Bathrobe Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢲⠉⢗⠒⠒⠠⠄⠒⠒⡺⠋⡖⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡇⠀⠀⠳⡈⢦⠀⠀⠀⠀⡰⢁⠞⠀⠀⢸⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢸⠀⠀⠀⠱⡈⢣⠀⠀⡼⢡⠎⠀⠀⠀⡇⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠈⡆⠀⠀⠀⠙⡄⢣⡜⢡⠋⠀⠀⠀⢸⠁⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⢷⠃⠀⠀⠀⠀⢸⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢀⣧⠀⠀⠀⠀⠀⡇⠸⡀⠀⠀⠀⠀⣼⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢸⠘⡄⠀⠀⠀⠀⢸⠀⢇⠀⠀⠀⢠⠁⡇⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⡇⠀⡷⠲⠤⠤⠤⠬⡇⣸⠒⠒⢲⢾⠀⢸⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢠⠃⠀⡧⠤⠤⠤⠤⠤⡿⢸⡄⣄⠼⢼⠀⠘⡄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡸⠀⡸⠁⠀⠀⠀⠀⠀⡇⢸⠀⢱⠀⠈⢇⠀⢇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⢠⠃⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠘⡄⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣀⡀⠀⢠⠁⡎⠀⠀⠀⠀⠀⠀⠀⡇⠀⢣⠀⢸⠀⠀⢱⠈⡄⠀⢀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠈⡇⠀⠀⣆⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⡖⠒⡏⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⡇⠀⢱⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡆⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢱⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠈⡆⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠠⠤⠤⠄⣀⣀⣀⣀⣀⣀⣀⣀⠸⠄⠠⠵⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡄⢶⣷⠸⣿⣿⣿⣿⢠⣷⡆⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣷⠸⣿⡆⢿⣿⣿⡇⣾⡿⢰⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⣷⠸⣿⣿⢠⣿⠇⣾⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⡆⢿⡇⣾⡿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⣷⠘⢰⣿⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣷⠸⣿⡆⣾⡿⢰⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠁⠀⣿⣿⣿⣿⣿⣿⡆⣿⢰⣿⠇⣾⣿⣿⣿⣿⣿⡏⠀⠹⣿⣿⣿⣿⣿⣷⡀
⠀⠀⢠⣿⣿⣿⣿⣿⡿⠁⠀⠀⢻⣿⣿⣿⣿⣿⣷⠀⣾⡿⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠹⣿⣿⣿⣿⣿⣷⡀
⠀⢠⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢰⣿⠇⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⡀
⣶⣬⣙⠻⢿⣿⡿⠁⠀⠀⠀⠀⠀⣭⣭⣭⣭⣭⣥⣬⣭⣤⣭⠉⣭⣭⣭⢩⣭⠀⠀⠀⠀⠀⠹⣿⣿⠿⢛⣩⣴
⠈⠛⠿⣿⣶⣬⡁⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⠛⣛⡛⢛⣛⣀⣛⣛⣛⣘⣛⠀⠀⠀⠀⠀⠀⣨⣴⣾⡿⠟⠋
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⣿⣿⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣤⣶⣶⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⡿⠿⠻⠿⠿⣿⣿⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⠀⠀⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠛⠿⣿⣿⠏⠁⠀⠈⠀⢠⡄⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⣤⠀⠉⠀⠀⠀⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⡀⠀⠀⠀⠀⠀⠀⢉⡀⠀⠈⠒⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠖⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠀⠀⠀⠀⢠⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠐⠂⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⡅⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠹⡄⠀⠀⠁⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⢀⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠊
⠀⠀⠀⠀⠀⣼⠃⠀⢠⠀⠀⠀⠀⠀⠀⠈⠁⠒⠠⢀⡀⠀⠈⠒⠄⠀⠀⣤⠋⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠥⠤⠤⠤⢀⡀
⠀⢀⠀⠀⡈⠉⠂⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠅⠀⠈⠲⡀⠀⠀⠙⠂⠁⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠠⠶⣶⣶⣶⣶⣶⣶⣶⠦⠄
⠀⠂⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠐⢂⠤⡀⢹⡀⠀⠀⠈⡄⠀⠀⢸⠄⠤⠤⢤⠤⢤⡀⡔⠂⠲⢄⡐⠁⣠⢀⣸
⠈⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⢠⠏⣈⠀⠈⠀⠇⠀⢇⠀⠀⠀⠰⡀⠁⠄⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⢱⡖⠋⠀⠈⡆⠀⠀⠀⠀⣀⣀
⡆⠀⠈⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⠀⡈⠀⠀⡆⠀⠈⢦⠀⠀⠀⠃⠰⠁⠀⠀⠀⠀⠀⠀⣿⠈⠣⣄⣀⡼⡓⠶⠶⠊⡆⠀⠀⠀⠀⠈⠈
⡇⠀⠐⠂⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠑⢄⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣄⠀⠀⠈⠆⠃
⠃⢀⠈⠀⠀⠚⣳⣤⣤⣀⣀⣀⣀⣀⡰⠂⠀⠀⡇⠀⡈⠀⠀⠀⠀⠀⠀⢣⠀⠈⡃⠀⠀⠀⠀⠀⢠⡏⠑⠤⠤⠔⢏⠀⠀⠈⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡠⠒⠙⠋⠼⠁⠀⠀⠉⠙⣦⠀⠀⠁⠀⠂⠀⠃⡰⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⡦⠤⠀⠤⣀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠒⠂⠀⠁
⠀⠣⣀⠀⠀⣀⠤⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠘
⠀⠀⢄⠀⠁⠀⡠⠀⠀⢀⡴⠋⠙⠂⠠⠀⢀⡀⠀⠀⠠⠤⠂⠀⠀⠄⢃
⠀⠀⢰⠏⠉⠙⠒⠒⠊⠁⠀⠉⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠄⠀⠰⠁⠈⠉⠉
⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐⢄
⠀⠀⢿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠄⠃
⠀⠀⠀⠀⠈⠉⢹⠒⢲⣶⡦⠤⣤⣤⠤⠀⣠⣀⢠⡄⢤⣤⡤⠔⠒⣆⣀⠀⡤⠤⠰
⠀⠀⠀⠀⠀⠀⢘⠀⢸⣿⠃⠀⣼⣿⠀⠀⢸⣿⢀⠀⢀⣿⠇⠀⠀⢸⣿⠀⠃
⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⠀⠀⠛⠛⠀⠀⣸⣿⠀⠀⢸⣿⡦⡀⠀⠘⠿⡀
⠀⠀⠀⠀⠀⠠⠦⢀⣼⣿⠀⠀⣷⣤⣀⠀⠙⢏⠀⠐⡚⠛⠃⠘⠓⠦⠀⠀⠀⠈⠁⠀⠄⠀⡀
⠀⠠⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⣐⠀⠠⢀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠑
⠀⠀⠀⠐⠀⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠃⠀⠀⡠⠤⠠⠄⠄⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⡀⣀⣀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡎⢿⣇⢩⣙⣛⣛⣉⡍⣸⡿⢱⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣌⢿⣆⢻⣿⣿⠟⣰⡿⣡⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡙⢿⣿⣿⣿⣿⣿⣆⢻⣧⠹⠏⣼⡟⣰⣿⣿⣿⣿⣿⡿⢋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣎⢻⣿⣿⣿⣿⣿⡆⢿⣇⢸⡟⣰⣿⣿⣿⣿⣿⡟⣱⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⡌⢿⣆⢱⣿⣿⣿⣿⣿⣿⢁⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡘⣿⡌⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣧⠹⣿⡘⣿⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⡇⢿⣧⢹⣿⣿⣿⢃⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣛⠻⠿⠿⠿⠿⠿⠘⠿⠊⠿⣛⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠿⠿⠿⠇⠿⠇⠸⠿⠿⠿⠿⠿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⠃⠀⣼⣿⣿⣿⡆⣶⡆⢰⣶⢸⣷⢸⣿⣧⠀⠘⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣸⣿⣿⣿⣿⡇⣿⡇⢸⣿⢸⣿⠈⣿⣿⣇⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⣿⡇⢸⣿⢸⣿⠀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⡇⢸⣿⢸⣿⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⣿⡇⢸⣿⢸⣿⠀⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⡇⢸⣿⢸⣿⠀⣿⡷⣷⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⣙⣃⣾⣿⢸⣿⠠⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠋⠈⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⡖⠒⠒⠒⠒⠒⠒⠒⡶⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⢧⠀⠹⡄⠀⠀⠀⠀⠀⡜⠀⣰⠋⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢳⡀⠹⡄⠀⠀⢀⡞⠀⡰⠃⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠳⡄⠹⡄⢀⡞⠀⡼⠁⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠹⡞⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠘⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠈⣦⠘⡄⠀⠀⠀⠀⣶⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢠⠇⢧⠀⠀⠀⠀⠀⠀⢿⠀⡇⠀⠀⠀⢰⠋⡇⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⡼⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⣸⠀⢹⡀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢠⠇⠀⢸⡤⣤⣤⣤⣤⣤⣼⠀⣧⣤⣤⣤⣯⠀⠀⣇⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡾⠀⠀⢸⣤⣤⣤⣤⣤⣤⣼⠀⣧⣠⣤⣤⣿⠀⠀⢸⡀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⣰⠿⠤⣤⣀⣀⣰⠃⠀⠀⡞⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠸⡄⠀⠀⣧⠤⠴⠒⠚⠋⢧
⠀⠀⠀⠀⠀⠀⠀⠳⠤⢤⣀⣀⡈⣹⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⣇⠀⠀⢧⡤⠤⠶⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠴⠶⠶⠶⠶⠶⠶⠶⠶⠦⠾⠦⠼⠦⠶⠶⠶⠶⠶⠦⠾⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣴⣶⣾⣿⣟⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠉⠉⠉⠛⠛⠿⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠀⠠⠒⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡈⠙⠋⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠉⠀⠀⠀⠀⠀⠉⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠃⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⢀⠐⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠙⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠢⡀⠀⠈⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣴⣶⣶⣶⣦⣤⠄
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⡤⠀⢡⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠄⠤⡀⠐⠀⠢⡀⠀⣠⠀⡁
⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⢂⠀⠀⠀⡀⠀⠃⠀⠀⠀⠀⠀⡗⢀⠀⠀⠈⡖⠁⠀⣸⠀⠀⠀⠀⢤⠤
⠂⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⣚⠈⠓⠤⠚⠉⠁⢚⣸
⠁⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⢸⡀⠀⢀⠀⠀⠀⠀⠀⠀⠁⢄⠀⠁⠀⠀⠀⠀⠀⠀⡿⢀⠀⢀⡰⠀⠀⠨
⠀⠀⠐⠆⢠⠚⠛⠛⠓⢖⠀⠀⠉⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⢀⡀⠀⢠⠁⠀⠉
⠀⠀⠀⠀⠀⣀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠀⠀⠀⠈⠁
⠀⠀⠁⠀⠉⡀⠄⠀⢀⠜⠈⠂⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⡀⠀⢀
⠀⠀⡌⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠁
⠀⢠⡇
⠀⠘⠃⠤⠄⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⢒
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢹⣿⠋⠉⣿⡏⠋⠉⣿⡏⠀⠐⣶⡆⠁
⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠸⠿⠀⠀⣿⡇⠀⠀⣿⡄⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠄⠀⣿⡇⠀⢰⣄⡀⠀⠻⡇⠀⠀⠿⠇⠐⠢⠀⠀⠀⠐
⠀⠀⠀⠆⠀⠀⠀⠀⠁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⣶⠖⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⠚⡀⠒⠒⢸⠓⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠁⠀⠘⡄⢣⠀⠀⠊⢠⠁⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠙⡄⢣⡀⢠⠃⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠁⠀⠀⠀⠀⠘⣄⠠⠁⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡇⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⡀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢡⡄⠀⠀⠀⢠⡏⠀⠀⠀⠀⠆⢠⠃⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢸⢱⡀⠆⠀⠸⠀⠀⠀⠀⡄⢀⠞⡆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠀⡘⣈⠉⠉⠒⢀⡄⢂⠐⠀⠐⢉⡄⠁⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠈⠀⡇⠮⠭⠑⠶⢶⠀⠈⠈⢩⡉⠥⢥⡄⠰⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠐⠦⣀⣀⠋⠂⠒⠒⠂⠹⠀⠸⡆⠀⡷⠒⢲⠡⠀⣀⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣀⡈⠀⡇⠀⠀⠀⠀⠀⡆⡇⠀⣧⠀⢸⠐⡍⢀⡠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠓⠄⠀⠒⡂⠀⡇⠁⠀⠙⠒⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠃⠀⠇⢀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠃⠀⠀⢸⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⠄⠸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢲⠆⠤⠤⠀⢶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⣀⣠⣀⣀⣀⣠⣾⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⣟⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡠⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⠟⠛⠛⢿⡿⢿⣿⣿⡿⣿⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⠀⠀⠀⡼⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⢹⢻⣿⣛⠶⠋⣾⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣿⠀⠀⠀⠀⠀⢿⣿⠛⣛⣃⣀⡀⠀⣠⣤⡉⠙⣼⣿⡏⠀⠈⢠⠄⡿⢿⣦⡀
⠀⠀⠀⠀⡀⣶⣶⡄⠀⠀⠀⢸⡄⣿⡆⠀⠀⠀⠀⣿⡟⢼⠛⣻⣿⣿⡒⠉⡉⠐⠀⣿⣿⣇⣆⣴⣄⣬⣥⣤⣿⣿⣦⣤⠄⠀⠠
⠀⠀⠀⠀⡇⠘⠋⠀⠀⠀⠀⢸⡇⣿⡇⠀⠀⠀⠀⣷⣷⡀⠀⠀⢉⠉⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⠈⣷⢻⣧⠀⠀⠀⠀⢻⣿⣷⠀⠀⠼⣿⠶⠆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⣀⣠⣿⡿⢿⡧⠀⠀⠀⠀⠀⠉⣿⢸⣿⠀⠀⠀⠀⢈⣿⣿⣷⡀⠀⠀⠀⠀⠀⢠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡆⠀⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣿⡇⠀⠀⣸⡇⢿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⡹⣿⣿⣿⣿
⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⢄⣠⣿⣷⣿⣿⣿⡿⣦⣤⣤⣶⠾⠿⣿⣨⣥⣤⣾⣿⣿⣿⣿⠀⢠⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⣿⣿⡇⠀⢀⣿⠻⠛⠛⢿⣿⣿⣿⡿⠀⣿⣿⠘⠃⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠙⣿⣿⣷⣶⣾⣷⣤⢀⣶⢺⣿⣿⣿⡇⢀⣻⣿⡆⠀⠘⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⣹⣿⢹⢿⣿⣿⣿⣿⣿⣧⠈⠸⣿⣿⣿⣿⣤⣼⣿⢸⣿⠟⠉⠄⢾⡏⢹⡧⠀⠀⣭⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢱⣿⣿⣿⡞⣹⣿⣿⣿⣿⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣾⡟⠘⠃⠀⠀⢸⡌⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠸⠆⠀⣀⣻⣿⣿⣿⠿⠟⠋⠉⣿⠁⠀⢀⣿⡗⠀⢲⡆⠀⣾⠁⠀⢻
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⡻⣿⣿⣿⣿⣿⡿⠿⣿⠀⠠⠑⢬⣿⣿⣿⠃⡘⠀⠀⠀⢹⠀⠀⣸⡇⠁⠀⣸⣇⠀⠀⢸⡆
⠶⠶⠀⠖⣢⡒⠛⣆⠀⠀⠀⣿⣿⣿⠁⢻⣿⡿⠋⠘⡇⠀⠘⣷⡐⠀⢸⣿⣿⣿⢠⠃⠀⠀⠀⢸⠀⠀⣿⡇⠀⠰⣾⣿⠀⠀⠈⣿
⠀⠀⠀⢀⣿⡇⠀⢸⠀⠀⠀⣿⣿⣿⠀⢸⣿⡇⠀⣰⣿⣤⠀⢿⡇⠀⠘⣿⣿⣷⠾⠀⠀⠀⣄⣾⠀⢸⡿⠁⠀⣀⠟⣿⣧⠀⠀⢹⡀
⢴⣶⣶⢾⣿⣇⣀⢈⡀⠀⣸⣯⣿⣿⣦⣿⣿⣧⢠⣿⣿⣿⡇⢸⡇⠀⠀⠸⡿⠏⢠⣤⣀⣠⡿⡟⠀⣼⠇⢀⣾⡏⠀⢸⣿⡆⠀⠈⠿
⣶⡦⠾⠿⢿⡿⠟⠿⠿⠀⣿⣽⣿⣿⣧⣄⣀⣙⣯⣻⣿⣿⣵⠸⣿⡀⠀⠀⠀⠀⠀⣯⠹⠃⠁⠁⠀⠏⢠⣿⣿⡇⣧⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠂⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⣿⣷⣤⣤⣤⣤⣼⣿⣃⣤⠴⠶⣲⣤⠻⣿⣿⣷⢻⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⢿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⠤⢤⣿⣿⣿⣍⢹⣄⣲⡆⢰⣿⠀⠙⣿⣿⣼⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⢻⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⡏⡼⣿⠀⢀⣿⣿⣿⣿⣿⠀⠙⡇⠈⣏⠀⠀⣨⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⣿⣿⡇⣸⣿⣿⣿⣿⡿⠋⣿⠃⡇⢿⡀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⡀⠀⢣⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⠁⣿⣿⣿⠇⣿⠃⠀⣿⠀⡇⠸⡇⠀⣿⣿⡇⢹⣟⣿⢸⡄⣾⣿⣇⠀⠘⡉⢿⡄⡀
⠀⣀⣀⣀⣀⣀⣠⣴⣦⠸⣿⡀⢸⣿⠀⣿⣿⣿⠀⡏⠀⠀⣿⠀⡇⠀⣧⠀⣿⣿⠇⠘⣯⡽⠦⠁⠸⣿⢹⣇⠀⠠⠀⣷⣧⡀⠀⡄
⠛⠛⠉⠉⠉⠁⠀⠀⠁⢰⣿⣆⢸⣿⠀⢿⣹⣿⠀⡇⠀⠀⡟⠀⣇⣸⣿⠀⠟⠁⠀⠀⣿⡇⠀⠀⠀⠹⠸⣿⡄⢀⡆⢹⣿⠇⠀⣁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⡶⠶⠦⢶⣴⣶⣶⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⣶⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣠⣽⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣴⣶⣶⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠉⠉⠠⣼⣿⣿⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀⡀⢀⣶⣄⠀⣀⡀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⡀⠀⢀⣂⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⣿⣿⣶⣿⣦⢰⡇⠀⣿⣂⣀⣾⣿⣿⢿⣿⡏⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣿⣿⣿⣿⣿⣄⣸⣿⣿⣿⣿⣻⣿⡛⣴⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⠛⠙⠛⠻⢿⢿⣝⢛⢿⣿⣿⣿⣿⣿⣿⣛⡉⣿⣿⣿⠟⣻⠯⠼⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⡀⠀⠀⠀⠀⠀⠂⠐⠒⠛⠉⠻⣿⣿⣿⣯⡀⢾⡛⠿⠂⠃⠰⠃⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢩⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⣿⡏⠀⠘⢷⡀⠀⠀⠀⠀⢸⠟⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣰⣾⣿⣧⡀⠀⣌⠘⣧⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠹⢆⣀⠄⠀⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡴⣿⢀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⠻⠿⣿⣿⡿⣿⣿⣾⡀⠀⠨⠳⠘⡰⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⡿⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠺⣿⣿⡇⠸⣿⣿⣷⡄⠀⠈⣢⣀⠀⠀⣼⣿⣽⡿⠿⣿⠿⣈⣋⣀⣀⠙⠻⢾⡇⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠻⣿⣿⣧⠀⢨⣿⡗⠀⣸⣯⡾⠋⣠⣤⠷⢞⣛⣭⣉⣙⠻⣄⢸⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⡔⢻⣿⣷⣆⠸⣿⣧⣴⣿⣿⣿⣿⣿⡵⠟⠋⠉⠉⢹⣿⡆⠈⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣦⣿⣿⣿⣘⣿⣿⠹⣿⣿⣿⠿⢋⣀⣤⣴⠖⠲⢿⣿⣇⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣯⣩⣴⣿⠟⡟⢱⠆⡀⢀⢹⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⠻⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿⣇⣼⣿⣼⣿⣧⢨⣿⠟⣿⣿⣿⣿⣿⣿⣿⣶⣄
⢀⡤⣠⢖⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⡀
⠈⡰⢁⠈⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⠁⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠰⠀⢣⠎⠜⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⡳
⠀⢣⠁⢊⠜⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣧⣹⣿⡿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⢫⡁
⠀⠀⢦⢊⠞⣴⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠻⢿⣿⣽⠛⡟⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠾⠎⠊⠁
⠀⠀⠘⣆⢚⡜⡵⣻⣿⣿⣿⣿⣿⣿⣿⣿⡐⢹⣿⣦⡀⠀⠀⠀⢀⡼⡏⠄⠀⠀⡆⠙⢻⣄⠀⠈⠁⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢀⠐
⠀⠀⠀⠈⢺⡜⡔⡵⡻⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⢿⣿⣦⡀⣰⣿⠃⠁⠀⠀⢠⠁⠀⠘⣿⣆⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡁
⠀⠀⠀⠀⠀⠉⠸⢜⢞⢜⣿⣿⣿⣿⣿⣿⣿⡀⢻⠘⠟⣿⣿⠏⠈⠀⠀⠀⠀⠸⠀⠀⠀⢈⠿⠿⢿⣿⣿⣟⣿⣿⣿⣿⢿⣿⡿⡿⡯⠛⠪⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠙⢿⣿⠿⡿⢹⡇⠀⠀⠀⢹⠇⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⡿⠮⠻⠝⠝⠛⠇⠙⢌⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⢿⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢰⠀⣰⣟⠧⠢⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⠙⠂⠂⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⠛⣛⣛⣛⣻⠿⢉⡙⠋⢨⣉⠻⣦⡀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣼⠟⣉⣩⣬⣤⣼⠿⣿⣿⣿⣾⣿⣷⣮⣿⣷⣌⠻⢛⣉⣭⠋⠻⠶⣦⡄
⠀⠀⠀⠀⠀⠀⣾⠛⢛⣩⣭⣶⣿⣟⣛⣯⣵⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡟⢥⣾⡃
⠀⠀⠀⠀⠀⠀⢙⣷⠮⣉⣽⣿⣿⣿⣿⣿⣿⣟⣛⠻⠯⣙⣻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣦⣀⣀
⠀⠀⠀⠀⠀⣠⡟⢁⣾⣿⣿⣿⣿⣿⡿⠛⢓⣂⣩⣿⣿⣿⣿⣿⣿⣥⣽⣿⣿⣿⣿⣯⣭⣙⣻⣿⣿⣿⣮⣉⠙⢷⡄
⠀⠀⠀⠀⢀⡿⣠⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⡿⠟⠻⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠄⢸⡇
⠀⠀⠀⠀⣼⡇⠋⣿⣿⣿⢛⣿⣿⣿⣿⣿⣟⣴⢢⣾⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢿⡇
⠀⠀⠀⠀⠙⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⡛⢫⣼⠇
⠀⠀⠀⠀⠀⣿⡸⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣭⣻⣿⣿⣿⣿⣿⣏⢻⣤⡿
⠀⠀⠀⠀⠀⠘⢷⣤⢸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⡇
⠀⠀⠀⠀⠀⠀⠀⢻⡌⡷⠿⠿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠛⠿⠏⠻⣿⠋⡀⠈⢴⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⠀⠀⠸⡇⠈⠯⠉⠙⠛⠿⠿⠯⠭⠟⠋⠛⠛⠎⠉⠁⢀⡤⠀⠀⠹⠀⣠⢎⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡜⡄⠀⠀⠁⠈⠓⠶⣤⣄⣀⣀⣀⠀⠀⠀⢀⣀⣀⣤⣶⣏⠀⠀⠀⢰⡘⡇⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡜⡄⠢⡄⠀⠀⠘⠋⠙⠛⠛⠉⠀⠀⠀⠈⠉⠉⠛⠃⠈⠁⠀⠀⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢇⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢛⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠸⡀⠀⠀⠀⠀⠀⢠⣦⣀⢀⣒⣈⣽⣶⠀⠀⠀⠀⠀⡴⢵⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡫⠞⠳⡀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠿⣿⣿⠀⠀⠀⢀⠌⠑⠢⣝⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠜⠁⠀⠀⠐⢀⠀⠀⠀⡿⢻⣧⣀⣁⣠⣿⡌⠀⣠⡔⠁⠀⠀⠀⠈⢮⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠌⠀⠀⠀⠀⠀⠀⢙⠲⠤⠔⠈⠛⠛⢛⣛⠩⡰⠟⠁⢀⠀⠀⠀⠀⠀⠀⠋⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⢁⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⡈⠑⠂⠤⠄⠊⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡰⡄⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠌⠒⠀⠠⠀⠂⠄⠀⠀⠀⠀⢘⠀⠀⠀⠀⢠⡞⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢘⠳⢤⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⠶⡎⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠈⢉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⡇⡻⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡞⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢃⠀⠀⡇⠈⠒⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢀⣠⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠶⠶⢶⣶⣤⣤⣤⣶⡶⠶⠾⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣾⣿⠛⠛⢻⠛⠛⠛⠛⠲⢶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠃⠀⢸⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠙⠛⠿⠟⠛⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⠟⠳⣄
⠀⠀⠀⠀⠀⣴⣿⣿⣿⠋⠀⣠⣤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⢭⣭⡁⠀⠀⠀⠘⢷⡄
⠀⠀⠀⢀⣼⠟⠛⠋⠀⢀⡞⠁⣠⣄⡀⠙⢷⡀⠀⠀⠀⣴⣶⣄⢸⢀⣴⣶⡄⠀⠀⠀⣰⠛⠁⣀⣤⡀⠙⣆⠀⠀⠀⠀⢻⣄
⠀⠀⢀⡾⠁⠀⠀⠀⠀⠈⢧⡀⠀⢀⡷⠀⠀⢹⣄⣀⣀⣉⡛⠃⢸⠀⠛⣋⣁⣀⣀⡼⠁⠀⠰⣇⠀⠀⣠⠏⠀⠀⠀⠀⠀⠹⣆
⠀⠀⣼⠃⠀⢀⣀⣀⠀⠀⠀⠉⠛⠉⠀⠀⣠⠞⠉⠁⠀⠈⠙⠳⣾⡴⠛⠉⠀⠀⠉⠙⢦⡀⠀⠈⠙⢋⣡⣀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⣸⠇⠀⣴⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣸⠧⢄⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⠤⢿⡀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⡀
⢀⡿⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⠀⠀⠈⠉⠓⣦⡤⢀⠀⣀⡠⣤⡖⠋⠉⠀⠀⢸⡇⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⣠⣶⣿⣇
⣸⡇⠀⠀⠈⠻⠿⠟⠋⠀⣠⡴⠶⠛⠋⠹⣆⠀⠀⠀⠀⠈⠁⠀⣨⡁⠀⠉⠀⠀⠀⠀⢀⡾⠉⠛⠳⠶⣤⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⢧⣀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠈⠳⢤⣄⣀⣠⡤⠞⠁⠙⠦⣤⣀⣀⣤⠴⠋⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠈⢙⣻⢿
⢿⣄⠉⠙⠓⠶⠦⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡤⠶⠖⠚⠉⢁⣼
⠀⠙⠳⠶⣤⣤⣀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣠⣤⡴⠶⠛⠁
⠀⠀⠀⡰⠋⠀⢉⡽⢷⣄⠀⠀⣴⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢲⠄⠀⢀⣴⠿⣍⠁⠈⢳⡄
⠀⠀⢰⡇⠀⢠⡟⠀⠀⠉⠛⠶⣬⣭⣉⣙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣉⣩⣭⡴⠞⠋⠁⠀⠘⣧⠀⠀⣷
⠀⠀⠀⢷⣄⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠳⢦⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⠶⠟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣰⠇
⠀⠀⠀⠀⠈⡇⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠉⠉⠉⢹⠉⠉⠉⠁⠀⠀⠀⠀⣀⣀⣀⠀⢀⣀⣀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠹⣄⠀⢰⠁⠀⠀⠹⠁⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠹⠁⠀⠀⢱⠀⣀⡼⠁
⣤⣤⣤⣤⣤⣤⣬⣽⣿⣷⣶⣶⣾⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣾⣯⣿⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣾⣶⣶⣶⣿⣿⣭⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣬⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⠀⢀⣱⣴⣴⢛⣋⠐⠒⠢
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣿⠿⣭⡉⠉
⠀⠀⠀⠀⠀⠀⠀⡟⠈⣾⡗⣌⣷⡈⠙⠈⠀⠀⢀⣰⣿⠋⣓⠀⣠⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠶⢻⡇⠈⢻⠙⠠⠀⠀⠀⡾⠁⢻⣷⡌⠸⢳⠏⣦⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢄⠑⢤⡀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠑⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠎⠉⠠⢄⠀⠀⠀⠀⠉⠒⠦⢄⡀⠀⠈⠑⠦⡀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠓⠺⡞⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠈⠑⠠⣀⠀⠈⠓⢄⡀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⢦⣀⠀⠙⢶⠀⠾⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢐⠤⡹⣧⣠⣄⡈⠶⣬⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⡤⠖⠋⠉⣀⠀⠚⢑⠻⣮⡾⠛⠓⠾⣧⡘⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⣹⢀⣴⠡⠜⡉⣤⣦⣾⣷⣿⣿⣿⣶⣄⠺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠖⠟⠳⠿⠿⠾⠷⠷⠛⠁⠁⠀⠀⠐⠀⠐⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠶⠾⠿⠛⠛⠛⠛⠛⠿⠷⠶⠶⣶⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⠶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣦⣄⡀
⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⣦⣄
⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄⡀
⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄
⠀⠀⣾⠇⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⣸⡏⠀⠀⠴⠿⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦
⢀⣿⠀⠀⠀⠀⡠⠚⢉⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠛⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⢸⡏⠀⠀⠀⡜⠀⣰⡿⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⢿⣄⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⢸⡇⠀⠀⢰⠁⢀⣿⣇⣠⣿⣿⣿⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡀⢸⣿⡀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⢸⡇⠀⠀⠸⡀⠈⣿⣿⣿⣿⣿⡿⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⢿⣿⣿⣿⣿⣿⠃⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⣷⠀⠀⠀⢱⡀⠹⣿⣿⣿⡿⠃⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠘⣿⣿⣿⣿⡟⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢘⡏⠀⠀⠀⠈⢿⣦⣌⣉⣉⣠⣴⡿⠋⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠻⣷⣄⡈⠛⠛⣋⣤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣾⠁⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀
⠈⢿⣄⣠⣤⣴⠶⢾⣿⡛⠛⠛⠉⢉⣭⡉⠉⠉⠉⠁⠀⠀⠀⣠⡿⣿⡍⠉⢉⣉⡙⠛⠛⣷⣶⣦⣄⡀
⠀⠈⠙⢿⣄⠀⢀⣾⠛⢿⣆⠀⢀⣿⠋⠻⣦⣾⠟⢿⣦⣀⣾⠋⠀⠈⢿⣶⠟⠉⠷⡴⠟⠁⠹⣆⣉⠻⠿⣦⣄⣀⣀
⠀⠀⠀⠀⠻⣧⣼⡇⠀⠀⢻⣆⢸⡿⠀⠀⠈⠁⠀⠀⠙⠛⠁⠀⠀⠀⠀⣀⡀⢀⡤⣄⣠⢤⣀⣀⣠⣤⣤⠤⠿⠟⠛⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⠙⠿⠇⠀⠀⠀⠀⠀⣀⣀⠀⢀⡾⠻⣦⣾⢋⣹⣿⣴⡶⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣼⡟⠙⢷⣿⣁⣤⣼⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⣿⠉⠻⣿⣟⣠⣴⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢰⣿⣦⠀⢀⣿⠃⠀⠉⢀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⢿⡇⠹⣧⣾⢃⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⢸⡇⢀⣽⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠹⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⠶⠦⣤⣤⣤⣤⣀⣀⣀⣤⣤⣤⣤⠶⠶⠛⠋⠉
⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣼⣧⣭⣧⣷⣶⣼⣼⣭⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣶⣶⣾⣿⣶⣶⣶⣷⣶⣶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠈⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣇⣬⠉⢰⠶⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠁⠀⢤⠀⣸⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣦⡄⠽⠶⣿⣿⠓⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⣸⣿⠟⠁⠐⠘⣿⣿⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⣿⡟⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠈⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⡇⢸⣿⠀⠀⠀⠀⠀⢸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢡⣿⠛⠳⢦⣤⡤⠔⠚⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣾⡏⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⢸⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⢀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡶⢀⠀⢸⣸⣿⠀⠀⠀⠀⠀⢀⣼⣿⡿⠁⠀⠁⠠⡐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠄⠀⣧⠀⡇⣤⠀⠸⣇⠙⢷⣶⣶⣶⣾⡿⣿⣏⣽⣁⣶⠴⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣋⠙⡄⣋⠀⡇⣾⠀⠀⣹⣧⣾⣿⢻⣿⣇⠀⠉⠀⠀⠈⢻⡄⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⢦⠀⣉⠀⡇⣿⠀⠈⣿⣿⣽⡟⠘⣿⠛⡜⢃⣄⣀⣠⣼⡇⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣼⠀⣷⣿⠀⢀⣿⢸⣿⠇⠀⣿⣼⠓⡌⠉⠋⡃⣹⡇⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⢀⠇⢰⠇⣿⠀⢸⡏⣾⣿⠀⠀⣿⡿⠠⠃⠀⢠⣶⢿⣧⡄⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣼⡆⣼⠀⣿⠀⣸⡇⣿⡿⠀⠀⣿⡇⠀⠀⢶⠀⠂⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢹⡇⣿⠀⡟⠀⡟⢱⣿⡇⠀⠀⣿⡇⡄⡄⠀⠃⠀⠀⠙⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢼⢁⡟⠀⣿⠀⣇⢸⣿⠁⠀⠀⣿⣿⡇⢃⠀⠀⠀⠀⠀⠱⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡏⢸⠁⣾⡟⠀⠀⠀⣿⡿⣇⢸⡀⠀⠀⠀⠀⡀⠜⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⢰⣿⠇⠀⠀⠀⣿⡇⣿⠀⣷⠀⠀⠀⠀⡅⠲⠛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠳⡾⣿⣿⠀⠀⠀⠀⢿⣿⠉⡆⠘⠛⠶⠏⠀⡟⣦⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣶⣿⠇⠀⠀⠀⠀⢸⣿⡆⢻⡀⠀⠀⠀⠀⡇⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⢻⣿⠀⠀⠀⠀⠀⢸⣿⠁⠈⢳⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⠀⠀⠀⠀⠀⢸⣿⣰⠀⠀⠀⠀⠀⠈⢀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡏⢆⠀⠀⢀⡸⠀⡌⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠈⠤⣀⣉⡤⠔⠃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣼⡏⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠄⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠃⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⡈⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠎⠁⠀⠂⢠⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣁⠀⠀⠀⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡡⠄⠊⠀⠀⢀⠄⠫⠀⠀⠀⣠⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠹⠟⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⣈⠴⠶⠤⠶⠂⢀⡴⠀⢀⣴⣶⣤⡾⠉
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠚⠒⠒⠓⠀⠀⠀⠂⠀⠀⠒⠈⢁⠀⠄⠀⠀⠺⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡩⢍⠢⡀⠀⠀⠀⠀⠀⠀⡠⣪⢭⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⠔⠀⠘⢄⠀⠀⠀⢀⠎⠀⠣⠬⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠦⠤⠤⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠈⠉⠀⠀⢀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠄⢘⠁⠄⠀⠈⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡶⠃⠐⢄⣀⣀⣠⠊⠢⢄⡠⠜⠀⠈⠳⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⢡⠎⠀⠀⠀⠀⣤⣿⠛⠉⠛⣷⣦⡀⠀⠀⠀⠘⢄⣑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡄⡔⠁⠀⠀⠀⠀⢸⣿⣿⣿⣶⣿⣿⣿⡷⠀⠀⠀⠀⠀⠹⡇⠈⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⡘⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠰⢰⣿⣷⡄
⠀⣠⠒⡢⠤⢄⠎⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠿⠟⢆⠤⠤⠒⢢⡀
⣸⡁⠙⡆⠀⢨⣀⡀⠤⡠⣆⠀⠀⠀⠀⡀⠀⠀⠀⠉⠁⠀⠀⠉⠁⠀⠀⠄⡀⠀⠀⠀⢀⠧⡀⢄⣀⣸⠀⠂⡆⠀⣱
⠳⠤⠭⠠⣤⡀⠀⠀⠀⠀⠈⢦⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡠⠊⠀⠀⠀⠀⠀⣠⡤⡨⠥⠴
⠀⠀⠀⢀⠃⠈⠉⢙⠧⣀⠀⠀⠉⠒⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠖⠋⠀⠀⢀⡠⢟⠉⠉⠀⢃
⠀⠀⠀⢸⠀⢀⣤⡾⢄⡀⠉⠒⠢⠄⣀⣀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⢀⣀⡀⠤⠒⠊⠁⣀⠼⡄⠀⠀⢸
⠀⠀⠀⢸⠀⢾⣿⠧⡀⠉⠒⠠⢄⣀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⣀⣀⠤⠒⠊⠀⡠⢇⠀⠀⢸
⠀⠀⠀⢸⠀⠀⢹⣄⠈⠑⠢⢄⡀⠀⠈⠉⠁⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⠉⠉⠀⠀⣀⠤⠒⠉⢀⡼⠠⣿⣿
⠀⠀⠀⠸⠀⠀⢤⡀⠑⠢⢄⡀⠀⠉⠁⠒⠂⠀⠤⠤⠤⠤⠤⠤⠤⠄⠀⠒⠂⠉⠁⠀⣀⠤⠊⠁⣠⠀⠙⠛
⠀⠀⠀⠀⢷⣦⢠⠈⠒⢄⡀⠈⠉⠐⠂⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠒⠈⠉⢀⣠⠔⠊⢰⡀⠀⠇
⠀⠀⠀⠀⠘⣿⠏⡗⠤⣀⠈⠉⠒⠢⠤⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠠⠤⠒⠊⠁⢀⡠⠖⣿⡇⡜
⠀⠀⠀⠀⠀⠙⢄⠈⢦⡀⠉⠒⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠐⠊⠁⣠⠞⢋⠜
⠀⠀⠀⠀⠀⠀⠈⠓⢶⣿⠲⢤⣄⡀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⣀⣤⠴⠚⣁⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠬⣹⠛⠛⢶⠶⠶⠶⠖⠒⠒⠶⠶⠶⢶⠞⠛⢻⠩⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠉⢹⠀⠀⢸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠑⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢪⠭⡐⠄⠀⠀⠀⠀⠀⢀⠔⡩⢍⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠐⠁⠈⢂⠀⠀⠀⢠⠊⠀⠃⠡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠧⠤⠤⢅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠈⠀⠀⠀⠄⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠂⢨⠀⠂⠀⢠⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⡚⠁⠀⠲⠤⣄⣴⣡⣑⡠⠔⠃⠀⠈⠻⡒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢡⠊⠀⠀⠀⠀⣴⣿⣍⡀⣈⣿⣷⡄⠀⠀⠀⠈⢦⣍⠢⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡷⡐⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⡀⣸⣦
⠀⠀⣀⠀⠀⠀⡰⠿⠟⢡⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⢁⢻⣿⣷⡀⠀⠀⢀⡀
⢀⠼⢠⠀⠉⠎⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠨⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠉⠁⠎⠈⠀⠘⢆
⡞⠂⠤⠁⠀⠓⠐⠂⠐⠋⢆⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠎⠓⠈⠒⠐⠃⠀⠁⠄⢚
⠈⠉⠉⠙⠗⠢⠄⢤⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⠀⢠⠀⠤⠒⠟⠉⠉⠉
⠀⠀⠀⢸⠀⠀⣀⡎⠉⠒⠤⣀⡀⠈⠉⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠉⠉⠀⣀⡠⠔⠊⠉⡆⠀⠀⢸
⠀⠀⠀⠀⠀⣾⣿⠀⠑⠦⢄⡀⠈⠉⠐⠒⠂⠠⠤⠤⠤⠤⠤⠤⠀⠒⠒⠈⠉⠀⣀⠤⠔⠉⢸
⠀⠀⠀⠀⠀⠙⣏⠉⠢⢄⣀⠈⠉⠐⠒⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠐⠒⠈⠉⢀⣀⠔⠊⢉⡄⣴⣶
⠀⠀⠀⢸⠀⠀⡏⠑⠦⣀⠀⠉⠒⠒⠤⠤⠀⣀⣀⣀⣀⣀⣀⣀⣀⠠⠤⠔⠒⠊⠁⠀⡠⠖⠉⡇⠛⢿
⠀⠀⠀⠈⣦⡄⠏⠲⢄⡀⠈⠒⠢⠤⠄⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠤⠤⠐⠀⠀⣀⠴⠊⡇⠀⡌
⠀⠀⠀⠀⢻⣿⢹⠦⣀⠈⠑⠢⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠒⠉⢀⡠⢾⡿⢠⠃
⠀⠀⠀⠀⠀⠫⡀⠱⡀⠙⠒⠤⢀⣀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢀⣀⠠⠔⠊⠁⡰⠛⡡⠃
⠀⠀⠀⠀⠀⠀⠙⠶⣾⡷⢤⣄⡀⠈⠉⠉⠉⠀⠐⠀⠒⠒⠂⠀⠈⠉⠉⠉⠀⣀⣤⠴⠋⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠬⢉⡟⠒⠶⠶⠶⠒⠒⠒⠒⠒⠲⠶⠶⠖⠚⣏⠩⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡇⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠉⢢
⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⢿⣿⣿⣿⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⠳⣿⣯⡾⠋⠉⢉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣿⡋⠀⠚⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠐⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⡀⣀⠀⣀⡾⣿⡿⢿⣿⣿⣿⣦⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢘⣿⢿⣧⢽⣿⣿⡈⠋⢀⡟⢻⣈⡿⣙⣿⣧⢿⣿⣿⣿⣝⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢰⣿⢃⡀⢀⢾⣿⣿⣿⡀⠈⢀⣜⠻⣀⡿⢸⣿⣆⣿⣼⣿⣻⣇⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⠈⠏⠈⢡⠾⠎⣿⣿⣿⣿⠀⣘⠿⢘⠋⢹⡀⢿⣿⢸⣿⣿⣿⠿⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢻⣧⠀⣈⡷⠋⡄⣸⡿⢿⣿⣿⡄⢻⣤⡛⣻⣾⣧⣼⣿⢸⣿⣿⣯⣶⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠜⠇⢾⠿⢁⡀⢠⣿⢠⣿⣿⣿⣿⣌⣿⡇⣿⣿⣿⣿⣿⣻⣿⣿⡿⣻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣤⣴⢛⣥⣾⣧⣼⡟⠻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⢹⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠏⠁⠘⠋⢉⣀⣼⡿⡟⠀⠙⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠿⢋⣸⠉⣿⣷⡇⠀⠀⠸⣧⠿⣿⣿⣿⣿⣿⠉⣿⣿⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢟⣉⠀⣡⣾⡇⠀⠀⢐⣤⣠⣀⣀⣠⣼⣿⠀⠈⠛⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⡀⠉⠹⣧⠐⣴⠏⢟⣻⣿⣻⢫⣿⡟⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡁⠀⣿⣿⢁⡼⡘⣯⠙⡏⣼⣿⣿⢸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡷⢀⡈⣷⡘⢃⣃⣿⢀⡏⣿⢿⣿⡔⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣞⢋⣹⡇⠸⢻⡟⠸⡷⠫⠜⢿⣧⢹⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⡙⢿⣿⢿⣿⠀⣾⣷⠸⡇⢱⣞⢹⣿⠸⣧⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢸⠇⠀⡇⠀⢿⠻⣿⡇⢸⡇⠀⣸⣼⣿⡇⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠳⠊⠀⣾⠀⠀⠸⢣⣿⡆⢰⠃⢀⣼⡌⣿⣇⢿⣷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢠⣾⠀⢸⣿⣤⢀⣷⣾⣿⠀⣿⡆⠀⢻⣧⣿⣿⠘⣿⠛⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢶⡾⠀⠀⣼⣿⣿⠏⢀⣿⣧⠀⢹⠇⢀⣸⡏⢹⣿⡄⣿⡆⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣼⣿⣟⠀⠀⣼⣿⠟⠀⣼⡄⠈⢹⡷⢸⣿⣷⢸⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠉⠙⣿⡿⠾⠟⢻⢷⡶⢿⣧⣶⣾⣷⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠉⠁⢉⡀⢻⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡿⠀⠀⢹⣿⠀⠘⠃⠀⠀⠘⠀⠀⠀⠘⠛⠙⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠃⢀⣿⡇⠀⠀⠀⠾⠀⠀⠀⠘⠀⠀⠀⠙⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠀⠀⢸⣿⡇⠀⠒⠀⠀⠀⠐⠂⠀⠀⠀⠶⠀⢠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠠⠀⢻⣿⡧⠀⠀⠀⣦⡀⠀⠀⠀⠄⠀⠀⠠⣶⣾⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⡀⠀⣼⡿⠀⠀⢰⣿⣿⠀⠀⣀⠀⡇⠀⠀⡀⠀⠀⠀⣤⠀⢀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣀⣷⡟⠁⣺⣿⡇⠀⠀⣾⣿⡏⢀⠀⠉⠀⣧⡀⠀⠀⠀⣀⠀⠉⠀⣷⣼⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢃⣀⣿⡿⠀⠀⣰⣿⣿⠁⠈⠀⢀⣶⣿⠃⠀⡀⠀⠁⠀⢀⠀⠋⣽⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣧⢘⣻⣿⡃⠀⠀⢸⣿⡿⠀⢀⠀⢻⣿⣟⡀⠀⠁⠀⠀⠀⠙⠀⣰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⣾⣿⣿⣷⡄⠀⣻⣿⡇⠀⠈⠀⣼⣿⡿⠃⠀⠀⠀⠃⠀⠀⠀⠻⣿⠿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⣼⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣾⣿⣿⣦⡍⢳⠀⠀⣀⣀⡀⠀⠰⠟⣠⣴⣶⣶⣮⣉⣿⣇
⠀⠀⠀⠀⢿⣿⠛⣌⡻⣿⣿⡇⢿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣆⣴⣿⣿⣿⣿⣧⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠘⣿⣤⣾⣿⣿⡿⠀⣌⣻⠿⢿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣧⣀⡌⠉⣿⣿⣿⣛⣛⡉⣾⣧⣿⣿⣿⣿⣿⢟⣀⢻⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠙⠁⠈⠓⠾⠾⠉⠑⠛⠻⢿⣯⣉⡁⠀⠀⢽⣿⣾⣿⣭⣵⠟⠛⠃⡬⢛⣋⣿⣾⡋⢽⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠰⢶⣄⣀⡀⠀⠠⠀⠀⠀⠈⠉⠛⠶⢶⣾⣿⣿⣯⣀⣄⣀⣀⣀⣰⣈⣉⣠⣾⣿⣿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠉⠻⣿⠿⠛⠋⠉⠉

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



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶⣦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⡿⠿⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⠶⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠁
⠀⠀⠀⠀⠀⠀⣾⣶⠀⠀⣠⣴⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⢿⣿⣴⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣧⣄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⣶⠶⠶⣶⠶⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⣯⠀⠀⠹⣆⣰⠏⠀⠀⣽⠛⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⠁⠀⠀⠘⣧⠀⠀⢹⠏⠀⠀⣼⠃⠀⠀⠈⠙⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠘⣧⢠⡟⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣀
⠀⠀⠀⠀⠀⣠⡴⠟⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠛⢶⣄
⠀⠀⠀⠀⠀⢻⣄⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠹⣦⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠻⣄⠀⠀⠀⠀⢀⡾⠁⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠹⣦⣴⡆⠀⣼⠁⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣴⠋⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡴⠋⢸⣇⣀⣿⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇⠙⢦⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣄⠀⠀⣠⣤⣤⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⣿⢀⡇⠀⠀⠸⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⣿⣼⠀⢠⡆⠀⢧⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⣿⡇⠀⡾⢳⠀⠸⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⣿⠉⠉⠁⠘⡆⠀⢧⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⣿⠀⠀⠀⠀⢷⠀⠘⡆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⣿⠀⠀⠀⠀⠘⡆⠀⢳⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠉⠉⠉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⢤⣿⣤⣤⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⠼⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⡛⠛⠿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⠣⣶⡄⠰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣀⠈⠀⠀⣻⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⡟⠀⠀⠀⣿⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣻⣿⣿⠟⠛⠿⣱⠂⡴⣘⠉⢓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠋⠉⠉⠉⡛⢷⣾⣾⠻⢾⠋⠉⠈⠉⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⢢⡀⣿⠀⣿⣿⣆⣿⡀⠀⠘⣇⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⢄⠈⢠⡑⣬⢰⢛⣻⠛⣿⠁⠀⠀⢻⣧⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⢒⡄⠣⠀⠓⡙⠘⢸⠘⠀⡇⠀⠀⠀⢸⣿⡀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠙⣦⣱⢘⡇⡀⢸⠀⠄⣿⠀⢀⠀⠀⣿⣿⡀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠴⠖⠷⢄⣿⣟⡞⣥⠁⣸⠀⡆⢿⠀⠀⡆⠀⢹⣿⡷⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣶⠼⠿⠀⠹⢿⣿⣿⣿⣿⣶⣧⣿⠀⠀⡇⠄⢸⣿⡟⠛⠳⢦⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⡴⠀⠀⢀⡼⠋⣻⡿⢿⣿⣿⣿⡇⣧⢸⠈⣿⡗⣾⠉⠈⠙⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⡇⠀⠰⠋⠀⣴⡟⣴⠞⢻⢿⣿⡇⣯⢸⠀⣿⣇⡿⢀⣼⣷⣤⣈⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⡇⣿⠀⡃⠀⠀⢨⣿⠀⣿⡄⣀⡻⢿⡇⣿⢸⡆⢸⣿⣇⣾⠋⠁⢀⣙⢛⣂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⣿⢠⡇⣾⠀⢸⣿⢀⣿⣿⣯⡉⢸⡇⣻⢸⡇⢸⣿⣽⡏⢀⣼⢿⢧⡟⠠⠬⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡇⠀⠀⣿⠀⢸⡿⢸⣿⣿⠋⠃⢸⡇⣿⠈⣷⠀⣿⠙⣰⠟⠁⢼⣸⣧⣴⣳⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢃⡄⣿⠀⣸⣿⠸⣿⣿⠂⠀⢸⠀⣻⠀⣿⠀⢿⡆⡿⠐⠀⢸⣿⣿⣿⡇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡧⢺⡇⣿⠀⢿⣿⠘⣿⣿⠀⠀⢸⡇⣿⠀⣿⠀⢸⣷⣿⣄⠐⣾⢸⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⢿⡇⢸⣿⠀⣿⡟⠀⠀⢸⡇⢸⠀⣿⡄⢸⣿⡏⣿⠀⣼⢸⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⢸⢇⢸⣿⠀⣿⢴⠀⠀⢸⡇⢸⡆⣿⢠⠈⣿⣿⣿⣷⣿⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣾⣷⣿⢀⣿⢸⠀⠀⣼⠁⢸⡀⣿⢸⠀⣿⣿⣿⣿⣿⣹⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣟⣿⡄⣿⣼⡏⢸⠀⠀⣿⠀⢸⡇⢸⠠⡄⢩⣿⣿⣿⣿⣿⣿⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡓⣼⠀⠀⣿⠀⢸⡇⢸⠀⡇⠀⠹⣿⣿⣏⠉⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡀⠀⣿⠀⢸⡇⢸⠀⡇⡆⠀⠹⣿⡿⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠙⡇⠀⢿⣿⡇⠀⣿⠀⢸⡇⢸⡄⠇⣿⠀⠀⠈⢿⣿⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⢸⣿⣿⠃⡞⢻⠘⠇⠀⣾⣿⡇⠀⣿⠀⢸⡇⢸⡇⡇⣿⠀⠀⠀⠀⠉⠁
⠀⠀⠀⣀⡀⢰⣿⢠⡤⢤⢯⡥⣠⣤⠀⢸⣿⣿⠀⡇⢻⠀⡇⠀⢿⣿⡇⠀⣿⠀⢸⣇⢸⣿⡇⢸
⠀⣴⠾⠿⢿⢻⣿⣿⡥⣴⣶⠖⡀⠈⠁⢸⣿⣿⠀⠁⡾⢀⡅⠀⣶⣿⡇⠀⣿⠀⢸⡇⢸⡏⠁⢸⡇
⠀⠿⠈⣿⣣⣼⣿⣏⠉⣈⣀⣺⡿⡁⠀⢿⣿⡟⠀⢸⡇⠈⠁⠀⣿⡿⡇⠀⣿⠀⢸⡇⠐⣇⠀⠈⡇
⠀⠠⣜⡟⠻⢟⣿⣟⠚⣿⣿⣿⣿⡟⠀⣾⣿⠁⢀⡿⠀⡦⠀⠀⣿⢃⡀⠀⣮⢸⢸⡇⠀⣿⢰⡄⢧
⠀⠀⠠⠀⠘⣿⣥⣭⣶⣶⣾⣯⣭⠁⣼⣿⠥⠀⠛⠁⡜⠁⠾⢠⣿⣄⣧⠄⠷⠈⢸⡇⠀⢿⢸⡷⠸⢀⣤⣶⣤⣄⡄⢀⣀⢀
⠀⠀⠀⠓⠰⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣍⣀⣀⣠⣇⣼⣷⣺⣟⢊⣀⡀⠸⢧⣀⠻⠞⢣⣷⣿⣿⣿⣿⣯⣿⣿⣿⣿⣈⣿⣤
⠀⠀⠀⠀⠀⠙⠻⠿⠛⠛⠿⠿⠿⠿⠿⢿⣿⣠⠟⠉⠉⠉⢭⡭⠿⠿⠿⣿⣿⠿⠇⡉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣵⣮⣥⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠙⠙⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣷⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠚⠉⠉⣭⣵⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⢀⡙⢶⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⢠⡀⡟⠹⠴⠃⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⣼⠉⡀⠀⠀⢀⠤⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠤⢧⡀⠀⠀⠀⢰⡞⠉⡇⠈⠑⢲⣧⠖⠋⢉⠟⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠘⠁⠀⠀⠀⣸⡆⠀⠱⣀⠖⠉⠙⣦⠴⡿⠒⠋⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢘⣑⣧⠀⠀⠈⠓⠦⠤⡾⠀⠉⢳⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⡯⠴⠶⡄⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢠⡀⠀⡀⠀⠀⣇⣇⣰⡠⡄⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⠳⣄⢳⡀⣄⠀⣀⠀⡰⠃⠀⠄⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠘⠶⠙⣏⣿⡿⠛⠁⣀⡠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⢸⢢⣴⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢤⣀⡀⠀⣠⠞⠉⢠⠄⠀⣮⢾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠉⢿⣅⡀⣰⣁⠀⠀⢃⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡤⣴⣫⢾⡄⠁⢠⠷⣦⣼⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣞⣉⡻⣿⣏⣤⣀⠎⡰⡋⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣉⣓⡒⠃⠀⡠⠺⠔⢊⣏⣀⡃⡇⠸⡜⢆⡰⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣒⡭⠽⠄⠓⢆⣘⣽⠒⠦⠾⠭⠽⡝⠀⠀⢸⠊⢡⣠⠗⣄
⠀⠀⠀⠀⠀⠀⣠⢖⠝⢋⣤⠔⣻⣷⣠⣾⡿⠛⢛⣿⡿⠋⠉⠁⠀⠀⠈⢻⡙⣄⣱⠊
⠀⠀⠀⠆⡄⡰⣱⠋⠦⢴⣹⡝⠻⣿⡿⠋⠀⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⢧⡇⠀⢠⠞⠉⠀⠀⠀⣤⡠⢬⣟⣿⣁⣀
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⡠⣞⣙⠒⠚⠯⠿⢻⠍⠉⢙⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⠩⠭⠭⠭⠭⠭⠝⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠤⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢧⣠⡿⠁⣠⣽⠛⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡁⣸⣿⣿⣵⠀⣀⡀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠛⠃⠰⠋⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣺⡟⢋⣠⠼⢿⣿⣾⣿⢗⠝⠋⠁⠀⠀⠀⢀⠴⠿⠿⢛⠁⠀⠠⠖⠟⠉⣧⠐⠎⠓⠀⠀⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠋⡄⡶⣷⣿⣿⣿⣿⢧⡀⠂⠄⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⢰⠁⠀⡘⢧⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣥⠟⢹⡿⢹⠉⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠐⠃⠈⠆⠀⠀⡄⠀⠀⣧⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⢼⣧⠌⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣡⠀⠀⢹⡀⠀⡀⠁⢰⠃⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠉⠀⠀⠀⠉⠁⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣧⠀⡀⠀⡞⠀⠠
⠀⠀⠀⠀⠀⠀⢀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠁⢠⠃
⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸
⠀⠀⠀⣰⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢼⠦⣄⣀⣠⢿⠀⣿
⠀⠠⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠜⠓⠀⠾⢊⡴⢂⣉⣿⡄⣿⡀
⢀⣈⣽⣿⣷⣷⣤⠄⡀⠀⣠⡀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠚⢙⠣⣃⠁⠚⣉⡐⢂⣔⣿⣿⣿⣷⠦⠄
⠀⢴⣿⣾⡿⠽⣿⡧⢹⣿⣿⣿⣿⡤⠀⡼⠙⠁⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣶⣿⣤⣴⣶⣮⣭⣥⣿⣿⣿⢿⣿⣿⢿⡟⠋
⠀⢸⣿⡟⠀⣀⡀⣸⣿⣿⠿⣯⠝⠂⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠻⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣭⢿⣄⠙⠆
⠀⣞⠏⠀⠉⠙⣿⠛⢉⡃⠈⠈⣀⠀⠀⡅⡀⢨⠀⠀⠀⠀⠀⠀⠀⢈⣉⣰⣾⡿⣽⣛⣉⡻⠦⠚⠛⠉⠉⠉⠉⠀⠹⣄
⠚⠁⠀⠀⠀⠀⠠⠀⠉⠀⠄⠠⢅⠀⠀⣧⡇⡈⠀⠀⠀⠐⠛⠙⠷⠿⠯⠶⠶⣿⣇⡱⠯⠻⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣉⡭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠖⠛⠛⢳⣦⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢋⡡⠀⠀⠀⠀⠀⠀⠠⠃⠀⠃⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⠂⣠⢶⡀⠀⠀⠀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡴⠊⠀⠀⢀⡠⠊⣀⡴⣿⣠⣾⡵⠞⠁⠀⢷⡰⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢀⣠⣴⣯⠴⠛⠉⠀⠟⠋⠁⠀⠀⠀⠀⠈⢿⣆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠻⠛⠉⣩⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠆⠘⡟⠂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⣀⣙⡳⠖⢀⡆⠀⠠⠴⠚⢁⡀⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⡟⠀⣼⠀⠀⠀⠀⣿⣿⡇⠀⠀⣿⢸⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠘⠢⠴⠂⢠⡏⠀⠀⠀⠀⠬⡫⠔⠀⠀⣷⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠙⠓⠂⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠃⠉⠉⠉⠭⠍⠉⠉⠈⠁⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣶⠦⡤⠤⠤⠤⠶⣾⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⣶⠞⢹⠁⠀⢣⠀⠀⠀⠀⢸⡏⢳⡦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠉⠉⠀⠀⡟⠀⠈⣧⠀⠀⠀⠀⠀⠀⣼⠀⠀⣧⠀⠀⠉⠉⠛⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠐⣄⠀⠀⠀⠘⡇⠀⠀⠈⢧⡀⠀⠀⢀⡾⠃⠀⠀⡟⠀⠀⠀⣼⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠘⢆⠀⠀⠀⢿⣤⠶⡆⠀⠙⢦⡴⠋⠀⣶⠶⡼⠃⠀⠀⢀⠃⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠦⣤⣸⣀⣤⠤⠟⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⢠⣟⡀⠀⠀⠀⠀⠀⠀⣏⠉⠉⠉⠉⠉⡇⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢿⣄⡉⠓⠦⣄⣀⣦⠀⢿⡀⠀⠀⠀⣀⡇⠀⠀⠘⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⡤⠖⠋⢁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠳⠶⢦⣬⣿⠀⠈⠙⠓⠖⠛⠁⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣤⡴⠶⠛⢻⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⣀⣸⣯⣀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠒⠶⠿⠦⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣇⣇⣀⣀⣤⣤⠶⠞⠛⠉⠉⠁⠀⠀⠀⠀⢸⡇
⠤⠤⠤⠤⠤⠤⠤⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⠶⢤⣽⣿⠿⠟⠛⠛⠛⠛⠳⠾⣿⣷⡄⠀⠀⠀⠀⠀⢀⡿⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣋⣹⠀⠀⠀⠀⠀⠀⠀⠠⢬⡻⣦⡀⣀⣀⣠⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠦⣤⣤⣤⣤⣤⣤⣤⣤⡦⠶⠶⠿⠿⠶⣦⣤⣄⣀⡀⢤⣝⡲⣝⢾⣿⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠍⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢯⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣤⠀⠖⠡⠙⠛⠳⢽⣶⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠴⠣⠀⢃⠘⠂⠀⠈⣿⠁⠀⠀⠘⣿⣠⠀⠁⢯⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡰⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠠⣸⣿⣷⡀⠀⠀⡼⠡⠇⠀⠀⠇⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣏⢷⣠⠛⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠘⢠⡏⣿⣻⣷⠀⠀⠇⠀⠀⠁⢠⢀⡀⠀⠀⠀⠀⠛⠀⠦⠌⣉⠻⢼⣏⣴⣣⡴⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡿⠀⠹⡟⠃⠀⠈⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⣩⡵⢈⣿⣶⣤⡙⣦⣤⣁⠀⠈⣿⠂⢀⠠⢒⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢴⠶⢾⡏⠠⠞⠈⢿⡈⢻⣸⣇⣙⣧⣴⣼⣿⡏⠶⢭⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣼⡀⠁⠀⠀⠘⣷⠀⠉⠉⠁⡰⢋⣴⣿⣿⣧⠘⡇⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠹⠆⠀⠀⣟⡤⠋⣸⠛⠟⠘⠷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠁⠀⢠⡏⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢉⣉⠁⠀⠀⡁⢀⡀⠀⠀⠀⠉⠉⠉⠉⢙⠃⠀⠀⠠⠤⠄⠀⠀⠀⠉⠉⠁⠐⠒⠠⠀⠀⠀⠀⠹⡇⠀⢾⠆⣾⢰⠚⠈⠉⡉⠈⠠⠤⠸⠋
⠀⠀⠀⠠⣤⡀⠘⠛⠻⠶⡶⣡⢤⣴⣷⣶⠀⠀⠀⠀⠀⣤⣤⣤⣤⠀⠀⠤⠈⠙⠁⢀⠀⠠⢀⣀⡀⠐⠒⠠⠄⠈⣷⡀⠐⢀⡟⠀⡛⠂⠀⠀⠀⠠⠿⠛⠃
⠀⠀⠀⠀⢴⣟⣩⣤⣶⣆⢀⡤⠀⠀⠈⠉⠁⢀⠀⠀⠀⠀⠀⠀⠛⠀⢤⣶⣆⣥⣄⣀⢀⢀⠀⠀⠀⠁⠀⠀⠙⠃⢙⠈⠂⢸⠃⠀⠶⠶⠶⠒⠂
⠀⠀⠀⠀⢠⣶⣤⡀⠀⠈⠸⣇⠀⠀⢴⣶⣶⣯⣤⣿⢠⢣⣶⡤⠄⡄⠀⠀⠛⠋⠉⠉⠀⠀⠤⠶⠶⣧⣶⣤⣠⣀⢈⠀⢄⣉⠀⢀⠀⣀⡀⢀⣤
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠴⡦⡴⠴⠆⢦⡄⢀⠀⣤⢀⣀⡈⠀⠈⠀⠀⠃⢠⠟⠛⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠈⠁⠉⠉⠁⠀⠀⣦⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠔⣧⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠁⠶⠶⠶⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣷⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⣠⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⣹⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠰⠆


⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡀⠀⠙⠻⣷⣶⠆⠀⠀⠀⡾⠟⠁⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⡠⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢉⣗⠚⠙⠁⠀⠘⠉⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠸⡟⠀⠠⠀⠀⠀⠀⠛⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⠠⠔⠁⠀⠀⠀⠀⢀⡠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠴⠒⠒⠒⠒⠒⠒⠋⠁⠀⢀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠯⠤⢄⣤⣀⡀⠀⠠⠤⠤⠒⠋⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠴⠾⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣀⣀⣀⣀⡤⠖⠋⠁⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠈⠉⠉⠉⠉⠉⠉⠉⠉⠐⠆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⢪⡅⠐⠒⠈⠉⠉⠀⠀⠉⠉⠀⠐⢢⣤⡀⠀⠀⠁⢂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠙⢣⡀⠀⠀⣀⠠⠤⠄⠒⠒⠈⠉⢀⡀⠀⠀⣀⣀⡀⣈⣉⣑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠹⡞⠋⣉⡀⠤⠔⠒⠂⠀⠀⢈⠠⢄⠺⢋⣽⠁⠋⠙⢄⠙⢢
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣀⠤⠄⠚⠟⠀⠀⠀⠀⠀⡀⠠⠀⢀⠔⠂⣠⠊⡀⠀⠈⣄⠈⠢⡀⢧⡀
⠀⠀⠀⠀⠀⠀⢀⡰⠛⢆⢀⡰⠋⠀⠀⣀⠜⠀⠀⡀⠠⠈⠀⢀⡠⠊⠀⠀⡐⠁⢠⠁⠀⠀⠈⢣⡀⠈⢾⣧
⠀⣠⠴⠊⠉⠉⠈⢳⣤⡴⠛⠁⠀⠀⢉⡀⠐⠈⠁⠀⠀⡀⠖⠁⠀⠀⢠⠊⠀⠀⠆⠀⠀⠀⠀⠀⠹⡆⠀⠙⡄
⡞⠁⠀⠀⠀⡠⠊⠁⢀⣥⡤⠖⠂⠉⠀⠀⠀⠀⣠⠒⠉⠀⠀⠀⢀⠔⠁⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢡
⠱⣆⠀⠀⢠⠁⠀⠀⢀⠁⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⢀⡠⠖⠁⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠈⠓⢤⣸⣄⠀⣀⠞⠀⠀⣀⠤⠒⠁⠀⠀⠀⠀⣀⠔⠋⠀⠀⠠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡌
⠀⠀⠀⠀⠉⠉⠛⣁⡠⠄⠛⠁⠀⠀⠀⠀⢀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⢫⡀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢀⣷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣠⠖⠉⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠉⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠳⣄⡀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⡀⠀⠉⠐⠢⣤⣀⣀⡀⠀⠀⠀⠀⡀⣀⣀⣀⠀⠀⣤⢤⡶⢋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡈⣱⠀⣀⡀⠀⠀⠀⠉⠥⠛⢋⣿⠉⢹⡏⠉⠙⠣⠤⣀⣠⣗⣡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⢹⠟⣧⢈⡡⠀⠀⠀⣠⠄⠂⡙⠧⠿⠦⣿⢆⡀⠀⠀⣉⣿⠋⠫⢀⡂
⠀⢀⠤⠄⠀⠈⠛⠀⣀⡰⠋⠀⠋⠀⠀⠀⡠⠋⠙⣦⡔⠀⠀⠀⠀⢸⠀⣷⡀⠀⠁⠁⠘⢄⡀⠈⠛⠒⠲⠶⠦⣀
⡔⠁⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣰⢾⡄⠈⠁⠶⠶⠶⠾⣾⠀⠑⠄⠀⠀⠀⠀⠈⠉⠉⠉⠲⠀⠀⠈⢃
⢣⡀⠀⢀⠁⣦⡉⢢⠀⠀⠀⠀⠀⠰⢁⠄⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⡄⠀⠣⡀⠀⠀⠀⠠⠉⣉⠆⠰⠀⣠⠎
⠀⠙⠲⠈⠓⠄⠒⠂⠀⠀⠀⣠⡾⠃⠁⠀⠀⠀⠀⡾⠃⠀⠀⠀⠀⠀⣷⡄⠈⠢⡀⠙⢆⠀⠀⠀⠒⠘⠚⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣟⠉⠃⠀⠀⠀⠀⣰⡅⡀⠚⠃⠀⠀⠀⠀⠋⣙⢄⠀⠘⠦⣀⠱⣄
⠀⠀⠀⠀⠀⢀⡤⠛⠇⠀⠁⠀⡀⢀⣴⠀⠀⠉⠀⠛⠀⠀⠀⠀⠀⠤⠀⢋⠈⠄⠀⠀⠈⠳⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠘⢳
⠀⠀⠀⠀⠀⣿⠀⡰⠀⠀⠀⢤⠁⠀⢦⡶⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⣀⠙⠃⠀⠃⠀⠀⠠⠀⢀⠀⠀⠀⢀⣀⣀⣀⣀⣠⢊⡀⠤⠞
⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠉⠁⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠸⠀⢺⣀⠴⢦⠉⠉⠁⠀⠀⠀⠀⠀⠀⢧⡀
⠀⠀⠀⠀⠀⠀⠹⣶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠰⢎⠂⣰⠆⠀⠀⠀⠀⠀⠀⠀⣀⠀⡇⠀⠀⡀⠃⠘⠃⢀⣀⣀⠈⠁⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠟⠀⣠⡄⠀⠠⠔⢊⠀⢤⣄⠀⠀⠀⠀⠈⠐⠂⢁⣀⠀⠀⢰⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⣡⡄⠀⠀⠐⠛⠀⠀⠁⠀⡀⠀⠀⠀⠛⢰⡄⠁⢰⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠤⠤⢀⣀⡀⠀⡤⣀⠓⢠⡶⠀⠀⠀⠀⢀⡼⠃⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠛⠛⣿⠓⠂⢶⠚⠛⠛⠋⠁⠀⠀⠀⠀⠙⠛⡶⢶⣦⣶⡶⠶⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⠈⠙⢁⠄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢹⠀⠀⠓⠒⠀⠸⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⣿⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠹⣇⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡀⠀⠀⠤⠬⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠀⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠾⠁
⠀⠀⠀⠀⠀⠀⢠⠶⠏⠈⠋⣹⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠘⠀⠀⠰⢶⠞⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⠁
⠀⠀⠀⠀⠀⠀⠘⠶⠆⢀⠀⠙⡆⠀⠀⢠⡟⢀⡇⠀⢀⠀⣂⠀⠀⠀⠈⠤⠀⠀⠉⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⡀⠀⠀⠐⠒⢿⠁⠈⠀⢿⡔⠉⠀⢸⣷⣤⣟⠀⣽⠶⣿⠀⠀⠠⠺⣤⣽⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⡐⠁
⠀⠀⠀⠈⠙⠛⢦⣴⠂⢨⡶⠆⠀⠀⣥⡤⠀⠀⣯⠤⣿⠀⣿⠤⣦⠀⠀⠲⢶⣈⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢀⠊
⠀⠀⠀⠀⠀⠴⠺⡏⠀⢘⠁⠀⠀⠀⡏⠀⠀⠀⠘⠶⠞⠀⠻⠶⠃⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠊⠂⠤⠤⠤
⣀⣀⣀⣀⣀⣤⣤⣋⣀⣘⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢏⣉⣹⡿⠻⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣮⣅⣽⣷⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢒⣶⣿⣶⡂⠀⠀⢤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⠏⢻⠉⠉⠷⠈⡿⠋⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠈⠐⡀⠀⠈⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣾⢿⠓⠀⠀⠀⠀⢠⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⢠⡀⠀⠀⠀⠀⣆⡀⣠⣷⣴⣦⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣶⣽⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠑⠒⠓⠒⠉⠏⠉⠍⠉⢉⡙⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠒⠂⠂⣉⣁⣀⣤⡴⠒⠚⠀⠀⢠⢤⠖⠂⠁
⠀⠀⠀⠀⠀⢀⣀⣀⣢⣤⠤⠶⠶⠶⠾⠿⠟⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠈⠑⣶⣤⢤⠈⠁
⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠾⠿⠛⠛⠉⢀⡸⠀⠀⠀⠀⠀⣀⠔
⠀⠀⣀⠀⠤⠤⢄⡠⠤⠶⠞⣛⣩⣭⣤⠶⠶⡶⡶⠶⠶⢶⢦⣤⣤⣤⣤⣤⠤⢤⡶⢞⣉⣦⠀⣀⠠⠔⠈⠠
⠠⠠⠀⠒⠒⠒⠒⠚⠛⠉⠉⠉⠀⣀⣀⣀⡤⠤⠒⠒⠴⠒⠉⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠉⠀⣦⣤⣤⣶⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣡⠤⠂⠀⠀⣀⡠⠤⠐⠀⠘⠇⠀⠀⠀⠀⠀⡠⢎⣤⡷⢖⣸⡟⢈⣩⡁
⠀⠀⠀⠀⠀⠉⠉⠉⠁⠚⠛⠉⠉⠀⠠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠈⣑⡫⠔⠋⠀⠉⠁⠈⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠛⠉⠀⠀⠈⣻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠣⠙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠸⡙⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣃⣀⣀⠀⠀⠀⠢⣄⠀⠀⠀⠈⠳⣦⡀⢆⠘⠢⠈⢻⣷⣤⣤⣠⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢿⣿⣶⣤⡀⠻⣦⡀⠀⠀⠈⠁⠈⢧⡀⠀⣼⡟⠉⠉⠉⣉⣉⠉⠩⠿⠿⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠉⠙⠷⠿⠷⠶⠟⠃⣌⠓⠀⠀⠀⠀⠀⠈⠛⢶⡿⣷⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢧⣀⣄⠀⠀⢄⣰⣄⡨⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣬⠉⠁⠀⠀⠈⠋⠈⠁⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⢿⣧⡐⠖⢀⡀⠀⠀⠀⣠⣿⠉⢻⣦⡀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠈⠻⣿⣍⠉⠀⢀⣠⣞⣋⠁⠀⠀⣹⣿⣦⣄⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠈⠻⣿⣿⣿⡻⢿⣿⣿⣿⣿⣿⠏⠙⢿⣷⣄⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣮⣝⠻⣿⠋⣤⣤⠶⠿⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿⠷⠋⠒⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡄⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣦⡀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⡄⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡄⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⠑⠂⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⣿⡄⠀⠀⠀⢠⡼⢿⣿⣿⣿⣿⣿⡇⢹⡏⠻⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢀⣿⣿⣿⣿⣶⣦⣤⣄⢀⣠⠾⠛⠀⣀⠚⢁⡀⢀⡴⠋⠀⠀⠙⠻⣿⡿⠟⠁⣼⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⠉⠁⡠⠀⣘⠇⢈⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠟⠀⠀⣾⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣾⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠂⣙⢦⡀⠀⠀⡠⠀⣠⠐⠀⠀⠀⠀⡀⠀⣸⠇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⣿⠀⠈⠻⣿⣿⣿⣿⣶⣤⣄⣀⡀⣀⣀⡼⢁⣿⢹⡖⠯⠔⠋⠀⠀⠀⠀⠀⠀⡇⢰⠏⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠘⡠⠋⠀⠀⠉⠻⠿⠿⠟⠀⠉⠉⠉⠉⠀⣸⡟⢸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⡷⠉⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢡⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣾⣿⡿⠛⠁⠀⠀⠀⠈⠉⠛⠶⣶⣦⣅⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣤⣤⣶⠾⠟⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢶⣤⣈⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠾⠟⠛⠉
⠀⠀⢀⣀⣠⣤⡶⠾⠛⠋⠉⠁
⠴⠿⠛⠋⠉




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⠛⠿⠿⠿⢻⠟⢫⡙⠛⢿⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣟⣛⣻⣿⣟⣛⣛⣛⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠓⠶⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡨⠇⠒⠉⠒⢄⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠀⠄⣀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠓⠒⠒⠦⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⡀⠀⢀⡶⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⢠⠊⠀⠀⢀⠶⠀⢠⠄⣀⣀⣛⡓⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠀⣀⠀⠀⠀⠀⠀⠀⠈⠲⠏⣀⠤⠤⠬
⠀⠀⠀⣀⣀⠀⠀⠀⡠⠊⠀⢀⠤⢤⣄⢺⡀⠀⠀⠘⠷⢦⠆⠘⠷⠂⠀⠉⠉⠉⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⢀⡴⠋⠁⠀⠈⢑⠎⠀⠀⢰⠃⠀⠀⠈⠳⡉⠓⠒⠒⠒⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⠈⠉
⡾⠀⠀⠛⠠⢀⠃⠀⠀⠀⠘⠷⢤⣄⣀⣆⠙⢀⠀⠀⠀⢿⢦⣀⡀⠀⠀⠀⠀⣀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠃⠀⠀⠀⠀⢀⣠⠴⠂⠁
⠹⢤⣀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⡌⠠⠆⠀⠀⠑⠌⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⢀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢀⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣥⣴⣯⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⣀⡀⠈⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠲⠶⣤⣤⠤⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⠻⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢄⡀⠀⠈⠉⠒⠀⠀⠀⠀⣀⠔⠊⠁⠢⢄⡀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠉⠑⢢⣀⢀⠠⠴⠒⠉⠀⠀⠀⠀⡈⠀⠈⠉⠒⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⠤⣤⣄⡄⢀⠀⠀⠀⢠⣴⣊⠁⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢅⣀⣀⣉⠀⠤⣉⡉⠓⠚⠋⠛⣿⠦⡀⠀⡖⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠉⠉⠉⠉⠑⠲⢤⠖⠉⠲⢼⣼⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⡏⠉⡟⠀⠙⠛⠂⠒⢲⡞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣦⣼⣆⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⢶⣾⠢⣤⣄⣀⣀⢀⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣀⣀⣈⣻⣾⣿⠥⠴⣟⣿⠋⣙⣳⣶⣒⣒⣿⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠒⠒⠚⠋⠉⠀⠀⠉⠒⠬⢙⣛⠫⠄⣀⣀⣹⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠚⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢰⢄⢤⡆⠶⠠⠄⢠⠤⡤⠴⠄⠀⠀⠀⠆⠒⠐⠀⠂⠆⠒⠐

⣿⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⠀⠀⣿⠇⢿⣿⠃⠀⣾⠛⣿⠋⠸⣿
⠏⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠇⠀⠀⠂⠈⡿⠀⠀⠙⠀⣾⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠈⠀⢀⠀⠀⢻⣄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣯⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠁⠙⠿⠿⣿⣿⣿⣿⣿⣿
⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠘⣿⣿⣿⡿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣠⠛⠟⠋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢸⣿⡹⠃⠈
⠁⠀⠀⠀⠀⠀⢀⣤⣾⡿⠋⠉⠉⠛⣷⣦⡀⠀⠀⠀⠃⠀⠀⡄⢠⡿⠀⠀⣲⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡹⠇
⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠙⣿⣿⡄⠀⠀⠀⠀⢀⠇⣿⣷⣤⣌⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢸
⠀⠀⠀⠀⠀⢸⣿⡿⣄⣀⡀⢀⣀⣀⣠⣿⣿⣷⠀⠀⣀⠀⠘⢰⢿⣿⣿⣿⣿⡏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡠⠄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⣟⣿⣿⣿⣀⣀⣿⣿⣿⣿⣿⡟⠀⠀⠙⠈⠀⢸⣿⣿⡿⣿⣿⡇⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⡄⠀⠀⠀⠀⠀⠹⣏⣀⣀⣀⣀⣀⣀⣀⣨⣿⡅⠀⠀⠀⠀⠀⣼⣿⡟⣳⡏⣹⡇⠁⣰⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⡇⠀⠀⠄⠀⠀⠀⠈⠛⠿⠿⣿⣿⠿⠛⢫⠀⢷⠀⠈⠃⠀⡰⣈⢸⡇⢸⣇⢹⣷⣀⡟⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠰⠟⣩
⣇⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠐⡆⠈⠀⠛⣠⡯⠈⣧⡈⣠⣤⢿⣿⡆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣬⡞⣿⣷⣿⣿
⠻⣿⡿⠟⠻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠄⠘⠀⠀⠛⢿⣷⣾⡿⢛⣯⣿⡎⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠸⣹⣿⣤⠶⠿⢿⣿⣿
⢀⣠⣯⣀⣀⣤⡔⠀⠀⠀⠀⣀⣀⣤⣼⠏⠀⠀⠀⠀⠀⠀⠀⠌⠿⢿⡿⠙⢛⢣⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠿⠻
⡟⢉⣿⠉⠁⠀⡛⠛⢿⠂⠀⣸⣿⣏⣽⠂⢠⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠈⠉⠉⠈⠤⣰⣆
⣹⡈⠁⠛⠡⠄⢱⣧⣼⣤⣤⣿⣿⠋⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠤⠀⠶⣖⣭⣿⣄⡤⣠⠴⢣⣀
⣉⠡⡄⢀⣴⠂⠒⣯⣿⡃⠈⠉⠉⣤⣴⣆⡌⠁⠀⢀⡀⠀⣠⠖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠁⠀⠙⠺⠾⡙
⠟⢣⣤⠸⢿⣤⣤⠉⠈⢛⣶⣶⠖⠁⠈⣿⣤⠼⠇⢀⣽⣚⣧⠀⠈⠁⠀⡀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀
⣤⡈⢁⣴⣼⣯⢼⣦⣤⣾⣿⣿⣿⣦⠚⠛⣧⢀⣌⣁⣀⠹⣿⣷⡄⠀⡠⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀
⣿⣥⣿⣿⣯⣽⣄⣤⡟⢬⡅⠀⠀⡋⠀⠀⣿⡎⢹⢉⣿⣥⣿⠻⡃⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⠈⡋⠀⢰⡀
⠻⣿⣿⣿⣿⣿⣿⣿⣵⣾⠟⠐⢺⣷⣤⡴⣯⡙⣿⡏⣿⣿⣿⢺⣿⢲⡇⠘⠀⠀⠀⣀⠂⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⣹⣦⡟⠁
⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣦⡀⠤⠛⢿⡛⣏⣳⣿⠿⣾⣿⣧⢸⡟⡿⠀⢸⠀⠐⠀⣿⠀⠀⠀⠀⢈⠀⠇⠀⠀⠀⠀⣿⣉⠁
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⢳⡶⢾⣤⣿⣿⣿⣿⣆⠻⣿⣿⢠⡅⡄⠀⢸⠀⠀⠀⠋⠀⠀⠀⠀⢺⠀⣿⠀⠀⠀⠀⠛⣿⡶⠴⠂
⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣴⠏⠀⠂⠀⢰⠆⠀⠀⠀⠀⠘⠀⠃⠀⠀⢀⠀⡀⣟⠃
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⣇⠀⣄⠀⠈⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠈⢸⡏⣿⡄⠀⠀⣖⠠⡦⠘⣳⠂
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠋⡀⠈⠀⡄⠗⢠⠀⠀⠀⠀⠀⡟⠀⠀⠸⣠⣧⢸⣿⠀⠀⢈⡰⣿⣿⠁
⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣸⡟⣿⡏⠙⠉⠉⠻⣿⢿⣿⠸⣆⠀⣦⠠⠿⠀⠃⠀⣼⠀⠀⠀⠀⠀⣷⠀⠀⠀⠹⡇⢸⣿⡿⠛⠀⠶⠋⠉
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣾⠛⢻⣿⡟⠈⠉⠣⡍⣿⣿⣿⠋⠀⠀⣨⠀⢩⡄⢢⡀⠀⢰⡇⠄⠀⠀⠀⠀⢻⠀⠀⠀⠀⠛⢼⣿⡍⢷⢚⡂
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣤⣿⡟⢀⡀⢀⡴⡇⠈⠁⣀⣀⣄⣨⣿⡆⠀⠀⢸⣰⢈⡆⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠺⣿⣷⡶⠛⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⣿⢠⣿⠄⣴⣿⡈⢙⣿⣷⣈⣿⣿⣷⠀⣴⢸⡏⢸⡇⠀⠀⠀⠀⡄⢠⡄⠀⢀⠀⠄⠀⢴⣷⣿⡧⢄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⢸⣿⡎⣹⣿⠇⠈⣿⣿⣿⣿⡏⢿⣎⠋⠈⣇⠸⠀⡶⠀⠀⠀⠀⢻⡁⢀⢈⠃⣤⣀⣰⣿⣧⣤⣄⡇
⠀⠀⠀⠀⠀⠀⠁⢠⣿⣿⣿⣾⣿⢾⣿⣿⢿⣿⠀⠀⡏⣿⣿⣿⡇⣸⣿⣶⣰⣈⡀⠀⠀⠀⠀⠀⢀⣾⠁⢺⣶⣘⡟⠋⠙⡿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠐⢄⣿⣿⣿⣏⣌⣿⠸⣿⠀⢩⡆⢰⣿⣿⣿⣽⣿⣿⣿⣿⣿⡿⠁⠀⣆⠀⠀⡀⢻⣿⣿⡎⠁⣍⢠⣶⢦⡞⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣿⠀⣿⠀⢸⡇⢸⣿⣿⣿⡿⢿⣿⣿⣿⡇⠀⠀⠀⢉⡈⠀⣠⣼⠻⣿⢁⣴⣾⣉⣳⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣟⣠⠗⢤⣸⣶⣹⣿⣿⣿⣿⣿⣿⡟⢁⣁⡀⠀⣠⠀⠉⠻⠛⠋⠑⠿⢟⣉⣤⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠉⠉⠉⠀⠀⠂⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⣀⡀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠈⠁⠀⠀⢀⣀⣀⡀⠀⠁⠪⠀⠀⠀⠀⠉⠢⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡤⣒⣚⠉⠁⠒⠀⠤⠀⢀⠁⠈⠑⠂⠄⣀⠀⠀⠃⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠀⠀⠀⠀⠀⠉⠀⠐⠠⢀⡀⠈⠐⠠⢀⠀⠀⠉⠂⠬⡀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠹⡦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠄⡀⠈⠒⢄⡀⠀⠈⠐⠤⡀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⡀⠹⣄⠁⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⢈⠐⠤⡀⠀⠈⠑⠄⡀⢂
⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⢀⠃⠀⠈⢦⡀⠀⠈⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠥⠢⣄⣀⣈⠊⠄
⠀⠀⠀⠀⢀⠎⠀⠀⠀⢀⠌⠀⠀⠀⡠⠙⠲⣄⡀⠀⠀⠈⠐⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠛⢉⠊⠄
⠀⠀⠀⢀⠎⠀⠀⠀⡠⠊⠀⠀⢀⠔⠁⠀⠀⠀⠙⠡⢐⡀⠠⠀⡀⠀⠈⠁⠐⠒⠀⠀⠀⣠⠤⠴⠒⠀⣩⡵⠟⠐⠉⠅⠈⠢⡀⠀⡀
⠀⢀⠠⠂⠀⠀⡠⠊⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⠁⠤⠀⠀⠀⠬⠠⠠⠔⡂⠛⠂⠀⠀⠐⠂⠉⡰
⠐⠁⣤⡤⠒⠁⣀⠠⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢲⠙⠅⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠏⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠀⠰⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢨⠐⠀⠀⠒⠉
⠀⠀⠌⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢡
⠀⠀⢄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠜
⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⠄⣀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⣀⠀⠄⠐⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⡿⠟⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡯⠀⠀⣀⣤⣴⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡀⣿⢿⣿⣋⣠⣶⣿⣿⣿⣿⢿⣏⠻⣿⡻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣶⣿⣿⣿⠁⣾⢿⣿⣯⣙⣶⣿⣓⣠⡴⣳⡁⠈⢹⡇
⠀⠀⠀⠀⠀⠀⢸⠟⡿⡿⠛⣻⣿⣥⣶⣶⣟⣷⣾⣿⣿⣿⡿⣿⣽⣿⣿⣿⣷⣒⣀⠀⡁
⠀⠀⠀⠀⠀⠀⠁⢀⣤⣾⣿⡿⣿⣿⣿⣟⣿⣞⣿⣟⣿⢿⣿⣾⣚⣿⢿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⣽⣿⣿⡟⢷⣿⣿⡽⣿⡛⠟⣿⢿⣿⣿⢸⠏⠿⢿⣿
⠀⠀⠀⠀⠀⣰⣿⣿⢏⢟⢱⣿⣿⣿⣟⢾⣿⣿⣿⠻⣏⠀⠈⢸⣿⣿⡗⠄⠀⠈⠁
⠀⠀⠀⠀⠀⡿⠙⠈⠂⠀⣾⣿⣿⡌⠚⠁⣿⣟⠦⠄⣿⡂⠀⠊⠙⠙⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⡝⠌⠀⠀⢻⣿⠦⠀⣸⡧⣾⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣠⣩⠴⣿⢿⡷⠉⠛⢿⡙⢿⣟⠉⠉⠲⢤⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣾⣿⣛⣟⣑⡉⠉⢺⣇⣤⣤⣤⡃⣘⣉⢡⣄⡒⢢⣝⣓⣾⣷⣦⣤⣶⣦⣤⣄
⠀⠀⠀⠀⠤⠤⢤⣀⣈⡠⠤⠀⠀⠘⠛⠛⠛⠲⢛⣿⢺⣗⠤⠄⢦⡄⠐⠛⠏⠬⠽⠾⡟⠛⣉⣉⣉⣁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠾⠛⠉⠉⠉⠀⠀⠀⠀⣾⡇⢰⡆⣿⡇⣸⣠⠎⠀⠒⣒⣲⣿⣭⣤⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡦⠿⠀⣺⢼⠙⢑⠿⣵⣹⡔⠀⠀⢉⣻⣿⣿⡿⠷⠶⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠔⠚⢿⡿⠿⠃⢠⣇⢾⡗⢯⠓⠬⢿⣿⣷⣶⣶⣿⣯⣥⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠑⠀⠠⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠈⢦⠁⢈⣀⠀⠄⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠈⠁⠈⠀⠀⠀⠂⢨⠀⢁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣬⠐⠀⠐⠀⠠⣢⢠⢁⠀⠀⠢⢠⡾⠀⠉⠠⠿⠇⠄⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠾⢮⡁⠁⠈⠉⠹⣘⠉⣀⡄⠀⠀⠆⠐⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠐⠁⠐⠋⠓⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣠⡇⢀⠶⣾⣤⣤⡿⡦⠀⡀⣾⣷⣴
⠀⠀⠀⠀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠉⠉⠀⠀⠁⠘⠚⠀⠀⠀⠀⠙⠀⠈⠁⠈⠋
⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠂
⠀⠀⠀⠂
⣀⣀⣀⣐⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣐⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⡟⠀⢠⣾⣿
⠀⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣵⣿⣿⣿
⠀⠀⠙⠻⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿
⣾⣿⣄⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠉⠉⣿⣿
⠛⠛⠋⠉⠀⠄⠀⠀⠻⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣘⣛⣲⣿⣿⣷
⠀⠉⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠙⠻⠛
⣶⣴⣶⣴⣦⣶⣤⣤⣼⣿⣿⡿⠿⠟⠻⠷⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠉⣋⠋⠛⠿⠛⣛⣉⣉⣉⡉⠁⠀⠀⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠄⠀⢀⣠⣴⣿⣿⣴⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠆⢀⣠⣦⣾⣿⣿⣿⣿⣿⡇⣻⣿⣿⠿⠛⠛⠛⠛⠿⠿⠿⠿
⣛⣿⣿⣿⣿⣿⣿⣿⣿⡵⠀⣠⠐⠃⣠⣶⣾⣷⣿⣿⣇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠃⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀
⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠋⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⠃⢀⢤⣤⣤⣀
⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⣹⣿⣿⣿⣿⣿⣿⣟⡛⠋⠙⠓⠀⠀⠛⠉⠉⠉⠁
⠺⠛⠟⠻⣿⢿⣿⠿⠿⣭⣏⢉⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣅⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⠟⠉⠹⣿⠟⣿⣿⣷⣦⡄⠁⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠹⢾⣇⣿⣤⣼⣿⣿⣉⠋⠉⠉⠀⠀⣈⣿⠁⠀⠙⠂⠉⠙⠒⠀⠀⠀⠀⢀⡐⢀⣇⠀⡀⠐⠚⠋⠁⠀⠀⠀⢸⠀⠈⠁⠀⠙⠷⣄⡀⣀⡀⠀⠀⣀⣨
⣤⣤⣄⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀⣺⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠹⣿⣎⡠⠤⠀⠀⠀⠀⠀⠀⣸⠀⠀⣀⣀⣀⣀⣈⣸⣯⣄⣀⣴⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⡟⠀⠀⠀⠀⠀⠀⠒⠒⢿⡄⠛⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿
⣤⣬⣥⣽⣿⣿⣿⣽⣿⣿⣿⣿⣥⣤⣤⣤⣽⣿⣿⣿⣯⣀⠀⠀⠴⠦⠤⠤⠀⠤⠤⣤⣴⣶⣾⡧⠤⢤⣤⠤⠤⠤⠤⠴⠾⠿⠀⠀⠀⠀⠀⠀⠟⠛⣷⠾⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣛⣉⣉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠶⣾⣿
⢿⣿⣿⠿⢿⣿⡿⠿⠁⠐⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⡶⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠒⠚⣃⣐⣒⠀⣀⣤⣤⣶⠶⠶⠖⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠖⠳⠴⠖⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠂⣀⠀⠀⠀⠄⠀⠢⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠐⠊⠉⠀⠐⡠⡀⠀⠀⠀⢀⠠⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⠤⠤⠐⠂⠀⠈⠒⠤⣁⡂⠄⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠄⢆⣒⣒⠰⡂⢸⠯⢓⠫⠝⠉⠢⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠏⡆⠀⠀⠀⠨⠄⠤⠀⠀⠀⠀⠀⣴⣥⠉⠉⠉⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⡠⠊⠱⡀⠀⠊⠉⠉⠉⠉⠁⠀⠀⡰⠁⠀⠓⠤⣄⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠉⠀⢀⠠⠛⠲⢤⡄⣀⣀⣀⠤⠐⠊⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠉⠀⢉⣠⠀⠀⠀⠀⠉⢓⣄⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠑⠦⠀⠀⠀⠀⠀⡀⠐⠉⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠆⠠⠤⠤⠄⠒⠈⠁⠐⠂⠀⠈⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠒⠒⠒⠒⠂⠐⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠓⠙⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣭⠭⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠭⠕

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠻





⠀⠀⠀⠀⡀
⣷⣶⣶⣶⣧⣶⣦⣤⣤⣾⣤⣀⢀⣦⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⢀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣤⣾⣷⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣒⠒⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠉⠁⠀⠀⠀⢰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠛⠻⠉⠃⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠫⠃⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠟⢻⡍⠉⠀⣈⠀⠀⢀⠀⠀⢀⠁⠤⠀⠐⠠⠀⠀⠠⠀⠀⠀⠀⠈⠀⠈⣁⢤⣴⣿⣿⣿⣿⣿⣿⣿⢿
⠛⠁⠀⠀⠀⡤⠆⠀⠩⡗⢂⣀⠀⠀⠐⡀⠀⣀⠃⢀⡀⠀⠀⡀⠀⠀⠀⠀⠙⠀⠛⠉⣻⣿⣿⣿⣿⣿⣿
⢈⡃⠀⠀⠈⡀⠒⠋⠀⠐⠞⠉⣀⡠⠀⠁⠀⠀⢠⡄⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣶⣿⣿⣿⣿⣿

⠀⠀⢀⡠⣤⢤⠀⠰⠞⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⡀
⢼⣴⡋⠀⠀⠀⠀⠀⠀⠀⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣹⣶⣤⡀⠷⣦⣄⡀⠀⠄
⠀⠀⠧⠲⣴⣦⣷⣶⣿⣲⣿⣦⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠛⠉⠛⢾⣿⣷⣦⣗⡴⢛⡏
⠀⠀⠀⠀⢹⣧⣾⣯⣾⣿⢿⣿⣥⡈⢿⠆⠀⠀⠀⠀⠀⠀⠀⠘⠛⢦⣤⣤⣤⣾⣿⣿⣽⣿⣃⡞⠃
⠀⠀⠀⠀⠸⣿⢿⣿⠛⢩⠟⠋⠀⠉⢻⡇⠀⠀⠀⠀⠀⠀⢠⡷⠂⠀⣀⡀⢺⣹⣷⣾⡿⡟⠿⢀
⠀⠀⠀⠀⠀⣽⢺⣿⠧⣤⣤⡤⠔⠁⠀⢷⠀⠀⠀⠀⠀⠀⢁⣤⡾⠋⠈⠉⠛⢿⣬⣬⣿⣶⡤⠈
⠀⠀⠀⠀⠀⣿⣼⡿⣍⣿⠁⠀⠀⣀⢤⢺⡄⠀⠀⠀⠀⢠⠞⡟⠀⠀⠀⠀⠀⠀⠀⠀⣱⢣
⠀⠀⠀⢴⠒⡟⠛⡿⠛⡇⠒⡖⠉⠢⠉⡼⠁⠀⠀⠀⠀⠀⣸⡷⠄⠀⠀⠂⠀⠃⠈⠀⣧⡯
⠀⠀⣠⣼⠤⠄⢀⣁⠀⠁⠀⠃⠀⢀⣶⠃⠀⠀⠀⠀⠀⡼⢹⣇⠀⢀⢀⣀⣤⣤⣤⣴⣸⣤⣀
⠀⠀⠹⢦⡄⠀⠀⠀⠉⠛⠂⠚⠃⠈⠁⠀⠀⠀⠀⠀⠀⠁⢠⠟⠚⠋⠉⠀⠀⠠⢶⡶⠶⠆⠈
⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⡠⣶⠀⠀⠀⠀⠀⠀⣄
⠀⠀⣹⢃⡀⠀⡄⠀⠀⣰⠏⠀⣠⣾⣿⡿⠇⠀⠀⠀⠀⠀⣿⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠
⠀⠀⠿⣆⡻⣄⡀⠀⣠⠀⡠⠊⠁⠈⢩⠃⠀⠀⠀⠀⠀⠀⡜⣇⠙⢢⣄⠀⠀⠀⢀⠀⣀⡤⠒⠈⠁⠜⠃
⠀⠀⠀⠸⠛⣻⠏⠉⢻⣯⣄⣀⣤⠞⢟⠁⠀⠀⠀⠀⠀⠀⠘⠈⠷⢮⣿⣿⠁⠀⢻⡿⠿⠀⠀⠀⢁
⠀⠀⠘⣅⠀⠀⠀⠀⠀⠙⠈⢁⡀⠐⠾⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⠀⠀⠀⠀⠈⠈
⠀⠀⠀⢸⡟⠶⠦⠄⠴⠒⠚⠉⠻⡗⢤⡀⠀⠀⠀⠀⠀⠞⢡⣯⠉⠛⢢⢄⣀⣀⣤⠴⡶⠓⣻⠄⠄
⠀⠀⠀⢰⡿⠄⠠⢀⡀⢀⠀⡀⠀⢸⡎⢇⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⡰⡇
⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠈⠀⠀⢩⡇⠈⠀⠀⠀⠀⠀⠀⠀⠠⣰⠃⠁⠀⠀⠐⠂⠀⠚⣇⢣
⠀⠀⢯⡉⠘⠒⠲⢤⡀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣇⣤⣠⣤⢤⣤⣄⣤⣀⣈⡄
⠀⠀⠀⠃⠀⠶⠂⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠄⣤⡶⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠉⢿⣿⠷⠂⠀⠀⠂⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢻⣟⡒⠀⠀⠀⠀⠈⣶⣮⡖⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⣾⠟⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠆⠀⠀⠀⣴⡏⠔
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠧⠟⠟⠠⠤⢀⣠⡟⢸
⠀⠀⠀⠀⠀⠂⠤⠄⠀⠀⢄⣀⡬⠀⢀⡀⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠑⢮⡝⠛⠂⡬⢍⣀⠒⠂⠓⠀⠒⠒⠒⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠑⠤⠞⣷⠄⠀⠃⠈⡄⠀⠀⠉⠐⠖⠂⠀⠤⠌
⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠻⡄⠀⠀⠀⠀⠀⢝⠂
⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⢀⠔⠂⠋⠈⠉⠁⠀⢰⢠⠀⠀⠀⠀⠀⠀⣄⠰⠄
⠀⠀⠀⠀⠘⢦⣀⡤⠄⡊⠐⠚⠓⠠⣀⠀⠀⠀⠀⠻⣷⠧⠲⡀⠀⢝⢆⢠
⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠈⠑⢦⣄⡰⠀⢀⣠⠜⠳⠶⣨⡰⠂
⠀⠀⠀⠀⠀⠀⠘⠥⣀⣀⡀⠀⠀⠀⠀⢀⣀⠠⡄⢒⣃⢔⡳⠎⠙⠣⡸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡯⡨⠭⠀⢷⣴⣿⠡⠞⠋⠁⠀⠀⢢⠑⣜⠂⢰⠒⣁⣈⠉⠉⡐⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢁⠀⠀⡜⢩⣅⡴⠊⠀⠷⡀⠀⠀⠱⡘⠓⡉⠁⠀⠈⠶⠉⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⢠⠁⢨⠁⠀⠀⢀⡼⠂⠀⠀⠀⢸⠀⠉⠢⡀⠀⠗⡶⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⢀⠇⠈⡗⠈⡄⠀⢠⠊⠀⠀⠀⠀⠐⠁⠀⠀⢀⠃⢸⡶⠧⢴⡞⠁⢜⠖⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠆⡀⠀⠀⠀⠀⠀⣽⠀⢄⠈⢇⠙⡄⠈⠑⠤⣀⠀⣀⠀⠀⠀⠀⠎⠀⠀⠓⠂⠉⠀⠙⠆⡠⠂⢐⡒⢊
⠀⠀⠀⠀⠀⠀⢁⠈⠆⠀⢲⣶⣾⣿⣿⠏⢰⣎⢆⣡⠀⠀⠀⠀⠀⡙⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣼⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠂⢸⡆⠘⣍⣉⢭⣏⣤⣿⣿⡟⣘⠀⠀⠀⠀⢸⣔⣶⠖⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠸⡁⠸⣿⣤⠁⠈⠙⡿⠟⠻⢻⠯⣾⣽⣿⣿⣿⣿⣿⡶⣤⠀⠀⠀⠀⠀⠀⣠⠄⠐⠖⠀⡲⠠⢴⠞⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠑⣘⣶⠁⠠⡞⠋⠀⢠⠇⢾⠀⠀⣉⣟⠛⠿⠿⣿⣿⣿⡀⢀⣀⡀⣴⠅⠒⠒⠲⢄⡘⠀⢀⣘⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠝⢧⠀⠀⠀⠀⠀⠀⠼⠋⡩⠿⠬⢷⣆⢀⠀⠀⢀⡽⠎⢭⠎⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠚⠊⠁⠀⣀⡀⠰⠿⠭⠒⠪⢍⠉⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠐⠀⠁