Scrub Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠒⠢⡔⠉⠙⢦⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡄⠀⠀⠌⠀⠈⠉⠒⠔⠁⣄⡽
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠭⠇⠀⠀⡀⠀⠀⠀⠀⢠⠼⠴⠤⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠈⠁⡰⠐⡄⠘⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⣠⠽⠿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃⢀⣀⠠⠤⠐⠒⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠑⣆⠠⠀⠁⠀⡠⠌⠀⢠⠔⠀⠀⠂⢻⡀
⠀⠀⠀⠀⠀⠀⡼⠙⢢⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠄⠀⡷⡞⠁⠀⠈⠐⠀⠐⢁⣠⡴⢶⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠑⠈⢩⡄⠱⠀⠀⠂⠠⠀⠀⠀⠀⠀⠐⠈⠉⠀⠀⠀⠀⠀⣱⠃⠀⢀⣴⠀⢀⠀⢨⠇⠀⠀⠉⠁
⠀⠀⠀⠀⡀⠀⠀⠠⠄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠐⠸⠃⠀⢠⠎⠀⠓⠤⠶⠋
⠀⠀⠀⠨⠀⡀⠀⠀⠀⠀⢀⠁⠂⠀⠀⡀⡀⠀⠀⠀⠤⠒⠈⠁⠀⠀⡀⢀⠀⠀⢩⣉⠉⠁⢢⡀
⠀⢀⠠⠄⠂⠁⠀⠀⠈⠀⠈⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠈⠗⠒⢌⠳⡄
⡔⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠂⢠⠀⠀⠀⠀⠀⡀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢠⠂
⠑⠤⠤⢀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠊⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠇
⠀⠀⠀⡌⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⡠⠀⠐⠈⠁
⠀⠀⠀⠈⠒⠀⠠⠤⠤⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠒⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠉⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣄⡀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠉⠻⠀⣀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠙⠃⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⡟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⢸⡇⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡿⠀⠀⣿⠀⠀⠘⣷⣤⣤⣤⣤⣤⣤⣤⣤⣾⣯⣤⣤⣤⣤⣤⣤⣤⣾⣯⣤⣤⡀
⠀⠀⠀⠀⠀⢠⣶⣶⣶⣤⣤⣤⣄⣀⢹⣇⠀⢸⡇⠀⠀⣿⡄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠈⣿⠻⢦⣄⠀⠀⠉⠉⠻⣿⢦⣼⣇⠀⠀⢸⡇⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⢿⡄⠀⠙⢷⣄⡀⠀⠀⣿⠀⠈⠻⣶⣄⠸⣷⠀⠀⢠⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠉⠻⣦⡀⢿⡄⠀⠀⢸⣿⣦⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⢈⣹⣿⣇⠀⠀⢸⣿⠘⣿⡇⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡶⠾⠛⠛⠉⠉⠙⠷⣦⣐⣿⠀⠘⣷⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣤⡀⠀⠀⠀⢀⣀⣨⣿⣿⣀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣶⣿⣛⠉⠉⠀⠀⠙⢷⣼⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⢻⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⠇




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

⠀⠀⠀⠀⠀⠀⠀⣠⢴⣒⣒⣒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠦⣄
⠀⠀⠀⠀⠀⠀⢰⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡄⠀⠀⣤⠴⣣⡇
⠀⠀⠀⠀⠀⠀⠘⣧⣉⣙⣛⡛⠒⠒⠲⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠶⠶⠒⠒⠒⠛⣛⣋⣉⣼⠃
⠀⠀⠀⠀⠀⠀⢠⠇⠀⢨⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠸⡄
⠀⠀⠀⠀⠀⠀⣼⢠⠀⣾⢰⠀⡆⢠⠀⢀⡇⣀⠀⢸⠀⡄⠀⡆⢀⠀⢰⠀⡀⢸⠀⢰⠀⣷⠀⡆⠀⡇⠀⡄⢻⠀⢰⠀⡇⣇
⠀⠀⠀⠀⠀⠀⢿⣼⠀⡏⢸⠀⡇⢸⠀⢸⡇⣿⠀⣼⠀⡇⠀⡇⢸⠀⢸⠀⡇⢸⡇⢸⠀⣿⠀⣧⠀⡇⠀⡇⢸⠀⢸⡀⣧⡿
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠛⠛⠛⠛⠛⠚⠷⠛⠛⠻⠾⠳⠾⠷⠾⠦⠼⠶⠷⠾⠗⠾⠖⠛⠒⠿⠞⠛⠛⠛⠛⠛⠙⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣦⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣠⠶⠋⠁⢠⣤⡈⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⢁⣤⡀⠀⠈⠛⠁⠀⠀⠻⣥⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠋⠉⠀⠀⠀⠻⣿⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄⠀⠀⠀⣿⣤⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣾⣿⣦⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣉⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⠋⠁⠀⠀⠈⠉⠁⠀⠀⣠⣴⣾⣿⣅⣨⣿⠿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢀⣴⣾⡟⠉⢿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣤⣴⣶⠛⣿⣿⣷⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣋⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢲⡄⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠤⠶⠶⠖⠒⠒⠒⠒⠲⠶⠶⠶⠦⠤⢤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠈⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣼⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠙⣷⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢸⣇⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣸⡆⠀⠸⡇
⠀⠀⠀⠀⢠⡶⠛⠹⢄⣀⣼⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣧⠀⠀⣿⠲⣤⡀⠀⠀⠀⠀⠀⢠⡞⠙⣦
⠀⠀⠀⢠⡏⠀⠀⠄⣀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠛⠋⠉⠀⢻⡄⠀⠀⠀⠀⠀⠙⠚⠃
⠀⠀⠀⣼⠀⠀⠀⠀⠀⠈⠉⠑⠒⠲⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠒⠒⠈⠀⠀⠀⠈⣧⠀⠀⣀⣀
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡖⠋⠉⠉⢳⣄⠀⣠⠶⣄
⠀⠀⠀⢸⡟⠲⠦⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⢺⡏⠀⠀⠀⠀⠈⠋⠛⠁⠀⢹
⠀⠀⠀⢸⠀⡄⠀⠀⠀⠀⠈⠉⠉⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉⠉⠉⠉⢀⠀⠀⠀⠀⡇⠀⠀⠙⠂⠀⠀⠀⠀⠀⠞⠓⣆⣀⡀
⠀⠀⠀⢸⠀⡇⠸⠀⢸⠀⠀⠀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⡄⡀⠀⡀⠀⠀⢀⠤⢼⢀⠴⣤⠖⢿⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠉⠀⠙⣦
⠀⠀⠀⠘⠦⣇⡀⠀⣸⠀⠀⠀⡄⡿⠀⠀⠀⠀⡇⢰⠀⠀⠁⢸⠀⠁⣀⠰⠃⠀⠀⠏⠀⠀⠀⠘⠀⠀⠊⠀⠀⠀⠈⠁⠀⠀⠀⠲⡄⣠⠟
⠀⠀⠀⠀⠀⠈⠉⠛⠻⠦⣤⣄⣀⣇⡀⠀⠀⠀⡇⠈⠀⠀⠀⣸⣀⣀⣁⣀⡄⠀⠀⠀⠀⠀⠀⣄⡀⠀⢀⣄⣀⣀⣤⣤⣀⣠⣤⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠉⠉⠉⠉⠉⠙⠓⠛⠳⠶⠶⠞⠉⠉⠉⠉⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⠤⠶⠶⠶⠤⢤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡴⠶⠶⠶⠶⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠉⠤⠴⠒⠒⠂⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠔⢋⣴⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢦⣙⠓⠶⠶⠦⠤⠤⠶⠶⠶⠚⠛⣛⣋⣉⣉⣉⣉⣉⣉⡉⠙⠛⠛⠶⠶⠶⢤⣤⣤⣤⡤⠶⠞⠋⣡⡟⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠉⠛⠳⠶⠶⠶⠶⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠲⠶⠶⢤⣤⣤⣤⣤⠴⠶⠛⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⠂⢠⡇⠀⣤⠀⡆⠀⡆⠀⢸⠀⠀⡇⠀⠀⡄⠀⡇⠀⡀⣶⠀⠀⣶⠀⣤⠀⢠⠀⠀⠀⠀⡆⠀⣇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⣾⠀⢸⡇⠀⡟⢸⡇⠀⣷⠀⢸⡆⠀⡇⠀⠀⡇⠀⡇⠀⡇⢹⠀⠀⣿⠀⣿⠀⢸⡀⠀⢸⠀⡇⠀⢻⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣤⣼⣤⣠⡇⢸⡇⢀⣏⠀⢸⣇⣀⡇⠀⢀⣇⣰⡇⠀⡇⢸⣀⣀⣿⣀⣹⣀⣸⡇⠀⣸⣧⣧⣤⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠛⠛⠉⠉⠛⠛⠛⠋⠉⠉⠛⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣀⣶⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣇⢏⣧⣥⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠄⠀⠐⠠⠀⣐⢁⠘⢲⣦⣹⣾⣿⢻⠞⣋⡀⠀⠀⠂⠶⠀⠘⠁⢠⡄⠀⠒⠀⠀⠀⢢⡄⠀⠀⠀⣄⠀⡃⠶⠀⣀⡀⠼⠂
⠀⠈⠀⠀⣴⣷⡄⠈⠀⠀⢿⢟⢧⣿⣿⣽⣛⣓⡤⡴⠀⠀⠀⠀⡀⣀⡘⠃⠀⠀⠀⠀⠐⠀⠄⠀⠀⣄⣨⢀⡈⠁⣄⠁⠀⠴⠆
⠀⠀⠤⠙⠩⢋⡁⠀⣐⡤⣻⣿⣿⣿⣿⣿⣿⣯⢭⣬⢅⣠⢀⣀⠀⠰⣌⣉⠉⠁⠀⠀⢠⡄⠈⠁⡤⠀⠈⠉⠹⡄⠉⡈⣴⠂
⠀⠀⠀⠀⠐⠀⣡⠤⢤⡅⠙⠿⢿⣿⣿⣿⣿⣟⢰⠭⠩⡀⠀⠀⠀⠀⠀⣀⣀⡆⣴⣶⡒⣀⠀⠀⠀⠛⠋⠁⠰⠶⢾⣿⣞⢁⣀
⢠⣦⢠⠙⢣⠁⢸⣏⣀⢡⣄⣄⣈⢿⣿⣿⡿⢁⠀⠀⠃⢄⠀⠀⠀⠁⠈⠛⠛⠁⠈⣉⠉⠉⠉⠀⠀⣴⣶⡴⠐⠒⠒⡀⠈⠁⠉
⠸⠿⠞⡳⠈⣩⢈⠒⠉⠁⠉⠋⠉⠋⠛⡛⢩⣠⢤⣤⠐⠀⠆⠀⠀⣠⠄⠤⠀⠀⠉⠛⠀⠀⠀⣀⣤⠀⢀⣤⣤⠀⠀⠀⢠⣠⣤
⠀⠀⢈⡥⣒⠀⠳⠈⢠⣤⠴⠀⣀⢶⣿⢽⣿⣿⣯⢫⣷⣶⡶⣁⠀⠴⠿⠶⠶⠿⠄⢀⡀⠀⠀⣀⡀⠒⠈⠉⠴⡾⠀⠀⠨⠖⢯
⢠⣔⣿⣶⣿⢨⡼⡟⢈⠁⣶⣷⣽⡿⢿⣻⠿⣿⣿⣽⣿⠛⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠙⠛⠓⠉⠁⠀⠀⠀⠀⢰⣗⡀⡀
⠐⠿⠿⠿⠿⠿⠿⢿⡷⠾⠟⠩⠄⢹⣿⣿⣿⣿⣿⣿⣿⠳⠂⢀⣤⣤⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠾⠿⣿⣿⣴⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠒⠢⡔⠉⠙⢦⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⡄⠀⠀⠌⠀⠈⠉⠒⠔⠁⣄⡽
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠭⠇⠀⠀⡀⠀⠀⠀⠀⠠⠼⠤⠤⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠈⠁⡰⠐⡄⠘⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⣠⠽⠿⢀⡀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⣀⠠⠤⠐⠒⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠑⣆⠀⠀⠁⠀⠠⠌⠀⢠⠐⠀⠀⠂⢻⡀
⠀⠀⠀⠀⠀⠀⠼⠉⢢⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡷⡞⠁⠀⠀⠀⠀⠐⢁⣠⠴⢶⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠑⠈⢩⡄⠱⠀⠀⠂⠠⠀⠀⠀⠀⠀⠐⠈⠉⠀⠀⠀⠀⠀⣱⠃⠀⢀⣴⠀⢀⠀⢨⠇⠀⠀⠉⠁
⠀⠀⠀⠀⣀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠸⠃⠀⢠⠎⠀⠓⠤⠶⠋
⠀⠀⠀⠨⠀⡀⠀⠀⠀⠀⢀⠁⠀⠀⠀⡀⡀⠀⠀⠀⠤⠒⠈⠁⠀⠀⠀⠀⠀⠀⢩⠉⠉⠁⠢⡀
⠀⢀⠠⠄⠂⠁⠀⠀⠈⠀⠈⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠓⠄
⡔⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠂⢠⠀⠀⠀⠀⠀⡀⠀⠠⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠁
⠑⠤⠤⢀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠊⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠃
⠀⠀⠀⡌⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⡠⠀⠒⠈⠁
⠀⠀⠀⠈⠒⠀⠠⠤⠤⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠀⡀⣀⣀⣀⣀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⠒⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠦⣄⠁⠀⠀⠀⠀⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠁⢀⡠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠙⠒⠒⠒⠉⠉⠉⠉⠉⠉⠁⠀⠈⠉⠒⠦⠤⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠚⠉⠉⠀⠉⠁⠙⠄⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢀⡤⠖⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠒⠉⠁
⠀⠀⠺⣀⣀⣀⣀⠠⠤⠤⠒⠒⠛⠉⠀⠀⢀⡠⠔⢫⠒⠛⠓⠆⠀⠚⠋⠉⠙⠓⠒⠒⠠⠤⢤⣤⠒⠚⠉
⠀⠀⢾⡁⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⢰⠁⠐⠒⠮⣦⣀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠉⢏⠉⠉⠉⠉⠉⠈⠁⠀⠀⠀⠘⣄⠀⠀⠀⠈⠙⠛⠛⠛⠓⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀
⠀⠀⠀⠀⠀⠉⢳⡐⠐⠒⠋⠉⠀⠀⠀⢸⡁⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠃⠒⠉⠙⠐⠀⠑⣄⠀⠉⠓⠒⠢⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠹⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠉⠁⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡒⠢⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀⠀⠀⢀⣀⠠⠤⠒⠊⠉⠉⠉⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤




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

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣛⣯⣭⣭⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⡼⢢⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣏⠓⠶⠶⠶⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡥⠤⠶⠶⠶⠚⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠚⠛⢻
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢀⡇⢠⠀⡀⠀⠀⠀⢠⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣠⠀⢀⠀⢠⠀⠀⠀⢠⠀⠀⡀⢠⠘⡇
⠀⠀⠀⠀⠀⠀⠀⣾⢠⡇⢸⠇⣿⠀⡇⢸⠀⠀⣾⠀⡆⠀⢸⠀⣶⠀⢸⠀⣤⠀⢸⠀⣠⠀⣿⠀⣿⠀⣿⠀⢸⠀⢸⡆⠀⡇⢸⡆⠀⣇⢸⡇⣷
⠀⠀⠀⠀⠀⠀⠀⢿⣼⠀⣸⣀⣇⠀⡇⢸⠀⠀⣿⠀⡇⠀⣾⠀⣿⠀⢸⠀⣿⠀⢸⠀⢻⠀⢿⠀⣿⠀⣿⠀⢸⡇⢸⡇⠀⡇⢸⣇⣀⣿⠀⣧⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉⠉⠛⠛⠛⠛⠛⠻⠞⠛⠛⠛⠶⠛⠶⠿⠶⠿⠦⠾⠶⠾⠶⠿⠛⠿⠛⠛⠛⠻⠟⠛⠛⠛⠛⠛⠉⠉⠉⠋⠉

⠀⠀⠀⠀⠀⡰⠺⠛⠛⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠲⡄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⡄⡇
⠀⠀⠀⠀⠀⢫⣙⣓⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣛⣩⠃
⠀⠀⠀⠀⠀⡇⠀⡄⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⢀⠀⡀⠀⢀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⣱⠀⡇⡇⡆⡄⠀⡇⡆⢠⠀⡆⢸⢰⠀⡇⠀⢸⠀⡇⣇⢸⠀⡇⢸⢸⡄⢢⢸⣹
⠀⠀⠀⠀⠀⠙⠚⠛⠓⠓⠓⠲⠷⠗⠺⠶⠧⠾⠼⠤⠧⠾⠼⠶⠷⠓⠾⠶⠓⠚⠒⠓⠛⠚⠁

⢀⣤⣶⣶⣶⣶⡶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⢶⣶⣶⣶⣶⣤
⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣿⡿⠿⠿⠿⠿⠿⢿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠿⠿⠿⠿⠿⢿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸
⢻⣧⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⣠⣤⠀⠀⠀⠀⠀⣤⡄⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠘⢿⣷⣤⣤⣤⣾⡿⠁⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠈⠉⠛⠉⠁⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣤⣤⣤⣶⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠗⣀⡺⣿⢟⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠼⣿⣿⡌⣾⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⢟⣴⣮⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⡌⡡⣿⣿⣿⡿⣧⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⢿⢟⣼⣿⣶⣝⠋⣾⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⡏⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣱⣬⡻⣿⡟⣵⣷⣮⡻⠇⠀⠀⠀⠀⣸⣿⣿⢟⣴⣄⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣿⣿⢢⣜⢿⣿⣿⢻⡇⠀⠀⠀⣠⡝⣿⣷⡜⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣝⠟⣵⣿⣿⣷⡍⡱⣿⡇⠀⣠⣮⣛⢏⣿⣿⡇⠈⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣫⣶⣮⡻⡿⣫⣾⣿⣦⣝⢛⣼⣿⠏⢸⣿⣿⠀⠀⠀⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢘⡳⣿⣿⣿⢟⣴⣝⠿⣿⡿⣱⣷⣼⠋⠀⣸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣮⡙⢣⣾⣿⣿⣿⢎⡸⢿⣿⠃⠀⢰⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣼⣷⣭⡻⠟⣵⣿⡿⠃⠀⠀⠀⠈⠛⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣫⣦⣝⠿⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄
⠀⠀⠀⠈⠠⠀⠂⣀⣀⡀⠀⠀⠀⠀⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡼⠁⠀⠀⠀⠀⡀⠀⢴⣤⣠⣴
⠀⠠⠀⠀⠀⠀⡴⣻⣿⣿⣿⣶⣶⣤⡧⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⣧⠀⠈⠀⠉⢠
⠀⠀⠆⢸⣄⣼⢷⣿⣾⣿⣿⡿⡿⣿⣿⣿⡀⠀⠐⠀⠀⠀⣠⠀⠀⠀⢸⢸⡇⠀⠀⣰⣤⣾⠿⣧⡄⠈⠐
⠀⠀⠼⣆⣿⣷⣾⣿⣷⣤⣿⠟⠛⣿⣿⣿⣷⠀⠀⠠⠁⢀⣸⠀⣠⠀⣇⣾⠀⠀⣺⣟⡅⢇⣠⢈⢙⠀⠻⢈
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣂⠠⣴⣿⣿⣷⣦⣤⣀⣸⣮⣡⣸⣼⣷⣿⣛⣻⠋⠙⡿⣿⣾⣿⡆⠂
⠀⠀⠀⣿⣿⡟⢿⣿⡿⣴⣿⡿⣻⣿⣀⣹⣿⣿⡿⣿⣿⢿⣿⢿⣿⠿⣿⣻⣿⡿⣿⣧⣾⣟⡿⢟⣿⣿⣾
⢀⠀⠙⢿⡿⣿⣿⣿⣘⣧⣤⣿⣿⣦⡶⡛⢛⣿⣿⣿⣿⣿⣿⣿⣻⣶⣿⣯⢹⣛⣾⡏⠽⢿⡿⣿⣿⣿⣿⢀⣀
⠙⠀⡀⢀⡿⡿⢂⣿⡻⡿⡛⠋⣩⢎⣙⣛⣇⡻⣿⡇⣘⣿⣿⣿⣿⣿⣿⣿⡳⣿⢻⣇⠀⣸⣿⣟⣻⣯⣿⠀⠁
⠀⠙⡅⠃⢀⣤⣿⡞⢝⣯⣼⠻⣴⣠⠟⡸⣶⢃⣿⣿⣿⣻⣿⣿⡿⡿⣿⣿⣧⣿⡿⡽⣿⣿⡟⣯⣟⡻⢟⡇
⠀⠀⠰⡛⣏⣹⣷⣃⣅⣯⠿⣹⣾⣭⣴⣿⣸⡿⠿⢿⣿⣿⣿⣿⣷⣿⣿⡏⣈⡙⣽⣿⣿⣷⢻⡟⣿⣷⣿⡇⠂
⠀⣀⣀⢰⣿⢿⣯⣭⣙⣿⣿⣿⣿⣿⣿⣿⡏⣠⣷⣗⣿⠿⡇⢉⡉⢘⠛⣓⠾⣷⡏⣿⣿⣟⡟⣋⢿⣾⣉⠁⢁
⠰⠐⠢⢼⡗⢼⣿⣿⣿⣿⣙⣿⣿⣿⣿⣯⣿⣩⣿⣿⣿⣷⣥⣮⣤⠒⣷⣿⣴⣾⣿⣿⡟⠛⠢⡐⠖⣿⣼⡋⠁
⠀⠀⠀⠈⣿⣻⣿⡿⠃⣠⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⡟⢿⣧⢴⡿⠟⡛⣿⣃⣸⣇⣴⣾⣷⢴⡏⣹⠋
⠀⠀⠀⠀⢿⡿⣽⡵⣰⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣧⣰⣤⣾⣿⣿⣿⣀⣋⣥⣀⣽⣿⠏
⠀⠀⠀⠀⠘⠀⠻⠐⠁⠀⠀⠁⠙⠋⠁⠈⠙⠁⠀⠉⠉⠙⠛⠙⠛⠛⠛⠛⠙⠋⠉⠙⠋⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠗⠀⠀⠀⠀⠀⠡⡐⠆⡄⡰⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣊⣲⣿⡇⠀⣉
⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢺⠿⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠍⠹⡑⢄⠒
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⠄⠀⢸⣑⣿⠄⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠛⠁⢰⣶⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠒⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠀⠀⡀⠀⠀⠰⠀⠀⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⣠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠘⠀⠀⠀⠀⡀⠀⠀⢿⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢻⠀⠀⠸⡇
⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢣⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠙⠃⠀⢸⠀⠀⠀⠁
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠃⠀⠀⠉⢀⠀⠀⠀⠀⣤⣟⠀⠀⢀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠂⠐⣤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣤⠀⠛⠃⠀⠀⠀⠋⠿⠀⠐⠈⡁⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠱⡆⣾⠀⡠⠀⠺
⠀⠀⠀⠀⠀⠰⠂⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣿⢱⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡠⠹⣿⣠⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢠⠏
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴
⠈⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⣀⠐⠋⠁
⠀⠀⠀⠈⠓⠦⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣀⣠⡤⠤⠤⠤⣤⣀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣠⠤⢤⡁
⠀⠀⠀⠀⠀⠀⠈⠰⠄⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⣀⣀⣀⣀⡀⠈⠉⠓⢤⡀⠀⠀⠀⢀⡀⢸⡁⠀⠀⡷⠀⠀⢀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⢠⠞⠁⢀⡤⠚⠉⠁⠀⠀⠀⠉⠙⠶⣄⠀⠙⢦⠀⠐⠋⠀⠀⠙⠒⠚⠁⢀⠀⠹⢤⠞
⠐⠂⠀⠠⢤⣄⡀⠀⠀⠀⠀⢠⠇⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠈⣧⠀⠀⠀⣀⣤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⠀⠀⡟⣒⣛⣛⣯⣭⣭⣭⣭⡙⢛⣛⠒⠚⡇⠀⢸⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣰⡋⣁⡀⢿⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠧⣤⠼⠀⠈⢹⡆⠀⠀⠀⠀⢸⣁⣹⠆
⠀⠀⠀⠀⠀⠀⢀⡿⣝⣺⠭⣷⣒⣒⣶⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣒⣒⣿⠵⠖⣫⣷⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠸⣟⡒⠮⢬⠃⢀⡈⠉⠉⠉⠉⠉⠉⠛⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠰⢒⣻⢀⠴⠒⠲⣄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢿⠭⣥⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢒⣒⣛⡭⠵⢾⠇⠀⠀⠀⠘⠛⠞⠉⢳
⠀⠀⠀⠀⠀⠀⠀⣿⢀⠠⠀⠉⢉⠉⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠋⠉⠉⠁⠀⠀⠀⢸⡄⠀⠈⠳⡄⠀⠀⠀⠸⢳⣄⣀
⠀⠀⠀⠀⠀⠀⠀⡧⢸⢼⠀⣷⣰⠀⠀⣀⠈⠀⠀⠀⡀⠁⠀⠀⣀⠀⠃⠀⢀⡴⢌⣡⠴⣧⠼⡇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣄⣀⣿⠈⠀⠀⣿⠸⠀⠀⠀⡇⠇⠀⠀⣿⠐⢧⠤⠞⡀⠐⠃⠠⣄⠀⠀⣠⠖⠀⠈⠁⠉⠀⠀⠈⠇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠾⣄⣀⣀⣀⣇⣀⣀⣠⠾⣤⣿⣀⣘⣁⣀⣀⣀⣈⣀⣀⣀⣀⣀⣠⣤⠤⠤⠤⠤⠴⠋
⣿⣿⠟⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡆⢸⡃⣀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠘⠃⠐⠦⢉⣡⣰⣆⡔⣄⣆⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣼⣿⣾⠃
⠀⠀⠀⠀⢀⣤⡸⠇⡐⠀⠀⠂⠲⠀⠀⠀⠀⠠⣀⣸⠆⣘⢶⢿⠿⡦⡖⠞⠀⠁⠀⠀⠀⠀⠀⠀⠙⢿⡿⢊⣡⣤
⠀⠀⠀⣰⠞⢉⡔⠊⣩⢀⠀⠠⠈⠀⠀⢀⣻⠧⣄⣸⠇⣼⣷⣿⡟⠁⣉⣋⡿⠀⠀⠀⠀⠀⠀⠀⠀⡬⠀⠘⠿⠟⠁
⠀⠀⢰⠏⠀⢼⠀⣼⠦⠦⢤⠀⠀⡆⠀⠀⣿⡖⣳⡀⢐⢛⣻⣿⣿⣿⠛⠿⠘⠄⠀⠀⠀⠀⠀⣰⣾⣅⣦⣶⣤⡀
⠀⢀⡞⢀⡿⢁⣿⢋⣩⠂⠀⠂⠄⠀⠀⠀⠸⠿⣿⣤⣁⣨⢉⣩⠇⡛⠄⠀⠀⠀⠀⡤⠀⠀⣤⣿⣿⣿⣿⣿⣿⡏⡿⢰⡄
⠀⠀⣿⣿⣽⡟⣱⣟⠉⠀⠀⠰⠷⣄⠀⠀⠀⠈⠛⢿⣷⣾⣉⣵⣤⠣⣀⣴⣤⠎⠈⠀⠀⣶⣿⣿⣿⣿⣻⡏⡝⠁⠀⠘⣱⡆
⠀⠈⣿⣯⣾⣿⣻⣄⡄⢡⡄⠁⠀⠀⠑⠀⠀⢀⠤⠀⠁⠛⠩⠿⣧⠀⣧⢉⠂⢀⣦⣼⣿⣿⣿⣿⣿⡿⢿⣿⣀⠀⠀⠈⠉⠰
⠀⠀⠸⣿⣿⣿⠛⠝⠁⠀⠀⠀⠀⠀⠀⢠⣆⣈⡠⢀⣮⠆⠀⣠⠀⠈⣿⠀⢠⠀⢻⣿⣿⣿⣿⣿⣋⣘⠐⣿⡯⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠠⣤⣀⡀⠀⢠⡀⠀⠿⣿⣿⣾⡏⡀⠀⣿⡇⠀⢸⢠⠏⣀⠈⣿⣿⣿⣽⣿⣿⣿⣿⡟⠃⢢⣔⠒⠦⣌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣷⣷⣿⣶⠢⠄⠱⡀⢱⢰⣾⣿⣿⣶⢰⡏⠀⠈⣆⠜⢻⢟⣽⡿⠉⢏⡋⡄⠀⠀⢉⣳⣦⠄
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣇⣦⡘⢳⠸⣾⣿⣿⣿⣿⣸⠀⢀⡾⠁⠀⡜⠻⣯⣴⠄⣸⢣⣇⢴⡳⡼⠞⠁
⠀⠀⠀⠘⣿⣇⠀⠐⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢻⡍⢻⣿⣿⡇⣿⢠⡞⠀⠀⣼⢁⡤⡄⠁⠈⠉⠋⠙
⠀⠀⠀⠀⣉⣉⣳⣞⡠⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠳⣸⣿⣿⣥⣻⠟⠀⡄⠀⠇⢸⠿⠃⠀⣠⠁
⠀⠀⠀⠐⠻⠟⢁⣜⠁⠠⣀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠞⣿⣀⣃⣿⠀⣶⣾⠗⠁
⠀⠀⠀⠀⠀⠀⠈⠉⢳⣴⡷⠒⠒⠂⣉⣀⡐⢀⣨⣿⣿⣿⣿⣿⣟⠠⠀⣀⣴⣿⢿⣿⣿⣿⣿⣥⣤⠄
⠀⠀⠀⠀⠀⠀⠦⠾⠁⠾⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠏⢰⣿⣿⣿⢿⡜⣸⠟⠛⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢽⣿⣿⣿⣿⣿⡿⠟⣿⣦⡿⠋⢀⣴⣦⣜⠷⣿⡟⣸⣃⣴⣾⣶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠋⢀⣴⣿⣿⠧⠂⢈⣉⣛⡿⡆⢿⢹⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠀⠀⠀⠀⠹⢿⣿⣿⢰⣿⣿⣟⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⠿⠿⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⣤⣤⣤⣤⣴⣶⣒⣒⣒⣂⣀⣀⣒⣒⣒⣒⣒⣲⣶⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣾⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⢻⠃⡌⠸⠃⠀⢸⠈⣿⠸⡇⠀⢸⠀⠀⡆⠀⠰⢸⣿⣿⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣘⠙⣸⢸⠀⠁⠀⠀⠀⣸⠀⣿⠀⡇⠀⢸⠀⠀⣇⠀⠀⡌⣾⣼⢰⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣻⣿⣀⣆⣰⣀⣀⣿⣀⡇⢀⡁⢀⣿⠀⠀⣏⢀⣄⣧⣿⣿⣴⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠈⠁⠉⠉⠉⠉⠉⠉⠁⠉⠀⠈⠁



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠭⡧⠤⢼⠭⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⣸⣀⣀⣇⣀⣸⣀⣀⣏⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡇⠀⢸⠀⠀⡇⠀⢸⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⠉⠉⡏⠉⢹⠉⠉⡏⠉⢹⠉⠉⣏⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡟⠒⢺⠒⠒⡗⠒⢺⠒⠒⡗⠒⢺⠒⡲⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⡧⠤⢼⠤⠤⡧⠤⢼⠤⠤⡧⠤⡼⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣀⣇⣀⣸⣀⣀⣇⣀⣸⣀⣀⡧⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠙⢤⡇⠀⢸⠀⠀⡇⠀⢸⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠙⢏⣹⠉⢉⣏⡭⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠉⠳⣄⠀⠀⣀⠴⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢈⡷⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⣍⠇⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣠⠴⠃




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄⠀⠀⣀⣀⣠⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⣉⣴⡾⠿⠛⠛⠉⠉⠉⠙⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡄⠘⠟⠉⣰⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣶⣴⣾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣸⡷
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⣉⣉⡛⠻⢿⣷⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⣌⠻⣿⣷⡦⠈⣀⣤⣶⡶⠛⡷
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣷⣿⠟⣠⣾⣿⡇⠋⣠⣾⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠻⣿⡏⢰⣿⡿⠋⣠⣾⣿⡿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣇⠸⠋⣠⣤⣤⡼⠛
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⣌⣉⠉⠁⠀⠀⠀⢀⣴⣿⣿⠆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣉⣭⣭⣭⣭⣭⣭⣤⣄⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⣠⣿⣿⣿⣿⠛⠛⠛⠛⠛⢛⣠⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠟⠡⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⠲⢤⡔⠉⠙⠲⡄⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⢄⠀⠀⠀⠐⠆⠀⠛⠒⢤⣠⠎⢁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠤⢾⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⢀⣞⣊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠀⡀⠐⠢⠀⠀⠀⠀⠀⠜⠉⠉⠉⠙⢦
⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢠⠂⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⡀⠀⠁⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠹⡀⠈⠒⠊⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⡠⠖⠛⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⡀⠐⢂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠁⠀⣀⣀⠤⠤⠒⠒⠈⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢦⠀⠄⠀⠆⠀⢠⠤⠃⠀⡀⠘⠂⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠢⡀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢮⣤⠛⠀⠀⢔⠡⠀⠀⠖⠀⢀⣠⢶⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠣⠤⠦⢃⠀⢎⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠐⠂⠈⠁⠀⠀⠀⢰⡾⠀⠀⠀⢁⠄⠒⢀⠀⢹⠋⠁⠈⠓⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠁⠀⢀⡴⠛⣄⠈⠂⣠⠞
⠀⠀⠀⠀⡠⠐⠒⠒⠒⠒⠒⠒⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠒⠈⠀⠘⠀⠀⢀⣞⡀⢄⣀⠉⠉⠁
⠀⠀⠀⠀⠑⠠⡄⠀⠀⠀⡀⠀⢀⠀⠈⠀⠀⠤⢀⡀⢀⡀⠠⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⠉⠢
⠀⠀⡠⠤⠐⠊⠀⠀⠤⠈⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⢠⢀⠒⠘⠀⠀⠀⠀⠀⠂⠀⠠⠙⠢⡀
⡰⠋⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠀⠐⠀⠀⠀⠀⠃⢠⢀⠐⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠁
⠁⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠠⠔⠠⠜⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢳⠄
⠀⠀⠀⠈⡇⠀⠀⠀⠘⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢀⠀⠀⠔⠀⠀⣀⡠⠔⠁
⠀⠀⠀⠸⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⡀
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠒⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠒⠒⠈
⣿⣿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⣶⣶⢠⣾⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⢌⣿⣿⡈⢿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣾⣿⢟⣭⣶⣷⣶⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠱⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠼⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠙⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣷⣶⣤⣌⣉⠉⠉⢁⣤⣾⣿⠇⠀⠀⠀⠀⠈⠙⢷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⢤⣶⣿⣿⣿⣿⣿⣿⣟⣫⣭⣝⣛⣣⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠋⠉⠙⠛⠻⠿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧
⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣅⣾⣤⠉⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠄⠘⣿⣿⣿⡟⠁⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⡆⠀⣷⠀⢸⠀⣼⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠪⣄⣀⠀⠀⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⠀⢸⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢻⣿⡷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣟⣀⣸⣃⣀⣟⣀⠸⠀⢹⣿⣿⡿⠁
⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⠀⠀⠘⠛⠀⢁⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠉⠉⠉⠙⠉⢀⣠⣴⡎⢻⡿⠃⣦⣤⣀
⢀⣠⣴⣾⣿⣿⣿⣿⡿⠿⠿⠶⢦⠄⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⢨⣧⢸⣿⣿⣿
⠙⢿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠶⣶⣶⣶⣤⣤⣶⣶⣶⠶⠿⠟⠛⠉
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠠⡄⠀⠀⢀⡀⠀⠀⠀⡂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⣬⠉⠉⣷⣦⢶⣄⢊⡀⢳⡀⠀⠘⢿⣷⢀⣴⣿⣿⢠⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀
⠀⠀⠀⣀⣰⣧⠛⠃⠀⠹⠛⠻⠛⢁⡶⠆⠹⡷⡞⠋⢁⠿⢁⣨⡄⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠒⠛⠛⠁⠀⠀⡀⠀⠀⠀⣀⣀⠀⠀⢰⠘⢰⣤⣤⣷⣿⣿⡇⠀⣺⣤⣤⡀⠀⡄⡀⠀⠀⡠⡀
⠀⠀⠀⠀⠄⠀⢀⠢⠷⣦⣀⠀⠉⠙⢶⣤⣿⢃⡁⣩⣏⣿⣿⢿⣿⣅⣈⣿⢉⣐⢾⢟⡄⡀⣀⠁⠠⣄⠀⠈⢀
⠀⠀⠀⢄⠠⠴⠎⠃⠀⣽⣈⣄⣀⠀⠀⢍⡉⣲⣿⣿⡿⣷⣿⣿⣿⣿⣷⣿⠁⢸⡃⣤⣹⣿⣿⡴⣶⢋⢀⣀⡆
⠀⠀⠀⢸⠇⡄⠙⠃⠀⢹⡟⢻⣿⣷⠰⢾⣴⣿⣿⢻⣷⣿⣿⣿⣿⢿⣿⣿⣧⢘⣿⢙⣩⣿⣿⣿⣿⣷⣔⠸⠓
⠀⢰⠀⠰⠀⡇⠀⠀⠀⣾⡆⢸⡟⢙⣀⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣍⣸⡿⠀⢀⣿⣿⣇⣼⣶⣛⡑⠓
⠀⢸⠀⣂⢸⣇⣀⣴⣴⣿⡇⢹⣴⣿⣟⣻⣖⣿⣿⣿⣿⢯⣽⣿⣿⣷⣽⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠟⠁⠀⠘
⠀⢸⣁⠈⢘⡏⠛⠡⣭⢹⣏⢹⣯⣿⣿⣍⣫⢿⣿⣿⣿⢿⣿⠏⠉⠹⣿⣿⣿⣿⣿⣇⣿⣿⢋⣏⡴⠠⠆
⠀⠺⣿⢇⡐⡇⠀⠀⠠⣼⣟⣸⡏⣉⣽⠛⠉⠛⣻⣿⣿⣛⣿⣷⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠄
⠘⠲⡽⠊⠈⠃⠀⠐⠂⠙⣿⣿⡇⠀⢹⠀⠤⠶⠀⠰⠼⠿⣷⣤⡤⠄⢻⣿⣿⣿⣿⣿⣿⣿⠏
⢀⣠⣽⠏⠀⠀⠀⠀⠤⣿⣟⠋⠀⠀⢹⡀⠀⠀⠀⠀⠀⠠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⠠
⢀⠽⡯⠀⠀⠀⠀⠀⠀⠉⢿⠀⠀⢀⣈⡄⠀⠀⠀⠶⠿⠉⠉⠛⠛⠛⠟⠛⠻⠿⡋⠙⠻⠿⣧⠠⠀⠀⠀⠒⠲⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⣻⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⡃
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠛⠛⢁⣿⣿⣿⣿⣿⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⣀⠀⢀⣀⣸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠻⠿⠿⠇
⠀⠀⠀⠀⠀⠀⢀⣠⣀⠈⢳⡀⠀⣿⡿⠟⠛⠋⠁⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠚⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠠⠀⡞⣾⣿⡧⠈⣧⠀⣿⠁⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣓⡀⢀⣀
⠀⠀⠀⠀⢀⠸⡸⣿⣿⣅⠀⣿⠀⣿⢠⣴⣶⣾⣿⠀⠘⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⡘⣷⡄
⠀⠀⠀⠀⠈⠀⢣⣻⣿⠏⢀⡏⠀⣿⡞⣿⡿⠭⢿⣤⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠞⠀⠀⣿⣇⢿⣿⣹⣹⣽⣿⣿⡇⠀⠀⠀⠀⣼⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣿
⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣾⣿⣿⣿⣿⠁⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⡘⢿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠛⠛⠉⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⡈⣿⡄⠀⠀⠀⠀⠀⠀⣹⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⡘⢷⠀⠀⠀⠀⠀⠀⠸⠾⠇
⠀⠀⠀⠀⠤⢤⣤⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡈⠆
⠀⠀⠀⠀⠀⠀⢀⣈⣉⣍⣽⣿⣍⣽⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠘⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⢟⣻⠀⠖⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⢸⡇⠀⠀⢸⡇⠀⠀⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠸⠀⠀⠀⠀⠡⡀
⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣿⣶⣤⣤⡀⠀⠀⠀⠈⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣼⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠒⠈⢉⡀⠀⠀⠀⠀⠀⠀⠁⠂⢀
⠀⠀⠘⠟⠻⠿⠛⣿⠿⠿⠿⠿⠟⠛⠇⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠴⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠆⠀⠀⠀⠀⣀⣼⠇⠀⠀⠀⠀⠘⠛⠿⢿⡿⡿⣿⡿⠛⠗⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⢀⡠⠄⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠸⠿⠿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⡀⠖⠀⢰⡶⠖⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣾⣷⠄⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣶⠄⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠚⠛⠛⠛⣿⣿⣿⣷⣄⣐⠀⠀⠀⠀⠀⡀⠀⢀⣼⠿⠟⠛⠃⠀⠀⠀⠀⠀⠲⠯⠭⠭⠭⠭⠷⠂⠘⣆⠀⠀⢻⡄⠀⡀⠀⠀⢿⣿⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠬⣝⣛⣛⣛⣛⣭⡄⠀⢙⣦⠀⠀⠙⢋⠀⠀⠀⠀⠻⣿⣶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣒⡲⢶⢶⣖⣒⠉⠛⠋⠉⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢱⣿⣿⣿⡏⢘⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡼⢿⣿⣿⡟⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡦⠀⠀⠀⠀⢀⣿⣿⡇⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠹⡟
⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⣴⡆⠀⠀⢻⡿⢻⣦⠀⠘⠃⡄⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⠛⠛⢠⡀⠀⠀⠀⠀⢨⠢⠀⠀⠀⠀⠀⢄⠑⠶⠀⣰⣦⡀⠀⡇⠀⠀⢰⠇
⠀⠀⠀⠀⢀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣦⠀⢀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢠⣼⣿⣿⣧⠀⡇⠀⠀⠿
⠀⠔⡀⣿⣿⣿⣻⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⢧⢹⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢻⡖⡋⠿⣿⠏⠀⡇
⠀⠀⠀⢿⣿⡟⠏⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⠈⣎⠁⢀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⡆⠁⠀⢸⠀⠀⡇
⠀⠀⠀⢸⠁⠁⠀⠀⠀⢀⡘⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⢹⡄⠈⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⢸⠀⢀⡇⠀⠀⠀⠀⠀⢀⡄⢰⣿⡄
⠀⢰⠀⢸⡄⢠⣤⠀⠀⠘⠷⢶⣄⠀⠀⠀⠀⠀⠀⠀⠈⡇⢠⣤⡌⣧⠀⠀⣮⠛⢀⠀⡀⠀⠀⠉⠀⠀⢹⡌⢆⢠⡄⠈⡗⢤⡀⠀⠀⠀⠈⠀⠾⠛⠏
⠀⢸⡇⢸⣷⣿⣿⠀⠀⠄⠀⣶⠈⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⠿⣄⢹⡄⠔⠉⠀⡏⠀⠛⠀⢀⣀⡤⠀⢸⡇⠘⡎⡇⢈⡇⡀⠳⡄⠀⠀⠀⠀⠂
⠀⠀⢻⣿⠊⢻⣿⣶⣿⢟⣿⠃⠀⠀⢀⠀⠈⠙⢿⡉⠉⠟⣇⠀⢹⡎⣿⡆⠀⣸⡇⠀⠀⠀⠐⠻⠆⠀⠀⣷⠀⢻⣷⢰⡇⢡⠀⢹⡄⠀⠀⠀⠀⠀⢀⡔
⠀⠀⢸⠸⡁⢹⡟⠉⣙⣯⣿⣀⡀⢀⣸⠀⠀⠀⠀⡿⣄⠀⣿⠀⠀⣷⢹⡁⠀⡿⠀⠀⢠⠀⠀⢀⠄⠀⢀⣿⣀⢈⣿⣾⡇⢸⣤⠀⢻⡀⠀⠀⠀⣠⡾
⠀⠀⣼⠀⣇⣹⣿⣿⢿⣿⣿⣯⠛⢉⣿⣶⣾⣷⡄⢹⣿⣷⣼⡆⠀⢸⣾⡇⢰⡇⠀⠀⣴⠀⠀⣼⠀⠀⠈⢻⡙⠛⢿⣿⡇⢸⡿⠀⠈⣧⠀⠀⠾⣿⠃
⠀⠀⣿⡄⠹⡇⢸⢹⡀⢟⠛⢿⣿⠾⣿⣿⣿⣿⣧⠸⣿⣿⣿⡇⠀⠀⣷⣿⢸⡇⠀⣀⠃⢀⣼⣃⣴⠏⠀⣿⡿⡄⣸⣿⡇⢸⡇⢡⠀⢹⡇⠀⢠⡟
⠀⢠⣇⡇⣦⣇⢸⡇⣷⠈⢳⡀⣷⠀⢸⣿⣿⣿⡿⠀⣿⣿⣿⡇⢠⠀⢹⣹⣼⠀⠀⢹⢰⣠⡿⠻⣇⠀⡜⢹⡇⢳⡏⢹⡷⣾⣇⠈⡆⠘⡇⣧⣾⠇⢰
⠀⢸⠉⡟⣿⣿⢻⣷⢸⣵⣾⣷⢸⣆⣼⣷⣽⢻⡇⠀⣟⡏⠈⣇⢸⠀⢸⣿⣿⣶⣿⡿⣿⣿⠿⣷⠿⣸⠁⢸⡇⢸⣇⢸⡇⣿⢹⠓⢷⠀⡇⣿⣹⡀⠀⡇
⠀⣿⠀⣿⡇⢿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⡷⢸⡇⠀⣿⡇⠀⣿⢘⡇⢘⣿⣿⣿⠙⣇⢻⡏⣰⠋⢀⡏⠀⢸⣁⣸⣿⢸⣇⣏⢸⠀⢸⠷⣟⡿⡿⠃⠀⢱
⠀⣿⠀⣽⣧⣼⡿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣷⢸⡇⠀⣿⣧⠀⣿⠸⡇⢸⡿⣿⣯⣠⡏⣼⣡⠏⠀⢸⠃⡤⢾⠏⢸⣿⣿⣿⣿⣸⠀⠈⡇⣿⣇⡿⣼⠀⢸⡀
⠀⣿⢠⣿⣏⢹⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⡇⢠⣿⣿⡀⢿⣐⣇⢸⡇⣿⣿⣿⢻⣿⣾⣦⣦⣿⠟⠀⢸⠇⢸⣿⣿⣿⣿⣿⣢⠖⡏⣿⣿⡇⢹⡀⠀⡇
⠀⣿⣤⣿⣿⢸⡇⣿⡏⣿⣿⣿⠛⣿⣿⣿⣼⣿⣿⣾⣿⣿⣧⣿⣿⣿⢸⡆⣿⢻⣿⢸⣿⣿⣿⣹⣿⣄⠀⡾⠀⠘⢿⣿⣿⣿⣿⡅⠀⡇⣿⣿⣇⠸⡇⠀⡇
⠀⣿⡟⣻⣿⣸⡇⣿⣷⣽⣿⣿⣠⣿⣸⡟⠈⡿⡿⡟⢻⠃⣟⢻⠛⡋⣾⡄⡇⠀⣿⣼⣿⣿⣿⣿⡇⠀⢀⡇⠀⡇⢸⣿⣿⣿⠘⣧⠀⡇⢹⣿⣿⠀⣧⠀⣷
⠀⣿⠁⢹⣿⣿⣷⣿⣿⠿⣿⢻⠿⣿⢹⡇⠀⡇⣿⡇⢸⢰⢸⣸⠀⡃⣿⡇⡇⠀⣿⣿⣿⢏⡟⣼⠁⡀⢸⡇⢠⣧⠿⣿⣿⣿⠀⠀⠀⣧⢸⣿⣿⠀⣿⠀⣿
⠀⣿⠀⢸⣿⡿⡃⢹⡿⣆⣿⢸⠀⢿⢸⡇⠀⡇⣿⠃⢸⠸⢸⣿⠀⠁⢸⡇⡇⠀⢻⠃⡇⣾⣷⣿⣟⡉⢹⡇⢸⣿⠀⣿⣿⠉⠀⠀⠀⣿⡿⣿⢻⠀⣿⠀⣿
⠀⣿⠀⢸⢹⡇⠀⣿⡇⠀⣿⢸⠀⢸⢸⡇⠀⡇⣿⠀⢸⡇⢸⣿⠀⠀⣿⣷⡇⠀⢸⠀⡇⡿⠋⣼⠈⠃⢸⡇⢸⡇⠀⣿⡇⠀⠀⠀⠀⣿⠇⣿⢸⠀⢻⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣿⣭⣭⠽⠿⠶⠶⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢳⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠿⠀⣿⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⣿⠀⠀⠉⠉⠛⠳⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣟⠓⠶⠶⠚⠛⠉⠉⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢠⣤⠶⠶⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠈⠙⠛⠶⣦⣄⣀⠀⠀⠀⢹⡆⠀⠀⠈⣧⠀⠀⣿⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢦⣼⣇⡀⣀⣀⣿⣤⠶⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣶⣤⣈⠙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢋⣥⠾⠛⢻⡟⣛⠻⣟⠳⢦⣄⡀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⠋⠀⠀⠀⢸⣸⣿⣷⢹⣷⣤⠾⢿⣷⣶⣶⣶⣿⣿⣥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⣧⡻⡿⣸⣿⣥⠶⢻⣿⣿⣿⣿⡿⠋⢿⡍⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⠉⠀⠀⠸⠿⠿⠷⠤⣤⣤⣼⠗⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⣀⢀⣶⣿⣿⣿⣶⡀⢀⣠⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⡿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣤⣶⠟⣻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣄⡀⠀⠀⠀⠇⣴⠛⢋⣀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡝⠻⣷⣄⠀⠈⠥⠾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣷⣦⡙⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢀⡀

⠀⠀⢠⠤⢠⡄⣤⢠⠤⠠⣤⠄⣤⡀⣤⢠⡄⡄⢠⣤⠀⡤⡄⢠⠀⢠⠤⠀⢠⠤⣄⣤⠤⢤⢀⡄⣤⠄⣤⠀⣠⠤⡄⡤⣤⢠⡄⣤⢀⡤⠄⣤⢠⡤⣤⠄
⠀⠀⠨⡽⠘⢧⠟⠨⠽⠀⠿⠸⠛⠧⠿⠸⠙⠇⠾⠻⠄⠯⠗⠿⠤⠸⠯⠀⠸⠤⠟⠿⠭⠈⠿⠁⠿⠅⠿⠄⠷⡤⠇⠟⠉⠸⠻⠹⠗⠯⠅⠏⠻⠇⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣠⣶⡶⠦⠀⠬⠀⣶⡶⠦⣠⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣀⣈⠀⢁⠀⠀⢀⣠⣄⣀⠀⣀⣸⣇⣁⠀⡀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣿⡿⣿⠛⣯⡘⣿⡀⠉⠉⣿⠡⣿⠙⣿⡟⣙⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⢛⣿⣿⣶⣿⠧⠤⠽⣾⣶⡿⠰⠛⠦⠼⢧⡿⡼⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⢿⣿⣿⣿⡿⢻⢿⣿⠿⠿⠿⣿⣿⣿⣿⡿⣿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡧⡇⣿⣿⣿⣿⣿⡇⣼⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣾⣿⣿⡿⣶⡿⣶⣾⣶⡷⣼⣿⣿⣿⣿⣷⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⣯⢿⡽⢿⣮⣵⣤⣿⡟⣧⢻⣿⣿⣶⣾⣥⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣟⣿⣿⣿⣿⣻⣯⣽⣧⣿⣇⣻⣮⣿⣿⣏⣽⣣⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣼⣿⣿⣿⣼⣿⠏⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⢾⠿⣿⣿⣿⡿⠷⣼⢿⣿⣿⠿⣿⣿⣿⣿⡟⣧⠁⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢻⢿⣿⡿⣾⡿⣿⢿⣿⣿⣿⢿⡿⣿⣟⣿⡟⠻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣻⣿⣍⡸⣾⣿⡷⣻⡻⢿⣸⡏⢹⣿⣸⣬⡟⠛⠁⠀⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣽⣿⣿⣷⣿⣿⣿⣿⣷⣾⣾⣧⣬⡷⠼⠋⠁⠀⠈⡇⠀⡭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⣇⣶⣿⣿⣿⣷⣿⠿⢿⠏⠁⢄⠀⠀⠀⠀⡰⠃⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠛⠛⠉⠉⠉⠀⠀⠀⠸⠃⠀⠀⠉⠉⢉⠉⣀⢀⣀⣓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠈⠃⠙⠙⠃⠉⠈⠁⠀⣠⡀⠁⠈⠈⠉⠙⠉⠋⠙⠉⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡃⠀⢀⠜⠉⠉⠉⠐⢀⠀⢸⡅⢀⡴⠋⠉⠉⠙⢠⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠈⡇⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡅⠀⠘⢦⡀⠀⠀⣠⠆⠀⠾⣷⡄⠡⣀⣀⡀⢀⠜⠃⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⡛⣿⡇⣠⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠉⠉⢉⣉⣉⣉⡉⠉⠉⡅⣿⡏⠉⣉⡉⠈⢉⠉⠉⠉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡅⠀⢠⠊⠀⠀⠀⠈⠠⠀⡤⣿⡇⠈⠀⠀⠀⢀⣀⠄⠀⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢈⢹⡟⢻⣿⣯⠀⠀⠇⣿⠇⠈⣿⠛⣿⣿⡉⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⢸⡇⢘⣿⣿⠃⠀⡓⢻⡆⠀⣿⠀⢸⣿⡟⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⣸⡇⢈⣿⣧⡠⠶⡇⣼⡇⣴⣿⠀⢿⣿⡤⠴⠐⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⢲⡶⠆⠀⢠⠁⣀⠀⣀⠘⠀⠀⡇⢻⡇⡀⢀⡀⢀⡀⢡⠀⠀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠆⠀⠉⠀⠀⠀⠀⢀⠀⠀⡄⣼⡇⠁⠀⠀⠀⠀⢺⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⣀⣸⡧⠆⠀⢲⡙⢛⣉⣛⣯⣰⠓⡒⢿⢵⣌⣿⠛⣿⣿⢀⣤⣤⣤⣄⣄⣤⣄⣀⣀⣀⣀⣄⣤⣄
⢴⣦⣾⣿⣶⣷⣶⣶⣶⣶⣶⣾⠅⠀⢸⣿⣱⡆⠀⢸⠁⣿⣀⣀⣀⣀⣀⣀⣄⢀⣇⣀⠀⡉⠀⠀⠀⠀⣿⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣶⣦⣤⣤
⠙⢿⣿⣿⣛⣿⣭⣭⣿⣿⡿⠉⠉⢹⣿⣿⡷⢶⠒⢾⠗⢹⣿⣿⡟⢻⣿⢿⣿⡿⠿⠛⠛⠛⠛⠟⠻⠿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠿⠛⠉
⠀⠀⠉⠹⡿⣿⣿⣿⣿⣿⣷⣶⣶⣾⡿⠿⠾⠿⠿⠶⠗⠲⠖⠶⠽⠯⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⣯⣭⣭⣥⡿⠟⠋⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⡯⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⡿⠿⠿⠿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠭⠹⠃⠀⠀⠀⠀⠀⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣥⣤⣤⣬⣥⣤⣤⣤⣬⣭⣭⣥⣬⣭⣭⣭⣭⣥⣤⣤⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠟⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢬⠂⡔⢂⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡇⣠⣶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠉
⠀⠀⠀⠀⢀⢶⡀⠀⡴⣺⣫⣟⣗⢦⠀⠀⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⡰⠰⠰⠔⢆⠀⠀⢠⡄
⠀⠀⠀⠀⡜⣸⠀⢸⠥⣯⢬⡧⢼⠤⡇⠀⣇⣳⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣚⡃⣛⢘⣓⢛⡃⠀⠘⣷
⠀⠀⠀⠀⡇⢧⠣⡈⢦⣷⠲⡗⡾⡴⢃⡜⡹⢹⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠘⣃⢩⢨⣏⡛⠃⢀⣾⣿
⠀⠀⠀⠀⠙⣄⠳⠙⢆⠉⠛⠛⠉⣰⠋⠜⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣆⠀⠀⠀⠈⠀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠈⢧⠀⡜⠀⠀⠀⠀⢣⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠸⠴⠃⠀⠀⠀⠀⠘⠦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⣿⠃⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠃⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣙⠖⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠀⠠⠀⠈⢢⠀⣀⠔⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠁⠙⡀⠚⠀⠀⠈⠽⠍⢀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠇⠀⠀⠀⠀⠀⠀⠛⠄⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠈⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠗⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⢤⣤⡀⠀⠀⠀⠀⠀⢀⣤⡶⢈⡦⢄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠄⠀⠀⢀⠀⠀⠈⠀⠰⢆⢭⣦⢤⣄⣨⣑⣄
⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠘⠻⠷⠚⡁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠠⠀⢀⡓⠲⡤⠤⠼⢥⣴⣾⣀⣆
⠀⠀⣾⣿⡟⠀⠀⠀⢀⣤⠂⠀⠀⠀⣀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⠠⠄⠀⠀⠄⠀⠀⢀⠀⡉⠹⢯⡽⠒⠒⠏⠀⠀⢁⡠⠷⡀
⠀⠀⢿⣿⡇⠀⢀⣴⣿⡿⠋⠀⠀⠛⠄⠀⠂⡀⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠐⠀⠀⠂⠀⠐⠐⠠⣀⠈⠂⠌⠀⠛⣋⠛⢀⠀⢃⣀⡤⢞
⠀⠀⠈⠿⣿⡄⠉⠛⠻⠷⠀⠒⠋⠑⠊⠂⠀⠲⠆⡤⠀⠀⠀⠀⠀⠁⠀⠔⠄⠀⠀⠘⡇⠀⠆⠀⠹⡔⠀⣀⡀⠂⣠⠖⠀⠀⠰⣯⣭⣭⣴⣾⡿⠀⢀
⠀⠀⠀⠀⠀⢁⠀⠀⠀⡀⠔⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠅⠀⠀⣆⠀⠇⠠⠀⢀⠞⣁⠀⠀⣴⣾⣿⣿⣿⠛⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡠⠀⢀⠀⠀⠀⠀⠀⢀⢄⡀⠀⠒⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠤⠒⠂⠖⠁⠁⢉⣥⠾⢴⣥⣩⠖⠡⢦⣾⣿⣿⣿⣿⣿⠀⡀⣀
⠀⠀⠀⠀⠀⠐⠄⠀⡀⠀⡀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠿⣯⣖⠤⠋⠀⠉⠂⢄⠉⠉⠉⠉⠉⠀⠀⠐⠅⠠⠔
⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣽⣭⣽⣽⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣷⣿⣷⣶⣿⣷⣶⣶⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀
⠀⠀⠀⠖⠆⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠁⠤⣠⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠐⠐⠒⠒⠀⠂⠐⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠡⣅⠉⠉⠁⡀
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠓⠶⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠁
⠀⠀⠀⠣⣀⠂⣤⠂⢠⠂⡆⠂⡆⢠⠂⣆⠠⢰⠂⡂⡇⡆⠢⠂⡆⢰⠒⡄⠂⡆⢠⠂⡇⠀⡤⠂⣤⠂⡇⢠⠐⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠑⢄⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠴⠤⠖⠒
⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠑⡀⠀⠀⡤⠤⠀⠀⠀⠀⢀⠀⠀⠀⢄
⠀⠀⠀⠀⢀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠒⡥⠠⠀⠀⠀⠒⠒⠒⠞⠂⠠⠐⢃⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠠⠠⠤⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠛⠛⠉⠛⣿⠉⠙⠛⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠈⢻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⢀⣤⠴⠶⠾⠋⠀⠀⠀⠀⣰⡟⠀⠙⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠐⢿⡀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡀⠀⠀⠀⣠⣴⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠶⠛⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⠀⠀⢰⡟⠀⠀⠀⠀⢰⡶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠘⢧⡀⢀⣾⠁⠀⠀⠀⠀⢺⡇⢸⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠾⠇⠀⠀⠀⠀⠀⣸⠇⠀⠻⠶⠟⠙⣷⡀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢿⣤⣀⡀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠈⢙⣦⢠⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⢾⣷⡿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢧⣽⢷⣦⡀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣀⡴⢿⣩⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠈⠛⠀⠉⠻⢷⣦⣤⣄⣀⣀⣀⣠⣤⣴⣾⡟⠉⠠⣿⡟⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠙⣧⠉⠉⠉⠉⠉⠁⢠⡟⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣻
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣴⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣦⢤⣀⢀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⡔⠒⠒⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣉⣹⣯⠉⣾⠀⠀⠀⣿⠉⠉⢂⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⢸⡇⠀⠀⣿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣷⣶⣿⣶⠶⠶⠿⠂⠀⢸⠀⠀⠀⠀⠀⠀⠀⠦⠾⣅⠀⠘⠁⢀⣒⡿⠗⣊⠽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣿⠷⠶⠒⠲⡶⠶⠶⠶⠖⡾⠀⠀⠀⠀⠀⠀⣼⣷⡞⣽⠉⠃⢲⣉⣉⡠⡤⠤⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⢠⠿⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⠀⠀⢸⣿⡆⠀⠳⠤⠴⠃
⠀⠀⠀⠀⠀⠀⢀⡤⣼⣀⣿⣦⣤⣤⣤⣅⣤⠤⢞⣭⡄⠀⠀⠀⠀⠀⡠⣿⣿⡇⣹⣶⡶⠚⣛⣅⠀⢠⣶⣦
⠀⠀⠀⠀⠀⠀⠘⡄⡠⢤⣤⣤⡀⠀⠀⡤⠒⢒⣻⣿⣦⣠⣀⠀⠀⠀⠻⠾⢿⣭⣵⡶⢾⣟⣻⣭⠑⢻⣿⠟⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠿⠟⠉⠓⠚⠛⠙⠋⠈⠉⠀⠀⠈⠀⠀⠀⠀⠈⠓⠂⠀⠠⠊⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⣉⣹⠂⠀⠀⠀⠀⠀⠀⠀⠐⢸⣿⠍⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⣬⣶⣶⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⣴⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡟⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠀⠸⢿⣿⣿⣿⠏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡿⠄⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣿⣿⠟⠁⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠜⠋⢁⣴⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣮⣥⣶⣾⣭⢵⣾⣿⠒⠛⠛⠶⡄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠿⠿⠿⠛⠛⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠟⠳⠿⠿⠟⠛⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⠀⠀⡀⠀⡀⠀⢀⡀⠀⠀⣀⣀⡀⠀⠀⢀⣀⢀⠀⠀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣻⣿⡿⠿⠿⠶⠶⠶⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡾⣼⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠓⠇⢸⡷⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢸⡇⠀⠀⠀⠉⠙⠓⠲⠤⣤⣀⣀⠀⠀⠀⢀⣀⣠⠽⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠉⠉⠉⠉⠁⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢀⡀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⠛⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢰⠋⠉⢹⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠈⠉⠛⠶⢦⣄⣀⠀⢸⠀⠀⠀⢸⡄⢀⣸⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠳⣦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠦⠤⠴⠾⠛⠋⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣈⠙⠷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⣋⡿⠶⡴⠿⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⡴⠋⠁⠀⢰⡇⣾⣦⠹⣦⣉⣽⣷⣦⣤⣤⣤⣶⣛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⢧⠹⣿⢀⣿⣁⡤⢾⣿⣿⣿⣿⡿⠻⡍⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣾⠋⠁⠀⠸⠭⣭⣭⣥⣤⣀⡿⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⡀⢀⣴⣶⣾⣶⡄⠀⢀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣾⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⢛⣿⡿⠛⠁⠀⢸⣿⠀⠀⠉⠻⣿⣿⡻⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠁⠀⣴⣿⠋⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠻⣷⣄⠈⠛⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣏⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⢙⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣠⣿⠟⠛⠻⠿⣷⣾⣿⣧⣤⣄⣀⣀⣀⣀⣸⣿⣀⣀⣀⣀⣀⣠⣤⣿⣿⣶⡿⠿⠛⠻⣿⣆
⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⢠⣿⠏⠉⠛⠛⠛⠛⠻⠿⢿⣿⠿⠿⠛⠛⠛⠛⠋⠉⢻⣿⠀⠀⠀⠀⠘⣿⣆
⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⢾⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⣤⣤⣤⣤⣄⡀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⢀⣿⡇⠀⠀⠀⢰⣿⠋⠉⠉⠛⠁⠀⣿⣟⠉⠉⢻⣿⡄⠀⣿⡟⠋⠙⠿⠷⠀⠀⢀⣀⣀⣀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⢸⣿⣷⣶⣦⠀⠘⢿⣿⣶⣦⣤⡀⠀⣿⡿⠀⠀⢸⣿⡇⢸⣿⡇⠀⣤⣤⣤⠀⢸⣿⣛⠛⠛⠁⢠⣶⣶⣿⡇
⠀⠀⠀⠸⣿⡏⠉⠁⠀⢀⡀⠀⠈⠉⣿⡧⠀⣿⣇⠀⠀⣸⣿⠇⠸⣿⣇⠀⠉⣽⣿⠀⠈⠛⠛⠿⣿⡆⠀⠉⠉⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠚⠿⣿⣿⡿⠟⠁⠀⢿⢿⣿⡿⠿⠋⠀⠀⠙⠿⣿⣿⠿⠃⠀⠸⠿⣷⣾⠿⠃⠀⠀⢸⣿⠃
⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣀⣀⣀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⣀⣠⣴⣿⣷⣶⣿⠿⠿⠿⠿⠿⢿⣿⠟⠻⠻⠿⠿⠿⣿⣶⣿⣿⣤⣄⡀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠛⠉⠙⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣿⡿⠉⠙⠻⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠘⢿⣧⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣾⡟⠀⢀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣈⠻⣷⣄⠀⠀⠀⢸⣿⠀⠀⠀⢀⣴⣿⢏⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣶⣤⣼⣿⣤⣤⣶⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⠿⠿⠿⠿⣿⣿⣶⣤⣄⡀
⣴⣿⡿⠿⢿⣿⣿⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣦⣤⣦⣤⣀
⢿⣿⣤⣀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣶⣶⣤⣤⣀⣰⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠛⠻⢿⣿
⠈⠙⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠺⠇⣼⣿
⠀⠀⠀⠀⠉⠛⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠟⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀⣾⣿⠏⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⡿⠿⠛⠛⠛⠿⣿⣿⡏⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣷⣶⣶⣾⣿⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣷⣶⣿⡟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣯⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠐⣢⠋
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⢀⠀⠉⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠸⢋⣻⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⢀⡀
⠀⠀⢧⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠀⠀⣀⠀⠀⠐⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡀⠉⠃⣤
⠀⠀⢤⠀⠀⡀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣿⣿⣷⡿⢿⠟⠻⣷⣦⣤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠂⠀⠒⠐
⣆⠀⠴⠀⠀⠁⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⠙⠃⢀⣄⣀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⠙⠒⣆⢀⠃⠀⢰⠄⠀⠂⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠟⠆⠀⡀⠀⠀⠀⠀⠤⠈⠀⠀⠀⠀⢀⠆
⠻⣀⠀⠀⣈⠀⠀⢸⡅⢰⠀⠀⠀⠀⠀⠀⠀⢿⣾⣷⠁⠀⠀⠀⠀⢀⡀⠀⠀⠐⠀⠡⠀⣀⠀⠀⠀⠠⠀⠀⢲⠎⠈⢀⡀
⡀⡷⠶⡄⠀⠀⠀⠸⡇⢀⠰⠄⠀⠀⠀⠀⠀⠀⢹⣗⢁⠔⡟⢀⠈⠐⠁⠀⣀⠰⠀⠰⣤⡿⠄⠀⠀⠀⠒⢄⠚⣠⠴⠈⠁
⠀⢀⣤⡘⠀⠛⠀⢸⣦⣾⡄⠀⠀⠀⠀⠀⠀⠂⡄⢹⠊⢘⡀⢈⡤⠀⠀⣜⢁⡆⠉⠀⢴⡕⠄⠀⠀⠀⠀⠈⠳⢆⡀⢀⠘
⠀⠞⠁⢹⡀⢈⡀⢶⠀⣹⢿⡤⠆⠀⠀⠀⠀⣤⠀⡄⠀⠉⠠⠼⣄⡾⠓⠭⢰⡇⠸⡌⢿⡁⠀⢂⡀⠀⠀⠀⠀⠀⠠⢀⡀
⢀⠀⠠⣌⣣⢾⡃⢻⢆⠋⢼⣷⣄⠀⠀⠘⢸⡏⠘⢥⡀⡀⠑⠰⠀⠀⠉⠓⢀⣝⣧⡈⠁⠀⢀⠀⢘⢐⡂⢰⠂⠐⠄⠀⠁
⠋⣡⢀⠀⠀⣨⣤⣾⣄⠦⢠⢿⠈⣇⠈⣀⣺⣀⠀⢀⡘⢣⡮⢴⠆⠤⠀⠀⠈⣛⣿⠋⢛⠀⠀⠞⠉⣌⡱⠦⠉⠀⠀⢀⡀
⡀⠸⣋⠉⠽⢿⡄⣼⡇⠠⠌⡛⠀⠉⣠⣉⡝⠁⡸⠤⠉⠁⠃⣼⠂⢀⠶⣧⡄⣐⠿⠶⢊⡄⠺⠿⠈⠟⠸⢤⡠⣀⢀⣈⠱
⢶⠜⣿⡗⣠⣛⡛⢿⡷⠂⠀⢱⠈⣦⣤⣿⣷⣴⣥⣄⠀⠀⣠⡾⣫⢿⢰⡶⣏⡰⠀⠗⣺⢁⡃⢀⠀⢀⠀⢈⡛⢐⡍⠯⣴
⡴⢹⣟⡿⠿⢙⢻⡚⠁⠀⣠⡄⢸⣍⣯⡿⠿⣿⡏⠐⠤⠀⠐⣟⡿⠂⠙⡿⠿⡿⠓⢀⠖⠊⢉⠰⢆⣟⡿⣇⣤⣞⡧⣆
⠁⢼⣿⡠⣦⡀⣨⣴⣿⣿⡶⣲⢻⣇⠈⣔⡜⢻⣂⣠⡖⢠⣦⣏⡗⡁⣀⠃⢿⠑⠠⠈⡃⠸⢺⠀⠻⣽⢣⣻⡾⡿⣞⠿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⡉⠉⠛⠛⣻⠷⠀⠀⠛⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢻⡇⣀⡴⠛⠁⠀⠀⠀⣀⠶⡄⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢼⠾⠋⠀⠀⠀⠀⠀⡜⢁⢰⠇⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢠⡀⠀⠀⣠⠄⠓⠛⠁⠀⠀⢀⣄⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠘⣯⠙⠲⡌⢳⣄⡼⠛⠛⠋⠀⣀⠀⡴⠋⢸⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⢦⣑⡿⠀⠻⣅⠀⠀⠀⠀⣿⠸⣥⡥⠋⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢦⣽⣆⠀⠀⣠⡿⠤⠤⠄⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⣠⠴⠒⣓⣦⡀⣿⡴⠛⠉⠀⠀⠀⣀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠙⠛⠲⠶⠞⠁⣿⠀⠀⠀⠀⣠⠞⣿⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠛⠀⠀⣠⠞⠁⠀⣿⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⠀⢠⣾⣥⣤⣤⣤⣬⣽⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠋⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⢀⡼⢀⠀⠈⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠲⣄⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢠⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⢁⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⡟⠀⠀⠀⠀⢀⡴⠋⢠⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢸⡇⠀⠀⠀⢠⡞⠁⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣾⠀⠀⠀⠀⡿⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢀⡟⠀⠀⠀⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠘⡇⠀⠀⠀⢸⡇⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢠⡇⠀⠀⠀⠈⡇⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⡿⠀⠀⠀⠀⠀⢻⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⢃⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⡏⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⡼⠀⠀⠀⠀⢀⡴⠚⠀⠀⠀⠀⠀⠈⠰⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢀⡇⠀⠀⠀⣰⢏⡔⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣸⠁⠀⠀⣰⣏⡏⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⡆⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡝⠀⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣇⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢠⡇⠀⠀⣿⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢨⠀⠀⢸⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢸⡇⠀⢸⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⠀⠀⣴⢟⣭⣭⣍⠢⡀⠀⠀⢸⡇⠀⢸⣿⠀⢀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢀⡗⠀⠀⠀⣿⡀⢰⡇⣾⠉⠈⢻⣷⢱⠀⠀⠸⡇⠀⢸⣿⠀⡾⠁⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⣾⠃⠀⠀⠀⣿⡇⠈⢧⡻⣆⣀⣼⡿⡸⠀⠀⠀⡇⠀⢸⣿⢸⠃⠀⢀⡇
⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣿⠁⣸⡏⠀⠀⠀⠀⢹⣿⡀⠈⠛⢮⣭⡭⠖⠁⠀⠀⠀⠇⠀⣾⡇⣼⠀⠀⢸⡇
⢀⡴⠟⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠻⣧⡀⠀⠀⠀⠀⠹⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣴⣿⣇⣠⡟
⠙⠓⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠈⠙⠛⠿⠿⠷⠶⠶⠾⠿⠿⠿⠟⠛⠛⠉⠈⠉
⠀⠉⠒⠶⠦⣬⣍⣛⡒⠶⠦⣤⣤⣀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠦⣍⣡⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⣀⠀⠀⠀⠀⠀⠀⠀⠸⢃⡀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⢠⣤⡴⣶⣻⣿⠀⠀⠀⣠⣀⡙⣾⡀⠋⠀⠀⠀⠀⠀⠀⠞⠋⣉⣽⣤⣠⣤⡄⠀⢠⣶⣿⠟⠇⣄⣾⣷⣄⣀
⠀⠀⠀⠀⢀⡀⣀⣈⠻⠋⡟⠛⠀⠀⣲⣿⣿⢿⣷⣿⡿⠂⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣿⣿⣿⣦⠀⠀⠀⠀⣲⣾⣿⣿⣿⣿⣿⣇
⠀⠀⠀⣀⡿⣭⣷⣿⡗⠀⠁⠀⢀⣤⣿⣿⣿⣿⣿⣧⣿⣿⠂⠀⠀⠀⠀⣴⣷⣿⡟⣿⣿⣿⣿⣿⡟⠀⢀⣩⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⢘⣿⣿⣿⣿⣿⣿⠂⡀⠀⢣⣿⣿⣇⠘⠿⡾⢿⣿⣿⠇⠀⠀⠀⠀⠛⢿⠟⠛⡷⠋⢻⣿⡆⠀⠀⢘⠗⢻⡿⣿⠛⠿⢿⡿⡟
⠀⠀⠸⣽⣿⢺⠚⠛⣫⣤⣦⡀⠀⠀⠿⠂⡆⡾⣿⡟⠉⠁⠀⠀⠀⠀⠀⢰⢶⣶⡄⡇⠀⠈⠛⠁⠀⠀⢀⠀⠀⠀⡏
⠀⠀⠀⠈⠁⢸⠀⠀⠘⢙⢻⡇⠀⠀⠀⠀⡇⠣⠾⠧⢠⣴⣶⣶⣷⣦⡄⠰⠸⢿⠀⣧⣀⠀⠀⠀⠀⡛⣿⣿⠆⠀⡃
⠀⠀⠀⠀⠀⢸⠀⠀⠘⠺⠿⠷⣶⣷⣶⣴⣧⣀⡀⠀⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⣤⣷⣶⣶⣶⡄⠀⣦⣿⣿⣀⣀⣇⣀⣀
⠀⠀⠀⢀⣀⣼⣄⣠⣀⣀⣀⣀⡙⠻⢿⣿⣿⣿⣿⡷⠶⢿⣿⣿⣿⡿⢱⣶⣿⣿⣿⣿⣽⡻⠕⠁⠀⠀⠀⠀⢀⠀⡇
⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢜⡸⢿⡿⡿⠿⠶⢿⢿⣦⣾⣿⣿⣶⣾⣿⣿⣿⣻⣿⣿⣿⣿⣶⡄
⠀⠀⠀⢹⡿⣿⣿⣿⣽⣿⣿⠿⠿⣿⣟⣿⣿⣿⣮⣷⣤⣴⣎⣶⣎⣭⣤⣪⣾⣿⣿⣿⣿⣿⣿⢻⣿⢿⣿⣿⡿⣿⣿⣿⡟
⠀⠀⠀⠸⣿⣿⣿⣇⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣭⣉⠓⠛⢿⡏⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡟⢺⣿⣿⣿⣿⣾⣽⣿⡿⣿⣿⣿⣿⣿⡏⣹⣿⣿⡗⣿⣿⣿⣇⠀⠈⠃⠛⠛⠛⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡽⣇⣼⣿⣿⡗⠾⠿⠿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠾⠿⠛⠛⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡆⠀⣶⣶⣶⡄⢰⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠁⢸⣿⣿⣿⣧⠀⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡏⢀⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢠⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠁⠸⠿⠿⠿⠿⠿⠇⠀⠿⠿⠿⠿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣿⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣴⡾⠟⠁⢸⣿⠀⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠻⣿⣿
⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⢸⣿⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⢀⣛⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢈⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠐⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠘⢃⢐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣦⣄⡈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣴⣾⣿⠿⠛⠛⠛⢿⣿⣿⣿⣿⣷⣦⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⢠⣾⣿⣿⠁⣠⣶⣿⣦⠀⣿⣿⣿⣿⣿⣿⣧⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⣿⣿⣿⣿⣄⠈⠛⠛⠿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⡿⠃⣠⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡄⠘⣿⣿⣿⣿⣿⣿⣷⡀⢹⣿⣿⣷⣄⡈⠛⠿⠿⠿⠿⠟⠁⣴⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣆⡈⠛⠿⣿⣿⣿⠟⠀⣼⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛