⠀⠀⠀⠻⣇⡿⠃⠀⠀⠘⣿⣿⣿⠃⠀⠀⠘⣿⡿⠃⠀⠘⢣⠸⠟⠀⠀⠿⣸⣿⠇⠀⠻⠎⡿⠃⠀⠀⠀⠻⣿⠼⠃⠀⠀⠀⢈⣛⡁
⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠻⣿⠇
⠀⠀⠀⢰⣿⣟⣽⡆⠀⠀⣰⣿⣿⡆⠀⠀⢾⣿⡆⠀⠀⠀⣾⢀⢽⣷⠀⢰⡇⢹⣷⠀⢰⣯⣹⣿⡆⠀⠀⢸⣿⣹⣷
⠀⠀⠀⠀⠁⠾⠛⠁⠀⠀⠘⠻⠟⠃⠀⠀⠀⢉⠀⠀⠀⠀⠘⠢⠞⠋⠀⠈⠁⠃⠃⠀⠀⠛⠹⠛⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⢠⣾⣿
⠀⠀⠀⢀⣴⣰⣶⣄⠀⠀⢠⣶⣆⠀⠀⠀⠰⣿⣿⡆⠀⠀⣠⣶⠷⣦⠀⢠⢰⣶⡄⠀⢀⣶⣾⣶⡄⠀⠀⢰⡟⣷⡄⠀⠀⠀⠈⠛⠛
⠀⠀⠀⠘⣿⣿⣿⠟⠀⠀⠘⠯⠟⠀⠀⠀⢀⣉⣉⠀⠀⠀⢻⣧⠸⣿⠃⠈⠈⠛⠁⠀⠘⣇⡀⣿⠟⠀⠀⠈⠙⠋⠀⠀⠀⢀⣶⣷⣦
⠀⠀⠀⠀⣀⣉⠁⠀⠀⠀⣤⡶⣤⠀⠀⠀⢿⣿⣿⠆⠀⠀⢀⣈⡉⠀⠀⣰⠶⠶⡀⠀⠀⣈⣉⠁⠀⠀⠀⣴⣿⣷⡄⠀⠀⠈⠻⠿⠟
⠀⠀⠀⢸⣽⣿⡇⠀⠀⠀⠿⣿⠿⠀⠀⠀⠈⠉⠉⠀⠀⠀⠏⢸⣿⠀⠀⠻⠠⠊⠃⠀⢸⡍⣿⡇⠀⠀⠀⠙⠿⠟⠁⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⢠⣾⣟⣆⠀⠀⠀⠈⠁⠀⠀⠀⡠⠤⣄⠀⠀⠁⠉⠀⠀⠀⠀⠀⣤⣶⣤⠀⠀⠐⣿⣿⣿
⠀⠀⠀⠀⣴⣶⣦⠀⠀⠀⢸⣿⣿⣿⠀⠀⠈⠻⠿⠃⠀⠀⢠⣀⣶⡄⠀⠸⣇⡄⣿⠆⠀⣴⠶⣦⠀⠀⠀⠸⣿⣼⣿⠃⠀⠀⠀⠉
⠀⠀⠀⠀⠻⢿⠿⠁⠀⠀⠀⠙⠛⠁⠀⠀⢠⣶⣦⠀⠀⠀⠸⠑⠿⠇⠀⠀⢈⣉⡁⠀⠀⠇⠀⠿⠀⠀⠀⠀⢈⣉⣀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⣴⣿⣶⠀⠀⠀⢰⣿⣿⣳⡄⠀⠈⠻⠛⠀⠀⠀⢠⡎⣷⡆⠀⢠⡏⡌⣿⡆⠀⣴⢻⣦⠀⠀⠀⢰⣿⣷⣿⡇⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠘⠿⠿⠟⠁⠀⢠⣶⣶⡄⠀⠀⠈⠃⠛⠁⠀⠈⠻⠵⠟⠁⠀⠉⠈⠋⠀⠀⠀⠀⠙⠳⠛⠁⠀⠀⢠⣶⣶
⠀⠀⠀⠀⣴⣆⣤⠀⠀⠀⣠⣶⣦⠀⠀⠀⠈⠻⠟⠀⠀⠀⣠⢂⣰⡀⠀⢠⠐⣶⡀⠀⢀⣤⢲⣆⠀⠀⠀⢰⣾⣷⡄⠀⠀⠀⠈⠛⠛
⠀⠀⠀⠈⠻⠿⠟⠀⠀⠀⠙⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘⠹⠁⠀⠘⠲⠟⠁⠀⠈⠛⠼⠏⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⣴⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⣶⠖⣦⠀⠀⣤⢤⡀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠻⣿⡿
⠀⠀⠀⢸⣟⣳⠄⠀⠀⠀⠰⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⣟⡌⡇⠀⠀⢿⣿⣄⡿⠀⠘⠏⢾⠇⠀⠀⠀⠀⢿⣘⡿⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣨⢡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣦⠀⠀⠀⠰⣿⣿
⠀⠀⠀⠀⣾⣿⣧⠀⠀⠀⠀⣾⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠻⠾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢠⡀
⠀⠀⣤⡄⢠⣀⣀⣀⣤⡀⢀⣀⣤⣀⢀⣀⢀⡄⠀⢠⡀⣀⠀⠀⣀⡀⢀⢀⠀⡀⠀⠀⠀⠀⠟⠻⠶⣽⠆⠀⠀⠀⠀⠀⢸⡿⠸⣽⠇
⠀⠘⠛⠛⠚⠻⠟⠛⠛⠛⠘⠛⠛⠛⠙⠛⠘⠓⠀⠊⠃⠋⠘⠃⠙⠐⠛⠛⠀⠛
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⢴⠠⣦⣤⣠⠄⢀⠔⠢⣄⢠⣠⠄⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠀⠈⠉⠈⠀⠀⠉⠁⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠴⠀⠂⠰⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⢀⡤⠄⣀⡀⠀⠀⠀⠀⠀⢠⡤⢄⢀⣤⠀⠀⠀⠀⠀⠀⣤⠄⢀⣀⠀⠀⠀⠀⠀⠀⢠⡤⢠⣖⠀⠀⠀⠀⠀⠀⣠⠴⠀⣀⡀
⠀⠀⠀⠘⠦⠖⠷⠀⠀⠀⠀⠀⠀⠘⠧⠎⠳⠾⠀⠀⠀⠀⠀⠀⠻⠁⠻⠟⠀⠀⠀⠀⠀⠀⠘⠃⠘⠁⠀⠀⠀⠀⠀⠀⠻⠼⠛⣥⡇
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠒⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠆
⠀⠀⠀⠀⠘⠀⠀⡙⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢶⣀⡖⣦⡄⠀⠀⠀⠀⠀⠀⠀⡖⢠⠀⠀⠀⠀⠀⠀⠀⠐⢲⠀⣄⠀⠀⠀⠀⠀⠀⢴⡔⢸⡤⠀⠀⠀⠀⠀⠀⠀⡆⠀⡆
⠀⠀⠀⠙⠈⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠛⠈⠀⠀⠀⠀⠀⠀⠀⠘⠛⢠⠏⠀⠀⠀⠀⠀⠀⠉⠙⠈⠙⠀⠀⠀⠀⠀⠀⡀⠓⠂⠃
⠀⠀⡀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠆
⠀⠀⠀⠀⠰⠀⠀⠀⠀⡄⠀⠀⠀⢄⠀⠀⠀⠈⠐⠄⠀⠀⠀⣠⢄⢠⢁⣀⠀⠀⠀⠀⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠁⢄⠀⠀⠀⠀⠀⠀⠉⠈⠂⠉⠀⠀⠀⠀⠀⠀⠈⠣⢴⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠉⠀⠀⠀⠀⠀⠀⠈⠁⣀⠉
⠀⠀⢸⣷⡼⣧⢶⢶⡆⠀⠀⠀⠀⢰⡷⣼⡶⢦⠀⠀⠀⠀⠀⠠⡎⢙⣦⢶⡄⠀⠀⠀⠀⠀⣿⡽⢶⢶⡄⠀⠀⠀⠀⠀⣞⣉⡇⡴⣦
⠀⠀⠈⠀⠁⠉⠀⠈⠁⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠉⠀⠸⠋⠀⠀⠀⠀⠀⠀⠈⠉⠃⠉⠿
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢒⠀⠠
⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠸⡶⡃⡾⠃⠀⠀⠀⠀⠀⠀⣙⣣⣺⣇⠀⠀⠀⠀⠀⠀⠈⡇⠘⡗⠀⠀⠀⠀⠀⠀⣿⣠⢻⣰⡆⠀⠀⠀⠀⠀⠸⣶⠁⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣰⠄⠀⠀⠀⠀⡀⠔⢄⣐⣂⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠃⠀⠀⠀⠀⠈⠀⠰⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃
⠀⠀⢠⠀⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⡀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⣀
⠀⠀⠈⠿⠹⠇⠹⠿⠏⠀⠀⠀⠀⠠⠜⢣⠼⠿⠀⠀⠀⠀⠀⠀⠘⠇⢙⡞⠀⠀⠀⠀⠀⠀⠴⣥⢤⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡨⠀⠀⠀⠀⠀⠀⠀⠦⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠬⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠵⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⢀⡤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠛
⢸⠂⠁⣘⣉⠘⢸⠒⠈⠁⡗⠈⠁⠀⠀⠀⢀⢻⡄⠀⠀⢀⣀⡀⢀⡀⠀⣀⡀⡇⣀⠀⣀⣀⣈⡠⠀⠀⠀⡐⠉⠀⠀⣀⡀⠀⣀⠀⣀⣀
⢸⠟⠁⢿⢧⣄⢸⡟⠉⠀⡟⠉⡀⠀⠀⠀⣸⠇⠷⣾⢻⢁⡟⣿⠃⢸⡎⢸⣽⡏⣩⢾⠎⢉⣽⠁⠀⠀⢸⡇⢀⣴⣾⠁⢸⡎⣸⢸⠏⠈
⣘⣀⣀⣘⣀⣈⣙⣓⣊⣁⣛⣊⣉⣀⣀⣀⣋⣀⣀⣛⣻⣋⣀⣛⣀⣘⣛⣋⣘⣛⣁⣀⣛⣋⣘⣀⣀⣀⣈⣛⣋⣀⣃⣀⣙⣛⣉⣚⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡋⣀⠀⠉⠛⢒⣲⣷⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠦⠤⠤⠉⣻⣅⢹⣿⣿⣿⣿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠢⡐⠂⠈⠻⠿⠟⣫⣽⣶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠂⣿⣿⣆⠀⠀⢀⡤⠀⡰⢊⣾⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡅⠡⢷⣾⡟⠋⠀⠀⠳⠌⢹⣂⣸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠓⠒⠒⠚⠿⠇⢀⣴⣧⡀⠀⢹⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀⣤⣤⢤⣄⡀⠀⠀⠙⡿⠋⣀⣴⣾⣿⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣛⢉⣿⣿⡿⠁⣐⣶⠋⣴⣾⣿⣿⣿⣇⣀⣠⣶⠏⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡻⠖⠛⠁⠁⠘⠿⠿⣦⡙⢿⣿⣿⣿⣿⠿⠿⠋⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⢀⣀⠀⣀⣀⡀⢻⣿⣶⣝⡻⢿⣤⣴⢦⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣾⣿⣿⣿⣁⢿⣟⢻⣿⣿⣿⣿⣿⠃⠨⢯⣤⡅⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠋⠽⠛⠁⠈⠙⡿⢿⣿⣻⣽⣶⣿⡿⠁⡸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢀⣀⣠⡼⢀⣘⣿⡿⠿⠿⣿⢧⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢻⡽⠿⠇⢸⣿⡋⠀⠀⠀⢀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⢀⣴⡾⠃⣼⣿⠃⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⠀⠙⡿⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢦⣺⡁⠀⠀⢠⠏⠀⠀⠀⣠⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⡞⠀⠀⠀⣼⣿⡿⠛⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⣠⣅⠀⠀⠀⠹⣿⣿⣿⣿⣏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⣶⣤⣴⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠛⠛⠛⠛⠓⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠄⢄⠁⠀⠀⠀⣿⡏⢻⣧⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠃⠀⢰⠯⠚⣬⡆
⠀⠀⠀⠀⢠⢠⣀⠈⠀⠀⠀⣿⣧⣾⣇⠀⠀⠀⠃⠀⠀⠀⠀⢸⡿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣧⣴⡄⠀⣮⠃⡤⠬⡤
⠀⠀⠀⠀⡄⡀⠀⠂⠃⠀⠀⣿⣇⣨⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠀⠀⢫⢦⣀⢿⠁
⠀⠀⠀⢀⣒⠁⢀⡐⠈⠀⠀⠛⠛⠋⠁⠀⠀⡀⠀⠀⣀⡀⠀⣘⠛⠛⢉⢀⠀⠀⠀⠀⡀⡀⠀⠛⠃⠀⠀⠀⠈⠁⠃⠁
⠀⠀⠀⢸⣿⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡃⢜⡞⠁⠀⠀⢠⠀⠀⠀⠀⣿⣾⠀⢸⣿⣿
⠀⠀⠀⢸⣿⣶⣾⡇⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⣿⣯⡟⠀⠀⠀⠠⢠⠀⠀⠀⠀⣿⣿⣇⣼⣿⣿
⠀⠀⠀⢸⣿⠀⢹⡇⠀⠀⠀⠀⠀⠀⢂⠂⠐⣐⠀⠀⣿⠗⣻⡄⠀⠀⠨⠠⠀⠀⠀⠀⣿⡈⣿⣿⢹⣿
⠀⠀⠀⠈⠛⠀⠘⠃⠀⠀⠀⠀⣀⣀⡀⠂⠐⠀⠀⠀⣙⡀⠘⠙⠀⠀⠈⠀⠀⠀⠀⠀⠛⢁⣉⠉⠈⠛⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢨⠀⠸⠁⠀⠀⠀⣿⡟⢿⣷⠀⠀⢀⣾⠿⢿⣦⠀⠀⠀⠀⡔⠀⠀⠀⠀⢸⣟⢻⣷⠀⠀⠀⠛⢻⡿⠛
⠀⠀⠀⠀⠀⢰⠃⠀⠀⡂⠀⠀⣿⣇⣼⡿⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠴⠂⢠⠀⠀⠀⠀⣿⡟⠉⠀⠀⠀⠘⣿⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣧⢈⢿⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠈⠛⠉⠛⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠛⠛⠋⢀⡀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⢽⢷⠀⢸⡿⠀⠀⠇⠅⠐⠀⠂⠨⠨⠀⠀⢫⡧⡀⣽⠀⠀⢻⣷⢀⣿⠇⠀⠀⠃⠀⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⣿⠇⠀⠀⠅⢀⠂⠤⠠⠆⡂⠀⠀⠈⣇⣗⡃⠀⠀⠀⢻⣿⡏⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⢻⣿⡿⠀⠀⠀⠰⠀⠰⠀⠄⠀⠀⠀⠀⣐⡗⠓⣶⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠸⠟⠃⠀⠀⠀⠈⠂⠂⠀⠓⠐⠀⠀⠀⠁⠃⠀⠿⠀⠀⠀⠘⠿⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⡀⠀⡄⠀⠀⢀⠀⢀⠀⠀⠀⠀⡀⢀⠀⠀⠀⢠⠀⣄⡀⠀⠀⡄⠀⢀⢀
⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠁⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠈⠀⠀⠁⠀⠀⠈⠁⠈

⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⣰⢻⡏⢹⡟⣆⠀⢀⡞⣿⣇⣿⢳⡄⠀⢠⠛⢿⠘⣿⠢⠀⠀⡴⣿⡇⣿⡟⡄⠀⢠⠞⢿⠈⢻⠳⠀⠀⣰⠻⣏⠙⡟⠆
⠀⠀⢿⢹⡟⢻⡏⡿⠀⠘⣟⣿⡟⣾⣻⠆⠀⢸⣀⣼⠀⣿⣀⠀⠀⢇⣿⡇⣿⣇⡇⠀⠸⣏⣸⠃⢸⣉⠀⠀⢿⠁⡟⠁⡟⠁
⠀⠀⠀⠘⠃⠘⠃⠀⠀⠀⠈⠛⠓⠛⠉⠀⠀⠀⠙⠛⠚⠛⠁⠀⠀⠈⠛⠓⠛⠋⠀⠀⠀⠉⠛⠚⠛⠁⠀⠀⠀⠁⠃⠀⠃
⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⣀⡀⣄⠀⠀⠀⠀⣀⢠⡤⣀⠀⠀⠀⠀⣀⠀⡄⠀⠀⠀⠀⠀⣠⢀⣀⠀⠀⠀⠀⡀⡄⠀⡀
⠀⠀⡼⡙⣇⣈⡏⣃⠀⢀⣏⣿⣇⣿⣙⡆⠀⠘⡇⠀⡇⢸⠃⠀⠀⠀⣿⠀⡇⠈⡆⠀⢰⣫⢿⣸⢿⣹⠀⠀⡼⠁⡇⠀⡇
⠀⠀⠳⣽⡇⢹⣇⠟⠀⠈⢇⣿⡏⣿⡭⠃⠀⠠⣇⠀⡇⢸⡆⠀⠀⢠⣿⡀⣷⣤⠇⠀⠘⢯⣿⢹⣾⠹⠀⠀⠳⣠⡇⢀⣧⠄
⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠈⠘⠋⠉⠀⠀⠀⠀⠉⠙⠉⠁⠀⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⠈⠙⠋⠁
⠀⠀⠀⣠⣦⣤⣄⠀⠀⠀⠀⣤⡄⣦⡀⠀⠀⠀⣠⣴⢲⣤⡀⠀⠀⢀⣤⡖⣦⣄⠀⠀⠀⣠⣴⢶⣤⡀⠀⠀⢀⣤⡴⢦⣤⡀
⠀⠀⡾⢿⡿⢿⡿⢷⠀⢠⣧⣿⣷⣿⣿⡆⠀⢸⢹⣿⢸⣿⢹⠀⠀⣯⡿⣧⣿⣯⡇⠀⢰⢁⣿⢸⣿⢸⡄⠀⣾⣜⣧⡞⣧⡗
⠀⠀⠹⢸⡇⢸⡇⠋⠀⠀⠛⣿⡿⣿⠝⠁⠀⠘⢾⣿⣸⣿⠞⠀⠀⠳⠄⡇⠀⡇⠀⠀⠈⢿⣿⣺⣿⠟⠀⠀⠙⢸⡇⢸⡧⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⣠⣶⡟⢷⣦⡀⠀⠀⣴⡶⣿⢶⣄⠀⠀⢀⢰⡆⢰⡦⡀⠀⠀⠀⣶⡆⣶⠀⠀⠀⢀⣴⣶⢰⣶⣀
⠀⠀⠀⠀⠀⠀⠷⣤⠷⡴⠷⡄⠀⠘⣿⠀⡇⠀⡟⠀⠀⣏⢸⡇⢸⡇⣹⠀⠰⡇⣿⡇⣿⠀⡇⠀⢸⣼⣿⣼⣿⣼
⠀⠀⠀⠀⠀⠀⠙⠿⣆⡿⠗⠁⠀⠀⠛⠀⡇⠀⠃⠀⠀⠘⠾⢧⡼⠷⠃⠀⠀⠱⠏⢷⠹⠞⠁⠀⠈⠹⢿⢻⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣿⡇⣿⢦⡀⠀⢠⢼⣿⢸⣷⢦⠀⠀⠴⣿⠋⡿⠷⡄⠀⠀⣼⢿⣹⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣧⡿⣥⢿⡅⠀⠈⡏⠈⡏⠘⡏⠀⠀⣴⢁⡜⠁⡞⡁⠀⠸⣿⣴⢛⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠃⠟⠋⠀⠀⠀⠁⠀⠇⠈⠁⠀⠀⠈⠛⠧⠟⠋⠀⠀⠀⠙⠻⠼⠛⠁

⢀⠀⢀⣰⣆⣴⣶⣶⣤⣶⣶⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⡄
⠸⠚⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⠀⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⠋⠁⠀⣤⣿⣿⣿⣿⣿⣿⠃
⢸⢰⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣷⣷⣶⣶⣤⣤⣶⣶⣦⣤⣶⣿⣿⣿⣿⣿⣿⣧⣶⣤⣤⣾⣿⣿⣿⣿⣿⣿⠏
⢸⣾⣿⣿⣿⣿⣿⣾⣿⡛⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⢛⣛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠉⠸⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠫⠙⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠉⠁⠛⣻⣿⣿⣿⣿⡇
⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⢰⠟⠁⢹⣿⣿⣿⣿⣿⣯⢁⣀⣤⣤⣴⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠚⠻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⢀⣀⣀⣾⣿⣿⣿⢳⣢⣀⢀⡀⠀⠀⠀⢸⠀⠀⠀⠒⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢿⣿⡇
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣷⠀⠀⠀⢸⠂⠀⠀⢠⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢀⣿⡇
⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢶⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⡇
⢰⣮⣿⣏⣿⡛⠟⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣶⣄⡈⠉⠉⣹⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡇
⠈⣿⣿⣿⣿⣷⣄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡌⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⣽⣿⣿⣿⣿
⢸⣿⣿⣜⣿⣿⣿⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⡆
⢸⣿⣿⣿⣿⣿⣿⣷⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⠃⡘⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⡄⢽⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠤⠤⠤
⠀⢸⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⠘⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⢸⣿⡿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢴⣾⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄
⢠⡾⣿⣷⣿⣿⣿⣿⠃⢻⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⣿⣯⠻⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⣿⣯⠥⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢹⣷⢹⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⠛⠉⠀⠀⢸⣭⣭⣥⣤⡤⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⢻⢺⣇⣿⣿⣶⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣅⡙⠿⢿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⡿⠿⠟⣿⣿⣿⣿⠏
⠀⠀⠀⡠⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠸⠁⠃⠀⠈⠀⠀⠀⠀⠀⠙⠻⣿⣿⣟⣿⣹⣭⣭⣬⣶⣿⣿⡿⠟⠛⠁
⠀⢀⣾⣶⣤⣿⡿⠋⠁⠀⠙⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⠛⠛⠙⠛⠛⠻⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⣶⣆⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⡄⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⢹⣦⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠸⣤⣭⣦⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠋⠉⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠤⠾⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣝⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢠⣾⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠛⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣡⣄⣤⣤⣤⡀⠉⠁⠀⢳⠀⠀⢀⣶⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡧⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠏⠁⠈⠛⢻⣂⡀⠀⠲⣷⠀⢼⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠀⡀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢸⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⡆⠀⠀⢀⣀⡈⠻⣗⠀⠀⠜⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⢶⠶⠞⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢠⣀⢀⡴⠞⠋⠀⠀⠀⠀⠀⠀⠿⣿⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠟⠉⠀⠑⣄⠀⢀⢀⣠⣠⣄⢤⡈⠹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠺⡟⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢔⣽⣿⠟⢻⠉⠛⠯⠟⠳⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⣴⡾⠤⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠶⢾⣿⣿⣿⣿⣷⠶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢟⣫⣭⠶⠞⠛⠛⢋⠭⠭⡙⠛⠛⠻⠷⣿⣽⣻⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢟⣭⠞⠋⢱⠒⡄⠀⠀⠀⢹⡶⠶⢸⡄⠀⠀⣴⢦⠈⠙⠻⣾⣝⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⠶⠋⠀⠀⠀⢸⠠⠷⢦⡀⠀⣾⠺⠆⣸⠀⢀⠤⠿⣾⠀⠀⠀⠀⠙⢿⣮⡳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⢏⡴⠁⠀⠀⠀⠀⠀⢸⡇⢿⠇⡇⠀⠈⠓⠊⠋⠀⣟⠾⢂⢸⠀⠀⣾⢹⠀⠀⠙⢿⣌⢣⡀
⠀⠀⠀⠀⠀⠀⢀⡾⢡⠎⠀⣰⠋⠯⠑⡄⠀⠈⠓⠒⢋⣀⠀⢰⠋⣩⡇⠀⠉⠛⠉⠉⠀⠀⣿⠸⠖⢦⠀⠀⠻⣧⠱⡀
⠀⠀⠀⠀⠀⢀⡾⢡⠃⠀⠀⠹⡐⠶⢮⠁⠀⠀⠀⣰⢣⠤⠇⢹⡘⠖⣲⠀⠀⣀⡤⢄⠀⠀⣿⢀⣶⣸⠀⠀⠀⠹⣧⠱
⠀⠀⠀⠀⠀⣼⢃⠇⠀⢾⠵⠀⠈⠉⠁⠰⡿⠀⣤⠿⠸⢦⠀⠀⣈⠉⠁⠀⣾⢱⠆⢸⠀⠀⣉⢁⠈⠁⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⢠⡏⢸⠀⡾⢉⠖⠀⠀⠀⠀⡏⢙⠀⠛⣷⢰⠉⠀⢸⡆⣷⠲⠀⢈⣷⣶⢸⠀⠀⡇⣸⠀⣴⢶⠲⢖⢲⡀⣿
⠀⠀⠀⠀⢸⠇⡇⠸⣇⣸⠀⠀⠀⠀⢠⡇⢸⠀⠀⠙⠊⠀⠀⠀⡇⢋⡼⠀⠸⠬⠫⠃⠀⠀⡇⢬⠀⣿⣾⣇⣸⣆⠁⢸⡇
⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠸⣏⢾⢇⠎⠀⢀⡀⢀⠀⠀⠸⣇⣦⣱⠀⠀⠀⢀⡤⢠⡤⡳⠬⠇⠉⠁⠈⠉⠉⠀⢸⡇
⠀⠀⠀⠀⢸⡀⡇⠀⣾⢻⣍⢢⠀⠈⠉⠀⠀⢰⡏⣶⠆⢳⠀⢀⡀⠀⣀⠀⠀⠀⣿⣶⡆⢠⠁⠀⠀⠀⠀⣾⢻⣑⡄⢸⠇
⠀⠀⠀⠀⠈⡇⢹⠀⣿⣠⣿⣀⠀⠀⢠⢒⡢⠘⠧⠤⠤⠋⠀⢸⠁⣿⠊⡇⠀⠀⠻⠤⣼⢸⠀⠀⠀⠀⠀⣿⢀⠉⠁⡼
⠀⠀⠀⠀⠀⢹⠘⣇⠉⠁⠈⠀⠀⢀⢼⣎⠏⠀⠀⠀⣖⡆⠀⢸⢰⠖⠊⡠⣄⡤⢀⠀⠻⠜⠀⣤⢲⣤⢤⡈⠁⠀⢀⠇
⠀⠀⠀⠀⠀⠀⢣⠸⣆⠀⠀⠀⠀⠘⠦⠭⠎⠀⠀⠶⡁⣩⠇⠸⠤⠆⠀⡇⢿⢇⣼⠀⠀⠀⠀⢹⡌⢋⠞⠀⠀⠀⠊⡠
⠀⠀⠀⠀⠀⠀⠈⢢⠹⣆⠀⠀⠀⡤⢤⣤⡤⢤⠀⠀⡏⡇⠀⠀⠀⠀⠀⠙⠦⠚⠟⠀⣀⣄⣠⣀⠳⠏⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡘⢷⣄⠀⢿⠈⣴⡃⠃⠀⠀⠉⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⡱⠋⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡙⢷⣜⠋⠈⠛⠀⠀⠸⣧⠙⣫⠗⠀⠀⢯⣦⠜⠁⣤⣄⢸⡆⠇⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣝⠻⣦⣄⡀⠀⢾⡫⣦⣱⠀⠀⣴⣻⣛⣓⠀⠘⠮⠭⠔⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢭⣛⠳⠶⣤⣤⣀⣀⣀⣀⣀⣀⣀⡤⠤⢐⣊⣤⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠶⠮⣭⣭⣭⣭⣴⠶⠶⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠁⠘⠁⠖⢂⣀
⠀⣤⠀⠀⠀⢰⢆⡇⢀⡤⢰⣤⣄⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣿⣿⣿⣷⠏⡿⢹⣦⠤⣴⢶⢤⣀
⠀⣿⠀⣾⢳⢸⢸⣇⢸⠇⢸⢹⢻⢣⣇⣯⣦⡏⡾⣼⠀⠀⠀⠀⢾⠀⣿⡏⡎⢹⢠⡇⢿⡏⣸⡟⢸⢀⢋
⠀⠘⠀⠻⠸⠚⠘⠙⡚⠆⠟⠚⠘⡘⠘⠘⠘⠀⠃⠃⠀⠀⠀⠀⠸⣤⠟⢧⡷⢼⣼⣇⣦⣧⣿⢧⣮⠾⡼
⠀⠀⠀⠀⠀⠒⣫⠩⠯⠆⣤⣄⠸⠽⠽⠝⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⡟⡸⠈⢀⡇⣸⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡴⡧⢧⣧⡼⠷⠿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠺⣗⢶⡶⣞⠿⠊

⠀⠀⣴⡇⠀⠀⣂⠂⢠⡖⢠⡇⠀⣠⡄⢠⡄⣤⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢀
⠀⠀⣿⡇⠈⣾⢱⡇⣸⠇⣿⣀⢱⡿⠈⣼⠇⡿⣸⠇⠀⠀⠀⠀⢸⡇⢼⣷⡟⣯⢸⢁⣿⣷⢸⣿⣦⡆⡗
⠀⠀⠸⠃⠀⠙⢊⡓⡙⠀⠯⠻⠘⡇⢀⠟⠰⠃⠛⠀⠀⠀⠀⠀⠀⠁⠈⠈⠀⠀⠈⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢸⡇⣿⣸⢷⡟⢰⡟⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢠⣦⣼⣾⣰⢂⣷⣶⣴⣦⣤⣠⡄
⠀⠀⠀⠀⠀⠀⠾⠰⠃⠿⠸⠇⠘⠃⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠈⠉⠈⠀⠈⠉⠈⠁⠁⠃

⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣤⣀⡀⠀⠀⠀⣀⣀⠀⠀⠀⣠⣄⡀⠀⠀⢀⣤⣤⣄⠀⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⢸⣇⣈⡷⠀⠀⣾⠁⠙⠃⠀⠀⣿⠀⢹⡆⠀⢸⣇⣀⠀⠀⠀⢸⣁⡀
⠀⠀⠀⠀⠀⣼⠿⣧⠀⠀⢸⡏⠙⣧⠀⠀⢿⠀⢀⡀⠀⠀⣿⠀⢸⠇⠀⢸⡏⠉⠀⠀⠀⢸⠋⠉
⠀⠀⠀⠀⠀⠛⠀⠛⠀⠀⠘⠛⠛⠁⠀⠀⠈⠛⠛⠁⠀⠀⠛⠛⠋⠀⠀⠘⠛⠛⠛⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢶⡄⠀⠀⣴⠀⢰⡆⠀⠀⢶⡶⠄⠀⠀⠀⠰⣶⠶⠀⠀⢴⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⢸⡇⣤⣅⠀⠀⣿⣤⣼⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠸⣇⣠⡟⠀⠀⣿⠀⢸⡇⠀⠀⣸⣇⡀⠀⠀⣦⣀⡿⠀⠀⠀⣾⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠀⠈⠁⠀⠀⠉⠉⠁⠀⠀⠈⠉⠀⠀⠀⠀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⣿⡄⢀⣿⠀⠀⢸⣧⠀⣿⠀⠀⣴⠟⢳⡄⠀⠀⣿⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣧⣸⣿⠀⠀⢸⡟⣧⣿⠀⠀⣿⠀⢸⡇⠀⠀⣿⠶⠛
⠀⠀⠀⠀⠀⠀⠀⢿⣦⣤⡄⠀⠀⡿⠹⡏⢿⠀⠀⢸⠇⠸⡿⠀⠀⠹⢦⡼⠃⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣀⣀⠀⠀⠀⣀⣀⣀⡀⠀⢀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠈⣧⠀⠀⢸⣇⢈⣿⠀⠀⢸⣏⠙⠃⠀⠀⠀⣽⠁⠀⠀⠸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡿⠀⠀⢸⡏⠙⣷⠀⠀⢀⡉⢹⡆⠀⠀⠀⣿⠀⠀⠀⠀⣇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠀⠀⠘⠃⠀⠛⠀⠀⠈⠛⠛⠁⠀⠀⠀⠙⠀⠀⠀⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⢰⡆⢠⡆⠀⠀⢶⠀⢰⡆⢀⡆⠀⠀⢰⡄⣰⠆⠀⠀⢶⡀⣴⠀⠀⠀⠶⠶⣶
⠀⠀⠀⠀⠀⠀⠈⣧⣼⠃⠀⠀⢸⡇⡿⣷⣸⠇⠀⠀⠀⢿⡏⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⢠⡟⣷⡀⠀⠀⠀⣿⠀⠀⠀⠀⣾⣃⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⡀⠀⢀⠀⠀⣤⣤⣤⢀⣠⣒⣢⣼⠶⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⢳⡀⠀⠀⣴⣆⠀⠀⠀⠀⠀⢠⡴⠊⠻⠋⠛⢰⠋⠘⢀⠁⠈⠉⠉⠉⠛⣽⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠐⠀⠀⠀⠀⣠⠆⠀⠐⢲⡟⣧⠀⠀⠈⢶⣌⡀⡀⣀⡤⠏⠁⠀⠀⠀⣀⠘⠀⠀⡈⠀⠀⢀⣠⣰⣾⡿⠋
⠀⠀⠀⠄⠀⠀⣤⣰⣶⣶⣶⣶⣿⠙⠛⢿⣷⡶⠿⠦⠞⢇⣀⡀⠴⠿⠻⠋⠀⠀⠀⠀⠉⠙⠙⠛⠀⠀⣀⣄⣠⣤⣼⣷⣷⣾⡿⠾⠿⠿⠿⠟⠉
⠀⠀⠀⣀⣿⣶⠿⠛⣫⣾⣿⣿⣀⡀⠀⠀⣿⠶⠦⠶⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⠆⠴⠶⣦⣌⡁⠀⠀⠙⠉⠹⡏
⠀⠀⠸⣾⣿⣁⠀⢠⣿⠟⡉⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠯⠽⢜⣦⣅⣀⠁⢈⣷⣄⠀⠀⠁
⠀⠀⠀⠙⠉⠛⠛⠛⠁⠀⠀⢠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣶⣿⣿⣿⣿⣤⣔⣛⣙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣐⡆⠀⠀⠈⠙⠇⠀⠀⠀⠀⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠀⠽⠿⠿⠿⠿⠛⠁
⠀⢀⠀⣠⣤⠀⠀⢀⠀⡄⠈⠈⠁⠀⠀⠀⢀⡄⠀⠀⢠⣔⠻⣿
⠀⠀⠁⠋⠉⠁⠉⠛⢋⠀⠀⠀⠀⠠⠀⠉⠘⠁⠀⡹⠊⣿⡒⠻⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠄⠀⣠⠼⢃⡀⠀⢲⣤⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠒⠚⠋⠀⠀⠁⠀⢭⣿⣴⡆⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣄⣦⡖⣷⡀⣠⠇⢀
⠀⠀⠀⠀⠀⢀⠀⠀⢀⠆⣀⣤⢴⣦⠾⢷⠷⠾⢿⢛⡗⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠻⣀⠀⠘⣺⠯⣿⣽⠟⣈⡿⠿⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠐⠋⠟⠢⠜⠆⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠛⠛⠻⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⡉⠁⠀⢀⡀⠀⠅⠌⠀⠁⠀⠄⠏⠀⠁⠀⠁⠠⠹⠈⠀⠀⠀⠀⠈⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠈
⠆⢠⡀⡆⢐⠀⢠⠠⢴⣤⡄⠀⡤⠀⠀⢠⡆⠀⣦⣄⠀⢠⡤⠠⢌⠒⠀⠀⠀⠀⠀⠀⠀⣴⣦⢙⡃⠀⠀⡀⠀⣀⢀⣄
⠁⣤⡵⠉⢰⠀⣧⡀⢘⣁⡀⠀⡇⢠⣀⢸⡍⢀⡏⠁⠘⠐⣻⡀⢸⣤⠀⠀⠀⠀⠀⠀⠈⡃⢀⡸⡋⡅⢸⡿⠉⡟⢻⣄
⠂⠈⠀⠀⠈⠁⠉⢁⣾⠀⠀⠈⠉⠈⠁⠈⠁⠀⠀⠁⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠈⠁⠈⠁⠀⠉
⡀⠀⠀⠀⠠⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⢠⢠⠀⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤⠠⡀⠀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄
⠀⠀⠘⠀⠁⠐⠤⠇⠀⠀⠸⠸⠀⠧⠖⠀⠀⠐⠤⠄⠠⠄⠀⠀⠠⠠⠃⠀⠼⠀⠀⠐⠄⠀⠸⠌⠀⠀⠀⠀⠀⠀⠁
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠
⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⣄⢀⡄⢀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠆⠀⠀⠑⠀⠈⠀⠁⡇⠀⠀⠀⠃⠈⠁⠈⠐⠀⠀⠀⠀⠀⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠄⠀⠯
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂
⡂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⢢⠘⠁⠐⠲⠀⠀⠀⠀⠁⢤⠀⠆⠄⠀⠀⠀⢇⠀⡐⠠⢐⠀⠀⠀⠀⠸⠀⠀⠨⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂

⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠠⢀⢤⠀⢊⡆⠀⠀⠀⠈⠒⠁⠖⠀⠀⠀⠀⠀⠁⠆⠐⡄⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⢠⠀⡀⢠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⣄⠀⠀⡀⠀⠀⠀⢁⡌⢣⠈⠀⣤⡀⠀⠀⠀⡱⠀⠀⡄⠀⠀⠀⠀⠈⡎⠀⢄⠀⠀⠀⠀⠀⡐⠁⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢀⡇⠀⣰⠋⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⣰⡏⠀⢠⠞⠀⢰⠇⢀⡏⢀⡴⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣿⣀⠔⠁⠀⠀⡿⢀⡞⢀⣿⠁⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢼⡿⠁⣠⣤⡄⢰⣧⠎⠀⣸⡧⠚⠁⣴⡏⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⢸⡇⠸⣿⠉⣀⠼⡇⠀⠀⣿⠀⠀⢠⠿⠧⠟⠀⣠⠖⠲⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠒⢤⣀⠘⠿⠂⢸⣧⠀⠈⠉⠁⠀⢻⡀⠀⠹⣆⡴⠋⠀⠀⠀⠰⣏⠀⠀⠸⡇
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠿⠄⠀⠀⠀⣤⡄⠉⠒⢂⣀⣀⣠⣶⣦⣀⡀⠙⠒⠒⢲⡟⠚⢳⣦
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⣀⡤⠀⠀⢸⣧⠀⠳⠄⣀⣀⣀⣰⣿⠗⠒⠉⠉⠀⠰⡿⡼⠁⠀⠉⣷⠀⠀⣼⡇⢀⣾⡿
⠀⠀⠀⠀⠀⢻⡀⠀⠀⣼⡿⠁⠀⠀⢸⣿⠀⣀⣤⣤⠀⠀⣼⣿⠀⠀⠀⠀⣠⣾⡆⠀⠀⠀⣀⡄⠀⢰⡿⠀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠉⠂⢼⣿⡇⠀⠀⠒⣿⡏⠀⣿⡇⠉⠀⣴⣿⡟⢀⣾⢻⡇⠀⣿⣧⡶⣦⣾⡿⠟⣱⡿⠁⢸⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢀⣼⡟⠀⠀⠻⣧⡴⠞⠉⣿⣇⠈⠿⠾⠁⠀⣿⡯⠴⠋⠻⣧⡴⠛⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⣼⠇⠀⡘⣄⠀⠀⠀⠀⣀⠀⢀⠀⠀⠘⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⢸⣿⣥⣿⡮⠠⢘⡇⠀⠀⠀⠀⠘⣿⣿⣿⣷⣄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣹⣟⣿⣘⣓⣧⠴⠒⠒⠦⡄⠀⠀⢸⣯⣿⣿⣿⡦⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⢿⣿⣾⠟⢿⣯⣻⣷⣛⣛⡐⡄⠄⢚⠿⢿⡟⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⢀⣶⣸⣿⣿⢿⣧⣴⠏⠁⠀⢹⡈⠈⠉⠛⠉⠸⢉⣤⠛⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠋⠍⠙⢟⣥⠼⢿⣧⡀⠄⠻⢿⡿⣿⣶⠖⠛⠊⠉⣿⣤⣿⡟⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⡇⢻⡓⣶⣓⣻⢄⠀⣾⠋⠀⡤⠀⠀⢳⣈⡟⣀⣀⣠⠞⠉⠻⠍⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣟⡘⣿⡍⣉⠁⣀⡼⣿⡇⢶⣿⠀⠀⢸⠟⠋⠉⠁⠈⠱⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠀⠀⠈⢀⣾⢃⢹⣻⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⢟⡿⠈⢡⡤⢀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢠⠟⠐⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠀⠀⠈⠉⠉⠉⠉⠀⠀⠐⠂⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⡀
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⠁⢡⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠄⠀⠀⠄⠀⢠
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠨⠀⡀⠀⠨⠀⠀⠂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⣀⠀⣀⣀⢀⡀⠀⠈⡄
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠌⠀⠀⠀⠀⠀⠈⠄⠀⠠
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠘⢄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣂⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢀⣤⡀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⠀⠀⢀⣐⠂⠐⠂⢺⡌⠀⠈⢧⡀⣶⣶⡉⡞⠀⢀⡦⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣍⠛⣷⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠘⠁⢠⣮⣷⣷⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⣿⠾⢷⣦⣤⣀⡀⠀⠀⠐⠖⠂⢀⡄⠐⣮⣽⣿⣿⢿⡉⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡘⠂⠞⠛⠾⠛⠀⠀⣀⣀⡀⠀⠉⠋⠛⢾⣭⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠈⠀⢠⣤⠈⢷⡕⣦⡀⠀⢀⠀⣠⠚⣿⠃⣶⣄⠀⠀⠀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣆⠘⠷⠄⠈⣆⣴⡎⠈⢼⠇⢀⣿⣿⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡿⠟⠛⠁⠀⠹⣄⡤⠈⠟⠠⡐⡼⠀⢸⡏⣿⡷⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠆⠳⣆⡀⠰⠀⢀⡟⠁⠀⠀⠈⠻⡀⠀⣾⡿⠟⠁⠀⠰⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣦⣀⠀⠀⠁⠀⣀⡀⠀⠀⠸⣷⣄⡀⠈⠀⣤⣄⡀⠀⠀⣀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣧⣤⣶⣿⣿⠃⠀⠀⠀⠒⠢⠉⠇⠀⢯⠻⣿⣦⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢿⢿⣿⣿⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡏⠛⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠟⠋⠀⠘⣽⣷⣄⣀⢀⣤⢴⠆⢀⠉⠉⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠶⠛⠀⣼⣿⡄⠛⠻⠹⠟⢿⡿⠇⣠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⢀⣄⠀⠀⢻⣿⣿⣄⠀⠀⠀⢀⣀⡸⢟⣽⣽⠁⠈⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠿⠉⠀⠀⣸⣮⣿⣿⣷⠀⢠⡿⢫⣼⣿⣿⡇⠀⠁⠀⠠⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣤⣄⣤⣾⣿⠻⡍⠙⠋⠀⢈⣙⣉⠉⠀⢳⣿⣢⣤⣄⣀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠿⠿⣿⣿⣿⣧⠀⣴⣬⠶⠞⠉⠉⡴⠾⠏⣟⣛⣭⣮⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠘⠋⠁⠀⠀⠀⠀⠈⠛⠛⠋⠀⠉⠀⠀⠈

⠀⢀⠤⣦⡄⠀⠀⠀⠀⠀⢀⡄⠢⡄⠀⠀⢀⡤⠒⠒⢠⡤⠀⠀⢠⡄⠐⠦⣄⠀⠀⢠⡄⠀⠀⠀⠀⠀⣀⠤⠶⣄
⠀⢶⡀⠈⢿⡆⠀⠀⠀⠀⢸⡟⣦⡃⠀⠀⣿⠀⠀⠀⠈⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⣧⠄⢠⠀⠀⠀⢿
⠀⠘⡽⠁⡼⣿⡄⠀⠀⠀⢸⡟⠁⣿⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣼⠃⠀⠀⡇⠀⠀⠀⠀⠀⣿⠉⠑
⠀⠀⠀⢠⠏⢹⣷⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠉⠓⠒⠉⠈⠀⠀⠈⠉⠀⠉⠁⠀⠀⠀⠁⠀⠀⠁⠀⠀⠉
⠀⠀⠀⣟⣀⣀⣻⣆⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡄⠀⠀⢠⠀⠀⠀⠀⠀⡄⠀⠠⠄⠀⠀⠀⠀⠰⣶
⠀⠀⢰⠉⠁⠀⠈⣿⡄⠀⠀⣇⠀⠀⢤⠀⠀⣽⢀⡤⢸⠇⠀⠀⢸⠀⠀⠀⠀⠘⡇⠀⢸⡇⠠⡀⠀⠀⠀⡃
⠀⢠⡏⠀⠀⠀⠀⢸⠿⡄⠀⠈⣰⡄⠘⠀⠀⣿⡀⠀⠀⠇⠀⠀⢈⡄⠀⠠⡦⠘⠀⠀⢸⡇⠀⠱⠄⠀⠀⠇⠀⠸
⠀⠛⠋⠀⠀⠀⠀⠈⠋⠙⠂
⠀⠀⡀⠀⠀⠠⠰⡄⠀⠀⠀⠀⢰⣖⠀⠖⣶⠀⠀⠀⢀⠄⠀⠀⠒⢦⡀⠀⠀⢺⡟⠈⠳⡄⠀⢠⡖⠁⠈⠉⠲⣄
⠀⠚⠁⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⡿⣆⠀⣿⠀⠀⠀⡎⠀⠀⠀⠀⠀⣿⠀⠀⢸⣷⠦⠴⠃⠀⣿⠀⠀⠀⠀⠀⣹⠆
⠀⠀⢠⠀⠀⡀⠀⠈⠧⠀⠀⠀⠀⣧⠘⢧⣿⠀⠀⠀⠱⡀⠀⠀⠀⢠⠏⠀⠀⢸⡇⠀⢠⡄⠀⠙⠆⠀⠀⢀⣠⠟
⠀⠐⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⢰⣶⠒⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣤⠤⠄⠀⠀⠀⠀⠒⡤⠀⠀⠐⣶⠀⠀⢲⣆⠀⠀⠀⠰⠂
⠀⠀⣿⠀⢀⣿⠇⠀⠀⠀⠀⠀⢸⣄⡀⠀⠀⠀⠀⣰⡞⠁⣠⡄⠀⠀⠀⢀⡜⠀⠀⠀⠀⣯⠀⠀⠀⢿⡄⠀⢠⠃
⠀⢀⣿⠘⠫⣄⠀⠀⠀⠀⠀⠀⠀⠉⢺⡆⠀⠀⠀⣿⡀⠀⢟⠇⠂⠀⠀⢸⡇⠀⠀⠀⠠⣿⠀⠀⠀⠈⣷⡀⠆
⠀⢨⣿⠀⠀⠐⠷⣄⡿⠀⠀⠰⢤⣀⠰⠃⠀⠀⠀⠙⠷⠤⣀⡠⠊⠀⠀⠘⠻⠦⣤⠄⠀⠿⠄⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠰⠟⢓⡙⠛⠙⢒⠛⠀⠈⣇⡏⠀⠀⠻⣿⡄⠀⠀⠛⠉⠀⠀⠀⡏⢹⣧⠀⠀⠀⣽⡏⠀⠈⠁⡀⠉⠋⢉⣽⠎
⠀⠀⢀⣾⠀⠀⢀⡟⠀⠀⠀⣿⡇⠀⠀⠀⠙⢿⢆⡞⠁⠀⠀⠀⠘⠁⠈⣿⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⢸⣯⠀⠀⢼⡇⠀⠀⠀⣾⡇⠀⠀⠀⠀⢀⢿⣷⡄⠀⠀⠀⠀⠀⠀⢿⣇⠀⢀⣿⡇⠀⠀⠀⠀⢀⣤⠊
⠀⠀⠈⢿⣦⣀⢘⣿⣄⣀⣠⣽⣇⠀⠠⡤⢀⣋⠀⠙⣿⣦⠀⠀⢀⣄⠀⠀⠉⠉⠁⢸⡇⠀⠀⠀⢀⡾⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠉⠁⠀⠈⠈⠀⠁⠀⠀⠀⠀⠛⠉⠀⠀⠘⠉⠉⠀⠈⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠓⠛⠉⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠾⢛⠋⠉⠁⠀⠀⠙⠻⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠟⠋⠀⢀⠈⠀⠀⠀⠀⠀⢲⡛⠙⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣯⠿⠋⢤⡄⠀⢠⣹⠀⠀⠀⠀⠀⢀⠀⠓⢀⣤⣨⣤⣽⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣼⠟⠋⠁⠀⠀⠀⠀⠀⠈⠈⠢⣤⣀⣀⣀⡁⠀⠀⠀⣼⣷⢦⣤⣽⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣰⢾⡇⢀⡴⠶⢤⠴⠊⢉⡳⢶⡀⠀⠀⠀⠀⠉⡇⠀⠀⢠⣿⣥⡾⠿⣿⢿⣿⣿⣧⡀
⠀⠀⠀⠀⣰⢏⠳⣼⠋⠀⠀⠀⢠⠓⠒⠤⠸⡄⠀⠠⢀⡤⠞⠁⠀⠀⢻⣿⣿⣶⣠⣤⣾⣿⣿⣇⠀⠑⠢⠄
⠀⠀⠀⢀⣿⠃⡰⠋⠀⠀⠀⠔⠁⠀⢀⡀⠘⢷⣄⠀⣹⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⣴⣦⡴⠂
⠀⠀⠀⢸⡏⢸⡇⠀⠐⠇⠀⠀⠀⡴⠛⠉⣱⠀⢿⡀⣿⠁⢀⣀⠀⠀⠀⠈⠻⣯⣿⣿⣿⣿⣿⣿⣷⣞⢸⣟⠁
⠀⠀⠀⣿⣯⣼⡅⢀⠈⠀⣷⡀⠀⢡⠼⡋⠉⢠⡌⢷⣿⣆⣸⣿⡇⠀⠀⠀⠐⠚⠿⣿⣿⣿⣿⣿⡿⠛⣫⣼⣷⡄
⠀⠀⠀⢹⣿⡌⣷⠀⠀⠀⠎⠉⠢⣌⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣇⣦⣦⣆⡀⢀⣴⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⡗
⠀⠀⠀⠘⣿⣇⣿⠀⠀⢈⠄⠀⠀⠙⢯⡽⣶⣟⡷⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠹⣿⣿⣷⣶⣅⠤⠐⠌⠀⠀⢀⣠⣿⠛⠶⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠙⣿⣿⣦⣟⣷⣶⣶⣤⣴⠟⢩⣎⢷⡈⢶⣾⣿⣿⣿⣿⣟⣻⣿⣿⣿⣤⣤⣤⣭⣭⣿⣷⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣿⣹⡆⠈⠳⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⡃⢤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠙⠻⢿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣯⠙⣿⣿⡟⢩⣿⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠈⢿⣄⣾⣿⢰⠤⣿⣿⣿⣿⣿⣿⣿⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣾⣿⣿⣏⠘⢰⡟⣿⣿⣿⣿⣿⣿⣶⣶⡄⢤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⡅⣋⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡏⣿⣿⣿⣿⣿⣿⣿⣬⣧⡌⢿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠛⠛⠋⡞⢻⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣻⣍⣿⢿⣿⣿⣿⣯⣿⡿⣿⣿⣦⣝⢿⣷⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⣀⣤⣴⣿⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢟⣵⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣽⣦⡙⣿⣾⣿⡀
⠀⠀⠀⠀⠀⢀⣴⡵⠋⠙⠿⠯⠩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡹⣿⣟⣿⣌⢻⣿⣧
⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⠁⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣯⢻⣆⠙⣿⡄
⠀⠀⠀⢀⠀⢂⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⡦⣿⣿⣿⣿⣿⣿⢿⣭⣾⣿⣧⣙⡉⠛⠛⢿⣿⣿⣿⣿⣧⠹⣯⣽⣧⢨⠃
⠀⠀⠀⣿⠁⠀⠠⣄⠀⣰⣆⣿⣿⣿⣿⡿⡆⢠⣿⣿⣿⣿⣿⣿⢰⣿⡿⢻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⠈⠻⣿⣿⣿⣎⠙⣿⣻⣎⢣⡀
⠀⠀⠀⠉⣄⢀⣠⣿⣾⣿⣿⣿⣿⣿⠁⠀⠀⣸⣿⣿⣿⡿⢿⣴⣿⣿⣿⣾⣧⠀⢸⣿⣿⠟⠉⢻⡏⠉⠷⣤⡙⢷⣦⡘⢿⣿⣿⣧⢿⣷⢻⡎⠁
⠀⠀⡘⠀⠀⠀⠀⠙⣿⢟⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣟⣿⣾⠉⣿⣿⠙⠻⣿⣆⠘⠉⠁⠀⠀⣸⠇⠀⠀⠩⠹⣶⣿⣷⣄⠈⢻⣽⠀⢿⣧⠻⠸⡆
⠀⠀⡇⠀⡄⠀⠀⣾⣿⠘⣿⣿⣿⣿⣿⣆⠸⣿⣿⣿⣿⣿⣿⡇⣻⣥⣴⣦⣼⡷⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠈⢘⣿⣿⣿⡄⠙⢿⣷⢈⣿⣆⠀⠛⡀
⠀⠀⡇⠀⢿⡠⣶⣿⣿⣇⣿⣿⣿⣿⡇⠹⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡘⢯⣿⣿⡄⢨⣿⡆⢹⣿⡗⠀⠁
⠀⠀⠷⠦⡼⣿⣽⡿⠛⢻⣿⣿⣿⣿⣇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣿⡆⠀⠀⢠⣠⣯⣀⠠⡂⠀⣀⣴⣍⣶⣿⣿⡇⠀⣻⡷⠈⠉
⠀⠀⠀⠀⠀⠁⠉⠁⠀⠻⠿⢿⣿⣿⡍⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡷⢨⣿⣿⣾⣳⣿⣿⣿⣭⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠻⠿⠗⠘⠻⣿⣿⡿⠋⠉⠀⠉⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⡤⡲⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠒⠒⠒⣲⣤⣤⣤⣄⠀⠀⠤⠄⡏⠉⠉⠁⢀⠐⠐⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⡇⠀⢀⠐⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣸⠃⠀⠀⣷⠀⠀⠠⠇⠀⠀⠀⠀⠀⢀⡴⢳⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠉⠀⠀⢸⡀⠀⠸⠆⢀⠄⠀⠀⣠⠟⠉⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣰⠦⠤⠀⠀⠘⡇⠀⢸⠀⠀⠀⠀⠐⠁⢈⣥⣿⠇
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠧⣦⣤⣤⡏⠀⠀⢀⠀⠀⢹⡄⢘⠀⠀⠀⢠⣢⣴⣿⠿⠛⠉⠀⠀⠀⣀
⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠦⠤⡍⠉⣉⣚⡛⠛⠻⠇⢘⣀⣤⣾⠿⠛⠉⠀⠀⠀⢀⡤⠶⠋⢩
⠀⠀⡖⠒⣶⠶⠶⠶⠶⠶⢖⣒⠒⠛⡇⠀⠈⢩⣅⣉⡉⠉⠙⠋⠉⠉⠀⠀⠀⣀⡠⠴⠊⡟⠀⠀⠀⢰
⠀⠀⡅⠀⡇⠀⠀⣀⣀⣀⠀⠈⢳⠀⠃⠀⠀⢸⡇⠀⠀⠌⠛⠛⠓⢒⡒⠒⠆⢻⠠⠁⠘⠁⠐⠀⠀⢻
⠀⠀⡇⠀⡄⠀⠀⠧⠤⠼⠂⠀⣰⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⢸⣀⣘⣀⣀⢀⡄⣀⣨
⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀⠐⠺⢅⠀⠀⠀⠀⢸⣇⠀⠀⢠⡖⠒⢦⣤⠤⠉⠠⢨⡭⡿⣿⠿⣿⣿⣿⣿
⠀⠀⡃⠀⠀⠀⠀⡎⠉⡦⠀⠀⠀⡇⠀⠀⠀⢸⡿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⢰⠒⠒⠒⠒⠻⠛⣻⣿
⠀⠀⡇⠀⡇⠀⠀⠉⠉⠀⠀⠀⣠⠇⠀⢠⣀⢸⡇⠀⠀⠈⠓⠂⠐⠢⡀⠀⠀⢰⡄⠀⠀⡠⠂⣴⢋⣿⠒
⠀⡀⠦⠤⠕⠖⠲⠒⠖⠒⠒⠈⠁⠤⠾⢸⢸⢸⣇⡈⢄⡀⠀⠀⠀⢀⣸⠇⠀⢸⠀⠀⡐⢁⣠⠷⠋⠁
⠀⠉⠉⠛⠛⠓⠶⠋⠉⠝⠋⠉⠲⠍⠉⠛⠛⠓⠦⢤⣍⣉⣛⡒⠮⠭⢄⣀⣀⢰⠇⣠⠶⠋⠁⠤⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠩⠭⣁⣒⣒⡦⠘⠛⠝⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠙⡆⠀⠀⠀⠀⠀⠀⢀⡞⠉⡆⢀⡴⠙⡆⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⡰⠁⠀⠀⠀⠀⠀⠀⣼⠁⢠⠃⣾⠁⢠⠃⠀⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠊⠀⠀⠀⠀⠀⠀⠀⢀⡟⢠⠊⢰⡇⡠⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⠀⠀⣀⡀⠀⣠⢒⡆⢸⡗⠁⠀⣼⠋⠀⢀⡞⡡⢄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠸⣿⡆⡐⢡⡇⢰⡟⠈⠀⣸⡇⠀⢠⣿⠀⠀⣼⠃⠑⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠁⢸⡇⡸⡇⠀⡔⠈⢧⣠⠎⢻⣀⡴⢻⡄⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠘⠟⠁⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⡠⠂⢢⠀⢾⣯⣷⠀⠀⡴⠃⢳⠀⣠⠔⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠋⢀⠐⡠⣀⠀⣼⠁⡠⠃⠀⠀⠀⠀⠀⣸⠃⣠⠃⣼⠃⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠘⢂⢨⡄⠉⠈⢠⣏⠜⠁⠀⢀⡀⠀⠀⠀⣿⠔⠁⢸⡇⢀⠔⠁⠀⠀⠁⠆
⠀⠀⠀⠀⠀⠀⠘⠃⢤⠀⠀⠀⣸⠇⠀⠀⣠⡏⢠⡆⠀⢰⣿⠀⠀⣿⠃⠁⠀⠀⠃⠃⠬⢐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢻⣦⠀⠚⢹⡇⡼⡇⢀⠏⣿⠀⢀⣿⠀⠀⠀⡜⠀⠀⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢸⡏⡆⠀⠘⠷⠁⢷⠞⠀⠻⣄⡜⠹⣇⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠖⠒⠀⡀⠀⠀⠠⠤⢄⠀⠀⠀⠄⠀⠄⢀⠀⠀⠆⠐⠂⡆⠀⠐⠂⠀⠲⠆⠀⠀⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠋⠠⠇⠀⠀⠀⠂⠀⡃⠀⠀⠀⠘⠀⠈⡇⠀⠀⡉⡏⡀⠀⠀⠀⠒⠎⠀⠀⠀⢐⣄⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⢒⠀⢰⠀⠀⠀⠢⠉⡍⠀⠀⠀⠰⠂⡠⠃⠀⠀⠀⠀⠅⠀⠀⠀⡏⠀⠀⠀⠀⠓⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠁⠀⠄⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⣀⣀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠀⡄⠀⠀⠐⠰⠀⠀⠀⠀⠀⠃⠃⠀⠀⠐⠁⠗⠁⠐⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡇⠀⠀⠀⠀⠀⠀⠔⠴⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠐⠂⠄⢤⠀⠀⠀⢄⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠃⠀⠀⠀⡄⠀⠀⠀⠀⠁⠐⠁⠀⠀⠀⠀⠚⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⡀⢀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠤⠀⠀⢄⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠠⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠁⠀⠀⠈⢁⠀⠀⡀⠀⠀⠀⠨⠅⠈⠀⠀⠀⡎⠀⠀⠀⠀⠀⠠⠆⠈⠂⠀⠐⠶⠶⠀⠈⠀⠀⣀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠀⠀⠀⠀⠀⠇⡀⢀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠗⠃⢠⠀⠀⠀⢰⠀⠡⠀⠈⠉⠥⠠⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠴⠄⢰⠀⠀⠀⠠⠶⠀⢰⠀⢀⢀⠄⠀⡀⠄⠠⡄⠠⠄⠠⡤⠄⡄⠀⠂⠒⡄⠀⠖⠐⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠇⠀⠀⠀⠌⠀⢈⠀⠰⠀⠀⠀⠀⠁⡜⠀⠀⠀⠀⠁⡈⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⠆⠀⠀⠆⠀⠀⠀⢠⠀⠠⡀⠀⠀⠀⢀⡂⢀⠀⠀⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡀⣐⣶⣻⣀⣶⠟⠳⣄⡶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢠⣉⠙⣋⣧⣹⣼⣇⡹⢧⣝⣀⣹⠷⣸⣧⣞⠲⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⢋⡴⣏⣈⡴⢾⠃⠁⢀⢉⣀⠀⣉⡀⠉⠃⠼⣾⡋⠹⢦⡟⢦⡀
⠀⠀⠀⠀⠀⠀⣤⣍⣹⢦⣄⠟⡙⣆⣌⢧⣿⢯⢿⣿⣾⡹⡟⣷⢲⢤⡈⠙⠻⢾⣵⣧⣀⡀
⠀⠀⠀⠀⠀⣴⠗⠊⠩⣿⣮⡁⢾⣻⣯⠻⠛⠉⠈⠁⠀⠉⠋⢙⠾⢧⢫⣥⠶⠹⡇⢟⣷⠙⢂
⠀⠀⠀⠀⣠⠴⣶⠷⢾⠈⣙⣯⣳⠝⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡕⡫⢄⠀⡿⣴⢺⡍⠹⠆
⠀⠀⠀⠀⡶⢤⡥⡾⠳⢦⣷⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠖⡽⡦⢵⣞⣫⣅⣤
⠀⠀⠀⢀⣛⡚⠷⡟⣀⣽⡶⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠽⢧⣀⣯⡭⠠⢌⡀
⠀⠀⠀⠘⣽⣯⣽⠋⠁⣞⣛⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⣽⠉⣥⠿⠖⠺⠁
⠀⠀⠀⠀⣉⣩⣧⢟⣠⠿⠭⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣓⡚⠈⣛⣷⣻⡇⡄
⠀⠀⠀⠀⠩⡴⢾⠛⣅⠐⠏⣛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠴⢀⣾⣭⣀⣨⠼⠃
⠀⠀⠀⠀⠀⢤⠶⣿⡧⢤⠀⢱⣫⣿⢠⣀⡠⠀⠀⠀⠀⠀⠀⠀⣀⣐⡢⣒⠟⢲⣹⠛⡋⢹⡟
⠀⠀⠀⠀⠀⠀⢻⡉⠃⣸⡇⣘⡁⠒⢧⣻⢻⡖⣷⢦⣤⣶⣰⣾⡿⡙⡿⣍⡱⠶⣌⠳⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠁⢲⡽⡟⢻⣿⠀⣀⣈⠉⠓⠻⢞⣾⠟⠓⠛⠁⣱⠰⢾⢋⡳⣌⡻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠑⣤⢛⡾⣩⣝⢷⡳⣦⡼⢿⠦⡖⣛⡛⢿⢷⠛⢧⡍⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⢻⣯⣷⠃⠿⡇⣸⠺⡷⣤⣷⠌⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠉⠋⠀⠈