Sense organ Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠤⠀⠸⠠⠤⠤⠀⠀⠴⠀⠢⠠⠄⠠


⠀⠀⠀⢀⠤⣄
⠀⢰⠁⢹⠀⢸⠒⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣊⢉⣁⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠐⡀
⡤⢸⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⢋⣀⣀⠀⠉⢆⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢇
⡇⢸⠀⢸⠀⢸⠀⢸⠒⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠉⡆⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸
⡇⠘⠀⠈⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⡰⢃⠇⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⢇
⡇⠀⠀⠀⠀⠀⡠⠊⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢰⠁⠎⡰⠁⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠳
⢇⠀⠀⠀⠀⠀⠁⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠈⠢⣀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠠⢄⡀⠀⠀⢀⡠⠤⣀
⠀⠀⠀⠉⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁⠈⠁⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⣤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠂⠤⠔⠒⠤⢄⡀
⠀⠀⠀⠀⢀⡠⠒⢹⢁⠖⠉⠉⢢⠈⡆⠀⠉⠲⢄⠀⠀⠀⠀⠀⠀⠀⠠⣶⠮⢥⠤⠤⠤⠤⣀⠤⠤⠤⠤⡬⠭⣶⠆
⠀⠀⠀⠠⡋⠀⠀⢸⡘⢄⠀⢀⡸⢀⠇⠀⠀⠀⣀⠝⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠀⠀⠀⠀⢸⠀⠀⠀⠀⡟⠉
⠀⠀⠀⠀⠈⠑⠢⢄⣑⠢⠭⠭⠔⠋⣀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠔⠊⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⢀⠉⠙⢦⡀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠉⠙⠦⡀⠀⠀⠀⠀⣠⠞⠉⠁⠀⠀⠈⠙⠲⣄
⠀⠀⠀⢠⠎⠀⠀⠀⠀⡅⠀⠑⡀⠀⠹⡄⠀⢀⡞⠀⠀⣀⠤⣀⡠⢄⡀⠀⠙⡆⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⢻⠀⢼⠀⠀⢊⣡⣤⣀⣠⢄⡘⠀⠀⢹⠀⢸⠃⠀⢠⠂⠀⠀⠀⠀⠰⡀⠀⢸⡆
⠀⠀⠀⢻⠀⠀⠀⢀⠀⡀⠆⢀⠂⠀⠀⡾⠀⢸⡀⠈⠀⠀⠀⠉⠁⠀⠈⠉⠀⣼⠀⠸⡆⠀⠘⠀⠃⠀⠀⠉⠐⠁⠀⢸⠃
⠀⠀⠀⠈⢧⡀⠀⠀⠐⢀⠠⠃⠀⢀⡴⠃⠀⠀⢣⡀⠀⠈⠉⠉⠉⠉⠀⠀⡴⠃⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠙⠢⢤⣉⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⣀⣠⠴⠊⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣠⠤⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠁⠀⠀⠈⠉⠓⢄⠀⠀⠀⠀⠀⣠⠖⠩⠍⠀⠀⠉⠙⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢀⠀⣤⣀⣤⣤⣀⠀⠈⢳⡀⠀⠀⡜⠁⠁⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⣾⣿⠟⡿⢩⡍⢻⢧⠀⠀⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠹⢦⣘⣮⡥⠊⠀⠁⢀⡇⠀⢸⡄⠀⠀⡀⠀⢀⡄⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠳⡀⠈⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⣀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣉⡁⠄⢐⢰⡄⠄⠀⡂⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠉⣿⣷⠀⢎⠠⢰⠄⡴⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣀⡞⠛⢳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⣀⢰⡏⠉⡇⠀⢸⡋⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠉⠉⠉⠙⠲⣄
⣾⠉⢹⡇⠀⡇⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣴⠞⠛⠛⠛⠶⡄⠈⢷
⣿⠀⢸⡇⠀⡇⠀⢸⡇⠀⣇⡴⠲⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⣇⡀⠀⠀⠀⠀⢹⠀⢸
⣟⠀⢸⠇⠀⡇⠀⢸⠇⠀⣿⠃⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣧⠀⠀⠀⠈⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⣼
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢰⠀⠐⠒⠚⠃⠀⠀⠀⠀⣴⠃
⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢸⡃⢀⡤⠶⣤⡀⠀⠀⣀⡴⠦⣄⠀⢸⡆⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠈⢳⣄⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⣤⠴⠈⠓⠶⠖⠋⠐⢦⣬⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣤⠤⠶⠛⠁
⠀⠀⠉⠓⠶⠶⠶⠶⠞⠋



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠦⣤⣀⢀⣤⠴⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⡿⠛⠉⠀⠀⠀⠉⠻⣿⠶⣄
⠀⠀⠀⢀⣠⣴⠚⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠙⢳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣾⠁⠀⠀⣠⣤⠀⠀⠀⠈⣧⠈⠛⢦⡀
⠀⠀⠀⠈⠻⣍⡉⠉⠛⠛⠛⠛⠒⠒⠒⠚⠛⠛⠛⠋⠉⢉⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⣇⠀⠀⠸⣿⣿⣷⠆⠀⠀⣽⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⣀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⢻⡄⠀⠀⠉⠉⠁⠀⠀⢠⠏⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠿⣦⣄⣀⣀⣀⣠⣶⠿⠚⠁
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣠⠖⠛⠉⠉⠉⠛⠲⣄⡀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠉⠙⠓⢦⡀⠀⠀⠀⠀⠀⢀⣠⠖⠛⠉⠉⠉⠛⠲⣄⡀
⠀⠀⠀⠀⣠⠎⠀⠀⠀⠤⠠⢍⢢⠀⠀⠹⣄⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⢠⡏⠀⠀⠀⠀⠄⠁⠀⠅⠃⠀⠀⢹⡄⠀⡾⠀⠀⡠⠒⠉⠑⠊⠉⠓⢄⠀⠈⣇⠀⢠⡏⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⢹⡄
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⡂⠀⡘⠀⠀⢀⡇⠀⡇⠀⠠⠔⠖⠯⠷⠾⠭⠶⠤⠀⠀⣿⠀⢸⡀⠀⠰⡇⣠⡀⠀⢀⣄⢘⠆⠀⢀⡇
⠀⠀⠀⠈⣇⠀⠀⠀⠂⠀⡐⠁⡠⠃⠀⠀⣸⠁⠀⢻⡀⠀⠀⠠⠤⡤⠤⠤⠤⠀⠀⢠⠇⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠘⢦⡀⠀⠀⣀⠠⠚⠁⠀⢀⡴⠃⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣤⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣤⣤⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣤⡤⠴⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠈⠉⠲⣄⠀⠀⠀⠀⠀⢀⡴⠚⠩⠅⠀⠀⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⢠⣀⣀⣀⣀⠀⠀⠈⢳⡀⠀⠀⢠⠏⠐⠀⠀⠀⠀⠀⠁⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⣤⣿⣿⢿⡟⣛⠛⡿⡆⠀⠈⡇⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠹⣄⠘⢄⣛⣡⠇⠈⠂⠀⡟⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⣸⠃⠀⠀⢻⡀⠀⠐⠁⠀⠈⠁⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠲⠖⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠶⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣤⡀⢊⢸⡁⠧⠐⠈⢸⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⢈⣿⣿⠀⠸⠀⠀⠧⠨⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⢠⠀⢀⡀⠀⢀⠄⢠⠀⣀⢀⢀⠄⢠⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠘⠀⠋⠐⠃⠀⠀⠃⠘⠀⠋⠛⠐⠃⠚⠀⠘⠂

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠖⠓⠲⢤⡤⡤⡖⠒⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⡴⠊⠀⣠⣠⣤⣴⣶⣿⣷⣿⣷⣆⣤⣀⣆⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⣶⣾⣿⠿⠿⠿⣿⣿⣿⣶⣄⠀⠐⣄
⠀⠀⠀⠀⢠⢧⣤⣴⣾⣷⣶⣶⣬⣥⣥⣥⣬⣬⣥⣶⣶⣿⣷⣦⣄⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠟⠋⢠⡆⠀⢀⣼⣿⣿⣿⣿⡿⣿⣿⣷⡄
⠀⠀⠀⠀⢸⣸⣿⣿⣿⠉⠀⠀⠈⠹⢩⣯⡏⠉⠁⠀⠀⠈⣿⣿⣿⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⣋⣴⡟⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢨⣿⣿⠻⠆
⠀⠀⠀⠀⠈⠻⣽⣿⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢺⣹⣿⢿⣷⣄⣀⠀⠙⢿⣿⣿⣿⣿⠿⠃⣠⢎⣿⠇
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠭⢭⣷⣦⣈⣉⣉⣀⣀⣩⠶⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠉⠉⠉⠉⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠐⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠑⠈⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠓⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠃⠻⠆⠨
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣰⣶⣾⢿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡶⠄⠠⢶⣾⠂
⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⢀⣾⣿⣿⣇⡸⣿⠿⠀⡀⠀⠀⠀⠀⠀⠆⠰⠆⠰⠋⠈⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡏
⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⢀⣾⣋⡉⠻⣏⠠⢻⠈⡅⡇⠀⠀⠀⠀⠀⡀⣀⠀⠈⠀⢀⡆⠀⢠⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠘⢠⣴⣶⣶⡟⠉⣩⠛⠄⠈⠀⠈⠀⠀⠁⠀⠀⠀⠀⠈⠁⠸⠂⠚⠉⠈⠉⠙⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⢀⠀⠈⣷⡄⠉⣋⠄⠀⠀⡆⠀⣀⠆⠄⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠘⠀⣾⣿⣷⡿⠋⠀⠀⡠⠀⢠⠏⡘⠀⠀⠀⠀⠀⠀⡆⠀⠀⠐⠀⠀⠀⠀⠸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡆⠀⠉⢁⠀⠑⠶⠐⠊⢠⠶⠃⠊⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠀⠀⠀⠀⠀⠀⠈⣷⣄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠊⢀⡠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢀⣴⡟⠉⢹⡄
⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠰⠀⣀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⢹⣴⣶⣾⣶⡄⠠⣤⣿⣿⣿⣷⣼⠃
⠀⠀⠀⠀⠀⠀⠄⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⣴⠿⢶⠶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⣻⡿⠿⠧⣼⣿⠿⠿⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⠀⡀⢠⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠉⠈⠈⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠈⠁⠁⠈

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡏⢳⡀⠀⢀⡴⡄
⠀⠀⠀⠀⠀⠀⢸⠈⣦⠀⠸⡇⠈⡇⠀⣸⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡀⢸⡄⠀⡇⠀⡇⢀⡇⠀⡏⢠⢤
⠀⠀⠀⠀⠀⠀⠀⣧⠀⣇⢰⡇⠀⡇⡼⠀⡼⢡⠏⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⣚⣻⣯⣭⣟⣒⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠘⠾⠀⠀⠉⠁⠀⡧⠏⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⡟⢁⣤⡀⠈⢣⠈⠙⠻⢦⡀
⠀⠀⢀⡤⢤⡀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣅⣀⠀⢧⡈⠻⠟⢀⡼⢀⣠⠴⠋
⠀⠀⠈⢧⡀⠙⢦⣀⡗⢦⡤⣄⣀⠙⠲⢤⣄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠒⠚⠛⠋⠉
⠀⠀⠀⠀⠳⡄⠀⠉⠀⠀⠙⢦⠈⠙⢦⠀⠀⣸
⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣄⡤⣤⣠⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢉⣉⣉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢠⡞⠉⠁⠈⠙⢲⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡘⢦⡀⠀⠀⠀⡇⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⠀⠀⣰⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⣴⠃⢀⣀⡼⠀⣰⠃⣸⠁
⠀⠄⠀⠀⢀⡠⠖⠋⠉⠉⠓⠚⠉⠉⠓⠢⣄⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⢀⣀⣠⣤⡀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⢼⡴⠋⠁⠀⡴⠃⡴⠃
⠀⠀⠀⢠⣯⠤⠤⠴⠒⠒⠶⠖⠒⠒⠶⠤⠬⣵⠄⠀⠀⠀⠀⠀⠉⠓⠒⠂⠈⠀⠈⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠙⠲⢤⣀⡀⠀⠀⠀⠀⢀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡀⢀⣀⣀⣀⣐⡹⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⡴⢾⡟⢻⣿⣿⣿⠻⣿⣯⣷⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⠣⢀⠀⠀⡄⠀⣄⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠸⣿⣿⣿⣿⠏⢀⣤⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢀⣀⠈⠀⠀⠀⢀⣀⢹⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠩⠛⠓⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠙⠓⠒⠀⠁⠘⠋⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⣀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢘⠀⠃⡅⠈⠀⠓⡄⢇⠘⠀⠢⠀⠀⠀⠀⠀⠄⠀⠀⢀⡴⢉⡤⠤⣍⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢰⠋⠄⠁⠈⢧⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⡐⠘⠂⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⡆⢀⡀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⣒⡒⣒⡲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠱⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣾⣿⣭⣽⣭⡽⣿⣾⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⣠⠏⣀⠀⠀⡴⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡹⣿⠅⠀⠀⠉⠁⠀⠠⢽⡿⡹⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠊⣠⠞⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣹⡀⠀⠀⠀⠀⠀⠀⣸⣱⠃⠀⠀⠀⠀⠀⠀⠀⠸⣇⡤⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⢀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⣠⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠶⢦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⣋⣡⣤⣤⣤⣤⣤⣀⠉⢻⡳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⣤⣤⣿⣿⣯⡶⢻⡍⢿⣿⣿⣿⢁⡇⠀⠉⠓⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠉⠉⠙⢦⡑⢄⡻⢦⣉⣉⣥⠞⠁⠀⠀⣀⣠⠽⠶⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢭⣓⡒⠲⠖⠒⣒⣋⡭⠟⠒⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡚⠷⢦⣄⠀⠀⢸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠺⠤⠴⠟⠁
⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠈⠛⢦
⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠉⠑⠢⠄⠒⠋⠉⠑
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⢰⣤⣦⣤⣤⣤⣄⡠⠤⠴⠶⢶⣶⣤⣤⣴⣶⣶⣤⣤⣤⣤⣀⣈⣲⣤⣤
⠀⠀⠀⠀⠀⠀⠱⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢈⡩⠛⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠦⠤⠤⠴⠶⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣠⠞⠢⡄⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠐⣝⠀⢩⢢⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠨⠨⠀⠀⣧⢠⠀⠀⠠⣊⠅⠶⣲⡦⢅⠢⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⣀⣔⠈⠒⠂⢁⣢⣀⠀⠀⠀⠀⠑⠍⢀⣠⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢐⠀⠀⠀⢁⠂⠀⠀⠘⠄⡀⠞⡻⠆⡀⠜⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠙⢄⠈⢁⡈⠁⡠⠋⠀⠀⠀⠰⠈⠁⣸⠆⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⠆⠀⠀⠎⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠂⠌⠒⠊⠀⠀⠀⠀⠀⠁⠂⠐⠉⠀⠀⠀⠀⠀⠠⣐⣢⠎⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠉⠉⠉⠀⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⡴⢤⠤⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠘⠀⠠⣙⡋⠄⠀⠁⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠐⢄
⠀⠀⡠⠔⠒⠀⠀⠒⠠⡀⠊⠀⠀⠀⠀⠈⠑⠠⠀⡀⠀⠤⠒⠁⠀⠀⠀⠀⠈⠂⢀⠄⠒⠀⠀⠒⠢⢄
⢀⠊⠀⠀⢂⠨⠀⠢⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠉⠀⠀⠀⠀⠀⠑
⡄⠀⠀⠀⠖⠀⠀⠁⠃⠀⠀⠃⠀⠀⠀⠀⠀⣀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠃⠂⠠⠄
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠆⢀⢡⡘⠰⠂⠀⠀⠀⠀⠀⢀
⠐⠄⠀⠀⢄⢀⡠⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠈⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⢂⠀⠈⢄
⠀⠈⠒⠄⣀⠀⢀⡀⠤⠊⠀⠀⠀⠀⡖⠂⡖⢠⡄⠀⡔⠂⣐⠂⡖⠆⠀⠀⠀⠀⠑⠤⢀⡈⠉⣁⠠⠒⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢌⠇⢍⠸⠈⠆⢌⡅⢭⡁⠌⠇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠁⠀⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⡈⠀⢁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠈⠀⠈⢉⠈⠁⡋⠁⢘⠉⠀⠈⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠰⠀⠀⠀⢂⠀⠀⢀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⡀⠀⢐⠀⠀⠀⠀⠀⠄⠀⠰
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠐⠐⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠐⢄⠀⠈⠑⠀⠊⠀⠀⡠⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣥⣦⣤⣤⣴⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣦⣥⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣬⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄⣀⡀
⠀⠀⠀⢀⣤⠖⣻⠟⠉⣀⣀⡈⠙⢿⡛⢦⣄⠀⠀⠀⠀⠀⢀⡴⠖⠛⠉⠙⠳⡴⠛⠉⠙⠓⠶⣄⡀
⠀⢀⡴⠋⠀⢠⡏⠀⣾⠉⠉⠙⡆⠀⣷⠀⠈⠳⣄⠀⣀⣼⣋⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⣀⣈⣻⣄⡀
⠀⠀⠙⢦⡀⠘⣇⠀⠻⣄⣀⡴⠃⢀⡿⠀⣠⡾⠋⠀⠀⢿⡀⠀⢹⡅⠀⠈⠙⡟⠉⠀⠀⢹⠁⠀⢨⡏
⠀⠀⠀⠀⠙⠳⢾⣷⣄⣀⣁⣀⣤⣾⠵⠛⠁⠀⠀⠀⠀⠈⠛⠦⢼⡇⠀⠀⠀⡇⠀⠀⠀⢸⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠁⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠚⠛⠉
⠀⠀⠀⠀⢀⣠⣤⠤⣤⣀⡀⠀⠀⠀⠀⠀⣠⡤⣼⠋⢳⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⡾⠋⣀⣤⠤⣤⡈⠙⢦⠀⠀⠀⠀⣿⠀⣿⠀⢸⠀⢸⣤⣀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⡟⠀⡾⠁⠀⠀⠀⠙⣦⠈⣧⠀⠀⠀⣿⠀⣿⠀⢸⠀⢸⠁⢸⡇⠀⠀⠀⠀⢰⠏
⠀⠈⠃⠈⠛⠲⣄⠀⠀⠀⣿⠀⣿⠀⣴⠛⣿⠀⣿⠀⢸⠀⢸⠀⢸⡇⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠘⡇⠀⣼⠃⣰⠇⠀⣿⠀⣿⠀⠻⠀⠸⠀⠸⠀⢸⡇⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⣰⠃⣰⠃⢰⠏⠀⠀⣿⠀⢿⣤⣀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡞⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠒⠛⠁⣰⠏⢠⡏⠀⠀⠀⣿⠀⠀⠀⠉⠳⡄⠀⠀⠀⢸⠇⢀⡾⠀⠀⠀⠀⠀⠀⠈⠉⢳⡄
⠀⠐⣇⠀⠀⠀⠀⠈⢠⡟⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢻⠀⠀⢀⡞⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠙⢦⣄⣀⣀⡴⠟⠀⠀⠀⠀⠀⠀⠘⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠈⠷⣄⣀⣀⣤⠴⣶⣦⣤⠞⠁
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⠠⡴⠒⠀⠉⠀⠒⢦⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⢀⣀⡀
⠀⠀⠀⢀⡠⠐⠉⠀⠈⠀⡐⠉⡐⠹⡆⠀⢡⠀⠉⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠉⠀⠀⠈⠒⠁⠀⠀⠁⠒⠠⢀
⠀⠀⢐⠁⠀⠀⠀⠀⠃⠀⢪⣍⠀⡠⡧⠀⠨⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠀⠀⢠⣂⡥⠀⠠⠄⢀⠠⠤⢤⣄⡤⠤⢄⡀⠠⠄⠀⢈⣀⡄
⠀⠀⠀⠉⠃⠄⡀⠀⠈⠢⡀⠉⠉⠉⢀⠐⠁⠀⢀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣀⠉⠉⡃⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⡀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⢀⠁⠀⠈⡁⠤⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢧⠀⠀⠀⠀⠀⠀⠀⠤⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⣀⡀⠄⠊
⠀⠀⠀⠀⡀⠤⠤⠤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄
⠀⠀⡠⠈⢀⠤⠀⠀⠤⡀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⠀⢹⠀⠈⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠂⢄
⠀⠠⠀⣔⠀⡀⠀⠀⠀⠀⠢⠀⠡⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⢂
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠆
⠀⢀⠀⢂⠀⠀⠀⠀⠀⢀⠔⠀⠌⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⠈⠀⠀⠀⣧⠌⠀⠇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠈⠀⠀⢂⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠊⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⢀⠌⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⢠⠀⡁⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠒⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠂⡀⠀⠀⠀⠀⠀⢀⡄⠂⠀⢠⠁
⠀⠀⠢⠀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠐⠠⠤⠤⠐⠈⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⢹
⠀⠀⠀⠀⠀⠀⠀⢠⠊⢢⠀⠀⠀⡇⠀⢸⡄⠀⠀⢀⠔⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢇⠀⠀⡇⠀⠈⡇⠀⠀⡞⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⢀⣰⣶⡿⠛⠉⠈⢹⣿⣿⡇⠉⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠸⡀⠀⡇⠀⠀⡇⠀⢠⠃⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠈⠳⠼⠟⠁⠀⠀⢹⠄
⠀⠀⢠⠖⠢⠀⠀⠀⠰⠀⠀⢱⠀⡇⠀⠀⡇⠀⡎⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠘⠳⣦⣄⣀⣀⣀⣀⣀⣀⣠⠴⠶⠚
⠀⠀⠈⣆⠀⠡⡀⠀⠀⠀⠀⠸⡆⡇⠀⠀⡇⡸⠉⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠈⢧⠀⠈⠢⡀⢠⠄⠀⠓⠛⠀⠀⠓⠁⠀⢰⠃⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠠⠄⡀
⠀⠀⠀⠀⠈⢳⡀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠆⠤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⣠⡶⠒⠒⢦⣌⠂
⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠃⠀⠀⢀⡏⠈⢳
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠐⡀⠀⡔⠀⠀⠀⠀⠘⣦⣀⠤⠴⠊⠀⠀⠀⠑⠀⠀⠀⠀⢀⠤⠄⠤⠤⠒⠤⣀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠀⠀⢀⠜⠁⢀⣀⢄⡀⢄⡀⠀⠑⠄⠀⠀⢣⡀⠀⠀⠀⠀⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⢀⠊⢀⣴⣯⣤⣤⣧⣤⣬⣶⣄⠀⠀⠀⠀⠙⢦⡀⠀⠀⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠋⠉⠉⠙⠋⠉⠉⠙⠻⣷⠄⠀⠀⠀⠀⠙⢦⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠩⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠃⢀⣀⡀⠀⡀⠀⣀⡀⠄⠁⢠⠀⠀⠀⠀⠀⠀⠓⠤⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠁⠀⠁⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⣤⣤⡤⠤⠖⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡏⠉⠛⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣀⠴⠒⣚⡓⠒⠤⡀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢱⠀⠀⠀⣀⡀
⠀⠀⢀⡜⡡⠚⣉⠁⠈⠉⠲⡌⡆⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⣴⠛⣆⠀⠀⠀⡇⠀⠘⡇⠀⢸⠁⠘⡆
⠀⠀⡞⠘⢁⠞⠁⡀⠀⠀⢠⠇⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⡀⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⡇
⠀⠀⡇⠀⡞⡴⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢧⠀⠀⣷⠀⠀⣧⠀⡟⠀⠀⡇⠀⠀⡤⢤
⠀⠀⢹⠀⢹⡳⡀⠀⠀⡆⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠘⡆⠀⢹⠀⠀⢸⠀⡇⠀⠀⡇⠀⢸⠁⠸⠂
⠀⠀⠘⡆⠀⠑⠈⠙⠢⠽⠂⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢧⠀⠀⢳⠀⢸⠀⠀⢸⠀⡇⠀⠀⡇⠀⣸⠀⢸
⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⢠⢾⠁⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢸⡀⠀⠸⡆⠸⡄⠀⢸⠀⡇⠀⠀⡇⢀⡇⠀⣸
⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⡠⠀⠀⠸⡌⢦⡀⠀⠠⠖⠒⠲⠤⢀⡇⠀⠀⣇⠀⠀⢣⠀⡇⠀⠸⣄⡇⠀⠀⡇⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢹⠀⠀⠈⠛⠁⠀⠀⠉⠀⠀⠀⢧⠞⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠲⠤⣀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢀⠴⠚⠉⠉⠑⠒⠉⠉⠉⠲⢤⡀⠀⠘⢆⠀⠀⠈⠑⢄⠀⠀⠀⠈⡇⠠⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠠⠵⠒⠒⠛⠒⠲⠤⠖⠚⠛⠒⠒⠥⠀⠀⠀⠑⢦⡀⠀⠈⢧⠀⠀⢸⠃⠀⠒⢄⡀⠉⠉⠒⠢⢤⣀⠀⠀⠀⢸
⠀⠀⠀⠙⠒⠦⠤⠤⠤⠤⠤⠤⠤⠔⠚⠁⠀⠀⠀⠀⠀⠙⡄⠀⠀⠑⠒⠋⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⠤⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠊⠁⣀⡤⠴⠒⠚⠋⠉⠉⠉⠉⠉⠉⠓⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡸
⠀⠀⠐⠚⠉⠁⢀⡤⠖⣒⣒⡒⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⢞⡥⢚⠍⣩⠍⠉⡍⠒⢬⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠡⣄⣈⢧⣈⣋⣰⣃⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢳
⠀⠀⠀⠀⠀⡠⠒⣄⠀⠀⢸⠁⠀⢸⡆⠀⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⢇⠀⠸⡄⠀⠈⡇⠀⠀⡇⠀⠀⢸⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢀⣤⣶⡶⠞⠛⠛⢿⣿⣿⡍⠳⣄
⠀⠀⠀⠀⠀⠸⠄⠀⢣⠀⠀⡇⠀⠀⡇⠀⠀⡎⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⣿⠟⠉⠀⠀⠀⢶⣏⣿⡿⠃⠀⠈⢷
⣀⢀⠀⠀⠀⠀⡇⠀⠘⡆⠀⡇⠀⠀⣿⠀⢸⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠈⠁⠀⠀⠀⣀⣌⡡
⣇⠀⠱⡀⠀⠀⢰⠀⠀⢹⠀⡇⠀⠀⡿⢀⡯⠄⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠖⠶⠶⠖⠒⠚⠋⠉
⠘⣆⠀⠑⢄⠀⠀⡆⠀⠈⣇⣧⠀⠀⣇⡼⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠈⢧⡀⠀⠑⢄⠔⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠉⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⣉⣀⣉⠑⠢⡀
⠀⠀⠈⠳⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⡁⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⢾⠋⠀⠉⡹⠦⡈
⠀⠀⠀⠀⠹⡆⠀⣀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⢰⠁⠀⠙⡄
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠸⡀⠀⠀⠀⠀⡀⠤⠄⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠄⢀⠞⠀⠀⠀⠀⠀⠱⠦⠄⠒⠋⠀⠀⠀⠀⢈⠀⠀⠀⠀⡠⠔⠂⠐⠒⠋⠓⠢⣄⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠂⠈⠁⠀⠀⢠⠎⠀⣀⠤⠤⠤⠤⢄⠀⠈⠑⡀⠀⠈⢣⡀⠀⠀⠀⠀⢀⡣
⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠰⠃⢀⣴⣷⣤⣤⣿⣦⣴⣿⣦⣄⠀⠀⠀⠀⠙⢦⡀⠀⠀⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠙⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡟⠉⠉⠉⠉⠋⠉⠉⠉⠙⣿⡷⠄⠀⠀⠀⠀⠙⢦⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠓⢄⡀⣀⠠⢀⠀⢀⣀⠤⠋⠀⡄⠀⠀⠀⠀⠀⠀⠓⠤⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠉⠀⠉⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣤⣀⣀⣀⣤⠤⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣛⢒⢖⡶⢛⠟⠛⠟⡻⠟⣻⠟⢛⡿⢛⡻⠛⠻⢳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢈⠹⣳⠚⠒⠛⠚⠓⠚⠓⠛⠓⠒⠛⠒⠛⠒⠛⠒⠛⠛⠛⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠪⡢⣑⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠯⠢⡙⢼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⡱⡜⣾⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⡑⡕⣌⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⣷⡜⢼⠃⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠘⡜⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⣸⢅⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⡌⢜⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠿⢿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡝⣜⢎⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣦⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⣀⣠⡤⠤⠤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠚⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢦⡀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠘⢷⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠺⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⠳⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⡴⡶⢲⠞⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⠙⣴⠇⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢾⣤⣠⠥⠾⠶⠞⠳⣤⡀⠀⠀⠀⠀⠀⣀⣤⢾⢱⡎⣧⠟⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡙⣆⠀⠀⠀⠀⠀⠈⠛⢿⣒⠒⠞⢻⠉⠃⢸⣨⠷⠋⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⢦⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠓⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⠤⣤⣤⣤⣤⣤⠤⠤⠖⠚⠉

⠀⠀⠀⠀⢀⡤⠶⢦⢤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣄
⠀⠀⠀⠀⡟⠀⠀⢸⠀⠀⢨⠉⠉⠛⠓⠲⢤⣄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠈⠳⠤⠤⠴⠖⠚⠛⠙⠛⠓⠦⣄
⠀⠀⠀⠀⡇⠀⠀⢀⣇⣀⣸⣀⣀⣠⣧⠤⠶⠒⢛⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⢿⠉⠉⠉⡏⠀⠈⠇⢀⣀⡼⠶⠚⠋⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣀⠸⠤⠄⠒⠒⠒⠒⠴⠒⠁
⠀⠀⠀⠀⠘⣇⠀⠀⢘⡤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠴⠶⠚⠉⢀⡠⠤⠤
⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠆
⠀⠀⠀⠀⠀⢠⠖⠒⢄⡀⠀⠀⠀⠀⠀⠀⣀⡤⠤⣄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠙⠦⣄⡀⠀⠀⠀⠀⠀⣀⣠⠖⠋⠀⡄
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⠑⠲⠤⠤⠖⠋⠁⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠉⠛⠓⠚⠛⠛⠁⠀⠀⣠⢴⠇
⠀⠀⠀⠀⠀⠘⣇⠐⠂⠤⢄⣄⣀⣠⠤⠴⠚⠛⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⠘⠤⢀⠀⠀⠀⠀⠀⢀⣀⠴⠊⢁⠞
⠀⠀⠀⠀⠀⠀⠙⢶⡀⠀⠀⠀⠀⠀⠀⢀⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠉⠀⠛⠁⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠚⠒⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⣀⣠⠤⠖⠊⠁


⣶⣶⡶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⣤⣶⡿⢆⠘⠛⢳⡾⣿⣿⣇⣤⣀⠆
⠀⠀⣿⣧⣤⣼⡄⢀⣿⣇⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡧
⠀⠀⣼⡿⠉⠛⠟⠛⠛⣿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⠀⠀⠀⢠⣤⡶⠿⢂⠈⠀⠀⠰
⠀⠀⠻⠇⠀⠀⠀⠀⠀⠿⠸⠇⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡸⠉⠀⠀⢺⠃⠶⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣷⠖⠶⠟⠈⢿⠇⠀⡄⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢠⡤⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠁⠉⡅
⠀⢀⠀⠀⠀⡌⢰⣶⣦⡴⣤⣤⠟⠀⢀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠸⣄⣀⣄⠃
⠀⠹⠀⠀⠔⠀⠈⠛⢹⠃⠈⠉⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠼⠋⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠤⠀⠀⠀⠹⠀⠀⠀⠅⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠄⠀⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠉⠉⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠶⠶⠆⠀⠀⠀⠀⠀⠀⠖⠲⠀⠀⠲⠶⠖⠀⠀⠀⠀⠀⠀⠲⠄⠆⠀⠐⠶⠖⠀⠀⠖⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠐⠟⠚⠗⠀⠿⠗⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠀⠀⠞⠛⠆⠀⠘⠒⠚⠀⠀⠀⠀⠀⠀⠰⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣤⡀⠀⠀⠀⢀⠀⠀⢄⡀⠄⠀⢀⣀⣀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠛⠓⠃⠀⠐⠚⠛⠀⠀⠀⠀⠀⠀⠐⠛⠛⠀⠀⠀⠀⠀⠀⠸⠻⠗
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⡠⠖⠛⠉⠉⠙⠲⣄
⠀⠀⠀⠀⠊⢀⡴⠋⠉⠉⠓⢦⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⣒⣒⣒⣂
⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠈⣇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠈⣿⣿⣿⣧⣽⣿⠛⠶⣤⡀
⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠢⣸⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠠⢀⣹⣷⣭⣭⣾⣿⣤⡶⠋⠉⠁
⠀⠀⠀⠀⠀⠈⠈⠉⠉⠙⢦⠀⢹⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⢰⣶⡄⠀⠀⠀⢸⠂⢀⠇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣀⣀
⠀⠀⠀⠀⢀⣿⠁⢀⣠⠔⠁⠀⠘⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠘⢧⠜⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠏⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⣠⠶⠶⠶⠀⠀⡠⠃⠀⢠⠋⠉⡆⠀⢸⠀⠀⢸⠀⠀⡰⠉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠉⠀⠀⠀⠐⠊⠉⠀⠀⠀⠸⠀⠀⢸⠀⢸⠀⠀⢸⠀⢀⡇⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀⠀⡇⠀⢸⠀⢸⠀⠀⢸⠀⢸⠁⠀⢸
⠀⠀⠀⠀⢀⡤⠴⠦⠤⠤⠶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢹⠀⡇⠀⠈⡆⢸⠀⠀⢸⠀⡎⠀⠀⡏
⠀⠀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⡇⣇⠀⠀⡇⢸⠀⠀⢸⢰⠁⠀⢀⡇
⠀⠀⠐⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢡⢸⠀⠀⢣⢸⠀⠀⢸⡸⠀⠀⢸⠁
⠀⠀⠀⠢⢄⣀⣀⣀⣀⣀⣀⣀⣀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⣼⠀⠀⠘⠊⠀⠀⠘⠃⠀⠀⡸⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢀⣴⠞⠁⠀⣠
⠀⠀⠀⢀⠔⠊⠉⠑⠒⠒⠋⠉⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⣠⡾⠁⠀⣠⡾⠋
⠀⠀⠐⠁⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠀⠀⡸⠉
⠀⠀⠀⣠⣦⡤⠄⣀⠨⢄⡀⠸⢤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⣤⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠙⢷⣆⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠈⠀⠛⠛⢦⡀⠀⠀⡠⠛⠛⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⡠⡀⠀⢰⠀⠈⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠘⠀⠰⠀⠸⠀⠀⡇⠀⠰⠁⠰⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢀⣤⡶⠞⠋⢻⣿⣿⠓⢄
⠀⠀⠀⠀⠀⠀⠁⠀⢇⠀⡁⠀⡇⠀⡆⠀⡇⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠸⣇⠀⠀⠀⠓⠟⠋⠀⠀⠇
⠀⠀⡏⠑⡀⠀⠈⠀⠘⡀⡇⠀⡇⢰⠀⢰⠁⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠉⠳⠶⠦⠤⠤⠔⠒⠋⠉
⠀⠀⠘⣄⠀⠀⠀⢀⠀⠧⠇⠀⠧⠃⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⢦⡀⠐⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢄⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠒⣤⡀
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⠀⠙⡀
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢀⠀⠀⠀⠰⣀⢀⠠⠀⠐⠀⠀⠀⠀⠀⢀⠀⢀⡠⢀⡀⠀⠀⢃⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⢀⠔⠁⡀⠄⠠⢀⠈⠂⠀⠈⢆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠂⣠⡾⠶⣶⡷⠶⣷⣦⡀⠀⠀⠑⢦⠀⠨⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠑⢄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠉⠀⠁⠈⠁⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠶⠀⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠿⠶⠶⣦⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠾⠛⠛⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠰⠀⢀⠀⠀⠀⠀⠘⠯⣭⠉⢉⠉⠉⣉⣉⣩⡍⠀⡄⠀⣤⣀⣀⡓⠞⢄⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠄⠈⢀⡀⠀⠀⢀⠁⠐⡛⠀⠆⠈⠛⢿⣿⠏⠀⠈⠀⠀⠈⢻⣿⠟⠋⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢦⠀⠀⢈⠋⠀⢀⣡⣴⣿⠁⠀⠀⠀⠀⠀⠉⠀⠁⢀⣄⠀⠀⠈⠁⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠐⡈⠀⠰⠆⠀⡁⠉⠉⠛⠻⡀⠀⠀⡶⠦⠀⠂⠀⠀⠀⠀⠁⡈⢀⠂⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠡⣄⡒⣴⠅⣡⠀⡂⠀⠀⠀⠐⣅⡈⢂⠀⠀⠀⠉⠂⢤⣾⣾⣦⡄⢂⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⣸⡏⠚⡂⢠⢋⣾⣿⡄⠀⠀⠸⠟⠁⠀⠀⠀⠀⠰⠛⠀⠒⣀⣀⣤⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⢀⣿⢀⡍⠠⠂⠚⠋⢉⡉⢰⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⣸⠇⠛⠳⡀⠒⠀⠀⠀⠀⣾⣧⣤⡶⠶⠶⠶⠶⠶⢶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⢠⡿⢠⠀⡁⣴⣄⠡⠀⠈⠈⠉⠁⢀⡔⠀⠀⣈⢂⣻⠃⡀⠈⠉⠛⠻⢶⣄⡀
⠀⠀⠀⠀⠀⣼⠇⣀⢱⢀⣿⣿⠶⠄⠀⢂⠠⠀⠈⠓⢀⠲⢶⣶⡥⠀⠤⠈⡐⠠⡆⠀⣉⠻⢶⣄
⠀⠀⠀⠀⢠⡿⠠⠴⣿⠜⠋⠀⠀⠀⠀⠁⠀⣱⡌⠂⣀⠕⢦⡝⢋⠀⠀⢀⡹⡟⠲⣤⠞⣻⣠⠙⢷⡄
⠀⠀⠀⠀⣾⠃⠒⠀⠅⠐⠀⠀⠀⠰⡇⠀⢐⣿⡇⣁⠐⠶⢿⡀⢀⠀⠀⢀⡀⡽⠆⡁⠶⡇⣀⠀⠈⠻⣦
⠀⠀⠀⢰⡟⠀⠀⢸⣦⡱⣤⡀⠀⠀⡀⠄⢀⣨⣥⣴⣬⣥⡘⢳⡌⠀⠀⠌⣹⡥⠞⠛⠦⣽⡌⠆⠀⠀⡹⣧
⠀⠀⠀⣾⠃⡀⢀⣼⣿⣿⡜⣿⠟⢀⣤⡾⠛⠉⠀⠀⠀⠈⠙⢦⡁⠀⠂⡀⠀⠊⠃⡀⠉⠒⠀⡀⡂⢀⣇⢹⣇
⠀⠀⢰⣟⠈⢀⠀⠂⠀⠀⠈⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⢄⣀⣀⡀⠄⠃⠀⣀⣀⡀⡤⣼⣎⠆⢿
⠀⠀⠀⢿⡄⠀⢰⣤⠀⡀⠁⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠈⣿⡿⣱⢦⣠⢖⡜⣿⡇⠛⠢⠍⡀⢸
⠀⠀⠀⠈⠻⢶⣤⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠈⡔⠀⡜⡟⡀⠑⠌⠃⠀⠀⠆⢼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⢦⣄⠓⢰⢀⠀⠀⠱⠼⠂⢀⠠
⠀⠀⠀⣀⣤⣤⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣿⠦⠉⠓⢤⠄⢀⢐⣡⣾⢠
⠀⣠⡾⢋⠁⠀⠠⠀⠄⢈⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⠀⠈⠁⠀⠀⠀⠀⢀⠀⠠⠀⠉⠉⣸
⢰⡟⠀⠂⠀⢠⣤⠀⠊⠂⠠⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠊⠂⢠⣤⠀⠀⠆⣰⡆⠀⠁⠀⢠⡿
⣿⠩⠧⡐⢄⠈⠁⠀⣠⣤⡄⡀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⡀⣠⣠⣀⠀⠙⣀⢀⣼⣿⣧⠈⠄⢀⣾⠃
⣿⠀⠀⠀⠈⠀⠀⢹⠟⡉⠀⢅⡀⢻⣆⠀⠀⠀⠀⠀⢀⣠⡾⠃⢀⠅⠊⠉⢿⣤⠄⠛⠈⠉⠁⠉⠁⢠⡾⠃
⢹⣇⣴⠂⠀⠁⠀⠀⠀⠰⡘⣶⡬⠆⠙⠷⠶⡶⠶⠾⠛⠉⠄⠯⣴⡞⡰⠀⠢⢀⠆⠈⠄⠀⠀⢀⣴⠟⠁
⠀⢻⣆⠀⠀⠰⢋⠒⣐⣐⠔⡞⠀⠂⠄⠀⠀⠀⠂⠀⢀⠀⠂⠀⠘⡔⣀⣐⡐⠚⢸⣧⡈⢀⣴⡿⠋
⠀⠀⠙⢷⣄⠠⠀⠐⠨⡛⢿⡏⠀⠨⠄⢦⢜⡃⢀⣛⢥⡄⠠⠀⠀⣿⠟⡋⠐⡂⠞⣩⣶⠟⠁
⠀⠀⠀⠀⠙⠷⣦⣔⡀⠹⠇⠐⠀⡀⠘⠊⢦⡈⠟⣡⠞⠸⠀⡀⠐⠀⢋⣁⣤⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⣦⣤⣤⣄⣀⣉⣁⣀⣉⣥⣤⣤⡶⠶⠟⠛⠉⠁
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢹
⠀⠀⠀⠀⠀⠀⠀⡎⠉⡆⠀⠀⡇⠀⢸⠀⠀⠀⡴⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣦⣶⣦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢁⠀⢹⠀⠀⡇⠀⠘⡆⠀⢠⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣴⡿⠟⠉⠀⢀⡸⢿⣿⠇⠘⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢇⠀⡇⠀⠀⡇⠀⡜⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠾⣆⠀⠀⠀⠀⠙⠛⠉⠀⠀⢀⠇⡀
⠀⠀⢸⠉⠡⠀⠀⠀⠃⠀⠘⡄⡇⠀⠀⡇⢰⠁⠀⡼⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠤⠤⠤⠤⠖⠚⠋⠉
⠀⠀⠈⢧⡀⠑⢄⠀⠰⠀⠀⢇⣽⠀⠀⣇⠇⠀⢰⠃⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢳⡀⠀⠁⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣁⣀⣉⠐⠄
⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠑⠤⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢠⠛⠁⠀⢠⠛⢦
⠀⠀⠀⠀⠀⠀⠸⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⡀⠀⡠⠂⠀⠀⠀⢣⡀⢀⣠⠔⠂⠀⠀⠢⠀⠀⠀⠀⢀⡀⠀⣀⣤⣄⡀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠠⠀⠀⠀⢀⠔⠁⢀⣀⡀⣀⠀⠈⠢⡀⠀⠘⢆⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠠⠋⢀⣴⣍⣀⣼⣤⣩⣦⣄⠀⠀⠀⠈⠳⣄⠀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⢠⣴⠟⠋⠉⠙⠛⠉⠉⠙⢻⣷⡄⠀⠀⠀⠈⠳⡄⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⣀⠀⢀⠀⣀⡀⠐⠁⡠⠀⠀⠀⠀⠀⠈⠢⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠈⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠦⠤⠤⠖⠚⠉

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣶⣶⣴⣶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣠⣤⣤⣀
⠀⠀⠀⠀⢀⣴⣿⣶⣿⣿⣿⣿⣷⣬⣿⣦⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣾⣳⡄⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣶⣿⣷⣄
⠀⠀⠀⠰⣿⣿⣿⣿⣥⣤⣤⣤⣽⣿⣿⣿⡷⠀⠀⠀⠀⣾⣿⣿⣅⣀⣀⣄⣀⣈⣽⣿⣿⡄⠀⠀⠀⢾⣿⣿⣿⡿⢿⣿⣿⡿⠿⠿⣿⣿⡷
⠀⠀⠀⠀⠈⠻⣿⣿⣽⣿⣿⣿⣭⣵⡿⠛⠀⠀⠀⠀⠀⣿⣿⣿⣛⣛⡛⠛⣛⣛⣻⣿⣿⠇⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣷⡾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣯⣽⣿⣿⣿⣽⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣠⣤⠤⣄
⠀⠀⠀⠀⠀⠀⢀⡴⣶⣦⣤⣶⡶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣭⣿⣿⣿⣿⠿⣶⣾⡇
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣶⣦⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠋⠁⠀⠀⠈⠀⢸⣿⡗
⠀⠀⠀⠐⢿⣿⣿⣿⣷⣤⣠⣴⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠿⠿⢿⣦⣹⡄⠀⠀⠀⠀⠰⣿⣿⣋⡉⠀⠘⠃⠀⣉⣩⣽⣿⠃
⠀⠀⠀⠀⠀⠙⢿⣿⣯⣿⣿⣏⣩⣽⡿⠋⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣄⣠⣀⣀⣙⣿⣿⡄⠀⠀⠀⠀⠙⣿⣯⣛⣛⣿⣿⣿⣿⣷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠉⢙⠟⠛⠛⠛⠻⣿⣿⣄⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⣠⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣲⣦⣤⣶⡶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣡⣾⠏⠀⠀⠀⠀⠀⠀⠀⢀⡴⣶⣤⣤⡶⣤⡀
⠀⠀⠀⠀⢀⣴⣿⣿⠿⠿⠿⠿⢿⣿⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠛⠛⠻⢿⣿⣦⡀
⠀⠀⠀⢠⣾⣿⣿⣷⣤⣤⣶⣤⣴⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣥⣤⣠⣤⣤⣀⣶⣭⣿⣿⡄
⠀⠀⠀⠈⠻⣿⣿⣟⣿⣿⣿⠿⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⡿⠿⣿⡇
⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣲⣦⣴⣶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠿⠿⠿⠿⢿⣿⠷⡄⠀⠀⠀⠀⠀⠀⠀⣀⠤⣤⡀⢀⣤⢤⣀
⠀⠀⠀⣀⣀⣤⣶⣿⣿⣷⣶⣾⣭⣷⣶⣤⣀⡀⠀⠀⢠⣾⣿⣿⡷⠶⠶⠶⠖⠀⠀⠀⣸⣆⠀⠀⠀⢶⡾⠿⢿⣿⣿⣿⣿⣿⡿⠿⠿⢶⡶
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠟⠁⠀⠀⠈⢻⣿⣥⣀⡀⠀⢀⣠⣔⣠⣴⣿⠏⠀⠀⠀⠈⢿⣶⣤⣀⡀⠀⠀⢀⣀⣤⣶⡿⠁
⠀⠀⠀⠀⠀⠙⠿⣿⣽⣿⣿⣿⣥⡾⠟⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣟⣻⣛⣛⣽⣿⠏⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣟⣿⣩⣽⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉

⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⣁⣈⣉⡉⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣽⣿⣯⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡕⠒⠪⣝⢆
⠀⠀⠀⠀⠀⡠⠒⣈⣩⡤⢤⣍⡑⠢⣀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⣀⡠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠻⡑⠀⢸⢸
⠀⠀⠀⠀⠀⣴⠊⠀⡇⣤⡷⡁⠈⠑⡄⠀⠀⠀⠀⠀⠰⡞⠶⠤⢄⣀⣀⠤⠴⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠜⠀⡸⡆
⠀⠀⠀⠀⠀⠈⠑⠢⠌⣒⡊⠥⠔⠊⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⣀⡀⢀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠰⡱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⣉⠔⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣠⠒⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⢰⢹⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣒⣉⣉⣒⣉⣈⣑⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⠃⡗⢩⠃⠀⠀⠀⠀⠀⠀⠈⠻⡙⢻⠋⢻⠋⢻⢛⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⠀⠘⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⡶⠶⠶⠶⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢍⠓⠤⠜
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⣤⡈⠀⠀⠀⣀⠀⠀⢰⣶⠶⣦⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⣯⣹⠇⠀⠀⠀⠁⠀⡿⢹⡿⣾⡧⣀⣴⣦⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣠⣐⣿⣄⠀⠀⣇⠀⠸⠀⠀⡆⠸⡇⠀⣿⣻⣿⣿⡿⠛⠓⠀⠀⠆⠠⠖⠀⠀⠀⡤⢢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠉⠁⢹⣶⡀⠘⣿⣆⠀⢸⣇⣷⣄⢠⠏⣿⡟⠋⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⡄⢤⠄⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠃⠀⠆⢸⠋⠀⠀⠀⠀⠺⣻⠟⢡⢮⠙⠛⢸⡏⠁⢹⣿⢻⣿⡶⠶⠾⠇⡈⣿⡧⠀⢀⡀⠀⠀⢳⣦⢂⡰⢧⡿⠁⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠲⠶⠈⠀⠀⠀⠀⠀⠀⣿⠀⠈⠈⠀⠀⠀⢧⡀⢸⡇⢸⡟⠁⠀⠀⠈⠁⣿⠀⠀⠘⠂⠐⠁⠈⠀⢸⠁⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠂

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⣝⣟⣉⣙⢻⡟⣩⣿⣻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⣉⡙⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⡖⠋⠉⠉⠳⣄⠈⠂⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠒⠒⠒⠒⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⡟⠀⡞⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢀⡤⢚⡩⣴⡶⢛⡛⠻⣿⡶⢦⣄⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢹⡀⠀⠀⠀⡇⢸⡱⠃⠀⢀⠀⣀⣠⠇⠀⠀⠀⠀⠀⡠⠖⠁⠀⣿⡱⣿⣷⣥⢸⡇⠀⠈⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠦⠤⢾⡇⠀⠀⠀⡇⢸⠁⢠⠏⠉⠉⠁⠈⠀⠀⠀⠀⠀⠈⠒⠦⢄⡀⢙⣷⣭⣯⣵⣿⡥⠴⠚⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⢷⢸⠀⠸⡀⠀⠀⠀⣾⡷⠀⠀⠀⠀⠀⠑⢤⣀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠸⡄⠀⠀⠈⠒⠤⡀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⣄⣀⣀⣀⣀
⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠈⠒⠋
⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⣸⠁⠀⠀⠀⣧⡀⠀⠀⠀⠀⠘⢦⡀
⢃⠀⣤⣤⡀⠀⠀⠀⠀⣀⣤⡄⢀⠄⠀⠀⣿⠀⠀⠀⠀⢸⠙⢷⣤⣤⣄⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠒⠒⠒⠒⠒⠢⢄⡀
⠀⠀⠈⠉⠙⠲⠤⠤⠞⠉⠉⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⠀⠀⠹⡄⠙⢦⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠀⠀⠀⠀⠀⠃⠀⠀⠘⠦⡀⠙⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠠⠶⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠉⠛⠛⠒⠲⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠋⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠷⣄⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠉⠒⠂⠤⠤⠤⠤⠤⠤⠤⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⣧⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣀⡠⢄⣀⡀⢀⣀⠤⢀⡀
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⣿⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠉⠁⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠠⠃⠀⢀⣀⣀⣀⠀⢀⣀⣀⣀⡀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠁⣠⣮⣁⣼⣀⣀⣸⣁⣀⣨⣦⣨⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣤⠟⠃⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⢇⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⢸⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠘⠦⣀⣀⣠⠾⠛⠉⠙⠋⣀⠴⠃⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣤⡤⠤⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⣤
⠀⠀⠀⠀⣀⢀⠀⣀⣦⣀⣀⡹⣧⡄⠀⠀⠀⢀⣠⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠴⠦⠀⠀⠀⠀⠈⠌⣉⠑⠀⠀⠀⠀⠀⠀⠁⠁⠈⠁
⠀⠐⠀⢹⣿⣤⣤⣾⠉⠙⣻⣇⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⡀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⣼⠋⠈⢉⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠈⠁
⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠉⠈⠀⠁⣉⢀⠅⠀⠀⠀⠀⠀⠀⠀⠈⠋⠄⠀⠀⠀⠀⠀⠈⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⠿⠿⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡆⠀⢀⠀⠀⠀⠀⠙⠟⠾⠎
⠀⠀⠀⡌⠘⠿⠿⠇⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠈⠒⠀⢆⣀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣀⣀⠀⠈⡤⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠰⢖⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠋⠱⠆⢀
⠀⠀⠀⠀⠀⠀⢈⠩⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠂⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠁
⠀⠀⠀⢐⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⠀⠀⠁⣀⠀⠀⠀⠉⠀⠀⠀⢀⣴⡒⣹⡿⠑⢠⡄⠀⠀⠀⠀⠀⠛⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠛⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠛⠛⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠛⠓⠲⢤⡀
⠀⠀⠀⠀⠀⢠⠞⠁⠀⣀⣠⣄⣀⠀⠈⢳⡀⠀⠀⠀⢀⡞⠁⢠⠴⠚⠓⢢⠀⠈⠳⡄⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⡟⠀⡰⠋⣁⣰⣦⡌⠑⣄⠀⣷⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢸⠤⡄⠀⢻⠀⠀⠀⢰⡇⣀⡤⠴⠲⢤⠖⠢⢤⣀⠘⡇
⠀⠀⠀⠀⠀⣇⠀⢣⡀⠻⣿⣿⠇⢀⠞⠀⣿⠀⠀⠀⣿⠀⠀⢀⠀⠀⠀⠈⣸⠁⠀⣸⠀⠀⠀⢸⡄⠙⢍⡓⠒⠒⠒⢚⣩⠏⢀⡇
⠀⠀⠀⠀⠀⠹⣄⠀⠉⠒⠦⠴⠚⠁⠀⣰⠃⠀⠀⠀⠸⣆⠀⢸⡀⠀⠀⣠⠇⠀⣠⠏⠀⠀⠀⠀⢷⡀⠀⠉⠙⠓⠋⠉⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠘⠳⣤⣀⣀⣀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠈⠳⢤⣉⣉⣉⣁⣤⠞⠋⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⣀⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⣀⣤⡤⣤⣤⣀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢀⣠⣤⠤⣤⣀⡀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠁⣠⠤⠤⣄⠉⠳⣄⠀⠀⠀⠀⠀⣠⠞⠉⠀⡀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⡎⣴⠋⠉⠋⢳⠀⠘⣧⠀⠀⠀⢰⠏⠀⠀⢠⠇⠀⢹⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠉⡇⢀⣴⡞⠀⠀⣹⠀⠀⠀⢸⠀⠀⢀⠞⠀⠀⠈⢧⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⢈⠙⠦⠞⡼⠀⠀⢀⡟⠀⠀⠀⠸⡆⠀⠸⣤⢤⢠⠤⡼⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡈⠓⠶⠚⠁⢀⣠⠞⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠋⠁

⠀⠀⠀⠀⠀⢰⣟⣛⢀⡇⣤⡀⣤⣠⣤⡄⠀⢀⣤⣤⢀⣤⣄⢠⣤⣄⢀⣤⣤⢠⣤⣄⢠⣤⡄⠀⢀⣏⢠⣤⣄⣠⣤⣄⢠⣤⣄
⠀⠀⠀⠀⠀⢸⡏⠉⠸⡧⠸⣿⠇⢿⣿⡇⠀⠸⣿⡿⠸⣯⡿⢸⡇⣿⠸⣿⡷⠺⣿⡿⢼⣿⡷⠀⠸⡿⠸⣧⡗⠻⣤⡿⢸⡇⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣤⣴⣶⡦⡀⠀⠈⠀⠯⠓⠐⠁⠀⣀⠀⢒⡖⢒⣤
⠀⠀⠀⠀⠀⠀⠀⢇⢀⣴⣄⡀⢝⣶⣿⠇⣿⠐⠢⢠⣶⣲⣴⡶⠀⠀⡆⠘⠁⠈⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣟⣷⣿⣻⡟⠀⢰⡀⢠⣿⣿⣿⣯⠀⠀⠘⣇⢀⠀⡀⢸⡦⠀⠀⠀⢤
⠀⠀⠀⠀⠈⠃⠘⠀⠀⠀⠘⠛⢿⣿⢷⡄⣼⣧⢸⣿⢻⣿⣿⡀⠀⠀⢙⣶⣷⢝⣿⠇⡀⢀⡀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣤⠄⢠⣂⣈⣿⣾⣿⡏⠉⢹⣿⡞⣿⣿⠁⠀⠀⠘⠉⠉⠙⠋⠀⠀⠊
⠀⠀⠀⠀⠀⠖⠀⠹⣯⠰⠈⠉⠉⣹⡇⢸⡇⠀⠀⢿⣇⣽⣿⡀⠐⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣛⣛⣻⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠉⠉⠉⠉⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠋⠉⣉⣀⣤⣍⣉⠙⠓⠦⣀
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⡴⠛⣩⠥⠖⠈⠉⠻⣦⡀⠈⠳⣄
⠀⠀⠀⡴⠁⢀⣴⠾⠿⣷⣶⣶⣶⣶⣤⣤⣄⣀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⣰⠋⠀⡰⠃⠀⠰⣄⡀⠀⡈⢿⡀⠀⠈⢧⡀
⠀⠀⡼⠁⠀⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠻⢿⣿⣦⡄⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠇⠀⢊⡵⠖⢲⣤⠈⠁⠀⢱⢸⡇⠀⠀⠀⢧
⠀⢠⡇⠀⠀⢠⣀⣀⣦⣤⣶⣤⣷⣦⣤⣄⡀⠀⠈⠙⠛⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠙⣆⠀⠀⠸⢸⡇⠀⠀⠀⢸⡆
⠀⢸⡇⠀⠲⣶⣿⣿⠿⠛⢹⣿⣉⣽⣿⢿⡟⢶⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠑⠦⠀⠀⣀⣍⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇
⠀⠸⡇⠀⠀⠀⠀⠹⣆⠀⠈⢷⣝⣛⣯⠞⠁⠀⠙⢦⡀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⣼⠃⣸⠋⣴⠄⡴⠀⣼⠁⠀⠀⠀⢸⠇
⠀⠀⢳⡀⠀⠀⠀⠀⠈⠳⠦⣤⣄⣉⣀⣤⠴⠆⠀⠘⠋⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠘⠒⠁⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⡾
⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢀⣠⡤⠶⠒⠒⠒⠒⠶⢤⣄⡀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠞⠉⠀⠀⡄⠀⠀⠀⢠⡄⠀⠀⠉⠲⣄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠉⠳⠦⣀⣀⠀⠀⠀⠀⢀⣀⡤⠖⠋⢠⠞⠁⠀⠀⠀⠀⡇⠀⠀⠀⢸⠇⠀⠀⠀⠀⠈⠳⣄⠉⠳⠦⣄⣀⡈⠙⠋⠁⣀⣠⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠹⡄⠀⠀⠀⡞⠁⠀⠀⠀⠀⢀⣴⠀⠀⠈⢷⠀⠀⠀⢠⠏⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠈⠉⠓⠦⣄⠘⢦⡀⠀⠳⠄⠶⠶⠶⠀⠀⠶⠶⠶⠠⠋⠀⢀⡴⠋⣠⠴⠚⠉⠁⠀⠀⠀⠀⠈⠉⠓⠦⣄
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⡴⠋⠁⠀⠀⠀⠄⠀⠀⠂⠀⠐⠀⠀⠀⠈⠳⣄
⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠈⠙⠒⠲⠤⠤⠤⠤⠶⠚⠋⠁⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⡾⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⣀⣀⣤⣄⡀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢒⠀⠀⠀⠈⠀⠀⡁⠀⠀⠀⠀⢷
⠀⢰⠇⠀⠀⣀⣤⠞⣫⡅⢀⠈⠉⠉⣡⠀⠈⣝⠳⢦⣀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⡆
⠀⢸⠀⠛⠛⡉⠦⠤⠤⠶⠾⢧⣴⣴⣽⠷⠶⠦⠴⠶⢊⠟⠛⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠸⡆⠀⠀⠈⢦⡀⠀⠀⠀⠄⠆⠐⠠⠀⠀⠀⠀⡴⠁⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸⠇
⠀⠀⢳⡀⠀⠀⠀⠙⠒⠦⠤⠤⠤⠤⠤⠤⠴⠒⠋⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⡞
⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢸⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⣀⠀⠀⣀⣀⣠⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣄⣀⣀⠀⠀⣀⣀⣨⠤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⠀⠀⠀⠈⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⢁⣠⣤⣤⣤⣈⠉⠒⢤⡀
⠀⠀⠀⢀⡔⠉⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣠⠞⠋⡥⠖⠒⠂⠉⠻⣦⡀⠈⢢⡀
⠀⠀⢠⠏⢀⡴⠟⠛⠻⠿⠿⣿⣷⣶⣶⣤⣤⣀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢸⠃⠀⡜⠁⠀⠐⢤⠄⢠⠘⣧⠀⠀⠙⡄
⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠉⠙⠻⠿⣷⡄⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠈⠀⢸⠞⠉⠹⣧⠀⠀⠀⡇⣿⠀⠀⠀⠸⡀
⠀⢸⠀⠀⠀⢲⣤⣼⣶⣾⣷⡾⢿⣷⣶⣤⡀⠀⠀⠁⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠘⠧⠀⠀⠃⡟⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠙⠻⠿⡏⠁⠀⣿⢶⣾⡿⣹⠏⠻⣆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⢩⡄⢠⡶⢂⠀⡀⠀⡿⠀⠀⠀⠀⡇
⠀⠈⡆⠀⠀⠀⠀⠙⢦⣀⡈⠛⠒⠚⠁⣀⡀⠈⠷⠄⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢸⣠⠎⠀⠋⠘⠁⣼⠃⠀⠀⠀⢰⠃
⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⢀⡞⠀⠀⢀⣀⣠⣤⣤⣄⣀⡀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢠⠏
⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣠⠔⠊⠉⡀⠀⠀⠀⢀⠀⠉⠑⠢⣄⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠉⠲⢄⣀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠊⣡⠞⠁⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠈⠳⡄⠙⠢⣄⡀⠀⠐⠶⠒⠋⠀⣀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠚⠉⠉⠀⠀⡰⠁⠀⠀⠀⠀⠀⢹⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠈⠉⠑⠒⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⢷⠀⠀⢀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠤⢄⣀⠀⠀⠱⡀⠀⠀⢼⠁⠀⠀⠀⠀⠠⠞⠀⠀⠈⡇⠀⠀⢠⠎⠀⠀⣀⣠⠤⡤⠤⠤⣀⣀
⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡙⢦⡀⠈⠓⠚⠛⠛⠀⠀⠛⠛⠃⠚⠁⢀⡴⢋⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄
⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠙⠲⢄⣀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠱⣄
⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠈⠉⠉⠛⠛⠉⠉⠁⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⢠⠇⠀⠀⠀⢀⣤⠶⠚⠲⠶⠶⠖⠒⠶⢦⣀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⢸⠠⣤⡴⢞⣋⣑⣋⣠⣆⣀⢀⣾⣦⣘⣓⣉⣛⢦⣤⡤⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠈⢢⡉⠉⠉⠠⢉⣛⢛⣋⢡⠨⠉⠉⡡⠊⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡇
⠀⠈⣆⠀⠀⠀⠑⠦⣤⣀⣀⣀⣀⣀⣀⣀⠤⠞⠁⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⣰⠁
⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠈⠓⠤⣄⡀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⢀⣡⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠉⠉⠉⠙⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠊⠉⠉⠉⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣀⣀⣤⣤⣤⣀⡀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣴⠟⠋⠁⢠⣻⣿⠇⠙⢆⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠻⣦⣀⠀⠀⠉⠁⠀⣀⡬⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢤⣤⣤⡤⠴⠚⠉⢦⣀⣠⣴⠶⠛⠛⠋⠉⠉⠙⠛⠳⢶⣤⣀⣠⠎⠑⠢⠤⣤⣤⣤⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠄⠐⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠴⠀⠘⠀⠑⠂⠀⠀⠀⠀⠀⠀⠈⠠⠀⠄⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠂⠀⠀⠐⠀⣇⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⣷
⠀⠀⠀⢀⣠⠤⠖⠒⠒⠢⢤⣀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡄⠀⠀⠀⠀⢈⠄⠀⠀⠀⠉⠰⢀⠈⠀⣀⡨⠂⠀⠀⠀⣿⠀⠀⠀⠀⢀⣠⠤⠖⠒⠒⠤⢤⣀
⠀⢀⠔⠉⠀⣀⡀⠐⠀⠀⠀⠈⠑⢆⠀⠀⠸⣇⠀⠀⠰⡔⠀⠀⠀⠤⠀⠀⠀⠁⠂⢤⠀⠰⠋⠉⠀⠀⠀⠀⠀⢀⡿⠀⠀⢀⠖⠉⠀⠀⢀⠀⠀⠀⠀⠈⠑⢄
⢠⠏⠀⠀⠈⠁⠀⠘⠓⡄⠀⠀⠀⠀⢳⡤⠔⢿⡀⠀⠀⠠⡀⠠⠀⢀⡠⣤⣤⠀⣀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠀⣸⠗⠤⣴⠃⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠈⢧
⡎⠀⠀⠀⠀⠀⠀⠁⠀⡸⠀⠀⠀⠀⠀⡇⠀⠈⢷⡀⠀⠀⠉⢰⣿⣷⣾⠿⠭⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠈
⡇⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡟⠀⠀⠈⢳⣄⠀⠀⠀⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠘⡇
⢱⡀⠀⠀⠱⣄⠀⠀⠔⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠳⡄⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣄⣀⣀⣀⣀⣤⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⡴⠃
⠀⠀⠈⠳⢤⣀⣀⠈⠒⣂⣀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣀⡀⠀⢀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠛⠛⠛⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠤⠄⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠊⠀⠄⢀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢁⡴⠿⠶⢾⠶⠾⢷⣄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⠀⠀⠀⠀⠀⣀⠀⠛⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠠⡀⠀⠁⠈⠀⠀⠀⡠⠃⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠈⠉⠒⠒⠂⠚⠉⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢤⣀⣀⣀⡠⠤⠖⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠂⠉⠁⠀⠀⠀⠀⠀⠀⠈⠑⠢⠠⠄⠒⠈⠈⠁⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⣶⠠⠐⠈⠁⡀⠀⣀⣀⡀⠀⠠⠤⠤⠤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⢠⠃
⠀⠀⠰⠻⣆⠀⠀⠀⠉⠂⠄⡀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠂⠀⠀⠒⠒⠀⠉⠉⠇⡠⠁
⠀⠀⠀⠀⠎⢧⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠘⡀⢣⠀⠀⢀⣤⣄⠀⠀⣀⡀⠀⠀⠀⠀⠀⠉⠉⢹⠁⠀⠀⠀⠉⠉⠉⠨⠱
⠀⠀⠀⠀⠀⢡⠈⣇⢠⣿⣿⡏⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⡀⠸⣿⣿⣿⣦⣀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⢃⠀⢻⠛⠛⠛⠛⠿⢿⡟⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⡆⠀⡅
⠀⠀⠀⠀⠀⠀⠘⡀⠀⢂⠀⠀⠀⠀⠀⠀⠑⠦⡄⠀⠀⠰⠄⣀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠈⠐⠤⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⢰⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⠑⠂⠤⠀⣀⣀⣀⡀⠠⠄⠀⠒⠒⠒⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠠⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡎⠀⢱⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡁⠈⡄⠀⠇⠀⢸⠀⠀⡘⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣠⣴⡶⠒⠛⣿⣿⡗⠢⡀
⠀⠀⠀⠀⠀⠀⠠⠀⢱⠀⠀⠀⢸⠀⢀⠃⠀⠇⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠈⣟⠁⠀⠀⠐⠭⠿⠃⠀⠘⠆
⠀⠀⡖⠀⠀⠀⠀⠀⠀⡇⢸⠀⢠⠀⣜⠀⢸⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⠳⠦⣤⢤⣤⡤⠤⠴⠚⠊
⠀⠀⠘⡄⠀⢄⠀⠁⠀⢸⡸⠀⢸⡠⠁⢀⠇
⠀⠀⠀⠘⣆⠀⠐⠜⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢄⡐
⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠐⠉⢢
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⢇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠓⠀⠉⠀⠀⠀⠀⠀⠀⣠⠔⠀⠉⠉⠉⠑⠀⠀⠀⢣⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠁⠀⠀⠀⡐⠁⣠⣎⣉⣭⣁⣦⣄⠀⠀⠀⠑⢄⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⣀⣀⠄⠊⠀⠀⠀⠀⠀⠀⠀⢴⡞⠉⠉⠉⠋⠉⠉⠻⡷⠄⠀⠀⠀⠱⣄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠤⠀⠄⠠⠄⠀⢀⠄⠀⠀⠀⠀⠈⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⡀⠀⢀⣀⡤⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡯⣽⣟⣛⣛⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⢤⣤⣄⣀⠀⠀⠀⣀⣤⡤⠤⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠶⠶⣶⣶⠶⠶⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⢀⣠⣤⠶⠛⠉⢻⡁⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢸⡟⠉⠛⠲⣤⣄⡀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⢀⣤⠞⠋⠉⡇⠀⠀⠀⠈⣇⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⣸⠀⠀⠀⠀⡸⠉⠙⠳⣄⡀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢀⡴⠛⡇⠀⠀⠀⢸⡀⢀⣀⣤⣿⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣿⣤⣀⡀⢀⡇⠀⠀⠀⢸⠛⢦⡀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⣰⠇⠀⠀⡴⢿⠀⠀⢱⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⡎⠀⠈⡿⢆⠀⠀⠹⡆
⠀⠀⠀⠀⠀⡟⠀⢀⡞⠇⠀⢧⣠⣼⣿⣿⣿⠿⠿⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠿⠿⣿⣿⣿⣷⣄⡜⠀⡸⢷⡀⠀⢿
⠀⠀⠀⠀⢰⡇⠀⣾⠹⣜⣶⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣶⣇⠈⣷⠀⢸⡆
⠀⠀⠀⠀⠘⡇⠀⢿⣷⣿⣿⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⡿⢿⣿⡟⠀⢸⠁
⠀⠀⠀⠀⠀⢿⠀⠀⠙⠳⣆⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣵⠞⠋⠀⠀⡿
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢨⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡅⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⢀⡤⠤⠦⠤⣄⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⣄
⠀⠀⠀⠀⡴⠋⢀⡠⠤⣀⠀⠙⣆⠀⠀⠀⡴⠁⡤⠒⠒⡆⠈⠳⡄⠀⠀⠀⡴⠉⠀⠀⠀⠀⠈⠱⡄
⠀⠀⠀⢰⡇⣰⠁⣤⣿⣆⠙⡄⢸⠀⠀⢸⠁⠀⡇⠀⠀⠷⡢⠀⢹⠀⠀⢸⠁⣴⣒⣑⢒⣑⡲⡄⢹
⠀⠀⠀⠈⣇⠈⠢⢍⣛⡡⠜⠁⡼⠀⠀⠘⡆⠀⡇⠀⠀⢠⠃⢀⡞⠀⠀⠘⣆⠈⠲⠤⠤⠴⠊⢀⡞
⠀⠀⠀⠀⠈⠳⣄⣀⣀⣀⡤⠞⠁⠀⠀⠀⠘⠦⣌⣒⣒⣁⡤⠊⠀⠀⠀⠀⠘⠢⣄⣀⣀⣀⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣠⠤⠶⠦⢤⡀⠀⠈⠉⠀⠀⢀⣠⠤⠶⠦⢤⡀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢠⢖⠼⢖⢄⠉⢦⠀⠀⠀⣰⠋⠀⢠⠀⢀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠟⡄⣠⡼⠀⠘⡇⠀⠀⡇⠀⢀⠎⠀⠘⡄⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢀⡙⠤⣳⠃⠀⣸⠁⠀⠀⢧⠀⠸⠤⠄⠤⠜⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣉⣋⣁⣠⠞⠁⠀⠀⠀⠀⠳⢤⣀⣀⣀⡠⠞⠁

⠀⠀⠀⠀⣴⣖⢒⡆⡄⣠⣠⣄⠀⢀⣤⡀⣤⡄⣠⣤⢀⣤⡀⣤⡄⣠⣄⠀⢰⡆⣤⡄⣠⣄⢠⣤⡀
⠀⠀⠀⠀⠻⠉⠘⠇⠻⠇⠻⠿⠀⠘⠿⠛⠿⠏⠻⠸⠘⠿⠛⠿⠗⠻⠟⠀⠸⠛⠷⠇⠳⠞⠸⠻⠇

⠀⠀⠀⠀⠔⢊⣉⣉⡑⠢⡀
⠀⠀⠀⠀⡴⠁⠀⠀⠙⣆⠹⡄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⡶⢶⣤⣄
⠀⠀⠀⠀⡇⠀⠀⠀⠠⣸⡀⡇⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠾⠄⠀⣿⣟⣛⣽⣇⣬⠟⠂
⠀⠀⠀⠀⠉⠉⠈⠑⡄⠘⡇⡇⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠉
⠀⠀⠀⠸⣷⠀⠀⢀⠆⠀⢃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠈⠐⠢⠤
⠀⠀⠀⢸⣇⠔⠊⠁⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⢠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⡀⠀⢀⣠⠴⣦⠀⢀⠌⠀⠰⠒⢆⠀⡀⠀⢸⠀⢠⠒⢢
⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠐⠈⠀⠀⠀⢸⠀⢸⠀⡇⠀⢸⠀⡌⠀⢸
⠀⠀⠀⠀⠀⣈⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⢂⢸⠀⠘⠀⡇⠀⢸⢀⠃⠀⡌
⠀⠀⠠⠊⠉⠀⠉⠁⠀⠉⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠸⠈⠀⠀⡇⡇⠀⢸⢸⠀⠀⡇
⠀⠀⠒⠒⠛⠛⠓⠛⠛⠓⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⡇⠀⣇⡇⠀⢠⡆⠀⢰
⠀⠀⠀⠂⠤⠤⠤⠤⠤⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠸⡇⠀⠈⠁⠀⠈⠀⠀⠘⠀⠀⠀⡠⠄⠒
⠀⠀⠀⡀⠤⠤⢄⡠⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠎⠀⢀⠔
⠀⠀⠊⠀⢀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠁⠀⡠⠁
⠀⠀⡠⠦⠐⠠⠜⠠⠄⠢⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢀⣴⠆⠀⠀⠀⠀⠀⠲⣤⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠈⠀⣀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠈⠂⠄⣀⡀⠠⠊⠀⠀⠀⠀⠀⠉⠑⠄⠀⠔⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠐⠒⠂⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠉⠢⠤⠤⠤⢄⡀
⠀⠀⠀⠀⠀⡠⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⣀⡠⠔⠚⠒⠂⠀⠀⠀⠀⠈⠐⠒⠂⠐⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠈⠒⠢⠤⠄⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠐⠀⠒⠀⠀⠀⢀⡶⣻⣥⣤⣴⣵⣾⣝⡢⠀⠀⠀⠀⠀⠀⠄⠀⢀⣀⡀⠀⠀⠈⠉⠀⠉
⠀⠀⠀⢀⠔⣫⣭⣶⣴⣾⣷⣶⣵⠀⠀⠀⠀⠀⠀⢀⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⢻⣿⣯⣓⣀⣐⣭⣤⠤⠤
⠀⠀⢠⣧⡾⠛⣉⣋⣛⣏⣥⣼⡟⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⢿⣯⣷⠶⣛⣻⣿⣿⠇⠀⠀⠀⠀⠀⠀⢰⣿⡛⠿⠿⣿⣿⢿⢿⣷⠟⣱⠇
⠀⠀⣾⣿⣶⡾⠿⠛⠿⠉⠈⠙⣷⡀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣶⣷⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣴⣶⣷⡾⠟⣡⣾⠋
⠀⠀⠹⣿⣿⣄⣀⣀⣀⣀⣤⡴⣣⣿⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣭⣷⡾⠟⠁
⠀⠀⠀⠙⠿⣾⣿⣿⣷⣶⣿⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠉⠉⠉⠉⠐⢄⡀⠀⠀⠀⠀⡠⠤⠠⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡀⣀⠀⣀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠊⠉⠉⠁⠢
⠀⠀⠀⠀⠀⡀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠊⠀⠀⠀⠀⠀⠀⠈⠐⠤⢀⣀⣀⠠⠔⢊⣀⠀⠀⠀⠀⢈⠑⠂⠠⠤⠐⠚⠓⠂⠀⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠁⣐⣀⡈⠉⠁⢠⠊⠀⠀⠀⠀⠀⠀⡀⢀⣠⣄⡀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⡠⠃⠀⡴⣨⣗⡦⣀⣤⣤
⠀⠀⠀⠀⣠⣚⣭⣍⣉⣤⣤⣭⣶⣄⠀⠛⡍⠁⠀⠀⣠⣶⣿⣿⣿⣿⣿⣶⣄⡀⠀⠑⠒⠁⠀⠀⠀⠲⠀⢰⣽⠛⠿⣿⣾⣿⣿⣿⣆
⠀⠀⠀⣼⣿⣿⡿⢿⠿⡿⠻⠿⣿⣿⡆⠉⠀⠀⠀⣰⣿⣯⣭⣬⣧⣴⣾⣿⣿⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣷⣴⣶⣶⣬⣿⣧
⠀⠀⣰⣿⣿⡭⠦⠴⠤⠶⠴⣶⠟⣻⣿⡄⠀⠀⠀⣿⣿⡟⠛⠛⠛⠋⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣿⠋⠉⠋⠉⠉⠙⢻⣿⡏
⠀⠀⠙⠛⠿⣿⣷⣶⣶⣶⣦⣦⣼⣿⣿⠃⠀⠀⠀⠈⢿⣿⣗⠶⣶⣖⣚⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣏⠸⣦⣁⠂⠂⠤⣤⣤⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣾⣿⣿⠛⡛⣉⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠶⠦⣤⣀⣀⣀⣀⣀⣀⣤⡶⠶⠶⠶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⢀⣀⣀⡀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣒⣩⡥⠴⠖⠒⠚⠉⠉⠐⠒⠲⠶⠶⢦⣤⡴⠶⠞⠛⠋⠉⣉⠙⠛⠳⢶⣝⡻⢦⣀
⠀⠀⠀⠀⠀⢸⣢⡤⠶⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⠀⢀⣠⣿⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡀⠀⡉⠻⢶⣤⣄⣀⠀⠀⠃
⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢤⠞⠀⠙⠛⠛⠉⠙⠶⠶⢤⣤⣤⡶⠶⠦⣤⣤⣤⡤⠴⠶⠛⠷⠦⠴⠂⠙⠞⠁⠀⠀⠈⢹⠏⠀⠀⢀⡄
⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠶⠶⠶⠶⢶⣦⣤⣤⣤⠶⠶⠶⠶⠾⠿⠷⢶⡄⠀⠀⠀⠀⡜⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⢀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⣄⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠘⠉⢻⣂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠈⠙⢷⣆⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⢠⡏⠉⠉⠛⣿⠛⠛⠲⣦⣤⣤⣤⣤⡾⠋⠉⠉⠓⠆⠀⠀⠉⠀⢀⣴⠟⠁⠀⠀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠁⠀⠀⠀⠃⠀⠀⠀⡿⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣤⣀⣀⣀⣀⣁⣀⣀⣀⣀⣈⣠⣤⣤⠶⠶⠛⠉⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠷⠶⠶⠶⠒⠒⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣚⠉⠀⠰⠶⠆⠐⠒⠦⠐⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡀⠀⠀⠀⠀⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠓⠀⠀⠀⠀⠈⠓⠛⣿⣌⢳⣄⠀⠀⠀⠀⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⣠⣤⠴⠟⢻⣿⡃⢤⠀⠀⣀⣀⠀⢠⣨⣿⣿⠳⣝⠳⢦⡴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⢰⣾⢿⢻⢈⣁⡀⠉⠉⠁⡙⡇⠉⠇⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⡁⠀⠛⣿⣧⣽⣿⣿⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠛⢿⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣶⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠉⠂⠠⠀⡋⠀⡀⠀⠀⠀⢻⣿⡆⠀⠀⠀⣠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠀⠀⠈⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠶⠁⣀⠀⠀⠀⠡⠀⠀⢀⠀⠀⣼⢻⡤⠃⠀⠀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢊⠁⠀⠀⠀⠀⠀⠈⠱⠀⠀⠀⠀⠀⠀⠶⢦⡀⠀⠀⠀⢀⡴⠂⠀⠸⠆⡈⠳⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠙⡇⠘⣿⠇⣀⠀⢾⠃⠀⠀⠀⠄⠀⠀⣄⠀⠀⠁⠠⠀⠀⠀⠀⢀⡄⠀⠀⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⣋⠀⢹⣈⣛⣀⡀⠀⠀⢠⠄⠂⠃⠠⣽⡄⠀⠀⠀⠀⢀⠀⢀⣼⡇⠀⠻⠶⠀⠀⠋⠀⠀⠀⠀⠄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠊⢿⣇⠈⠙⢻⠋⠁⠀⠀⣼⠄⠀⠀⠀⢈⣿⣦⠀⠀⣻⡇⠀⣾⡟⠀⢤⠀⣤⣧⠀⠈⠃⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣶⠚⠛⠓⢢⡀⢀⠁⠀⠀⢀⡀⠁⡘⣿⣧⡻⠊⢛⣼⣟⠑⣀⠀⢦⡙⢿⣧⠀⠀⠀⠀⣾⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣤⡊⢀⣤⡇⠛⠀⠀⠀⡿⠁⠀⠀⢘⣿⣅⠀⣨⡿⠯⠈⣿⠀⠙⠵⠟⠁⠀⠀⢠⣿⣿⣿⡷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡹⢿⣿⠛⠁⠀⠀⠀⢸⡇⠀⠀⠠⡿⠏⠙⠛⠉⠀⠀⠀⢿⠀⠀⠀⠀⠀⠐⠠⠙⠻⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⡆⠰⣿⡀⠀⠀⠀⠀⠀⠀⣴⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⣠⠉⠃⢰⠀⠀⠀⠀⠀⠻⠀⢤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡶⠀⠀⠀⠀⠀⠀⡄⢠⣴⠋⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⡆⠈⡧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⡴⠀⠀⢹⠄⠀⠀⠐⢢⣿⠂⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣠⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁

⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣴⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡄⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⣾⣷⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⣩⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣲⣾⣦⣤⣶⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠚⠛⣛⠳⣿⣿⣿⣿⠟⣻⣿⢿⠹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣴⣿⣿⣧⣨⣯⣤⣶⣾⣿⣿⣼⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣷⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⣿⣿⣿⡟⠹⣦⡈⣹⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣯⣿⣯⣴⠞⠛⢿⡿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣟⣛⣿⣻⣿⣿⣶⣶⡆⢀⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⡯⠡⠏⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠿⢛⣵⣿⣿⣿⡟⠿⡧⠴⠶⠿⠛⠻⠟⠟⠋⠁⠀⠀⠘⠻⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠉⠿⠟⠿⣿⠀⢿⣾⣿⣿⠉⠀⠠⠤⠀⠠⠄⠀⠀⢀⣶⣿⣷⣤⣶⡄⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣴⣟⣿⣶⡘⣦⣌⠛⢃⣀⢀⣠⣀⣄⣀⣀⠀⠀⠀⠈⠻⢿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⢹⣿⡿⠟⠁⣨⣿⠁⠰⠿⢻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⡏⠀⠀⠀⣠⣶⣿⢠⡇⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣰⣾⣷⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇⣿⡗⣾⣿⢟⣀⣈⣠⣾⣿⣛⣟⡃⠿⣿⠃⠀⠀⠀⠀⠹⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠆⠈⢻⣿⡟⠋⠉⠀⠍⠻⠉⠙⠻⢿⣷⣦⣄⡀⠀⠀⠘⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡁⢰⢃⣼⡟⠀⠐⠲⠦⠄⠀⠀⠀⢊⠄⣩⡙⠟⠃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⡷⢸⠿⡃⠀⠘⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈⣡⠃⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⣷⡖⠛⢀⠀⠀⠀⠄⡀⠀⠀⠀⠄⠀⠀⠀⠒⠀⠀⠀⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢛⣿⠀⢸⣿⡦⡀⠀⠀⡐⢦⣄⡀⠀⠀⢀⣠⣄⠀⠁⠸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⣿⠀⢸⣿⡅⣄⠀⠀⠀⠀⠉⠙⠛⠉⣈⣻⡏⠧⠀⢀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡋⠀⢸⣿⣗⡙⣺⣶⠶⠦⣀⡀⢀⣈⡿⢻⣿⣀⠀⠋⡄⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⢿⣿⢿⣿⣿⣿⣿⣿⢇⡠⠟⠋⣿⣿⣿⣾⣿⢏⠠⡈⡇⡔⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⡟⠾⢿⡧⠿⠟⢽⡿⣿⡿⠛⠙⠙⣷⣾⣿⣿⡷⣾⠀⠫⠐⣢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣦⠤⣤⠀⣌⠉⢮⡉⠁⠀⠈⠙⠛⠛⠻⠇⢿⡄⢆⣀⣒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠙⠛⠉⡰⠛⠂⠛⠀⠀⠘⠛⢶⠀⠀⠀⠀⠀⢺⡏⠉⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣶⣇⣀⣄⣀⠀⠀⠀⠀⢠⡀⣷⣶⣤⣶⣶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠉⠛⠻⠏⠙⡟⠣⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⡜⠻⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠈⠉⠉⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡟⢿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⣠⣄⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠃⠈⣿⠿⠿⢉⡿⢿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣹⣿⣿⣇⣿⣿⣿⣿⣷⣾⣷⣴⣶⣧⣴⣦⣰⣦⣀⣉⣀⣶⡿⣿⣶⣶⣌⢿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠇⢉⣻⡿⢿⣿⣿⣾⣿⡝⣿⣷⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠁⣼⡿⠧⣬⣻⣟⡿⠛⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠘⢿⣦⣼⠟⣿⣿⣿⣟⣿⣿⣟⣿⣟⠻⢿⣿⣟⢿⣿⣿⣶⣤⣝⢀⣤⣧⡿⢃⡘⠻⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠛⠟⢋⡙⢿⣿⠟⢹⣿⣼⠷⣿⣿⣿⣧⣼⣿⣯⡀⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠉⠓⠚⠻⠶⠽⣤⡿⢿⣯⣹⣿⡃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠈⠹⠶⠖⠒⠖⠈⡽⠁⠲⠚⠛⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⣫⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢋⣡⡼⠧⠔⠒⠂⠈⠉⠉⠙⠓⠚⠒⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡸⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡜⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠊⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠂⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣤⣴⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡷⠀⠀⠀⠀⠰⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⠀⣀⠀⠀⢀⡠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠑⣴⠁⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢸⡄⡀⠀⠀⠀⣆⣀⣀⡀⠠⠤⠤⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⡄⠀⠀⠷⠀⠀⡄⠉⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠢⢄⣀⣀⠔⠉⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢀⠀⠀⠀⠄⠢⡀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣨
⠀⠀⢇⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣻⣿⣦⣤⠤⠀⢠⠤⠐⠒⠒⠂⠈⠉⠉
⡔⠀⠀⢵⡀⠐⠆⠀⡠⠂⠑⠀⠀⠀⠀⠀⠈⡇⢸⣿⣿⠁⠀⠀⠀⡄
⠑⠢⣠⡀⠀⠀⠀⠎⠀⢀⠊⠀⠀⠀⠀⠀⠀⢧⠸⡟⠳⣀⡀⠀⠀⢧⠠⠤⠤⠤⢤⣄⣀
⠰⣁⡀⠴⢤⡀⠄⠀⡤⠂⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⣄
⠀⠀⠀⠀⠀⠙⠒⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣀⡀⠀⠀⠀⣀⣠⡤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠓⠋⠉⠉⠑⠒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠸⠖⠒⠒⠚⠋⠉⠉⠉⠙⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⣸⠉⠉⠓⠢⡤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠤⣤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢠⡊⠉⣀⠴⢄⠀⠶⢄⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠉⠁⠀⢸⠀⢸⠀⠣⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠈⠑⠒⠤⠤⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣀⣀⡀⣀⣠⠤⠴⢶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣷⣶⣶⣤⣤⡇⠀⣇⣤⣶⣶⣿⣿⣿⣷⣶⣦⣤⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠁⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢠⠖⢩⠏⢠⠓⡽⡍⠲⡄⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⡳⠼⣯⣢⣖⣽⠧⢚⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⡆⠀⠐⠱⣆⡀⠈⠁⢀⣀⠈⠃⠀⣰⢁⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⢤⣀⡀⠀⡠⠞⠉⠀⠘⢆⠀⠀⠀⠈⠉⠉⠁⠁⠀⠀⡰⠃⠀⠉⠳⢄⠀⢀⣀⡤⠤⠤⢄⣀
⠀⠀⠀⠀⢀⠔⠋⠁⠀⣀⡀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠑⠦⣄⣀⡀⠀⣀⣠⠴⠊⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠈⠙⠢⡀
⠀⠀⠀⢰⠋⠀⠀⢠⠀⠚⠏⠦⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢠⠋⢳⠀⠀⠀⠀⠙⡄
⠀⠀⠀⡇⠀⠀⠀⠀⢠⢨⢰⠀⡀⠀⠀⠀⠈⡆⠀⠀⠀⢀⡤⠖⠊⠉⠉⠑⠒⢤⡀⠀⠀⠀⢰⠁⠀⠀⠀⠀⡏⠀⢀⡃⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠐⡆⠸⠼⠼⢤⠇⠀⠀⠀⠀⡇⠀⢀⡔⠁⠀⠀⠀⡔⢢⠀⠀⠀⠈⢢⡀⠀⢸⠀⠀⠀⠀⡴⠁⠀⢸⡸⡄⠀⠀⠀⢸
⠀⠀⠀⢣⠀⠀⠀⠸⡀⢱⠊⢰⠀⠀⠀⠀⣰⠁⠀⡎⠀⠀⠀⠀⢀⡑⢊⡀⠀⠀⠀⠀⢳⠀⠈⣆⠀⠀⠀⣙⠢⣄⡭⠒⡁⠀⠀⠀⡜
⠀⠀⠀⠀⠳⣄⠀⠀⠙⠒⠒⠁⠀⠀⢀⡴⠁⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⡆⠀⠀⠀⠀⠀⡇⠀⠈⢦⡀⠀⠉⠁⠀⠀⠉⠁⠀⣠⠞
⠀⠀⠀⠀⠀⠈⠑⠢⠤⣄⣀⡤⠤⠒⠉⠀⠀⠀⠘⡄⠀⠀⠀⣀⡈⡇⢸⢁⣀⠀⠀⠀⢠⠃⠀⠀⠀⠈⠒⠤⢤⡀⣠⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠚⠤⠤⠍⠭⠄⠀⠛⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢀⣀⣀⣀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⣠⠔⠃⠀⠀⣀⣀⣀⡀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠖⠋⠉⠀⠀⠈⠉⠓⢤⡀⠀⠉⠑⠒⠒⠊⠉⠀⢀⡤⠒⠉⠀⠀⠀⠉⠙⠲⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⢀⣀⢀⡀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⡤⢒⡒⢤⡀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣀⣔⣉⣀⣁⣀⣰⣄⡀⠀⠘⡆⠀⠀⠀⠀⢰⠃⠀⠀⡄⠀⠘⢸⠁⠈⠃⣧⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠛⠅⡏⠀⡇⠘⡇⠝⠋⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⢸⢸⣖⠀⠈⠇⠀⢠⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠳⣀⢀⡰⠃⠀⠀⠀⢠⠃⠤⠤⠤⠤⠘⡄⠀⠈⠎⠀⠀⠀⠀⠀⡏⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠙⠦⠔⠁⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⠀⠀⢀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⡀⠀⠀⣀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠙⠲⣶⣤⣄⣄⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠞⠋
⠀⠀⠀⠀⠀⠈⠻⣿⡛⠙⠀⠀⠀⠰⠂⠀⠀⢠⡤⠀⠀⣀⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣀⡀⠀⠠⢤⣤⠄⠀⠀⢴⡆⠀⠀⠚⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⢠⡄⠀⠀⠀⠈⠋⠀⠀⠀⠀⠏⠀⠀⠀⠸⠇⠀⠀⢀⢟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⢷⣶⣶⣆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣠⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣟⣲⣟⠿⠄⠀⠀⢠⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⡀⠀⢀⣀⢿⣦⣤⢴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⠙⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⢿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡒⠢⡤⠠⠠⢄⡠⠤⠤⢀⠄⠀⠀⣀⡀⠤⢄⡠⠀⠠⠴⠊⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠈⠁⠀⠀⠘⠂⠀⠀⠰⠀⠀⠀⠶⠀⠀⠘⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠒⠒⠒⠒⠒⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠋⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠛⠛⠷⣦⡀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⢀⣴⠟⠋⠁⠀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢹⡇⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⡞⢻⣷⡄⠀⠀⢸⡧⣼⠉⣿⡆⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⢸⡗⣾⣿⡇⠀⠀⢸⡇⢿⣻⣿⡟⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣼⣷⠀⠀⠀⠀⠈⠻⣿⠟⠁⠀⠀⣼⡇⠈⠛⠛⠀⠀⠀⠀⠀⠀⣰⡿⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⢀⣿⠋⠉⠉⠉⣁⠁⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢷⣄⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⢠⡶⢿⣏⠀⠀⠈⠻⣦⣄⡀⠀⢀⣀⣠⡾⠃⠀⠀⠙⠷⣶⣤⣤⣴⠾⠛⠁⠀⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠈⠀⠀⠙⠻⣦⣄⣀⠀⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⢸⡏⠛⠿⠶⣦⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣤⣶⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⠠⠿⠦⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣀⣠⠂⠀⠀⠀⠀⠉⢀⣀⣤⣾⠟⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⠶⠶⠶⠶⠿⠛⠋⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠷⠶⠶⠶⠶⣶⣶⣶⣶⣶⣾⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣴⡶⠶⠾⠿⠿⠟⠛⠛⠛⠛⠿⠿⠷⠶⣶⣤⣄⡀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣤⡀
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣄⡀
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⢠⣿⣤⣤⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⣿⠛⠿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⢀⣿⠀⠀⠀⠉⠙⠛⠿⣶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁
⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋
⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠋⠁
⠈⠉⠛⠻⢷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⡶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠷⠶⢶⣶⣶⣶⣦⣤⣴⣶⣶⣶⡶⠶⠾⠿⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡁⠠⠤⢄⡑⠄
⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⢸
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣉⡥⠬⢭⡅⣂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⠀⠀⡸⢸
⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠈⠰⣶⠆⠁⠀⢉⡷⠀⠀⠀⠀⠀⠀⠀⢐⠀⡀⠸⠀⡴⢁⠆
⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠈⠁⠒⠚⠢⠤⠴⠓⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⠀⠈⡠⠊
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⠚
⠀⠀⠀⠀⠑⠢⠄⠀⠉⠙⠉⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⢠⠉⢂⠀⢀⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⡀⠸⠀⢸⠀⡘⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡃⢠⠀⢸⢠⠃⠰⢠⠊⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠰⠼⠀⠘⠂⠀⣧⠂⡠⠁
⠀⠀⠀⠀⢀⠤⠒⠉⠑⠒⠂⠁⠒⠠⡀⠀⠀⠀⠀⠀⡠⠄⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠰⡅⠀⠀⠒⠂⠀⠒⠂⠒⠀⢈⠆⠀⠀⠀⠀⠱⡀⠙⢄⡌⠒⢆⠠⢄⡀⠀⠀⡆
⠀⠀⠀⠀⠈⠑⠠⠄⢀⣀⣀⠠⠄⠒⠁⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠈⠂⠀⠙⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⡀⣀⡀⣀⠠⠊

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣻⣟⣙⣫⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠓⣶⡐⠶⠀⠖⣱⠶⢛⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣀⣴⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣿⣶⡤⠁⠀⠀⠀⠀⠶⠟⣿⣿⠌⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣇⠀⠠
⠀⣶⠾⣧⣿⡁⣰⣇⣀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡶⣀⠀⠀⡀⢠⣉⠻⣿⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣘⠁
⣰⢟⣤⣿⣿⣷⣿⣟⣿⣆⣦⣾⣧⣆⣀⣴⠀⣀⠀⠈⠉⢻⣯⠚⠀⢹⣦⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⡤
⣸⣿⡙⣿⣿⣽⣛⣀⡀⢹⡏⢿⣿⣿⣿⣿⣾⣷⣄⠀⠀⠀⠀⡠⠀⠸⢗⠀⠀⠀⠀⠀⠀⢀⣠⣠⣤⣀⡀⣸⡄⣼⣿⡏
⠘⣿⣿⣾⣿⠿⢿⢿⣿⣿⣿⣄⠀⠀⢹⡟⣿⣿⣿⣟⣷⣠⢀⡷⣄⡀⢸⣤⣴⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢓⣶
⠘⡈⢻⣿⡇⠀⠀⠸⠿⠟⠃⠀⣠⡀⠀⣀⠉⣽⠿⠿⢿⡟⡸⠀⠈⠀⡿⠛⢿⠉⠁⠀⠈⠉⠉⠉⠉⠉⠻⣿⣿⣿⣿⣿⡿
⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⢺⠃⡇⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⠿⠃
⠀⢀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠒⠆⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠠⠤⠆⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠂⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⡀⢤⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⡀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢀⡀⠀⣾⣤⢴⣴⡶⠶⣶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠿⠛⠀⣿⣻⠿⠋⢠⡏⣠⠄⠀⠀⠀⠀⠈⠙⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠛⠁⠀⠀⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡆
⠀⠀⠀⣤⠞⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣤⣴⣶⣿⣷⣶⣶⣦⣄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⣠⠔⠒⠉⠒⠒⠊⠛⠒⠤⡀⠀⠀⢷⣀⣤⣤⣀⡾⠀⠀⣠⠔⠋⠋⠁⠀⠀⠉⠉⡓⢦⡀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠲⢿⡤⠤⡤⠤⠤⠤⠤⠤⡤⠤⢬⡷⠂⢸⡇⠀⠀⢸⡇⢰⠊⠀⠀⠀⠀⢰⣿⣤⡀⠀⢁⠀⠈⢳⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠒⡇⠀⠀⠀⠀⠀⡶⠊⠁⠀⠀⢸⠇⠀⠀⠸⡇⠈⠑⢤⡀⠀⠀⠈⠛⠋⠀⠀⠄⣠⠔⠋⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡾⠀⠀⠀⠀⢷⠀⠀⠀⠈⠓⠲⠦⠤⠤⠶⠒⠋⠁⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠈⠢⠄⠀⠤⠊⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⢦⣄⡀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⢀⣠⡴⠋⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠈⠉⠙⠓⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠚⠛⠉⠁⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠒⠚⠒⠲⠤⣄⡀
⠀⠀⠀⠀⢀⡴⠛⠉⢀⣀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⡠⠐⠒⠒⠒⢄⠈⠙⢦⡀
⠀⠀⠀⡴⠋⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⢀⠎⣠⠖⠀⠑⠢⡀⠱⡀⠀⠹⡄
⠀⠀⣼⠁⠀⠀⠀⠀⠀⢸⡏⢠⠠⡀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢸⠀⢣⡀⠀⠀⠀⠁⠀⡇⠀⠀⢻
⠀⢠⡇⠀⠀⠀⡠⣀⡀⠘⠃⠘⠀⠛⢹⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢦⠀⠈⠑⣦⠀⠀⡰⠁⠀⠀⢸⡇
⠀⠸⡇⠀⠀⠀⢡⠀⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⡼⠀⡰⠚⠁⠀⡰⠁⠀⠀⠀⣸⠁
⠀⠀⢷⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⢣⡀⠀⠀⠀⡸⠁⠀⠀⠀⢠⠏
⠀⠀⠈⢳⡀⠀⠀⠀⢆⠀⠀⠀⠀⠀⡸⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⢣⠀⠀⣠⠃⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠙⠦⣄⡀⠀⠑⠒⠂⠒⠈⣀⡴⠚⠁⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⣀⢀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠈⠛⠢⣤⣀⣑⣘⣁⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠒⠚⠛⢧⡀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⢰⠁⠀⢣⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⡇⠀⠀⠈⡆⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⣸⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢸⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢸⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠸⢖⣲⣄⠀⠀⢠⡶⣲⠞⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠁⠊⠁⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠁

⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠀⠀⠀⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣤⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡀⠀⠀⠄⠀⠀⠠⠶⠛⠻⠗⠂⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢸⣿⣿⡆⠀⠀⣴⢶⡄⠀⠀⠁⠂⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠀⠀⠀⠁⠠⠁⠀⠀⢀⡀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣦⣀⣴⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣠⣿⣿⡿⠛⠙⢿⣿⣿⡿⠋⠀⣼⡈⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠙⢋⠀⠀⠀⠀⠙⠛⠀⠀⠀⠘⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠗⢸⣮⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠛⢩⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣷⣀⣠⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣷


⠀⢀⡀⢀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠤⠤⠄⣀⠀⠀⠛⢋⣁⠠⠤⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠊⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠎⠀⠀⠀⠀⠀⠀⠈⠒⣄
⠀⠀⠀⠀⠀⢀⡀⠀⣀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⣶⣄⣀⡀⠀⠀⢀⣀⣠⣾⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠰⢀⡀⠀⢀
⠀⠀⠀⠀⣴⣿⡑⠶⠄⠠⠀⠀⠀⠴⣶⣶⣾⣿⡿⠿⠿⠛⠛⠛⠛⠿⢿⣿⣿⠿⠟⠛⠛⠛⠛⠿⠿⣿⣿⣶⣶⣤⡤⠤⠤⢤⣤⠤⠶⣿⣿⡄
⠀⠀⠀⠀⠁⠀⠉⠶⢄⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⡠⠆⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠗⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⢢⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⡖⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⢋⡤⠀⠤⠄⡀
⠀⠀⠀⠀⠀⢀⡴⠉⠑⢦⡀⣀⠰⠊⠀⠀⠀⠀⠉⠰⢆⡀
⠀⠀⠀⠀⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠠⠄⣀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⢀⣤⡀
⠀⠀⠀⠀⠑⠄⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠶⠦⠤⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠸⣦⣄⠀⠚⢢⣤⣤⡾⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠒⠒⠂⠀⡤⡤⢀⡤⠤⣄⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠌⠉
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠔⠒⠀⠁
⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠆⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠤⠄⠀⠀⣦⣀⣀⠀⠀⠀⢀⡀⠠⠤⠄⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣀⠉⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠐⠒⠂⢤⠀⠀⠀⠀⠀⣠⠔⠒⠒⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠉⠰⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢠⠄
⠀⠀⠀⠀⢀⣤⡀⠐⠶⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠲⠆⠀⣀⣄
⠀⠀⠀⠀⠀⠉⠛⢆⡀⠀⢤⣦⠀⠀⠠⠤⠠⠤⠠⠤⢤⡄⠀⠀⠛⢂⡤⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠄⠀⣠⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢦⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⠈⠛⠦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠰⠟⠁⠀⣀⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠈⠉⠒⠒⠀⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠒⠒⠋⠉⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠶⠂⠀⠀⢀⣀⣀⠀⠀⠀⠒⠂⠈⠉


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣏⣉⣛⣉⣻⣉⣙⣉⣹⣆⣉⣋⣻⣋⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣽⣿⣿⣧⣤⣿⣿⣭⣽⣿⣿⣿⣤⣬⣭⣭⣭⣥⣤⣬⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣤⠦⣄
⠀⠀⠀⠀⠀⠀⡞⠛⡇⠀⣿⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠛⠓⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⡟⠙⡇⠀⡇⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⡴⠚⠛⠓⢦⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⣿⠀⣧⡞⠓⡆⠀⠀⠀⠀⠀⠸⠁⠺⣤⡀⠀⠀⠀⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⡇⠀⠃⠀⠃⠀⠛⠀⣿⠁⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⡼⠁⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣀⠞⠁⠀⠀⠀⠀⠀⠀⣾⠀⣀⣤⡀⠀⠀⠀⣠⣄⡀⠘⡇
⠀⠀⠀⠀⠘⢆⡀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⣤⡤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣥⠤⠉⠲⠴⠚⠁⢤⣥⠴⠃
⠀⠀⠀⠀⠀⠀⠙⠒⠲⠖⠒⠋



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠛⠉⠉⠉⠛⢶⡦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣚⡉⠀⠀⠀⠈⠉⠁⠀⠀⠀⢉⣓⣦⣄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡾⠁⠀⣠⣤⠀⠀⠀⢳⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠙⢮⣉⠉⠉⠉⠙⠛⠛⠛⠉⠉⠉⠉⣉⡴⠋⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⣇⠀⠀⢿⣿⡿⠀⠀⢸⠃⢀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⣤⣄⣀⣠⣤⠤⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣽⣄⠀⠀⠀⠀⠀⣠⣏⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠒⠛⠋⠁

⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠉⠛⠲⢤⡀
⠀⠀⠀⠀⠐⠁⢀⡴⠚⠋⠛⠳⢤⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣒⣒⡒⠒⠂
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠈⢧⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⣿⡿⣽⣿⣉⣿⣿⠶⣤⡀
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢠⠘⡆⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠀⠀⢻⣷⣛⠿⣋⣼⡟⢀⣨⡿⠓⠆
⠀⠀⠀⠀⠀⠘⠗⠢⠤⠤⠤⡀⠀⠱⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠻⠿⠿⠿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠸⡄⠀⣿⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢿⣿⠆⠀⠀⠀⡰⠃⠀⡟⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⠤⠤
⠀⠀⠀⠀⠀⣼⡏⢀⡤⠴⠊⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠻⠴⠋⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢀⡴⠶⠿⡶⠀⠀⣀⠎⠀⠀⣸⠉⠉⡆⠀⢀⡇⠀⠀⡇⠀⠀⡔⠉⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠊⠁⠀⠀⠀⠴⠊⠉⠀⠀⠀⠀⢹⠀⠀⢹⠀⢸⡇⠀⠀⡇⠀⢰⠁⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢸⠀⠀⢸⠀⢸⠀⠀⠀⡇⠀⡸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣀⣠⣀⣀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⡆⢸⡀⠀⠘⡆⢸⠀⠀⠀⡇⢀⡇⠀⠀⡾
⠀⠀⠀⢀⠔⠋⠁⠀⠀⠈⠁⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢻⠈⡇⠀⠀⡇⢸⠀⠀⠀⡇⢸⠀⠀⠀⡇
⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠸⡄⡇⠀⠀⣇⢸⠀⠀⠀⡇⡎⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢇⢳⠀⠀⢸⣸⠀⠀⠀⣧⠃⠀⠀⢸
⠀⠀⠀⠈⠑⠢⠤⠤⠤⠤⠤⠤⠤⠤⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⣼⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⡠⠴⠒⠢
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⡰⠋⠀⠀⠀⡠
⠀⠀⠀⢀⠔⠊⠉⠉⠉⠓⠚⠉⠉⠉⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢀⠞⠁⠀⠀⡠⠊
⠀⠀⠠⠁⠀⠀⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢠⠎
⠀⠀⠁⢀⣴⣄⣸⠀⣀⣸⣁⣀⢠⢇⣡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⣀⣴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⣠⡴⠆⠀⠀⠀⠀⠀⠀⠀⢶⣤⡀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡄⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢃⠀⣠⣄⡀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠁⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⣀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⢦⣀⣀⡠⠊⠉⠉⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠁⣀⣀⣉⡙⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⢐⣋⣭⣭⣭⣉⡄⠩⠽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣍⣭⣴⣿⣿⣝⡲⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣇⢻⡇⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⠻⣌⠻⡿⣿⡎⣿⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⣹⣦⡹⣷⡽⣧⡄⣨⣿⣿⣏⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣾⣿⣯⣾⡿⠋⢉⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣡⡾⠟⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣷⣶⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⠙⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠁⠀⠀⣈⣭⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣶⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠤⠤⡤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁
⠀⠀⠀⣀⣀
⠀⠀⠀⡿⠿⠇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠰⠚⠲⠶⢤⡄

⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠱⣤⡄⣠⠔⡟⠲⡄⢀⢠⣀⠔⣠⣤⡔⢆⣯⣾⣿⠐⣶⣤⡄⢤⣀⠀⡀⡤⠀⡗⠰⡄⣀⠀⢻
⠀⠈⠀⢩⣿⣆⣐⣃⣑⣘⢯⠤⠄⠀⠤⠬⠥⠌⠉⠭⠭⠤⠭⠬⠄⠤⠤⢦⣼⡖⣂⣀⣀⣈⣫⠁⢉⠁
⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⠀⢀⣤⠐⠒⠖⠒⠒⠢⢤⡀⠀⠀⠂⢸⣿⣿⣿⣿⡟⠋⣿⣇⣾⡇
⠀⠰⣀⣸⣿⣽⣿⣿⣿⣿⣿⠀⢀⣼⣿⣿⠆⠀⣤⣤⣤⣤⣄⣧⠅⢠⠀⢸⣿⣿⣿⠿⠆⢰⣿⣄⣠⠇
⠀⠀⡟⣿⣿⣿⣿⣿⣿⣯⣿⠀⣾⣿⣿⡗⢇⡠⣟⡏⢹⣿⣟⣿⡆⡌⣇⢸⡿⣽⣿⠠⠯⣾⡏⠙⢻
⠀⠀⠀⣿⣿⣿⣿⣭⣿⡕⣿⠀⣿⢿⣿⡿⣼⣿⢿⣷⣾⣿⣿⣿⣿⡛⠟⢸⠰⣽⣿⣳⢲⣿⣯⠀⠘
⠀⠀⠀⣿⣿⣿⣿⣿⡏⣡⣿⠀⠘⣻⣿⣇⣽⣏⣿⣿⣿⣿⣿⣿⣻⡟⠀⢸⣎⢻⣿⡏⣸⣿⡯
⠀⠀⠀⣟⣿⣿⣿⣿⣳⣿⣽⠀⣀⠀⠛⠿⢟⣿⣿⣿⣿⣿⡿⠟⠋⢀⡄⢸⣿⣾⣿⣷⣿⣿⣿⠀⡇
⠀⠀⠠⠿⣿⣿⣽⣭⣭⣭⡽⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠸⣿⣿⣿⣿⣭⡽⠏⠄
⠀⢀⠀⠀⡹⠋⠋⠉⠉⣝⡁⡀⠀⠀⠀⠀⢀⡀⢀⢀⣀⢀⡀⠀⠀⠀⠀⢀⢹⣿⠉⠉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁

⠀⠀⠀⠀⣀⣤⣴⣤⣴⣶⣤⣄⡀⠀⠀⠀⠀⣠⣴⣦⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⣠⣾⡿⠿⠿⠿⣷⣦⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡄
⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⢾⣿⣯⣭⣭⣭⣽⣿⣿⣦⠀⠀⠀⢸⣿⣷⣦⣤⣤⣴⣶⣿⡿⠀⠀⠀⠀⠳⢤⣤⣤⣤⣤⣤⡴⠞
⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⢀⣴⡿⠿⣿⡿⠿⢷⣤⡀⠀⠀⢀⣠⣤⣶⣿⣷⣴⣿⣷⣦⣤⣀⠀⠀⠐⣾⡿⠿⠿⠿⠿⠿⠿⣿⠖⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣄⡀
⠀⠀⢿⣶⣶⣶⣤⣴⣶⣶⣶⠇⠀⠀⠀⠙⠿⣷⣮⣽⣿⣭⣶⡿⠟⠁⠀⠀⠀⠘⣿⣷⣶⣤⣶⣶⣾⠟⠀⠀⠀⠀⢾⣯⣉⣀⣀⣀⣀⣈⣭⣿⠂
⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠛⠛⠛⠉

⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⠀⠀⠀⠀⢀⣤⣄⣀⣀⣤⣀
⠀⠀⣴⣿⡿⠿⠿⠟⠻⠿⣿⣦⠀⠀⠠⢄⣠⣴⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢤⣶⣿⣿⠟⠿⠛⢿⣿⣷⡦⠀⠀⠀⣠⣴⣿⣾⣿⣿⣿⣿⡷⠂
⠀⠀⠻⣿⣷⣶⣶⣶⣶⣾⣿⠟⠁⠀⠀⠀⠙⠳⣿⣶⣾⣿⣿⠟⠁⠀⠀⠀⠀⠈⠻⣿⣿⣶⣾⣿⠟⠋⠀⠀⠀⠀⠙⠿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⢀⣠⣄⣀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠰⣿⣏⣁⠀⠈⠉⠀⢈⣹⣿⡆⠀⠀⢶⣛⡛⠛⠛⠛⠛⢙⣛⡠⠀⠐⢾⣯⣍⣉⣉⣉⣉⣩⣿⡶
⠀⠀⠀⠈⠛⠿⢿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠛⠋⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠾⠿⠿⠿⢿⡿⠷⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠛⢷⡄⠀⠀⠀⠀⠸⣧⣀⠀⢀⣽⡟⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣴⡿⢿⡅⠀⠀⠀⣸⡇⠀⠀⢀⣤⣤⣌⡛⠛⠛⠉⠀⣰⡟⠛⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠈⠻⠶⠶⠾⠛⠀⠀⣴⠟⠉⠀⠙⢿⡄⠀⠀⠀⣿⡀⠀⠀⠈⣻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠻⣦⡀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣆⣀⣀⣀⣼⣇⠀⠀⠀⠈⠻⢶⣶⠾⠋⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⣀⣼⣷⣶⣶⠿⢿⡿⠛⠛⣿⠋⠉⣿⠋⠛⠛⣿⠛⠛⢿⡶⢶⣤⣤⣀⡀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡿⠟⠻⣏⠀⠹⡄⠀⠷⠀⠀⠻⠀⠀⠸⠀⠀⠀⠟⠀⠀⠸⠁⠀⣸⠏⠙⢻⣷⣦⣼⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣄⣀⡀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠴⠋⠁⠈⣻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣄⣀⢀⡖⠀⠀⢀⡀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡆⠀⠀⡀⠀⢠⡀⠀⣱⣦⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣷⣶⣦⣾⣥⣤⣤⣿⠀⠀⠀⠀⠀⢹⣧⣠⣤⣷⣴⣶⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⣻⡿⠀⠀⠀⠀⢶⢸⣿⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⢸⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⢸⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠂⡟⢸⣿⢰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠂⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⡼⠰⠀⣼⡏⢸⣀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⣸⠁⡆⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⢀⡏⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⠀⠎⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⡀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃

⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⢦⡀⡇⠄⡟⢄⢸⠙⢄⣸⠀⠀⡟⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡦⠤⠤⠄⣀⣀
⠀⠀⠀⠁⠃⠀⠃⠀⠙⠀⠈⠈⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⡤⠖⠉⠁⠀⢀⡔⠉⠉⠉⠙⠲⣄
⠀⠀⠀⣤⡀⢰⠆⡆⠀⡆⢰⢀⠐⡖⢄⠀⠀⠀⠀⠀⠀⣠⡾⠟⠀⠀⠀⠀⢠⡿⠂⠁⠀⠀⠀⠀⠘⠦⣀
⠀⠀⠀⡇⠈⠲⠅⡇⠀⡏⠱⡼⢄⡇⠘⠀⠀⠀⠀⢤⡴⠝⠂⠀⣀⠀⠀⠀⠉⠀⠀⡄⠀⠀⠀⣠⣾⡏⠛⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⣠⡾⠃⠀⠀⢠⠆⠀⣼⠀⠀⠀⠈⣡⡿⢷⡄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢰⣊⣜⣉⠀⠀⡄⣠⠀⠀⢀⡇⠀⠀⠀⣼⠟⠁⠈⢿⡀⢦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣿⣿⣿⣿⣧⣴⣿⡅⠀⠀⣸⠇⣠⣤⣾⣿⣶⣀⡠⠼⣇⢠⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣼⣿⣿⡿⣿⡧⠈⢹⣿⣿⢿⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠿⠟⠋⡍⠀⠀⣸⠈⠉⠉⠁⠀⠀⠀⠸⠉⠁⠀⣿⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⠿⢻⡟⠉⣷⡀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠛⠛⠁⠀⠘⣷⠀⠹⣇⣰⠁⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠘⣿⡀⠀⢸⣿⣷⣄⡀⠀⠀⠈⠽⠅⢠⡾⢣⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⠀⣿⣷⡀⢸⣿⣿⠿⣤⣤⣀⡀⢀⣴⣿⡇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠤⣄⣀⣠⣾⣿⣯⣷⡀⣿⣿⣷⣌⣿⣃⣠⠀⠙⣿⣿⡟⢹⡏⢹⡏⠉⠛⢶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⣩⡿⠃⠂⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣴⣿⣿⣷⣷⠁⠀⠃⠀⠀⠀⠈⠓⠄
⠀⠀⠀⠀⠀⠀⠀⣴⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⢀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⢀⠀⠀⠀⠀⠁
⠀⠀⠀⢀⣤⣿⣿⠟⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣷⡄⠀⠀⠀⢢
⠀⠀⠀⠘⣻⣿⡏⠀⠀⠀⣀⠀⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠹⠃⠀⠀⠀⠁
⠀⠀⢀⡔⣿⣿⡇⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠃⠀⠀⠀⠘⠄
⠀⠀⢈⣴⣿⣿⣇⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠤⡄⠀⠀⣘⠄
⠀⠀⢀⣿⣿⣿⡏⢰⢰⠀⢀⠀⠀⣠⣶⣧⣶⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡰⡷⠡⣔⠌⠃
⠀⠀⠀⣹⡿⢻⡇⢸⣿⣦⣾⣷⣿⣿⡿⣿⣟⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡄
⠀⠀⠀⠁⠀⢸⣿⣶⢸⣿⣿⠿⣫⢋⣴⡿⠛⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠁⠸⣏⡿⠞⠡⠋⠀⠀⠛⠉⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡿⠿⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⠦⣤⣀⣀⠀⠀⠀⠀⢀⣀⡤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣁⡀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢀⣤⣄⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣧⣴⣿⡿⠿⠟⠒⠰⠶⠒⠿⠿⡿⠿⠿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣀⣀⣀⣤⣤⡀⡀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠿⠛⠃⠀⢄⠀⠀⠀⢢⠀⢀⠀⡀⠀⠀⠀⢶⠘⠛⠟⠋⠁⡀⠈⠙⠛⠛⠻⠛⠿⣿⠿⠿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠿⠋⣵⠂⠷⢖⣀⣤⣶⣶⣾⣷⣶⠾⡷⢷⣶⣴⣶⣾⣦⣤⠀⣤⣴⣇⣐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠿⠟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⠐⣛⢋⣉⣴⣾⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠻⣷⣮⣤⣀⠀⠀⡀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⣦⠎⣡⣾⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣆⠈⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠰⠟⠛⠁⣟⣠⣿⣿⡟⣹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢈⣿⣷⣦⣀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣶⠿⠦⠤⣤⣤⣤⣤⣤⣤⣷⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣄⣈⣁⣀
⠀⠀⠀⠀⠀⠀⠀⡀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣭⣿⣴⣶⣶⣶⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣯⠛⠻⠛⠿⠛⠿⠻⠿⢿⡿⠿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⣿⣹⣿⣿⣿⡟⢛⡿⠿⣿⡟⠋⠛⠋⠉⠉⠙⠉⠛⠁⠀⠀⠀⠀⠀⠘⠛⠿⠻⣿⣿⡟⠀⠀⠀⠀⣀⣀⣠⣤⡤⠶⠤⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣦⣾⣅⡀⣿⣇⢀⠀⠀⠀⣀⣤⣤⣤⣀⣴⣶⣄⡀⢁⣀⣀⣤⣦⣿⣿⣿⣦⣶⠞⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠙⠛⠿⠿⠟⠛⠿⠏⠈⠙⠋⠛⢭⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣟⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠀⠀⣀⣀⡀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣪⡥⠴⠒⠒⠊⠉⠉⠐⠒⠲⠶⠶⠶⡶⠖⠛⠛⠉⢩⡙⠛⠳⢦⣝⡷⣄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⣧⠴⠒⠉⠉⠁⠀⠀⠀⡀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣧⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢷⣄⣠⠾⣇⠀⠀⠀⠀⠀⢘⠃⠀⠀⠀⠀⠀⣿⣀⠀⢀⢧⣀⡤⠙⠻⠶⢦⡤⠀⠈
⠀⠀⠀⢲⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠙⠛⠛⠛⠛⠋⠉⠙⠛⠋⠀⠉⠀⠀⠀⠀⡾⠁⠀⠀⡆
⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣄⣀⣀⡀⣀⣀⣀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⡸⠁⠀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⣴⠞⠋⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⢀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠋⢻⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠈⠙⢶⡄⠀⠀⠀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⡟⠉⠉⠻⡟⠛⠓⢶⣦⡤⠤⣶⠞⠉⠉⠙⠆⠀⠀⠁⢀⣠⠾⠃⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠈⢣⠀⠀⠀⠀⣀⣤⠶⠛⠁⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠦⣤⣤⣤⣤⣤⣤⣤⠴⠶⠶⠚⠛⠉⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⠦⣤⣤⣤⣤⣤⡤⠤⠤⠤⠶⠒⠚⠉⠁

⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠙⢧⣆⠀⠀⠴⠦⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⣀⣰⣀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣴⣶⣶⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⢀⠀⠃⠠⡤⣤⡾⠿⠻⠿⣧⡀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢉⠀⠀⠀⠀⠀⢱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢠⠰⠶⠶⠦⢸⣿⣿⣿⣟⣿⣿⡶⠶⣦⣠⣀⣈⠙⠛⠛⠿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠉⠁⣀⠀⣄⢸⣿⣿⣿⣿⣿⣿⣅⡘⠛⠛⢛⣿⣿⣷⠶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣛⡁⣿⣄⣹⣿⣿⣿⣿⣿⣿⣿⡶⠿⢿⣿⣿⡿⠻⡹⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⣫⣿⣿⣿⣿⣿⣿⣷⢾⣶⡿⣿⣶⣶⠆⢹⣽⣿⣿⡿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣻⣿⣿⡿⣿⣿⣥⡘⢻⣿⣆⠸⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣒⣿⣿⣿⣿⠟⣫⣶⡿⢁⠖⠉⢛⣿⣿⣄⣾⡿⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⠿⠻⠟⣯⠿⣏⣾⣃⡞⢀⣴⣿⠛⣻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣧⣤⣼⣿⣿⣛⣿⣷⢿⠃⢯⠘⠉⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡬⢶⠶⠟⢋⠟⠋⠑⠀⠀⠹⠀⠀⢹⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⡀⣀⣀⣀⣀⣀⡈⢿⣿⡏⠳⠀⠀⠤⠤⣤⠤⠄
⠀⠀⠀⢀⢀⠀⠀⢸⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⣚⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⢸⢸⣷⢰⣾⢸⣷⡶⢶⢰⡆⠀⠀⠀⠀⠀⣰⠁⢰⡟⠛⠋⠍⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠁⠈⠈⠁⠀⠀⠀⠀⠀⣧⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢐⣾⣿⠀⠀⢄⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⡿⠿⠿⠶⠶⠦⠄
⠀⠀⠸⠁⣿⠀⣿⠀⡇⢸⠀⣾⠀⢿⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣶⣦⣼⡶⠿⠟⠛⠋⠁⠐⠋⣀⠀⠀⣠⣤⣴⣤⣄
⠀⠀⠀⠀⠈⠀⠋⠀⠁⠈⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠂⢒⠂⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠁⠉⠉⠈⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠘⢿⣿⣿⣿⡟

⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠲⠦⠟⠀⠙⠳⠋⠀⠀⠀⠀⠀⠘⢿⣗⣤⣀⡀⠀⣀⣤⣞⣻⡿⠃⠀⠀⢠⣠⣀⣦⣧⣴⣄
⠀⠀⠀⠀⠀⠀⠈⣦⣦⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠐⠀⠉⠩⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢿⣦
⠀⠀⠀⠀⠀⣠⣼⠟⣿⣿⠉⢷⡄⠀⠀⠂⠀⠀⠀⠀⣿⣆⣶⣶⣧⣸⡇⠀⠀⠀⠀⠀⣼⡿⢻⣿⣿⠷⠄⠈
⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠸⠿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠩⠠⢸⠁⢀⡤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣤⠀⠀⢠⢀⢀⢀⡀⠀⢺⡆
⠀⠀⠀⠀⠀⠀⢠⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠠⠈⠈⠄⠀⠀⠀⠀⠀⠘⣿⣧⠀⢸⣾⣾⣾⣧⣀⡿⠁
⠀⠀⡄⠀⢠⠀⢸⣧⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠜⣻⣿⣿⣿⢿⡟⠯⠁
⠀⠀⢰⣤⣿⣿⡿⠋⠉⡅⠀⠀⡄⠂⡄⠀⢀⡀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠇⠸⠀⠉
⠀⠀⠈⡋⢀⢀⠁⠄⣆⠁⠀⠀⣱⠠⠃⠐⠀⠀⠂⠐⠀⠡⠚⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡀
⠀⠀⠀⠀⠸⡅⢸⠤⠊⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⣾⢶⣷⣴⣦⠀⠘⠀⣦⡿⣾⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠚⠁⠀⡀⠠⠄⠀⠀⠀⠈⠘⠃⠉⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀
⠀⠀⢀⡀⣀⠖⠄⠀⠀⠀⠀⠀⠀⢠⢲⡁⢀⡀⠀⠀⠀⠀⣸⣼⣇⣿⣰⣇⣶⠀⠀⠀⠀⠀⡴⢠⣧⣤⣾⠀⣆
⠀⠀⢰⠭⠅⠀⣴⡶⣶⡄⣠⡶⣶⡆⠀⠨⠵⢳⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣼⣷⣼⣿⣿⣿⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠙⢛⣋⠁⠀⠀⡠⠂⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⢿⠇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠈⠢⣀⠀⠀⠉⠉⠉⠉⣉⠀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠹⢹⠇⠸⠀⢿⠈⠀⠀⠀⢸⠏⢹⠿⠿⠿⠻⣿⠈⣿
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠊⠀⠀⠀⠀⠘⠀⠘⠃⠀⠀⠀⠛⠀⠈

⣿⣿⠿⠿⢻⠿⡿⢻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿