Crosshair Emojis & Symbols

⠀⠀⠀⣀⠴⠤⡀⠀⠀⠀⠀⠀⠀⣠⠴⠤⡀⠀⠀⠀⠀⠀⠀⡠⠔⠤⡀⠀⠀⠀⠀⠀⠀⡠⣶⡤⡀⠀⠀⠀⠀⠀⢀⣤⣶⣤⡀
⠀⠀⠀⡇⠰⠂⢸⠀⠀⠀⠀⠀⠰⡇⢮⠆⡰⠀⠀⠀⠀⠀⢸⠀⢾⠆⠸⠀⠀⠀⠀⠀⢸⢾⣍⣿⡱⠀⠀⠀⠀⠀⢾⣏⠲⣹⡷
⠀⠀⠀⠈⠒⠒⠁⠀⠀⠀⠀⠀⠀⠉⠺⠒⠁⠀⠀⠀⠀⠀⠀⠑⠲⠒⠁⠀⠀⠀⠀⠀⠀⠑⠻⠛⠁⠀⠀⠀⠀⠀⠀⠙⠻⠛⠁


⠀⠀⠀⡠⠒⠲⢄⠀⠀⠀⠀⠀⠀⡤⠒⠢⣄⠀⠀⠀⠀⠀⠀⡤⠒⠢⡄⠀⠀⠀⠀⠀⢀⡤⠒⠢⡀⠀⠀⠀⠀⠀⢀⠴⠒⠢⡀
⠀⠀⠰⡂⠒⠂⢰⠀⠀⠀⠀⠀⠸⡀⠲⠒⢸⠀⠀⠀⠀⠀⢸⠐⢺⠂⢸⠀⠀⠀⠀⠀⢸⠐⢿⠖⡸⠀⠀⠀⠀⠀⢰⠐⣿⠒⡷
⠀⠀⠀⠙⠒⠒⠉⠀⠀⠀⠀⠀⠀⠙⠒⠒⠁⠀⠀⠀⠀⠀⠀⠑⠒⠒⠁⠀⠀⠀⠀⠀⠀⠑⠒⠚⠁⠀⠀⠀⠀⠀⠈⠑⠒⠊⠁


⠀⠀⠀⡤⠒⠒⢄⠀⠀⠀⠀⠀⠀⡤⠒⠒⢄⠀⠀⠀⠀⠀⢀⠔⠒⠒⢄⠀⠀⠀⠀⠀⢀⠔⠒⠢⡄⠀⠀⠀⠀⠀⢀⠔⠒⠢⡄
⠀⠀⠸⡀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠀⠀⠀⠸⠀⠀⠀⠀⠀⢨⠀⠀⠀⡸⠀⠀⠀⠀⠀⢨⠀⠀⠀⡸
⠀⠀⠀⠈⠒⠒⠁⠀⠀⠀⠀⠀⠀⠉⠒⠒⠁⠀⠀⠀⠀⠀⠀⠙⠒⠚⠁⠀⠀⠀⠀⠀⠀⠑⠒⠊⠁⠀⠀⠀⠀⠀⠀⠑⠒⠊


⠀⠀⠀⡔⠒⠒⢄⠀⠀⠀⠀⠀⠀⠔⠒⠒⢄⠀⠀⠀⠀⠀⢀⠔⠂⠒⢄⠀⠀⠀⠀⠀⢀⠔⠒⠒⠄⠀⠀⠀⠀⠀⢀⠔⠒⠢⡄
⠀⠀⠘⡀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡀⠀⠀⡸⠀⠀⠀⠀⠀⢸⡀⠈⠀⡺⠀⠀⠀⠀⠀⢸⠀⠒⠀⡛
⠀⠀⠀⠈⠒⠂⠁⠀⠀⠀⠀⠀⠀⠈⠒⠊⠁⠀⠀⠀⠀⠀⠀⠉⠒⠊⠁⠀⠀⠀⠀⠀⠀⠉⠚⠊⠀⠀⠀⠀⠀⠀⠀⠉⠒⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⢙⣋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠛⠉⠁⠀⢸⣿⣿⠀⠀⠉⠙⠻⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠸⣿⡿⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣸⣿⣧
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄⡀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣤⣄⣀⣸⣿⣿⣀⣀⣤⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⣿⡿⠿⠿⠟⠛⠉

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

⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⡀⠀⠀⠀⠀⠀⢀⡤⠖⠦⢄⠀⠀⠀⠀⠀⢀⢤⡤⣀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠠⠤⠄⢠⠄⠠⠤⠄⠀⠀⣤⣼⠁⠀⢹⣦⡄⠀⠀⢠⠇⠐⠀⠐⠀⢣⠀⠀⠀⢠⣧⣤⣧⣬⡇⠀⠀⠀⠀⠠⣾⠛⣷⠄
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠘⢲⣶⠚⠀⠀⠀⠀⠘⢆⠐⠀⠐⢀⡞⠀⠀⠀⠀⠣⢬⡧⠔⠁⠀⠀⠀⠀⠀⠉⠻⠋
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠉


⠀⠀⢀⡠⢤⡤⣄⠀⠀⠀⠀⠀⣀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠠⢖⠤⠀⠀⠀⠀⠀⠀⡠⠤⠦⢤⡀⠀⠀⠀⠀⠀⣀⣴⣀
⠀⢀⣎⠀⢸⡀⠀⣳⠀⠀⠀⡀⠘⠣⣤⠟⠀⡀⠀⠀⢰⢀⠀⠀⠀⢠⢠⠀⠀⠀⡜⢠⢒⡓⣆⢹⡀⠀⠀⣀⣜⣁⣸⣀⣣⣀
⠀⠈⣏⠉⠹⠉⠉⡹⠀⠀⠀⠀⣠⡞⠉⣦⡀⠀⠀⠀⠸⠈⠀⡀⡀⠈⠘⠀⠀⠀⠳⡈⠢⠥⠃⡼⠀⠀⠀⠀⠑⢄⣸⣠⠎
⠀⠀⠈⠓⠺⠓⠊⠁⠀⠀⠀⠀⠈⠀⠂⠀⠁⠀⠀⠀⠀⠀⠐⠶⠒⠀⠀⠀⠀⠀⠀⠈⠓⠓⠉⠀⠀⠀⠀⠀⠀⠀⠘


⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡤⣤⢄⡀⠀⠀⠀⠀⢀⣠⣤⢄⡀
⠀⠀⡜⠁⠄⠠⠈⢣⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠏⠁⠀⠀⠉⠹⠀⠀⠀⢰⠃⠀⡛⠀⠙⡆⠀⠀⢠⠋⡠⠒⢦⠙⣆
⠀⠀⢇⠀⠌⠡⠀⡸⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⡀⠀⠸⠃⠀⢀⠀⠀⠀⢹⡉⠁⣭⠉⢩⠇⠀⠀⠸⡀⠣⣉⠴⢀⡟
⠀⠀⠈⠑⠲⠖⠊⠁⠀⠀⠀⠿⠄⠀⠀⠀⠤⠇⠀⠀⠀⠷⠤⠀⠀⠤⠾⠀⠀⠀⠀⠙⠒⠿⠒⠉⠀⠀⠀⠀⠙⠲⠶⠖⠋

⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⡔⠁⢹⠁⠑⡄⠀⢀⡞⠉⣈⠈⠳⡄⠀⢠⠟⠁⡀⠉⢳⡀⠀⣰⠋⠉⠉⠙⢦⠀⠀⡔⠁⠀⠀⠑⡄⠀⢀⠞⢁⣀⡈⠳⡀
⠀⠀⠀⠐⡘⠄⠤⠤⠜⡙⠀⢸⡀⠘⠽⠃⢀⡗⠀⢻⠀⠃⡇⠃⢨⠇⠀⣟⠀⠘⠃⠀⣸⠀⠀⡅⠀⠘⠀⠀⡀⠀⠸⠀⠸⠤⠇⠀⡇
⠀⠀⠀⠀⠘⠢⠤⠤⠊⠀⠀⠀⠙⠦⣤⠴⠊⠀⠀⠈⠓⠤⠤⠴⠋⠀⠀⠈⠳⠤⠤⠔⠃⠀⠀⠈⠢⠀⠠⠚⠀⠀⠀⠑⠤⠤⠤⠋
⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢀⡀⡀⣀⠀⢀⡀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⢀⡞⠡⠀⠀⠙⣆⠀⢸⠀⠆⠀⠠⠂⡇⠀⠰⠉⠀⠀⠈⠳⠀⠀⡴⠋⠀⠀⠉⢧⠀⠀⠀⠂⠈⠀⠂⠀⠀⢀⠊⠀⡀⠀⠑⡄
⠀⠀⠀⠘⡇⠀⠘⠀⠀⡿⠀⢸⠀⡀⠛⢀⠀⡇⠀⢫⠀⠀⠀⠀⢨⠃⠀⢯⠀⠀⠀⠀⣸⠀⠀⠉⡀⠈⠀⠈⠁⠀⠸⡀⠐⠛⠀⢀⠇
⠀⠀⠀⠀⠈⠲⠤⠴⠚⠀⠀⠸⠄⠠⠤⠠⠠⠃⠀⠀⠑⠂⠤⠒⠁⠀⠀⠈⠓⠶⠶⠚⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠙⠂⠤⠐⠋
⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⢀⡀⠤⢀⡀⠀⠀⠀⢀⡤⠤⣄⠀⠀⠀⣤⠤⠤⠤⠤⣤⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⢀⡀⡤⢀⡀
⠀⠀⠀⢀⡞⠁⠀⠀⠉⣦⠀⢀⠋⠀⠀⠀⠘⡄⠀⢰⢀⠒⣒⢢⠰⡄⠀⡇⠀⠀⠄⠀⢸⠀⢀⡞⠁⢀⠀⠉⣧⠀⢠⠃⠀⠂⠀⠙⡄
⠀⠀⠀⠘⣇⡀⠈⠀⢀⡟⠀⠘⡄⠀⠀⠀⢀⠇⠀⢹⠘⢌⣋⠘⢡⠃⠀⡇⠀⠑⠊⠀⢸⠀⠘⣇⡀⠈⠁⣀⡟⠀⠘⡁⠁⠀⠀⢈⠇
⠀⠀⠀⠀⠈⠓⠲⠒⠋⠀⠀⠀⠈⠒⠒⠒⠁⠀⠀⠀⠈⠒⠒⠚⠀⠀⠀⠓⠒⠒⠒⠒⠚⠀⠀⠈⠓⠲⠒⠋⠀⠀⠀⠈⠒⠒⠒⠁
⠀⠀⠀⠀⢀⠀⢠⠄⢀⠀⠀⠀⢀⠀⢤⠀⠀⠀⠀⠀⢀⡤⡶⣄⡀⠀⠀⠀⡠⠤⠤⢄⠀⠀⠀⢀⡠⠴⠤⣀⠀⠀⠶⡄⠤⠤⠤⢠⠶
⠀⠀⠀⠀⣀⠁⢀⠀⢁⡄⠀⢀⣀⡀⠘⢀⣀⡀⠀⣰⡋⠀⠀⠀⢹⣄⠀⡌⠀⠒⠐⠀⢱⠀⢀⡎⠀⢀⠀⠈⢂⡀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢁⡄⠀⠀⢄⠁⠀⠈⠀⠀⢠⠀⠀⠁⠀⠙⣆⠀⠀⠀⣸⠋⠀⠡⡀⠀⠀⠀⡜⠀⠈⢇⠀⠀⠀⢀⠎⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠈⠙⠿⠋⠁⠀⠀⠀⠉⠒⠒⠉⠀⠀⠀⠀⠉⠰⠂⠁⠀⠀⠚⠉⠁⠉⠀⠉⠓
⠀⠀⠀⠀⢠⡴⠖⠶⣤⠀⠀⠀⣀⠤⠒⠠⣀⠀⠀⠀⡠⠔⠀⠤⡀⠀⠀⢠⠔⠚⠛⠲⣄⠀⠀⢀⠤⠐⠠⢄⠀⠀⠀⣀⠴⠲⠦⡀
⠀⠀⠀⢠⡏⢀⡸⣀⠀⣧⠀⢠⠁⠀⠄⠄⠈⡆⠀⠘⠀⠠⠠⠀⠈⡄⠀⡏⠀⢴⣲⠀⢸⠀⢀⡇⠀⢠⠀⠀⢁⠀⢸⠃⠓⠀⠊⠘⡇
⠀⠀⠀⠈⢧⡀⠘⠀⣠⠏⠀⠈⢆⠀⠁⠁⡠⠃⠀⠘⣄⠈⠈⠀⡴⠁⠀⠹⣄⣀⣀⣠⠞⠀⠀⢣⡀⠀⠀⣀⠆⠀⠘⣢⠊⠀⠑⣴⠃
⠀⠂⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⠀⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠛⠉
⠀⠀⠀⠀⢀⠔⠒⠒⢄⠀⠀⠀⣠⠖⠒⠲⢄⠀⠀⠀⣠⠀⠀⢀⡄⠀⠀⢠⠖⠛⠛⠲⣄⠀⠀⠆⠐⠒⠒⠀⢂⠀⠀⡠⠒⠒⠂⢄
⠀⠀⠀⢠⡇⠀⡀⡀⠀⣧⠀⢸⠁⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⠀⠄⢸⠄⠀⡇⠀⢠⠀⠀⢸⠀⢰⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠣⣀⣀⡀⡠⠃⠀⠈⢧⣀⠀⣀⡴⠃⠀⠀⠴⠀⠀⠰⠆⠀⠀⠙⢤⣀⣁⣠⠏⠀⠀⡁⠀⢀⠀⠀⢸⠀⠈⢦⡀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠉⠉⠉⠁⠁⠀⠀⠀⠈⠉⠁

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

⠀⠀⠀⠀⠀⠀⢀⣠⢤⡤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠁⠀⠀⠀⢠⠀⠀⠀⠀⠈⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⡦⣄⣀
⠀⠀⠀⠀⢠⠞⢁⠤⠲⡖⠤⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠸⠃⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠀⢀⡅⠀⠈⠳⣄
⠀⠀⠀⢠⠇⡰⢁⠖⠉⠋⠲⡌⢣⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠔⠘⠃⠢⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⢀⠔⠙⠋⠲⡄⠀⠘⡆
⠀⠀⠀⢺⡃⡟⠻⡂⠀⠀⢀⡟⢻⠒⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠸⡂⠀⠀⢘⠃⢘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡓⠒⠻⡓⠚⡗⢒⡟⠒⠘⡟⠂
⠀⠀⠀⠀⢧⡘⢦⡙⠲⡗⢋⡴⠃⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠈⢺⠂⠁⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠉⠲⡗⠋⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠙⠦⣌⣙⣏⣡⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢺⠒⠈⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣠⣇⣠⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⡤⠖⢶⠲⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⢿⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⢺⠒⠦⣄
⠀⠀⠀⢀⡜⠁⠀⠀⠘⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢀⣠⣾⣤⡀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⢀⣸⣀⠀⠀⠑⡄
⠀⠀⠀⢸⣀⡀⠀⠀⣀⡀⠀⢀⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⢠⡟⠁⣀⡀⢹⣆⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⡀⠀⣰⠁⣀⡀⢱⡀⠀⣸⡀
⠀⠀⠀⢸⠉⠁⠀⠀⠉⠁⠀⠈⠉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠀⠘⣯⡀⢉⠁⣸⠏⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⠀⠁⠹⡀⠉⠁⡸⠁⠈⢹⠁⠁
⠀⠀⠀⠈⢣⡀⠀⠀⢠⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠈⠙⢿⠛⠁⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠈⢹⠉⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠈⠓⠦⠾⠴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣾⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢼⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘


⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣅⣀⡀
⠀⠀⠀⠀⢀⠔⠉⠀⠸⡇⠀⠉⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⢸⡇⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠁⢀⡃⠀⠉⠲⡄
⠀⠀⠀⢠⡏⠀⠀⠀⠀⡀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠠⠊⠉⠉⠑⢆⠀⠹⡄
⠀⠀⠀⢸⠖⠒⠀⠀⠲⡗⠀⠀⠒⠒⡇⠀⠀⠀⠀⠀⠀⠀⠒⢺⠒⠒⠀⠀⠺⠇⠀⠐⠒⢺⡗⠒⠀⠀⠀⠀⠀⠀⠀⠐⢺⠒⠒⡗⠂⠰⠂⠀⢺⠒⠒⡗⠒
⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠘⠢⢠⣄⠴⠋⠀⡰⠁
⠀⠀⠀⠀⠈⠳⢤⣀⣸⣇⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣸⣇⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⣀⣀⣂⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠾⠿⠟⠛⠛⠛⠛⠿⠿⢶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠋⠉⠁⣿⡇⠉⠉⠛⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣀⣀⣀⣀⣀⣀⣀⣟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣘⣇⣀⣀⣀⣀⣀⣀⣀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠛⠛⠛⠛⠛⠛⠛⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⢛⡟⠛⠛⠛⠛⠛⠛⠛⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⡀⠀⠀⣿⡇⠀⠀⣀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⣿⡟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⣶⣤⣤⣄⣀⣈⣀⣠⣤⣤⣴⡶⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠠⠂⢉⣉⡉⠀⠠⡀⠀⠀⠀⠀⠀⡠⠒⠉⠉⠉⠑⠢⡀⠀⠀⠀⠀⠀⡠⠐⠈⣉⡉⠀⠢⡀⠀⠀⠀⠀⠀⣠⠐⠈⢹⡏⠁⠢⡄
⠀⠀⠀⠀⠎⢀⠊⢁⣀⡀⠑⡄⠐⠀⠀⠀⠀⡎⠀⠀⠀⣀⠀⠀⠀⠙⡄⠀⠀⠀⡘⠀⠔⠁⠀⠀⠁⠄⠈⡀⠀⠀⠀⡐⠀⠀⠀⠈⠀⠀⠀⠈⠆
⠀⠀⠀⠸⠀⢀⠀⢿⣿⡿⠀⡄⠀⠀⠀⠀⠐⡇⠀⠀⠒⢐⠐⠀⠀⠀⡇⠀⠀⠀⡇⠸⠀⠀⠐⠀⠀⠸⠀⡇⠀⠀⠀⡿⠖⠂⠀⠸⠂⠀⠒⠲⠷
⠀⠀⠀⠀⠣⠈⠢⢄⣀⠀⠔⠁⡔⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠰⡀⠑⠄⣀⡀⠔⠁⡠⠀⠀⠀⠀⠐⣀⠀⠀⢠⡀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠁⠂⠠⠤⠤⠐⠈⠀⠀⠀⠀⠀⠀⠉⠲⠤⠤⠤⠔⠊⠀⠀⠀⠀⠀⠀⠈⠂⠀⢤⠤⠀⠊⠀⠀⠀⠀⠀⠀⠈⠂⠀⠼⠧⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠠⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢴⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣾⡧⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⢄⡀
⠀⠀⠀⠀⠀⢴⣄⠀⢿⠀⣠⡦⠀⠀⠀⠀⠀⣠⠊⠁⠀⢤⢀⠀⠙⢆⠀⠀⠀⠀⢠⠞⠁⠀⠺⠃⠀⠙⢦⠀⠀⠀⠀⢀⠞⣡⠄⠀⠀⠤⡌⢢⡀
⠀⠀⠀⣤⣤⣀⡈⠀⣀⠀⢁⣀⣠⣄⠀⠀⢀⡃⢀⣌⠀⣀⡀⢑⡀⠈⣆⠀⢀⣀⣏⣀⠀⠀⣤⡄⠀⢀⣈⣧⣀⠀⠀⡎⠀⠁⠋⠀⠀⠁⠁⠀⢣
⠀⠀⠀⠙⠉⠉⣀⠀⠉⠀⣀⠉⠉⠋⠀⠀⠈⡅⠀⠁⠀⠉⠀⡠⠁⢀⠇⠀⠈⠉⣏⠉⠀⠀⠙⠁⠀⠈⢉⡏⠉⠀⠀⢇⠀⡀⠄⠀⠀⡀⡀⠀⡜
⠀⠀⠀⠀⠀⠘⠃⠀⣾⠀⠘⠃⠀⠀⠀⠀⠀⠘⢦⡀⠈⠙⠉⠀⡠⠊⠀⠀⠀⠀⠘⢦⡀⠀⢴⡄⠀⣠⠞⠀⠀⠀⠀⠈⠢⡉⠁⠀⠀⠈⣁⠜
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠉

⠀⠀⠀⠀⠀⡠⠔⠒⠀⠒⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⣀⡐⠂⠄⠀⠀⠀⠀⠀⠀⢀⠴⠒⠂⠐⠒⢤⡀
⠀⠀⠀⠀⡜⠀⠠⠀⠚⠀⠄⠀⢱⡀⠀⠀⠀⡀⠀⠀⠀⠨⠀⠀⠀⠀⡀⠀⠀⠀⠰⢁⠔⣡⣤⣤⡁⢂⠑⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⢸⠀⠠⡇⠀⠀⠀⠰⠆⠀⠇⠀⠀⠠⠦⠠⠠⠀⠀⠀⠀⠠⠤⡇⠀⠀⠀⡇⠄⢰⣿⠁⢙⣿⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢆⠀⠑⠤⣤⠠⠊⠀⡸⠁⠀⠀⠀⠁⠀⠀⠀⢐⠀⠀⠀⠀⠁⠀⠀⠀⠡⠘⢄⠙⠻⠛⢁⠜⢠⠃⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠈⠓⠤⣀⣈⣀⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⢈⣀⡈⠡⠔⠁⠀⠀⠀⠀⠀⠙⠦⢄⣀⣀⡠⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⠄⠂⠀⠐⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⢀⣀⣀⠀⠈⢢⡀⠀⠀⠀⠀⡴⠋⡀⠸⠠⢈⠑⢄
⠀⠀⠀⠀⣤⣅⣀⠀⠀⠀⣀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡐⠁⢈⠀⠑⡀⠀⢣⠀⠀⠀⡌⠀⠂⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠉⢅⠀⠀⢀⠀⠀⡸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⡀⠉⢏⠀⠛⠃⢈⠋⠁⡸⠀⠀⠀⡏⠉⠀⠀⠀⠀⠀⢀⠁⡙
⠀⠀⠀⠀⠀⠀⠑⠀⣿⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠑⠰⠀⠉⠀⡠⠃⠀⠀⠀⠘⢄⠀⠀⢠⠄⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⠤⠤⠖⠊⠀⠀⠀⠀⠀⠀⠀⠉⠒⠐⠂⠒⠉

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

⣿⣿⠛⢿⢛⠿⣿⢟⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠂⠈⡃⢸⠁⠀⠒⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⢀⡀⠄⠒⠀⠈⡃⢸⠀⠀⠒⠠⢀⡀⠁⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⠠⠊⠁⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠈⠑⠄⡀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⢀⡅⢸⡀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⢀⠎⠀⠀⠀⠀⠀⡠⠐⠈⣀⠠⡇⢠⠄⣀⠁⠂⢄⠀⠀⠀⠀⠀⠱⡀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠄⠀⠀⠀⠀⢀⠊⢀⠔⠉⠀⠀⡆⢨⠀⠀⠉⠢⡀⠑⡀⠀⠀⠀⠀⠠⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⠀⠀⠀⠀⠀⠂⢠⠃⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠘⡄⠘⠀⠀⠀⠀⠀⠃⠀⠆
⠀⠀⢀⠄⠤⠤⠤⠄⠦⠠⠦⠤⠤⠄⠄⠴⠠⠦⠤⠠⠤⠤⠠⠃⠘⠤⠤⠤⠤⠤⠴⠀⠦⠤⠤⠄⠄⠤⠀⠴⠠⠤⠤⠤⠤⡀
⠀⠀⠈⠒⠒⠒⠒⠒⠖⠒⠒⠒⠒⠒⠒⠲⠒⠖⠒⠒⠒⠒⠒⡄⢠⠒⠒⠒⠒⠒⠲⠒⠖⠒⠒⠒⠒⠒⠒⠲⠒⠒⠒⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⠀⠀⠀⠀⠈⠄⠘⡄⠀⠀⠀⠀⡃⢰⠀⠀⠀⠀⢠⠃⠠⠀⠀⠀⠀⠀⡄⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢂⠀⠀⠀⠀⠈⢄⠈⠢⣀⠀⠀⡇⢸⠀⠀⣀⠔⠁⡠⠁⠀⠀⠀⠀⠐⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠈⢆⠀⠀⠀⠀⠀⠑⠠⢀⠉⠐⠃⠸⠂⠁⡀⠄⠊⠀⠀⠀⠀⠀⡐⠁⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠈⡃⢸⠁⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⠐⢄⡀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⢀⡠⠂⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠈⠀⠂⠤⠀⠀⡅⢸⠀⠀⠤⠐⠀⠁⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠤⠄⢀⡄⢸⠀⠠⠤⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠜

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




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣿⣷⣶⣶⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠿⠛⠋⠉⠉⠉⣿⡏⠉⠉⠉⠛⠛⠿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⣿⡟⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⢠⣤⣤⣤⣼⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣯⣤⣤⣿⣧⣤⣼⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣤⣤⣤⣤
⠀⠀⠀⠀⠈⠉⠉⠉⢻⣿⡋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⠉⠙⣿⡟⠉⢹⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣻⣿⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣿⣧⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣶⣤⣤⣄⣀⣿⣇⣀⣤⣤⣴⣶⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⣿⡿⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃

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

⠀⠀⠀⠀⣠⢴⡧⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⡧⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠦⢄⡀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠦⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠦⢤⡀
⠀⠀⣀⢞⡀⢈⡁⢀⣳⣀⠀⠀⠀⠀⣀⣞⠀⡬⢥⠈⣳⠀⠀⠀⠀⠀⢀⡏⢀⣸⣆⡀⢱⡀⠀⠀⠀⠀⢀⡏⡾⠏⠿⢦⢱⡀⠀⠀⠀⠀⢀⡏⡞⢉⡉⢣⢱⡀
⠀⠀⠉⢯⠁⢈⡁⠈⡽⠉⠀⠀⠀⠀⠉⢯⠀⢓⡚⢈⡽⠉⠀⠀⠀⠀⠈⣇⠉⠹⠏⠁⡸⠁⠀⠀⠀⠀⠈⣇⢳⣦⣶⠞⡸⠁⠀⠀⠀⠀⠈⣏⢧⣈⣁⠜⡸⠁
⠀⠀⠀⠀⠙⢺⡗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢺⡗⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠖⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠲⠖⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠲⠖⠊⠁


⠀⠀⠀⢀⡤⠶⡶⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⢶⠶⢤⡀
⠀⠀⢠⣏⣀⣀⣇⣀⣹⡄⠀⠀⠀⠀⢠⡏⣀⣸⣀⣀⢹⡄⠀⠀⠀⠀⢠⠏⢀⣀⣀⢀⠹⡀⠀⠀⠀⠀⢠⡏⣀⣴⣦⡀⢹⡄⠀⠀⠀⠀⢠⣏⣀⣼⣦⣀⣹⡄
⠀⠀⠘⣇⠀⠨⡇⠀⣸⠃⠀⠀⠀⠀⠘⣇⠀⢸⠁⠀⣸⠃⠀⠀⠀⠀⠘⣆⠀⠘⠁⠀⣰⠃⠀⠀⠀⠀⠘⣇⠈⠻⠟⠁⣸⠃⠀⠀⠀⠀⠘⣇⠈⢺⠞⠁⣸⠃
⠀⠀⠀⠈⠓⠶⠷⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠾⠶⠚⠁


⠀⠀⠀⢀⡤⠖⠒⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠲⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠲⢤⡀
⠀⠀⢠⠋⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢠⠏⠀⢀⠀⠀⠹⡄
⠀⠀⠘⣆⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠘⣆⠀⠈⠀⠀⣰⠃
⠀⠀⠀⠈⠓⠶⠶⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⠶⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠚⠁


⠀⠀⠀⢀⡴⠶⠶⢤⡀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠲⢤⡀⠀⠀⠀⠀⠀⠀⢀⠴⠲⠖⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⢶⡶⢤⡀
⠀⠀⢠⡏⢀⠀⡀⠀⢙⡄⠀⠀⠀⠀⢰⡏⢀⢐⡂⡀⢹⡄⠀⠀⠀⠀⢠⡋⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⢠⡇⢀⢀⣀⢀⢹⡄⠀⠀⠀⠀⢠⣋⠀⢀⡀⢀⣹⡄
⠀⠀⠘⣆⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠘⣏⠀⠀⠀⠀⣹⠃⠀⠀⠀⠀⠘⣇⠀⠀⠈⠀⣹⠃
⠀⠀⠀⠈⠓⠶⠶⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠚⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠒⠚⠙⠉⠙⠙⠒⠲⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧
⠀⠀⠀⠀⠀⠀⠀⣤⠶⠾⠁⠀⠀⠀⢤⡠⠤⠤⡠⠄⠀⠀⠀⠹⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢹⡄
⠀⠀⠀⠀⢠⣶⠟⠇⠀⠐⠊⠑⠒⠢⠀⠀⠀⠀⠀⠔⠒⠒⠉⠒⠀⠘⠟⢷⣄⠀⠀⠀⠀⠀⢰⢻⢸⣷
⠀⠀⢀⡤⣾⠷⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠸⣿⣦⡀⠀⠀⠀⢸⣾⢸⣿⡀
⠀⠀⠸⣿⣿⣄⣀⣀⣸⡄⠀⠀⠀⢸⡇⠀⠀⠀⢀⡇⠀⠀⠀⢀⣾⣀⣀⣠⣾⣷⡟⠀⠀⠀⢸⢿⢸⣿⡇
⠀⠀⠀⠈⢿⣿⢿⣿⣿⣿⣷⣶⣶⣿⣿⣶⣶⣶⣿⣿⣷⣶⣶⣿⣿⣿⣿⢿⣿⠋⠀⢀⣠⣶⣿⢸⣿⠀⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠉⠙⠙⠻⣯⣿⠿⠿⣿⣿⣿⡿⣿⣿⣿⡿⠿⢿⣯⡿⠋⠛⠉⠁⠀⠀⠸⠟⠛⢻⠈⣿⠀⡟⠛⠻⠇
⠀⠀⠀⠀⠀⠀⠀⣤⣤⠖⠛⠛⠛⠛⠛⠉⠉⠉⠹⠛⠛⠛⠛⠳⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠤⠤⠶⣷⣤⣴⣤⣤⣤⣴⡷⠦⠤⠖⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠘⣿⡇⠁⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡇⢿⠀⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⢸⡇⢀⣿⡇⢸⣇⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠿⡏⡟⠏⠉⠉
⠀⠀⠀⠀⠀⢀⡤⠔⠉⡩⡤⠖⠂⢸⡇⢸⣿⣧⢸⣿⠀⠒⢤⢌⡉⠳⠤⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⣀⣤⣤⣿⣇⡾⣿⠿⣌⣿⣤⣤⣄⡀⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⣆⢸⠀⢸⢸
⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⡟⠉⠀⠈⠛⠀⠀⠀⠘⠁⠀⠉⢻⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⢿⠘⣦⠏⣸
⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⢀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠘⣧⠈⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⢶⡤⢷⣤⣴⢦⡴⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢀⣀⣀⢀⣀⣀
⠀⠠⠀⠋⠋⠛⠚⠛⠛⠓⠠⠆⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠂
⠀⠒⠉⠓⠀⠉⠀⠉⠒⠘⠀⠀⠀⠈⠀⠀⠀⠀⢀⢀⣙⠇⠀⢀⠢⡤⠀⠀⠀⠀⠀⠀⡀⠀⠠⠐⢀⡀⣀⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠄⠡⠀⠀⠈⠉⠀⠁⠁⣤⠈
⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠠⠀⠀⠰⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢧⡄⠀⠄
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡈⠠⠌⠀⠠⡀⠀⠀⠀⠀⠦
⠀⠀⠀⣤⣀⣤⡀⣀⣀⠒⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⢀⡹⠟⠚⠛⠛⡦⠆⠀⠀⠠⠉⠀⠀⠀⠀⣴⣼⣳⣿⡶⣤⡄⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⢰⠂⠠⠤⠂
⠀⠀⠀⠀⠘⠀⠋⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⢀⡞⠀⠈⠀⠀⠀⣀⠁⠐⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢁⠻⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣄⡀⠀⠀⠀⢀⣀⣠⡤⠶⠋⠀⠀⠀⠆⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠓⠒⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠢⢄⠀⠀⠀⠠⣀⢀⡀⡀⠀⢂⠤⣀⣠⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠻⠻⠟⠶⠓
⠀⠀⠀⠑⠒⠂⠀⠀⠀⠈⠀⠀⠈⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⣀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋


⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠀⠀⢤⣤⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣯⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⢀⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢗⠴⠀⢛⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⡏⣽⣛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⠠⠔⠂⠈⠉⢡⠼⠉⠈⠙⠛⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⡄⣀⢀⡀⢈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂
⣶⣿⣿⣿⣷⣮⣿⣦⣶⣭⣶⣶⣶⣖
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡃⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⣰⠏⣠⠞⢙⢒⣙⣧⡀
⠀⠀⠀⠀⠀⣼⠃⣼⡃⣰⠋⠉⠙⣎⣷
⠀⠀⠀⠀⣸⠇⣸⠇⡼⠁⣀⣄⡀⠸⣾⡇
⠀⠀⠀⢠⡏⢠⡿⣹⢡⡞⣡⢤⣙⡆⣿⣿
⠀⠀⠀⣸⠁⣾⠃⡇⡾⡾⢁⣀⠹⣿⢸⣿⡆
⠀⠀⠀⣿⢀⡟⣸⢹⢿⣧⢯⡿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣚⣖⣖⣲⣟⡿⠃
⠀⠀⠀⣿⢸⡏⣹⢸⣽⢸⢸⣿⣿⣿⠷⣿⡗⠒⠒⠒⠚⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⣝⣹⣋⣙⣭⣳
⠀⠀⠀⣿⢸⣧⢺⢸⢿⠸⣼⢯⢇⣿⢸⣿⡇
⠀⠀⠀⣿⠈⣷⢺⠸⡾⣆⠙⠋⣼⡏⢸⣿
⠀⠀⠀⢸⡄⢿⡜⡇⢳⡜⠦⠜⡿⢁⢿⡟
⠀⠀⠀⠈⣧⢸⡗⣹⡀⠙⠒⠛⢁⡞⣼⠇
⠀⠀⠀⠀⢹⡆⢷⡑⠳⣤⣀⣴⡫⣷⠋
⠀⠀⠀⠀⠀⠻⣎⢻⣔⠤⠊⣪⡿⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⠛⠉

⠬⠐⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠈⠀⠀⠹⡀⠹⠋⣳⡍⣿⡴⢿⣟⠉⡝⠀⠜⡩⠊⠰⢁⠞⠙⠁⡠⠞⠁
⢤⣄⠀⠀⠀⠀⠀⠁⠈⢢⣴⠦⠤⣤⣄⡀⠀⠀⠀⠀⢠⢖⠛⣧⣄⢸⢱⠟⠋⠀⠀⣻⡜⣁⣤⣀⣁⣀⣀⢄⣀⣤⡈⠀⠀⠀⠀⣠⣔
⣒⠠⠀⠒⠄⠀⠀⠀⠀⣟⡀⠠⢀⠤⣼⠋⠗⠓⢀⢴⢟⡀⠀⠈⠀⠚⠓⡶⠀⠀⠈⠋⠉⠉⠀⠁⠠⠏⠀⢀⠃⠀⢻⡆⡠⠐⠉
⡒⠀⠠⠤⣀⠀⠀⠀⠀⣽⠂⠀⡈⠂⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠈⠀⣀⡾⠃⠀⠀⠀⠀⢠
⠉⠛⠂⠀⠀⠀⠀⠀⠀⠈⢲⡆⠁⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⠈⠠⢿⠉⠉⡧⠀⠀⠀⢘⡆⠀⠀⠀⠀⠑⠉
⠤⠄⠀⠀⠀⠀⠀⢀⡠⠤⣴⢳⡤⠀⠀⠀⠀⠀⠁⠰⠐⠀⣀⠀⠀⢢⠈⡄⠊⠁⠀⠁⠀⠀⠀⠀⠘⠃⠀⡴⠚⣫⠄
⠴⠒⠦⠤⠀⢀⡜⠉⠛⠁⠘⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠛⠉⠉⠷⣶⢦⡄⢀
⡒⠖⠂⠀⠀⣸⡏⠁⣀⠔⠚⠀⠈⠒⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⣠⠟⣙
⢛⢉⡴⠎⠉⠃⠀⠸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⡷⠀⠀⠀⠀⠀⠀⠀⡀⠶
⠈⣿⣀⡀⠀⢀⠀⢀⡀⠀⢀⠀⠒⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢤⣤
⡒⡚⠻⠷⢶⣟⠀⠈⠳⢴⣎⡠⠀⠀⠀⠀⠀⠈⠀⢠⠀⠄⠆⠀⠀⠀⢀⠀⠠⠄⠈⠈⠀⠀⠀⠀⠀⠁⠀⠄⢰⡄⠀⠀⣀⣀
⢀⣀⡀⠀⠀⠘⠳⣤⣄⣀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠂⢀⠀⠀⠈⠀⠀⠀⠈⠀⠐⠄⠀⠀⠀⠀⠀⢴⢼⠁⢤⠚⠋⠉⠂⢉⣉
⠿⠁⠀⠀⠀⠀⢀⠀⠍⠁⣻⠀⠀⠀⠀⠈⠙⠉⡉⠀⡀⠀⢀⣀⡁⠀⢆⠀⠀⠈⠁⠀⠈⠉⠀⡠⠶⣤⡤⠞⠋⢀⡖⠀⠈⠐⠒⠄⠠
⠈⠀⠀⠀⡠⠂⠁⠀⢀⣴⠿⣄⣄⣡⠴⡄⠀⣠⡷⢚⠂⠀⠀⣹⡍⠂⢢⣄⣀⣤⠟⠦⠴⢧⣀⣀⣶⠏⠓⠲⠞⠋⠁⠀⠈⠀⢄⠐⠠
⣖⠔⠊⠀⠀⡠⠔⠋⠙⠁⠀⠀⠀⠀⠀⠉⠋⣱⠃⠸⣏⣠⣴⠋⢷⡄⠀⠀⢡⠇⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠁⠀⢀⡴⢋⡤⠊⢁⣀⣠⢂⡖⢠⢈⡠⠀⢰⢃⣴⣤⡌⢷⡱⢳⣧⣙⡃⢟⢉⠀⠀⠀⠁⠀⢰⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⣤⡀⠀⢀⣠⣤⡴⠶⢶⡶⡶⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡖⠲⠞⠁⡠⠟⠛⢫⣀⡤⠬⠧⠦⠷⠼⢤⣥⣹⢹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡷⠀⠐⠿⣍⡷⠋⠸⣄⠀⠀⠀⠀⠀⠀⠀⠙⢾⣀⢷⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣋⣤⣤⠀⠀⣀⠀⢿⠓⠾⠀⠀⠀⢀⣤⣴⠶⠶⠿⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠁⠀⢸⢠⠞⠉⠓⠾⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⢀⣀⣠⣤⡼⠿⠛⠛⠁⠀⠀⠀⠉⠙⠛⠻⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣷⠀⠀⠀⠀⠘⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢁⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠁⠀⠙⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⡛⠋⢙⡿⠁⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⢀⣴⠋⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠿⠛⠉⠀⠀⠉⠛⢷⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢀⡾⠁⠀⣿⡇⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣾⢁⣶⣷⢻⡀⠀⢠⡇⢀⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡏⣼⣿⡟⢈⣿⠞⠁⠉⣏⠀⢰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣽⡇⢿⠿⢁⣾⠇⠀⠀⠀⢿⠀⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠸⣷⣤⣴⠿⠁⠀⠀⠀⠀⠸⣧⠹⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠾⣫⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣟⡛⠛⠛⠛⠉⠉⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠂⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠈⠉⠉⠉⠛⠳⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠃⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤⣀⠀⠀⠀⠀⠙⠿⣿⣷⣦⣤⣀⣀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣄⡀⠀⠈⠛⠿⣿⣿⣿⡟⠛⠛⠛⢻⡍⠀⢀⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣤⣤⣤⣤⣤⣿⡒⠦⣄⣀⢻⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⢸⣇⠀⠀⠈⠙⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠛⠛⠒⠾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢀⣴⠶⠾⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣯⣥⣤⣴⠟⠁
⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⡿⢿⡿⠿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⠁⠀⠀⠀⡇⠀⠀⠀⠉⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⣀⣤⣤⣶⣷⣦⣤⣀⠀⠀⠀⠉⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⣠⣾⠿⠛⠉⠉⡏⠉⠙⠻⣿⣦⡀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⣼⡿⠃⠀⠀⣀⣤⣧⣄⡀⠀⠈⠻⣿⡄⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢰⣿⠃⠀⠀⣼⣿⣿⣿⣿⣿⡄⠀⠀⢻⣷⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠘⠛⣿⡟⠛⠛⢻⣿⡛⠛⠛⣿⣿⣿⣿⣿⣿⡟⠛⠛⣻⣿⠛⠛⠛⣿⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠈⢿⣧⠀⠀⠈⠻⢿⣿⠿⠋⠀⠀⢠⣿⠇⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠈⢿⣷⣄⡀⠀⠀⡇⠀⠀⣀⣴⣿⠋⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠉⠻⠿⣷⣶⣷⣶⡿⠿⠋⠁⠀⠀⣠⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣦⣤⣤⣧⣤⣤⣶⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⡟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀
⠀⠀⠀⠀⠀⢤⡤⣤⣤⠄⣀⢠⣤⣤⣄⣤⢀⡀⣤⢤⣥⣴⣞⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠛⠁⠀⠘⠃⠛⠘⠛⠈⠘⠃⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣀⡀⠀⠀⣀⣀⣀⢀⣀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠴⠚⠀⠂⠀⠉⠱⠟⠃⠈⠉⠋⠀⠛⠀⠈⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀⣞⠉⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡔⠒⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠐⡀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠁⠙⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣋⡄⠀⠠⠆⠀⠀⠀⠀⠀⡂⣺⠦⠋⠄⠀⠄⠀⠉⢍⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⢀⢶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢅⣀⣑⠂⠀⠀⠀⠀⠾⠟⠻⣷⡀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣷⠲⠀⠀⠀⠀⠀⠀⠂⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⣀⠂⠐⠒⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠐⠀⠀⠙⠁⡀⡀⠄⣰⠦⠤⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠬⠤⠖⢇⣠⣀⡤⣧⠀⠀⠀⠀⠀⢠⣅⣀⡤⠐⠛⠲⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢼⡆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠉⠑⠊⡀⢿⠃⡀⠀⠀⠀⣿⠉⠑⠋⠉⣉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⣀⣀⡀⠀⠘⠋⠙⠆⢉⠒⠛⠐⠁⢀⡄⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠴⠴⡾⠹⠤⣀⣰⣠⠖⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⣀⠀⠀⠀⣠⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂⠤⢤⡖⠒⠖⡇⠀⢀⠀⣿⠈⠑⠒⡋⠁⠈⠉⡦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠕⠀⡠⠒⠊⠉⠀⠔⠓⡴⣉⡊⠁⠃⠀⠒⠀⠀⠀⠐⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡷⠰⠀⠀⠔⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣴⡃
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠴⠋⠁⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠂⠒⠐⠒⠒⠂⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠐⠒⠒⠈⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⡖⠒⠛⠛⢛⠒⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡆⢹⠀⢹⡀⠸⡄⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢰⠃⠸⡀⠈⣇⠀⢳⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⡾⠀⠀⣇⠀⢸⡄⠘⣇⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢰⠇⠀⡶⢸⠀⠀⣧⠀⢹⡄⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣼⠀⢠⡇⠈⡆⠀⠸⡄⠀⢷⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠁⠀⢸⠀⠀⢱⠀⠀⠳⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⣿⡆⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⢞⡪⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠧⠹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠶⠒⢁⡠⠤⣄⡀⠑⠦⠤⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢰⠃⠀⠀⠀⠙⡆⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡆⠸⡀⠀⠀⠀⢀⡇⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠙⠲⠤⠴⠋⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣀⡤⠖⠛⠓⠦⣄⡀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠴⠚⠁⠀⠀⠀⠀⠀⠀⠉⠓⠾⠂



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀
⠀⠀⠀⠢⣄⡈⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣀⠤⣤⡀⢀⡀
⠀⠀⠀⠀⠀⠙⠳⡂⢌⡛⢶⠤⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠉⠉⠳⡃⠀⡤⠚⠉⠉⠲⣄⠀⠀⠀⠀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⡀⠈⠲⢌⠉⠓⠊⠙⠳⡴⠚⠓⠶⠉⠈⢀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⡇⠀⣀⠤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠲⣦⡽⠄⠀⠀⠀⠢⣄⠀⠀⠀⠀⠈⣇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠⠗⢋⣵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⢿⠄⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡙⠦⡼⠘⢤⠃⡇⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢳⡆⠀⠀⠀⢀⣠⣤⠿⠀⠀⠀⠀⠀⠉⢹⣃⣀⣤⣤⠶⠚⠉⠀⠀⠀⠀⠰⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⢈⣉⡷⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣁⣀⠀⠀⠀⠀⠀⠀⣠⠤⠬⠅⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠆⠀⠀⠐⠒⠛⠻⠶⡄⠀⠀⠀⠀⠀⠀⠀⡤⢝⣷⣌⡉⠁⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⢀⡼⠥⢄⠀⠀⠀⠀⠀⠀⠱⡄⠀⠈⠉⠓⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣲⠔⠀⠀⠀⠀⠀⠀⠀⠀⡸⢀⣴⣴⡀⣶⣾⡁⠚⠆⠀⠀⠀⠀⠀⠀⠀⢺⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠏⠘⠇⢷⡏⠃⠙⠀⠀⠀⠀⡔⠢⠤⣀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⣀⣴⡯⠴⠒⣞⠉⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠙⠒⢄
⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠙⠢⢤⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢠⡤⠖⠁⠀⠀⠰⣕⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣖⠚⠁⠀⠀⠀⠀⠀⠀⠁⠠⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢲⣶⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⡏⠹⡄⠀⠀⠀⢀⡄⠀⠀⠀⡇⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡘⠀⠀⠉⠓⠒⠚⠁⠘⠦⠤⠞⠁⠀⠈⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠰⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠀⠀⠰⣄⣀⠀⠀⢀⣠⣶⠾⠼⢶⣤⣤⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⢄⣽⣷⣶⣾⣿⣟⣥⣄⠀⠀⠈⠛⠻⢷⣄⡀⢤⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣬⣷⣽⠏⠁⡦⠊⠀⠀⠀⠀⠀⠀⠈⢲⣾⣿⣏⣴⡙⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣏⡄⠀⠀⠀⡠⠔⠚⠓⠒⠄⠀⠈⠙⠍⠙⢿⣧⣤⣤⡶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠐⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⣿⠁⠉⠲⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠻⡀⢠⠀⠀⠀⠘⣆⡀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡦⠀⠀⠀⠀⠉⠒⠒⠀⠀⠀⠀⠀⠀⠀⢀⣦⣼⣧⡑⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣭⣾⣷⣄⢀⡀⢤⣠⢤⡀⠀⠀⠀⡠⠀⠀⠐⢺⣿⠁⠈⠉⠓⠤
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠈⢦⣙⠿⠿⣿⡛⣆⣈⣉⣙⣳⣶⣍⣂⣀⣠⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⠉⠁⢈⠛⠻⠿⠛⡋⠉⠺⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠉⠛⠛⠉⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣁⣉⣉⢉⣉⣏⣉⣉⣉⣷⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠀⠚⠚⠛⠛⠛⠛⠁

⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⡾
⠀⠀⠙⠷⡄⠀⣧⡀⠀⠀⠋⠀⣠⠄
⠀⠀⠀⠀⠀⠀⢻⠻⢦⠴⢲⡟⠁⠀⢀⣤⣤⣤⠄⠀⣀⠄⡖⢰⢂⡐⠀⠤⡀
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠺⣤⣄⣀⠀⠀⠀⣠⠔⠃⣹⠔⠋⠁⠀⠀⠹⡄⠘⡄
⠲⠖⠒⠂⣠⣞⠁⠀⠀⣤⡾⠻⠥⠤⢰⠊⣇⠠⠖⠉⠀⠀⠀⠀⠀⠀⠀⡗⠈⡃
⠀⠀⠴⠚⠋⠉⠉⢻⣴⠋⣯⠘⠃⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣗⣉⣅⣀⣀
⠀⢀⣠⠀⠀⣴⠀⠘⠏⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠿⠛⠛⠋⠉⠉⠉⠙⠛⠛⠻⢷⡆
⠴⠋⠁⠀⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⣤⡤⠶⠶⠶⠶⠶⠶⠶⢤⣤⣼⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⢀⣠⣤⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⡷⠶⠤⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠴⠚⠛⠛⡟⠛⠿⠿⠿⣿⣿⣿⣷⣶⣶⣤⣤⣀⣿⠀⠀⣆⣤⣴⣾⡿⠿⠟⠛⠋⠉⠀⣷⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠘⢽⣿⣿⠏⠉⠙⠛⠛⣿⠀⠀⢻⢿⣿⣯⠁⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⣀⠀⠀⠀⠀⠀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠈⠛⠲⠶⠶⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⣼⡇⠀⠀⠀⠐⠋⣿⠛⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠘⣧⠉⠛⣶⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠴⢶⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⡿⠀⠀⠀⠉⢹⡏⠉⠉⠉⠉⢹⡏⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣷⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⡀⣾⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣽⠞⠹⡆⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢤⣄⣀⠀⠀⠀⣿⣀⣀⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠶⠦⣤⣤⣤⣤⣤⣤⣤⠴⠶⠞⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠉⠉⠉⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠐⠊⢁⣠⣶⠿⠿⠿⣶⣤⣀⠈⠉⠓⠒⠒⠒⠒⠒⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉⠁⢉⣀⣁⣀⣠⣤⣶⠿⠋⠀⠀⠀⠀⠀⠉⠛⠿⠶⣶⣶⡶⠶⠶⠶⣶⣤⡀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠾⠁⣠⣶⡿⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⠈⢇
⠀⠀⠀⠀⠀⠀⢰⠃⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠈⢦⡀
⠀⠀⠀⠀⠀⣰⠏⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠙⠶⣄
⠀⠀⢀⡠⠊⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⡀⠙⢦⡀
⠀⡴⠋⢀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⢻⡄
⣾⠁⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠈
⣿⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⡌
⠘⡆⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⢸⡇
⠀⣧⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠘⣧
⠀⡿⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠘⡆
⢀⡇⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸
⢸⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⢀⡾
⠘⣇⠀⠹⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⢀⡴⠛
⠀⠈⠳⣤⡈⠛⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⢀⡴⠋
⠀⠀⠀⠀⠙⠳⣄⠈⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠘⢿⣦⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣴⣾⠿⠃⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠙⠛⠛⠛⠛⠛⠛⠿⢷⣦⣄⡀⠀⠀⠀⠀⣠⣴⡿⠛⠉⠉⠉⣉⣉⣁⣀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣶⣶⣶⣤⣄⣀⠈⠙⠻⢷⣶⣶⡿⠟⠁⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⢀⣾⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣦
⠀⢀⣾⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠃
⢀⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡟
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

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

⠀⣾⡆⣶⡆⣶⣓⢰⠛⢶⡀⣴⢦⠀⡆⠀⠀⣰⠚⢳⡄⣞⡃⠀⢰⣆⣰⣆⡶⠛⢦⢰⣦⢰⣆⡶⠛⣦⢰⣛⡦
⠀⠇⠻⠃⠇⠿⠤⠸⠦⠞⠱⠟⠻⠆⠧⠄⠀⠙⠦⠼⠃⠏⠀⠀⠸⠇⠹⠇⠳⠤⠟⠸⠈⠻⠏⠳⠤⠟⠸⠙⠦
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀
⠀⠂⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⡀
⠀⢠⠤⠤⠛⡀⠀⠀⣤⠼⣮⣾⣽⣁⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢠⡏⠐⠀⠀⢹⣤⡤⠤⠚⡇
⠀⢀⡇⠀⠀⣩⠶⠀⠈⣹⣫⣟⣟⠋⢀⣠⢤⣀⣼⠉⠉⣿⢤⡼⠓⢦⡌⢧⡳⠤⢞⡼⠁⡇⠀⠀⣨⠗
⠀⠘⠂⠑⢤⠁⠀⠀⠀⠉⠀⠈⠛⠀⣯⠀⠈⢧⣸⠆⠀⠿⠴⠁⠀⡼⢦⡴⢎⠉⠁⠀⠈⠉⠙⠲⠇
⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⣰⠛⠲⣋⡷⠀⡀⢠⠄⢠⢤⡀⢠⡈⠓⠞⠁⣈⡷⠀⠀⠀⠀⠀⠀⣤⡀⢀⣤
⠀⡼⠁⠄⠄⠙⡆⠀⠀⠀⠀⠳⣤⣄⠀⢸⢢⠣⡘⡂⢸⢠⠇⠮⡇⡤⠀⣞⣹⣦⡄⠀⠀⠀⢠⣤⡾⣼⣯⢮⣀
⠀⢳⡰⣄⣠⢂⠏⠀⠀⠀⢰⠶⠷⠾⠀⠈⠀⠀⠀⠁⠀⡄⠀⠀⠀⠉⠀⠈⠀⠀⣇⠀⠀⠀⠀⠈⣿⡽⣟⡏⠉
⠀⠀⠉⢛⣛⣁⠤⢄⠀⠀⠸⣇⣠⣤⡀⣰⣀⠄⠤⡀⡀⢁⡠⢄⢐⡂⠀⢾⣉⣻⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠠⠁⠀⠁⠀⠀⡇⠀⠀⢀⡷⠞⠃⡁⠈⠠⠠⠂⠅⠬⠢⠸⠉⢁⡤⣤⡀⢹⠇⠀⠀⠠⡤⠤⠞⢃
⠀⠀⠀⠑⢄⠀⠀⡔⠀⠀⠀⠘⢦⣴⡞⣹⠆⠀⠀⠀⠀⠀⠀⢀⣀⠈⠳⣤⡟⠋⠀⠀⠀⠀⡰⠀⠀⢈⠵⠂
⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⣟⠁⢠⡞⢳⠆⢠⢤⠀⢻⣈⣳⣄⡼⠃⣀⣀⡀⠀⠀⠋⠉⠢⡄
⠀⠀⠀⠀⠀⠀⠰⡶⣄⡴⡆⠀⠀⢠⠏⠛⠋⢙⡟⠀⣾⠾⣇⢀⣻⢳⠀⢠⠋⠀⠠⠈⢧
⠀⠀⠀⠀⠀⠲⢿⣿⣿⣟⣲⡄⢀⡏⠀⠀⠀⠈⡿⠓⠻⡄⠙⠉⠀⠈⣇⠸⡠⣄⣀⡄⡼
⠀⠀⠀⠀⠀⠀⠸⠗⠻⣽⠀⠀⣸⠀⠀⠀⠀⢸⠁⠀⠀⢳⠀⠀⠀⠀⢸⡄⠉⠓⠒⠋
⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢿⠀⠀⠀⢸⡆⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢠⠖⠢⡤⠠⣄
⠀⠹⡉⠁⠘⠢⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡆⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⡸
⠀⠴⠤⢄⢰⠋⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⡏⠀⣘⣟⣦⣞⡇⠀⠣⡀⣠⠔⠁
⠀⠀⠀⠀⠉⣠⠞⠉⡉⠳⡄⢀⡇⠀⠀⠀⠀⢀⡇⠀⠀⢸⠀⠀⠀⠀⢸⡇⠘⠻⡿⣿⣯⠽⠆⠀⠈
⠀⠀⠀⠀⠀⣿⢠⠀⢀⡄⡗⢸⠁⠀⠀⠀⠀⢸⠇⠀⠀⢸⠀⠀⠀⠀⠀⢧⠀⠘⠛⠙⠾⠂
⠀⠀⠀⠀⠀⠈⠳⠭⠭⠚⠁⡟⠀⠀⠀⠀⠀⣼⠀⠀⠀⠘⡇⠀⠀⠀⠀⠈⢧
⠀⠞⠉⠳⠒⠲⡄⠀⠀⠀⢸⣃⡀⠀⠀⠀⢀⡏⢰⢦⣀⣤⡿⡄⠀⠀⠀⠀⠈⣳⡄⠠⡤⠤⠊⡇
⠀⢆⠀⠀⠀⢀⠆⠀⠀⠀⠀⠈⠉⠙⠒⠦⠼⠶⣞⣷⣿⣾⣤⡹⣄⣀⡤⠖⠋⠁⠀⠀⡕⠀⠀⡨⠕
⠀⠀⠣⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠕⢻⣻⠁⠀⠈⠁⠀⠀⠀⠀⠀⠈⠉⠉⠢⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠹⣮⢳⡐⡄⠀⠀⠀⠀⠀⠀⡄⣾⠈⢁⡀
⠀⠀⠀⠀⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⣷⣧⢳⡀⢀⣤⣤⣤⣀⣷⡸⢀⣾⡇⠀⠀⢀⣶⣮
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⣸⣿⣟⣷⣿⣿⢟⣛⣿⣿⣷⣼⣿⣷⣶⣷⣿⣿⣃⡄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢻⣏⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⢹⣶⣾⣿⣿⣿⡿⢿⣾⣿⣿⣷⣿⣿⣭⣿⡿⣹⣿⡟⠁⠀⢀⠍⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢦⣤⣄⠀⠄⢘⢓⣏⠀⣠⣿⣎⣻⣿⣿⣿⣿⣯⣭⣻⡿⣿⣿⣿⡿⠉⢰⣿⣏⣤⠀⠀⠈⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⢿⣷⣷⡦⣈⠁⠀⣾⡟⣛⢛⣿⡿⡿⣿⣟⣭⣽⣷⣶⣾⣿⣡⠀⠈⢿⡿⣿⣾⣶⣶⣀⣀⠈⠀⠀⠀⢀⣀⣤⣀
⠀⠀⠀⠀⠺⡦⠀⠀⠀⠀⠀⠀⠉⠳⢶⣦⣝⣲⣿⣿⣁⣿⣿⣿⣿⣯⣹⣿⣿⣽⠛⠛⢿⣧⣎⣴⣿⣷⣹⣿⣟⣿⣿⣿⣿⣾⣵⣿⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠼⣿⣿⣿⣿⣽⣿⣿⣭⣿⠏⠀⢿⡛⠩⠀⠀⠘⠃⣸⣷⣍⢻⣟⣮⢻⣼⣿⠿⠛⢋⣉⣤⣴⠂
⠀⣀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠁⣀⣿⣿⣿⣿⣿⣿⠎⠋⢐⡂⠈⠐⢶⣶⠄⠘⣧⣽⣭⠛⢻⡟⢛⣉⠭⠔⢒⡈⠉⣉⠡⠤⠴⠶⡂⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣼⡿⣽⣉⣿⣿⡿⡿⠆⣐⣿⠀⠀⠀⠀⠁⠀⢀⡿⢿⣿⠀⣠⢫⣧⣶⣾⣿⣯⣭⣶⣶⠖⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⠀⣤⣾⢠⣿⢧⢸⣿⣿⣟⢷⣿⠀⠙⠁⠀⠀⢠⣾⣧⡤⠉⣠⣾⣷⣦⣭⡾⢿⡿⣿⣟⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠉⠀⠀⠁⢼⣿⣿⣎⣻⣿⣿⣾⣿⣦⡀⣀⠴⠆⣼⣿⣿⡠⠐⠋⠻⠻⢿⣟⣱⡏⣶⡏⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⣽⣿⡿⠻⠛⠛⢉⣨⣿⢇⠈⠉⠁⣩⣿⣿⠿⠛⠀⠀⣠⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⡿⣦⣤⣠⣶⡿⣿⣿⣟⡷⣶⣿⣿⣏⡀⠀⠀⠓⠘⢿⣿⡿⠁⣸⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡴⠟⠉⡈⣩⣴⢿⣿⣧⣽⢷⣼⡿⣿⣿⣤⣬⣽⣻⣿⣎⡓⡄⠀⢈⡻⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠀⠀⠀⠀⠉⠁⠀⠉⠹⠿⢷⣽⠶⠾⠿⠿⠿⠿⣿⣿⣿⣿⡿⣆⠢⡹⣿⣧⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⠟⠀⠀⠀⠀⡈⠀⠀⠀⠙⣧⢻⣎⠻⣷
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⢻⣆⠈⠁⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡴⢋⡥⠿⢠⡙⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⠵⢺⠳⢭⡳⣄
⠀⠀⠀⠀⠀⠀⣼⣥⡏⠀⣤⡀⢙⣤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣏⠀⠀⠀⢀⣳⣽
⠀⠀⠀⠀⠀⠀⠹⡄⠲⣄⢈⢀⡴⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢧⡀⢀⠀⣀⠎⡼
⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣿⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢭⣽⣯⡵⠞⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠠⢊⠠⠀⠠⡑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⣸⡇⠈⠹⣦
⠀⠀⠀⠀⠀⠐⠢⡁⠄⠀⠴⠀⠀⢈⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠧⠤⢴⣿⣿⠶⠶⠾
⠀⠀⠀⠀⠀⠀⠀⠐⢌⠂⠠⠐⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢹⡇⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠛⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠋⣿⠉⠙⠻⣶⠾⢿⣬⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢧⣴⠟⠛⠳⠶⣼⣧⣀⣤⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⠶⢿⣴⣾⣿⣷⣤⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠉⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣷⡿⠿⣿⣿⣿⣿⠿⣻⣿⣯⣵⣾⣿⡆
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⣯⣝⣻⠿⠏⠀⠀⠀⠉⠀⠈⠐⣦⠀⠹⣯⣶⠿⢟⣛⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⢲⣟⠿⠿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣤⣀⠀⠀⠀⢲⣀⣀⣀⣀⣰⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣤⡼⠿⢷⣶⣶⣿⣿⠛⢻⣟⣋⣥⣤⣤⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣾⠿⢻⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠠⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠏
⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⢛⣛⣛⣛⣛⣿⣿⡇⠀⠀⢰⢸⣿⣿⣿⣿⣿⣛⡛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠚⠃⠀⡀⢸⣾⣿⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣤⣶⣿⣿⣾⣿⣿⣷⣀⣀⣀⡀
⠤⠤⠤⢤⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣤⣤⡤⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⠶⢾⡷⠶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠛⠉⠁⠀⠀⠀⢸⡇⠀⠀⠀⠈⠉⠛⠻⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠒⢺⡗⠒⠶⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⣿⡆
⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⠀⠀⠀⠠⢶⡶⡄⠀⠀⠀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣸⣇⣀
⠉⠉⢹⡏⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠀⠀⠀⠘⠿⠿⠃⠀⠀⠀⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⢹⡏⠉
⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⢼⡧⠤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣀⡀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣀⣤⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⢿⡿⠿⠿⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⣠⣾⣿⣿⡀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡿⠿⠿⠛⠛⠿⠿⢿⣿⣿⣶⡄⣾⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠇⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣶⣤⠀⣠⣾⡿⢛⣛⣛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⢀⣾⣿⡿⠛⠉⠀⠀⠀⠀⠉⠛⣫⣾⡿⠋⠀⠈⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⢠⣿⣿⠋⠀⠀⣀⣤⣶⣶⡄⣠⣾⡿⠋⣾⣿⡄⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣿⣿⠃⠀⠀⣼⣿⠟⠛⣩⣾⡿⣋⠀⠀⠸⣿⣿⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⠀⠀⢸⣿⣿⠀⠸⠿⠋⣼⣿⡇⠀⠀⣿⣿⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣿⣿⡄⠀⠀⢻⣿⣦⣤⣤⣴⣿⡟⠀⠀⢠⣿⣿⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠘⣿⣿⣄⠀⠀⠉⠛⠿⠿⠛⠉⠀⠀⣠⣿⣿⠃⠀⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⡀⠀⠈⢻⣿⣷⣤⣀⠀⠀⠀⠀⣀⣤⣾⣿⡿⠁⠀⢀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⣠⣬⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣷⣶⣶⣤⣤⣶⣶⣾⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣮⣴⡄⠴⣮⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⣿⠀⠈⠀⠀⠀⠀⣶⣤⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣿⣷⣶⣶⡿⣿⣇⠀⡨⠝⠀⣘⣿⠿⣿⣷⣟⣳⡞⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡽⠷⣼⠿⠛⢣⣬⣿⣄⢘⠈⠀⣿⡁⠀⠘⢛⡻⠿⠿⠿⠿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⠿⡷⠶⠼⡿⢤⣼⠿⢿⣿⣦⠠⣿⣯⡍⠠⠀⠈⠁⠀⠀⠱⠶⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⢀⠀⣄⢠⠤⡄⣤⠄⡀⢴⠄⢠⣤⣦⣤⠀⡤⢰⣦⠤⣶⣆⣠⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⣏⢸⣶⡗⣻⡀⡇⠹⠀⣸⢉⣿⣿⡀⠃⢸⡍⢶⣭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢸⢤⣧⣿⢤⡇⢴⡇⡮⢈⣿⣽⠃⡈⢸⣇⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢾⣸⣿⣿⣸⡷⢿⣁⣿⢸⣿⢻⣆⣉⠸⡟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠉⠉⠉⠉⠀⠉⠉⠉⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡛⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢸⡇⠀⢺⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠸⠇⠀⠠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⡀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠏⣀⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣆⠀⠀⠘⠓⠀⢈⣀⠀⠈⠁⠀⣠⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡄⠀⠀⠀⠼⠿⡿⠆⠀⠀⢠⣿⣿⣿⣿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣄⣠⣄⠀⠀⢳⣤⣤⣤⣾⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣆⠀⠀⢹⣿⣿⣷⣿⣿⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⣀⠀⠛⠿⢿⣿⣿⡿⢷⣶⣤⠈⢻⡟⠋⢁⣀⣤⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⢿⡷⠦⠄⡈⠉⠁⠀⠉⢉⣥⣄⣿⣷⣿⡿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⢳⠄⠀⠀⢸⣇⣠⣤⣬⣿⣿⣷⣶⣤⢍⣙⠿⣯⣿⣇⠀⠀⠀⣠⠤⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣿⣤⡀⠲⠘⠃⠹⠿⣏⣻⡤⣿⣭⣿⢶⣟⡻⠶⠀⠿⠓⠀⠀⣿⠛⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠸⣿⣿⣷⣦⣤⣄⡀⠀⠉⠐⠻⠍⠛⠊⠉⠀⠀⢰⣤⣀⣴⣶⣎⢻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣿⣿⣮⣝⣻⣿⣿⣮⣭⣦⣤⢤⣀⣶⣈⣤⣴⣿⣿⣿⣿⣿⡏⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡁⣿⣿⣿⣿⣿⠶⣿⣩⣿⡼⠷⠼⣿⣤⣿⣻⣿⣾⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⣿⣿⣿⡛⡿⠒⠉⠀⠀⠀⠀⠀⠛⡀⠀⠙⠳⢾⡟⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⣯⣽⣛⣯⣹⣧⣤⡄⠀⠀⠘⠺⣇⠀⠀⠀⠀⠙⢟⣹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⡾⠁⠿⠿⠷⣿⡋⢴⡶⠄⣀⣄⢹⡅⠀⠀⠀⠀⠈⢿⣽⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣷⣾⠁⢰⣄⣤⠠⡚⢧⠸⠀⢸⡿⠛⣿⣧⡐⠇⠸⠟⠀⠈⣯⣼⡗⢄
⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⣿⣧⣾⠀⠀⢙⠃⡠⠷⢄⣄⠀⠘⠣⣤⡿⣿⢃⣀⢻⡿⠀⠀⣿⣬⣿⣌⢧⡀
⠀⠀⠀⠀⠀⢠⡞⢁⣾⣿⣿⣷⣾⠀⠀⠈⠁⠀⡶⠂⣹⡄⠀⠘⢿⠇⠀⣽⣿⢰⡇⠀⠀⣷⣤⣿⣿⣷⣝⢦⡀
⠀⠀⡀⢀⡰⢯⣾⣿⣷⣯⣿⣿⣤⡄⢼⣷⠀⠀⣶⣿⣉⠷⣄⠀⢸⣄⠠⣬⣿⡚⢃⡀⢰⣧⣿⣿⣿⣿⣿⣿⣟⣦
⣠⠞⠋⡉⠷⠿⢿⣿⣿⣿⣿⣿⣷⣶⢆⠿⠀⠀⢠⠀⠩⠶⠙⢿⡴⣿⡆⢻⣿⣿⠏⣱⣦⣼⣿⣿⣿⣿⣿⣿⣿⣷⡙⣶⣦
⠙⠿⠦⠞⠛⠶⠶⢤⣌⣉⣉⠙⠛⢷⣾⠓⣄⣀⣴⣇⣀⣀⣀⣤⣴⣿⣷⣾⡽⣥⠞⣷⣼⣿⣿⣿⣿⣿⣿⣽⡿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠘⢻⣯⣼⡷⣤⣤⣀⣀⣀⣀⢠⡤⢶⣧⣹⣿⠻⠷⠚⠛⠉⠉⠁⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡉⢻⣿⣷⣾⣷⣼⣿⣾⣿⣾⢿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠹⣿⣿⣿⣿⣿⣿⡿⣁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠹⣿⣿⣿⣿⡟⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⢿⣿⠟⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡸⠏⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡰⢤⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣷⣀⣀⣠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⠿⠿⠁⠙⠛⢛⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⠀⠀⠀⠀⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠉⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣤⠀⣶⡶⠾⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠛⠋⢉⣿⢻⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣤⣀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣺⣿⡿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⠛⢛⣛⣛⣛⣛⠛⠻⠶⣯⣽⣻⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⣩⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣌⡙⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣰⡟⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣦
⠀⠀⠀⠀⠀⠀⣼⠏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠹⣧
⠀⠀⠀⠀⠀⣸⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⣧
⠀⠀⠀⠀⢀⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⡆
⠀⠀⠀⠀⢸⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⡇
⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⡇
⠀⠀⠀⠀⢸⣧⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⣿⡀⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⠃
⠀⠀⠀⠀⠀⠸⣧⠘⣿⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣼⡏
⠀⠀⠀⠀⠀⠀⠹⣧⡘⢿⣦⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣌⠻⣿⣦⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⠙⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣡⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣌⣙⠛⠿⠿⣿⣿⣿⣿⣿⠿⠿⠛⢋⣡⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠶⣶⣦⣤⣴⣶⠶⠾⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠙⢦⡞⠁⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠙⡦⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣢⠤⠠⠤⢤⣊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⢀⣀⠤⠤⠤⢄⣀⠈⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢀⡴⠊⢁⠤⠄⠀⠀⠤⣀⠉⠢⡀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢠⠋⣠⡎⠁⠀⠀⠀⠀⠀⠀⠙⣆⠈⢢⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⡇⠰⢁⣤⣄⡀⠀⠀⠀⠀⣀⣤⣌⢳⠀⢃⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠀⠂⢸⣿⠉⠓⠀⠀⠀⠰⠋⢹⣿⠈⠀⢸⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠸⡀⠸⠀⠉⠉⠀⠀⠀⠀⠀⠈⠉⠁⡸⠀⡘⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠱⡀⠱⣄⠀⢀⣀⠀⢀⣀⠀⢀⡔⠁⡰⠁⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠘⠦⡈⠑⠢⠬⠉⠩⠤⠒⠁⡠⠞⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠈⠑⠢⠤⠤⠤⠤⠒⠉⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠤⠤⠤⠄⠒⠊⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⣠⣤⣤⣤⣀⢠⢠⣖⣸⡭⣭⡥⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠗⣌⠹⣻⠋⢿⢀⡼⢯⡀⠀⠀⠀⠙⢋⣓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣾⠋⠀⠈⠓⠈⡙⠨⠟⣿⣟⡿⣷⣌⠀⠀⠀⢩⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠀⠀⠀⠒⠙⠁⠁⣼⡄⠀⠀⠀⠀⠀⠀⠐⠖⠀⠈⡈⣉⣡⡔⠀⠀⠀⢋⢁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣛⣻⡅⠀⠀⠀⠀⠠⣌⡀
⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣴⣿⢇⡀⠀⠀⠀⠀⢢⢥⡀
⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠠⢤⣀⡀⠀⢠⣿⣷⠛⠋⠃⢹⣄⠀⠀⠀⠀⠢⡴⢄
⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠈⢧⠀⠀⠀⠀⠈⠲⣛⢢
⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠉
⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠄⡏
⠀⠱⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡞
⠀⠀⠹⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⡜
⠀⠀⠀⠘⢦⡈⠦⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣠⠋
⠀⠀⠀⠀⠀⠙⢦⡉⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡠⢠⡐⠊⠣⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠆⠝⣘⠥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢬⣑⡤⣀⣉⠡⠔⠍⠄⣀⡀⣂⠀⠀⠀⢐⡤⠔⠊⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣿⣿⣿⣶⣶⣶⣶⣶⣶⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣀⣩⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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







⣿⣿⡿⠿⣿⡿⢿⢿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣴⣿⣶⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢻⣿⣷⣷⣶⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⣀⣀⡀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⠀⢀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠹⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡿⣿⣿⡿⢹⣿⣿⣿⣿⠏
⠀⠀⠀⠹⣿⣿⣿⠋⠈⣿⡃⠀⠈⠙⣿⠟⣿⣿⣿⣿⣿⣿⡿⠋⠙⠉⠀⠀⠀⠈⠐⠉⠙⢿⣿⣿⣿⣿⣿⣿⠘⣿⠉⠀⠀⠈⡿⠀⠘⣿⣿⣿⠏
⠀⠀⠀⠀⠘⣿⢏⠀⠀⠸⡅⠀⠀⠀⣿⠀⣿⣿⣿⡉⠀⢩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠁⠈⢹⣿⣿⣿⠀⣿⠀⠀⠀⣨⠃⠀⠀⢿⣿⠃
⠀⠀⠀⠀⠀⠘⢧⠘⠀⠀⢱⡄⠀⠀⣿⠀⣿⣿⣿⣷⠶⣾⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⢶⣾⣿⣿⣿⠀⣿⠀⠀⢀⡌⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢳⣄⣠⣿⠀⣿⣿⣿⡅⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⣹⣿⣿⣿⠀⣿⣤⣤⡟⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⢻⣿⣿⢠⣿⣿⣿⣿⣷⣾⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣶⣷⣿⣿⣿⣿⢰⣿⣿⠟⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⡀⢀⡹⣿⣼⣿⣿⣿⣿⣿⣿⣿⣤⣤⣴⣤⣦⣬⣴⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣼⣿⡏⠆⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢽⠛⣿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡍⢧⣀⠅⠀⢀⠀⠀⠀⡴⣟⡦⠀⠀⢀⠤⠒⣾⡟⢃⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣜⢿⡣⡀⠃⠀⣾⣈⡎⠁⠀⢠⠁⣱⡾⢋⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡙⣃⣼⣾⣗⣁⠑⠒⢂⣁⣾⠟⣡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢆⠙⠮⠙⣟⣿⡦⣛⣵⡛⣛⠥⠊⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡛⣯⣧⡀⠹⡆⠙⣿⣀⣹⣥⣠⣾⡿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡆⡤⠰⠿⠒⠿⠿⡁⠸⠟⠛⠻⠗⠿⠛⠋⠉⠀⠀⠀⠀⣤⣤⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢋⡶⣄⠀⢿⣥⡜⢃⢮⡱⠀⢿⠀⠀⣴⠋⠐⢂⣾⡦⢼⠆⢠⡝⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⡇⣿⢀⠈⠳⠈⠺⠋⠑⠓⠚⠒⠒⠘⠒⠒⠀⠛⠀⠘⠂⢰⡆⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⡇⣭⡉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡇⣏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⠁⠈⣇⣀⣤⣴⢴⣾⡟⠨⣗⠺⠝⢿⡗⢤⣤⡀⢰⡇⠀⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣤⡐⣦⣌⡙⠻⣿⣟⠓⠋⠁⠀⠀⠀⠚⢰⣮⡿⠛⣡⣴⡆⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⠹⣿⣿⣷⢦⣉⡓⢦⣄⡀⢀⣤⠶⢋⡡⣠⣿⣿⡿⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⣠⢿⡄⠻⣿⣿⣿⣿⢿⠖⠿⠟⠛⠳⠞⠷⣼⣿⣿⣿⡇⣼⢷⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⡟⣧⠰⣬⡿⠛⠈⢠⣴⠶⠒⠳⢆⠈⢀⠊⢿⣾⣿⢀⠿⣯⣿⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢭⡞⠁⠸⣤⢏⠀⠄⠀⣿⡅⢀⠚⡇⠀⣿⡄⠑⠌⢈⢏⡰⠀⠈⣧⠌⡣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢽⣾⡇⠀⢀⡿⠂⠁⠀⢀⣯⣄⠘⡶⠇⡰⢏⣼⡆⠀⡄⠺⣇⠀⢠⣷⣾⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠟⣧⠴⣻⡇⢸⠁⠀⢈⣿⣯⣭⠄⢐⡟⠀⢸⠄⠀⠠⠈⣿⡳⢬⣿⢿⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣶⠞⣡⣾⢿⣷⡈⠂⢠⣿⠏⣁⠀⠠⡿⢀⣄⠈⠀⠀⠀⣪⣿⣬⡀⣙⠦⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠴⢋⣡⣾⣿⣿⣿⣿⣦⡀⠻⣧⡛⠀⢀⣴⣄⣿⡷⣆⡤⠀⢁⣾⣻⣿⣿⣾⣷⣌⠳⡤⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⠀⣛⣛⣛⣛⣃⣀⣀⣛⣿⣒⠌⠻⠦⢿⣵⠿⡿⠟⡋⢤⣶⡿⡟⣛⣛⣋⣉⡛⢋⡃⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠊⠁⠀⠘⣿⣹⣍⣭⠀⠀⠈⢻⢷⣴⣦⣶⣶⣥⣮⢞⡟⠀⠀⣰⣯⣽⢏⣿⠀⠀⠙⠶⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⢛⣷⡖⢆⣨⣎⢿⣿⣿⣿⡾⠁⣾⣤⡔⢶⣯⠛⠽⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣟⡳⠦⣽⡌⢿⣿⣿⠃⣼⣯⡷⢞⣋⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠺⢷⠘⣿⡏⣸⠿⠛⠓⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠘⠐⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⠀⣠⠞

⠀⠀⠀⠀⠀⢀⣀⣀⣠⡀⣤⢠⡄⣤⢀⣤⣤⢀⡄⣤⢠⣤⣤⣠⢠⡄⣀⣠⡀⣄⢠⢠⣤⣄⣤⣤⣤⡄⣤⢠⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⡟⢸⡍⣿⠀⡇⣼⠈⡇⣿⢸⢿⡷⢹⢬⡏⡇⣿⠃⣏⣸⢸⢹⣷⣿⣿⢿⣄⣿⣼⡟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⠿⣿⣿⡇⣿⢹⣷⣿⢢⣇⣿⢸⡇⡟⣿⢸⣧⣾⢼⠥⡇⣿⡇⡿⣿⢸⣿⣿⣿⣿⣿⡟⣿⢸⡯⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣿⣸⣿⣿⣾⣿⣿⢿⣏⡇⣿⢸⣏⡯⣼⣵⢧⣿⣟⣿⢾⣿⡟⣿⣿⣿⣿⢾⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣾⣾⣿⣷⢯⣾⣤⣷⣿⣿⡾⠿⣿⡷⢾⠿⠿⠿⠾⠿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠾⣿⣄⣨⡿⠶⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣼⣷⣿⡅⠀⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣽⣿⣿⣿⣿⣋⣾⣿⣿⣿⣽⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢸⣿⣾⡿⠟⠛⠋⠉⠉⠀⠹⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣹⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⢿⣿⣦⣀⣀⣀⣀⣠⣾⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⣿⣿⣿⠟⣫⢿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡉⠛⠟⠋⡾⠛⠛⢻⡏⠛⠉⢉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠿⣦⡀⣾⣷⣀⣀⣸⣿⣆⣠⢾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⣧⠈⠻⢿⡏⠉⢉⣭⠿⠋⠁⣼⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡤⡄⠀⢠⡶⣤⡎⣴⢋⣿⡀⠀⠈⠻⠛⣁⠀⠀⠀⢸⣏⠻⠉⣷⣶⣄⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠈⣷⡘⢦⡸⡆⡇⡿⢡⣾⢦⣧⠀⣠⡀⠶⣉⠐⠀⢀⣿⢻⡁⠀⠈⠙⠿⢷⣤⠼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠙⣷⣾⣿⣭⣿⣾⠟⣰⣿⣿⣅⣈⣀⠀⣾⣿⠂⠙⢷⣦⣀⡴⠛⠁⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠙⢷⡟⣋⣵⡾⠟⠛⠛⠛⠛⠛⠿⣿⣽⣿⣃⣠⠟⠋⠀⡤⢼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠈⠈⠑⢀⣽⡿⠋⡀⢠⠞⣃⣐⣒⣶⢦⣀⠙⢿⣿⡁⡀⠀⠜⢀⣾⠃
⠀⠀⠀⠀⠀⣀⣤⠾⠋⠂⠀⠀⢀⣴⣾⡟⠀⠞⣡⠖⠋⠉⠋⣥⠾⡆⠙⣧⠀⢿⣷⡯⠓⠀⠀⢙⣷⣄
⠀⠀⠀⣴⣟⣫⣥⣤⣀⣠⣄⣀⣈⣿⣿⠁⣄⢰⡏⠀⠀⠴⠟⠀⠚⢷⡀⢸⡇⠉⣿⡇⠈⠚⠱⠿⠁⠙⢷⣄⣀⡀
⠀⠀⠀⠉⠉⠉⠉⣹⢹⡏⠉⢩⣯⢹⣿⠀⢸⡎⢳⣤⡈⠀⠀⠀⢀⣾⡡⢼⣗⠀⣿⣷⢶⡶⠶⣾⢶⡶⠶⠿⣭⡿
⠀⠀⠀⠀⠀⠀⢰⡟⠳⠙⣆⠠⢻⡎⢿⣄⠘⢷⡈⣿⠁⠀⣴⠷⠾⠿⢃⣾⢋⣀⣾⡛⣦⢱⠆⣠⣾⠁
⠀⠀⠀⠀⠀⠀⢰⣟⠳⠤⣶⣠⣿⠟⣿⣿⣧⡀⠙⠿⣯⣟⣋⣀⣤⡴⠛⠁⣠⣾⣏⠻⣛⣾⣠⣵⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣟⡴⠛⠉⠠⠂⠘⠩⠿⣿⣶⣄⣀⠀⠈⠉⠁⣀⣠⡶⠟⠃⠈⠛⢯⣬⠔⠋
⠀⠀⠀⠀⠀⠀⣴⣞⣁⣀⣀⣀⣀⣀⠈⠅⠀⠀⠙⣿⣿⡿⠿⢿⣿⣿⠉⠀⠀⠈⠀⠀⠀⢹⡗⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⠉⠉⠉⢻⣧⠠⠀⠀⣸⣿⣿⣧⣴⣏⣿⡀⠀⠀⠀⣰⣦⣶⣶⠾⠶⠶⠿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡖⠂⢃⣿⢥⣿⣿⣿⣯⡼⡇⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡂⣸⣿⣼⢿⣿⣏⠻⡟⢿⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⠉⢾⣸⡇⣿⡀⠙⢾⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠈⠿⠛⠿⠀⠀⠘⠋

⠱⠄⠈⢁⣀⣵⡙⠳⡿⠄⠀⠀⠀⠀⠀⠀⢀⢸⠃⠀⢀⠀⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠐⢕⣤⠀⠀⣠⠊
⢀⣴⣕⠄⠛⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠉⠀⠛⠀⢀⡀⠀⠀⠀⡔⢠⠀⠀⠀⠘⠁⠀⠜⠁⠸⣆
⣝⠂⠙⢀⣴⠄⠓⠀⠀⠀⣠⠰⠲⠲⠆⠁⠀⠀⠴⠀⠒⠠⠀⠀⠈⠀⠀⠀⠀⠀⠁⠤⡄⠀⠀⠀⠀⠠⠀⠀⠈
⡙⠂⠀⠌⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣰⡚⠶⠄⠀⠀⢀⠥⠒⢄⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠀⠀⠀⠀⠘⠉⠁⢢⠀⠀⠀⠈⠀⠀⢸⠒⠒⢀⡀⠀⠀⠀⠁⠀⠔⠀⠀⠀⡠⠚⠁
⠀⠀⢠⠀⠤⠰⠇⠀⠀⠀⢰⠃⠚⠁⠠⡄⠀⠀⢁⠇⠰⠀⠀⠀⢰⠤⠐⣀⠸⠂⠒⢀⠰⡄⠀⢀⡀⠀⠀⠀⠠
⡰⠈⠙⠂⠀⠈⡱⠔⠶⠤⠌⢠⠆⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠜⠀⠸⡀⠀⠉⣠
⠳⠦⠀⠀⠀⠀⣁⠀⡤⠬⠗⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢠⠄⠀⠠⠅⠀⠠⠒
⣦⠀⠀⠀⢰⠋⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢈⠂⠀⠀⠉⠉
⠀⠈⡁⠀⠘⠠⠂⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⣤⡤⠤⠄
⣤⡦⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣴⡶⠖⠂⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒
⣼⡷⠖⣋⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀
⢴⡶⠟⣋⠄⠀⠀⣠⠔⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠢⣌⠙⠿⣿

⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⡯⡟⣩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡉⢍⣿
⠀⠀⡟⡇⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⢸⣿
⠀⠀⡇⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⣿
⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⡏⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⡇⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠘⠐⠀⠈⠂⠂⠘⠀⠈⠀⠋⠁⠀⠈⠂⠀⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⡧⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⡇⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⡇⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⡇⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⡇⡇⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡇⠀⣿
⠀⠀⡇⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⣇⣣⣝⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣧⣆⣿
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

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

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡛⣙⣟⣩⡛⣻⣛⣻⣟⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠄⠀⠐⠈⠉⠉⠑⠢⠀⠀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡠⠀⠀⠀⠙⠂⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠂⠀⠀⠤⠄⠀⠀⡄⠀⠀⠀⠑⠖⠖⢀⣀⠄⠀⠀⢀⣄⣀⠄⠀⠀⠈⠃⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠑⠉⠀⠀⠀⠒⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢀⢀⡉⢣⠀⠀⠀⠀⠐⠦⠤⠄⢀⣀⡀⠀⠢⠤⠔⠊⠒⠃⠀⣠⢀⠄⠀⠀⢠⠀⠀⠀⠈⢢
⠀⠀⠀⠰⠊⠁⠀⢀⠀⠀⣈⣧⣀⠉⡉⠀⠙⠓⠖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠛⠁⠀⠀⠀⢀⡜⣠⠀⠀⠀⠀⠁⢳
⠀⢀⡤⠂⠀⠐⠊⠹⣄⡀⢀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⡀⠀⢀⡜⠀⠀⡀⠈⠹⠄⠀⠀⠀⠀⠀⠒⠉⠈⠀⠀⠀⡴⠀⠀⠈⠀⢤
⠀⠊⠀⠀⠒⣆⠀⠀⣀⡍⠀⠀⠀⠑⢪⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠉⠀⠉⠉⠀⠀⠀⠀⠠⣄⡀⠐⠆⠀⠒⠁⠒⠒⠋⠀⢀⠦⠔⠄⠈⠇
⡀⠀⠀⠀⢤⡈⠁⠀⠰⡁⠀⠸⣄⠀⡀⠑⠂⢄⠀⠰⣄⡀⠄⠀⠀⣀⠀⠀⠣⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢄⣰⠤⠂⠈⠋⠁⢀⠄⠀⠀⡀
⢇⠱⠄⠀⠀⣉⠁⣠⠀⠉⠀⠀⢀⠉⡀⠀⠀⠀⠉⠁⠀⢀⠀⣉⡉⢀⣀⡠⢄⣈⠉⣉⣁⡀⠠⣄⣠⡄⠀⠀⢤⡀⠀⠀⠈⠉⠁⠠⠖⢊⡁
⠈⠢⠀⡄⣄⠈⠀⠻⠀⠀⠙⠤⠈⠉⣁⡜⠐⠋⠈⡐⠊⠁⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠀⠀⣀⣜⠃⠀⠀⠀⠠⠴⠒⠊⠀⠄⠈⡄⠊
⠀⠀⠀⠈⠢⡁⠀⠤⡀⠄⠐⠂⠀⠀⠀⠈⠋⠉⠉⠀⣿⠀⠀⠀⢰⠀⡇⠰⠀⠀⠀⠀⡼⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠀⣀⠀⠚
⠀⠀⠀⠀⠀⠉⠒⠂⠐⠤⡍⠉⢀⣐⡊⡐⠒⠀⠀⠖⡿⠀⠀⠀⢸⠀⢇⡇⠀⡈⠠⢸⠃⠒⠓⠒⠂⠀⠀⠉⡈⣁⣀⡠⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠑⠄⠀⢺⡀⢈⠸⠈⡇⠸⠀⢃⠇⡆⡿⠖⠤⠒⠐⠊⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡆⡀⡇⡄⠠⣸⢰⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷⡇⠁⠀⡇⡏⡼⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡼⢇⡠⠴⢧⣇⣇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠌⠉⠁⠀⠀⠀⠀⠀⠁⠘⠋⠳⠐⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⢠⣴⠦⣴⠠⢤⣤⡄⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠲⠄⠠⣿⡇⣿⠀⢸⠀⢸⢣⠔⠢⠤⠆⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⡿⠀⡇⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣧⡇⠀⠘⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢳⡇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⢀⠴⢦⠀⠀⢈⠤⢤⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠁⠣⠀⠀⠀⠀⠋⠑⡀⠀⠀⠉⠀⠀⠁⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠀⠀⠔⢢⡤⡈⠂⢀⡀⢩⠤⠒⢤⢤⡀⠙⠀⠐⠳⡄⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠀⠠⠄⠀⢤⡀⠀⠀⠀⠀⠀⠈⠀⠐⠆⠀⠀⠑⠲⠀⠈⠓⠀⠈⠈⠋⠂
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠇⠀⠀⢠⠀⠀⠀⠀⣀⠶⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⢧⠀⢿⣶⠆
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⢀⠀⢠⡟⠀⡴⢃⡴⠛⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠔⣡⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢹⡀⠀⠘⢀⠞⠱⠋⠀⠀⠀⠀⠀⠀⠀⡀⠘⠁⠀⠀⢀⣀⠀⠀⠆⠀⠁
⠀⠀⠀⠀⠀⠒⠌⠉⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠬⠰⠂⠀⠰⠀⠀⠈⠛⠛⠷⠶⠶⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⢀⠀⠀⢀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠉⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠈⠙⠒⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⢀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠉⠲⡄⢤⡀⢀⡀⢀⡰⠒⠚⠁⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⣾⣿⡿⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠤⠂⠐⠐⠒⢆⣀⡀⠀⠀⠀⠀⠀⠀⠰⠆⠙⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⠀⠉⠙⠂⠀⠀⠀⠀⠄⠀⠈⠀⢀⡒
⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⣷
⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⡀⣁⢀⡀⠀⡀⠀⣀⠤⢤⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣸⠏⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢀⡉⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠐⠁
⠀⠀⠀⠀⠀⠀⣾⣤⣷⣶⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠐⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠠⣄⡀⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⢿⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢊⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠘⠣⢔⠂⢀⠀⠠⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢠⡶⠤⠤⠤⠀⠀⢴⣭⠷⣤⠀⠈⠒⠛⠀⠀⠀⠀⣤⠞⠠⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⢀⣠⠄⣀⠸⠛⠃⠒⠀⠒⠒⢍⡀
⠀⠀⢰⡦⢒⠂⠀⠀⢂⠀⠺⠈⠀⠀⠠⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠤⠀⠀⠑⢄⣤⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠷⠂⠀⠈⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⢈⣰⠃⠀⠾⠆⠁⠈⠈⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⡀⠀⣀⡀⠀⡄⢠⣶
⠀⢈⠀⠀⠀⠈⠇⠀⠀⢀⣀⡀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠡⠀⠃⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠒⢖⣨⠖⠉⠉⠀⠀⠈⠂⠑⢎⠠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⢰⠋⠀⠀⠸⣷⠀⠀⠀⠰⠆⠀⠱⠄⠀⠀⠀⢀⡀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢊⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠤⠄⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⠀⠈
⠀⠀⠀⠀⠀⠑⠂⠒⠀⠘⠎⠁⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠘⠀⢸⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠐
⠀⠀⠀⠠⠀⢠⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⢠⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠏⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠆⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠐⢾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢀⠀⠉⠁⠀⢀⣀⡀⠀⠀⠊⢉⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠈⢹⡦⢀⠀⠀⠀⠀⣀⣠⡤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠘⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠉⠀⠈⠁⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣀⢤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠲⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠒⠆⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠤⠈⣦⠖⠀⠀⡤⠆⢠⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠐⠠⣘⠁⠀⠀⠀⣄⠀⠜⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣸⠄⠀⣡⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠃⢦⡀⠀⠀⢠⠤⠒⠋
⠀⠀⠀⠀⠀⠀⠀⣀⠀⢤⠀⠀⠀⠃⢠⣾⠛⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠹⡁⠀⢀⡆
⠀⠀⠀⠀⠀⠰⠀⢠⣔⠀⠣⠀⣤⣼⡟⢃⣠⡌⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌
⠀⠀⠀⠀⠀⠰⠛⠻⠿⠷⠶⠦⣤⡴⠶⠏⠘⠻⢱⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡔⠀⠀⠀⠀⠈⣠⡀⠀⠀⠀⠀⢰⠏⠉⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠛⠈⠁⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠋⠂⠀⠀⠙⠁⠀⡅
⠀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⢠⠰⣤⠀⠃⣀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⡀⠁⠈⠀⢀⣀⠀⠠⣤⠞⣉⠀⠀⠀⠲⠀⠀⠂⠀⠀⠀⠀⠀⠀⣄⠀⣀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⡁⠁⠀⠀⡤⣩⣤⣽⠏⠀⠁⠀⠀⠀⠈⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠟⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠉⠛⠛⠟⡏⠉⠉⠚⠁
⠀⠀⠠⠊⠀⠄⠀⠀⠀⠐⠷⠛⠉⠀⠀⠀⠀⠀⠀⠀⠤⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅
⠀⠀⠀⠀⠀⠀⢊⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡰⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⢋⠀⢀
⠀⠀⠀⠀⠀⠀⠙⠪⡁⠀⠀⠀⠀⠀⠒⠀⠀⣠⠎⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢠⢿⠂⠀⠘⡂⠀⠀⢀⠤⠄⠐⠚⠛⠃
⠀⠀⠀⠀⠀⠲⣀⠀⠀⠐⠦⠤⠄⠡⠀⠐⠂⠀⢀⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⠃⣦⠴⡀⢡⡄⠀⠌
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠤⣤⣤⣀⢀⣀⣠⠷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠀⠉⠁⠀⠀⠉⠀⡼⠂

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣀⣉⣈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⢀⣟⣆⢸⣭⡝⢸⠉⣥⢸⠭⠅⢙⡏⠀⠀⡇⡞⠉⠁⡏⠉⡇⣿⢦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠈⠀⠁⠈⠙⠉⠈⠛⠃⠈⠁⠀⠀⠁⠈⠛⠁⠉⠋⠁⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢷⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡟⢿⡏⠀⠀⠀⠀⠀⠀⠴⣶⣷⣶⠆⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣦⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠛⠘⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷
⠀⠀⠀⣿⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠏⠙⠷⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⣀⡀⠀⠀⣼
⠀⠀⠀⣿⠀⠀⠰⣾⣿⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣷⠆⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠿⣿⠁⠀⠀⣿
⠀⠀⠀⢿⠀⠀⠀⠛⠈⠛⠀⠀⠀⢀⣀⣴⣇⡀⠀⠀⠀⠚⠁⠛⠀⠀⠀⠀⠀⠠⢶⣿⣷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠟⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⡄⠀⠀⣀⣠⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⡇⠀⠀⣽⠿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⡿⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⢀⣠⣆⣀⠀⠀⠀⠉⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣿⠀⠀⢀⣀⣴⣇⣀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟⣿⠁⠀⠀⠀⠀⠀⠀⢀⣰⣧⣄⣀⠀⠀⢸⠃
⠀⠀⠀⠀⣿⠀⠀⠈⣹⠟⢿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⣽⠟⣿⠉⠀⠀⣸
⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣧⣤⠀⠀⠈⠁⠀⠉⠀⠀⢀⣶⣄⠀⠀⠀⠀⠀⠲⢾⣿⡶⠂⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠈⢿⣀⠀⠀⠀⠀⠀⠀⢽⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⢿⡟⠀⠀⠀⠀⠀⠛⠀⠙⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⠿⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⠿⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡉⠉⠒⠒⠒⠶⠶⢠⣄⠀⠀⠀⠀⠀⣠⣤⡀⠀⢀⣤⠶⠖⠒⠚⠉⠉⢉⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⠀⠀⠀⠀⠀⠀⠘⢣⠀⠀⡔⠛⠀⠸⠏⠀⡟⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣀⠀⠀⠀⠀⠀⠀⢸⡀⢸⡇⠀⠀⡀⠀⢸⠃⠀⠀⠀⠀⠀⢀⡜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢇⡀⠀⠀⠀⠀⠈⠳⠄⠁⠀⠀⠀⠦⠘⠀⠀⠀⠀⠀⢠⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡤⢼⡟⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⣿⡦⢴⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢶⡄⠉⢷⡜⠓⣶⠀⠀⠀⠀⠀⠰⡆⠛⣵⠟⠁⠠⠞⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠶⠴⢿⣦⠤⠴⠦⠾⠿⠿⠦⠴⢤⡤⠶⠤⢾⡷⠤⠶⣤⡤⣶⠷⠤⠦⠴⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣴⠀⢠⡆⢀⠷⡀⢰⠀⠀⢠⡄⠳⣄⠐⣿⠀⠀⠀⢀⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢰⡇⢛⠀⠀⠀⠈⢶⡎⠀⠟⠛⠇⢸⣇⣀⢸⣆⣀⠿⠘⠛⢦⠀⢰⡆⢻⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠾⡇⠘⠷⠶⠶⠶⠾⠷⠾⠶⠶⠶⠾⠟⠛⠳⠿⠟⠶⠶⠶⠶⠶⡾⠀⢿⠖⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⡀⢦⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⢀⣀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣠⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣸⠁⣼⣤⣤⡔⠶⠎⠛⢫⠉⠉⢉⣵⠏⠉⣯⣍⠉⠉⠙⠛⠉⠺⣗⠀⠿⠋⠁⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⠀⢀⡀⠉⠛⢶⣄⣐⠦⠔⠛⠉⠉⠈⠁⠈⠁⠙⠓⢤⣤⡶⠞⠛⠋⠀⡄⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⡇⠈⠁⠐⢢⡀⠈⠙⠶⣤⡀⠀⠀⠀⠀⠀⠀⣤⡴⠞⠉⠀⡠⠒⠈⠀⢀⣾⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⣿⡆⠀⡄⠀⠀⠁⠄⠀⣀⣸⠷⠶⠶⠴⠾⠿⣄⣀⣠⠄⠀⠀⠀⡰⠀⣼⠃⠄⢀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠃⠀⡄⢳⣷⠀⠐⠂⠀⢀⣴⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⢶⣄⠀⠌⠁⣠⣿⡄⢢⠈⡈⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠄⠁⣾⠛⣦⠀⢈⣶⠋⠀⠀⣀⣴⡶⠚⠛⠛⢷⡶⢦⣀⠀⠀⠈⢻⡄⠀⡿⠀⢿⡀⠐⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢣⣄⢀⡼⠃⠀⠹⣤⡞⠁⠀⢠⡴⢿⠁⠀⠀⠀⠀⠀⠐⢄⠉⢳⣄⠀⠀⠹⣿⠃⠀⠘⢣⡄⢠⡌⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠀⠃⠀⠀⣠⡿⠁⠀⢰⡟⠀⣌⠀⠀⠀⢀⣀⠀⠀⣈⣄⠀⠹⣇⠀⠀⢸⣇⠀⠀⠸⡀⠈⡁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⠰⠀⢰⣆⣠⡾⠛⡇⠀⠀⣾⠀⠀⠻⣀⠀⠰⠈⠉⠀⠀⠙⠁⠀⠀⣿⠀⠀⠈⡻⠷⣄⣸⡇⠀⠃⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢀⣼⠟⠁⠀⢠⡇⠀⠀⣿⠀⢀⡴⠛⠀⠠⠄⠀⠀⠀⠈⠀⠀⠀⣿⠀⠀⠀⣥⠀⠈⠻⢧⣀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⡾⠋⠁⡀⠐⠀⠘⢇⡀⠀⢸⣷⠈⠀⠀⠈⠁⠀⠀⠐⠂⠀⠀⠀⢠⡟⠀⠀⣸⡏⠀⠂⢀⡀⠙⢷⣄⣿
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠠⠀⠁⠀⠀⠀⠀⠸⣇⠀⠀⠙⢧⣀⠀⠐⠃⠀⠄⠘⠛⠋⢁⣰⠏⠀⠀⢰⡏⠀⠀⠀⠀⠈⠁⠄⠙⠷⣄⡀
⠀⠀⠀⠀⢀⣴⠞⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠙⠻⣤⣤⣄⣠⣤⣤⠾⠛⠁⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠛⠛⠒⠛⠒⠒⢶⠖⢀⠶⣶⡶⢶⡶⠒⠘⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠟⠳⠖⢶⡶⢶⣶⢶⣤⢶⡶⠒⠶⠶⠲⠞⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⡉⠰⠎⠠⠈⠹⢦⣄⡀⠘⢏⡙⠳⠶⠦⣤⡄⣤⡶⠶⢻⡟⠀⢀⣤⡴⠇⠀⠄⠙⠆⠙⣦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡀⠀⠈⢀⠀⠀⠘⠃⢾⣇⠀⠀⠀⠀⠀⠈⠀⠀⣶⡿⠛⠁⠀⠀⡈⠁⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⢷⡾⠃⠐⠀⠙⠀⢹⣄⠀⠀⠀⠀⡄⠀⣴⡏⠀⢀⡀⠃⠈⢳⡿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠞⣃⣀⣛⣴⣿⡄⠸⠀⠀⠁⢠⣿⣦⣴⣄⡈⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠈⢳⡄⢠⠇⠀⡼⠃⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁

⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀⠤⢰⠠⣄⠀⠀⠀⠀⠀⠀⡤⠄⡆⠤⡄⠀⠀⠀⠀⠀⢀⢤⢰⢠⣄
⠀⠀⠠⠤⠄⡣⠤⠤⠀⠀⠀⠀⠀⠭⠤⢘⠤⠬⠄⠀⠀⠀⠀⠠⠥⠤⡣⠤⠥⠀⠀⠀⠀⠀⠤⠥⢜⠤⠭⠄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⠦⢸⠠⠊⠀⠀⠀⠀⠀⠀⠧⠄⡇⠤⠇⠀⠀⠀⠀⠀⠘⠯⢸⠨⠟


⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⢀⡀⠀⠀⠀⠀⠀⠀⣀⡀⡆⣀⡀⠀⠀⠀⠀⠀⠀⡀⢰⠀⡀
⠀⠀⣀⡀⣠⢦⠀⣀⡀⠀⠀⠀⢀⣚⢀⡴⡄⢙⣀⠀⠀⠀⠀⣀⡃⢠⢦⡀⣃⡀⠀⠀⠀⢀⣈⢊⡴⣌⢚⣀
⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠲⣄⢈⢀⠔⠀⠀⠀⠀⠀⠀⣆⡀⡁⣀⡆⠀⠀⠀⠀⠀⠰⣖⢈⢐⡶
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⡄⠀⣤⡄⠀⠀⠀⠀⠀⠀⣠⠀⢠⡀
⠀⠀⠂⠒⠺⡕⠒⠒⠂⠀⠀⠀⢀⠚⣀⣤⡀⢙⢀⠀⠀⠀⠀⡀⡃⢠⣤⢀⠃⡀⠀⠀⠀⢀⢈⡊⡤⡌⢚⢀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠰⣄⢸⢀⠔⠀⠀⠀⠀⠀⠀⣦⡀⡇⣀⡆⠀⠀⠀⠀⠀⠰⣖⢸⢐⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘


⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠰⠋⢸⠈⠢⠀⠀⠀⠀⠀⠀⠏⠁⡇⠉⠇⠀⠀⠀⠀⠀⠰⠪⢸⠨⠳
⠀⠀⠀⠉⠁⡄⠉⠁⠀⠀⠀⠀⠀⢨⠈⢠⠀⣡⠀⠀⠀⠀⠀⠀⡌⠀⡄⠉⡅⠀⠀⠀⠀⠀⢈⢌⢠⢈⢄
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘⠘⠁⠀⠀⠀⠀⠀⠀⠉⠁⠃⠉⠁⠀⠀⠀⠀⠀⠀⠑⠘⠐⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠠⠒⠁⠙⠒⠁⣿⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠟⠀⣀⣠⢦⣠⠀⠈⢉⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡆⠀⣠⠟⠀⠀⠈⡗⠀⠈⠻⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣚⠁⠀⢀⡷⠤⡠⣴⠛⠀⠀⣰⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⠀⠸⣯⡀⢧⡀⠀⠀⣠⣼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠷⠲⣦⡿⢿⣌⡛⣦⢤⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⣷⡉⣿⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⢾⠁⣴⣧⣈⣿⣯⢹⡷⢶⣦⣤⡀⠀⠀⠀⠀⠀⢰⡟⠉⠋⠉⠛⠛⠳⡄
⠀⠀⢠⡞⣉⠀⢻⠀⢹⠑⢲⡄⠀⠀⠀⣠⡶⠟⠉⠀⡀⣼⠳⢬⣛⣛⣛⣩⣼⣷⣄⠀⠉⠻⣷⣦⡀⠀⠀⣼⠁⡈⠀⢰⠀⢀⡀⠹⡄
⠀⠀⣼⠁⢿⣀⣼⣀⣼⣀⣸⡇⠀⢠⡾⠋⠀⠀⢰⣾⡸⣧⡀⠀⠘⣿⣿⣿⣸⣿⣿⠃⠀⠀⠀⠻⣿⣆⠀⠻⣦⡽⢦⣈⠦⠤⠃⡀⢹⡆
⠀⣼⠛⠀⠀⣉⣛⣧⣄⣨⡟⢀⣴⠟⠛⢶⡄⠀⠘⣿⣷⣽⣿⣿⣾⣿⣿⣿⢿⠿⠋⠀⠀⡄⠀⠀⢼⣿⣧⠀⠙⠶⠶⢾⣶⠳⠛⠁⠀⢳⡀
⢀⣿⠃⠀⠀⠈⢻⡟⠉⠉⠀⢸⡟⠀⠀⠀⠁⠀⠀⠈⠛⠿⣿⣿⣿⣋⡿⠋⠉⠀⠀⠀⠘⣷⡀⢀⣽⣿⣿⣧⣀⣀⡀⢸⡇⠀⠀⠀⠀⠈⢳
⣼⠇⠀⠀⠀⠀⢸⣿⣤⣤⣤⣼⣿⠰⣿⣿⣦⠀⠀⠀⠀⠙⢿⣿⠿⠁⠀⠀⠀⠀⠀⠒⠚⠛⠻⣾⣿⣿⣟⣿⠟⠛⠛⠻⣧⡀⠀⠀⠀⠀⢨
⣿⡀⠀⠀⠀⣠⡿⠛⠉⠈⣉⣿⡟⠇⣿⡃⣼⣧⠀⠀⢰⠀⠀⢠⠀⠀⠀⠀⢀⣀⣤⣄⠀⠀⠀⠈⣿⣿⡾⡁⠀⠀⠀⠀⠈⠑⠢
⠘⣷⡀⠀⠀⠀⠀⢤⣤⣴⣿⣿⡇⠀⢸⣧⣻⠿⢷⣤⣼⢠⡀⣏⣀⡀⣠⡶⣿⣯⢏⡽⠟⠒⢀⣼⡹⣿⣿⣷⣤⣀⣀⣀⣴⣀⣠⣠⡄⣀⣤
⠀⠘⠷⣤⣶⣶⣶⣶⣿⣿⣿⣿⣷⣠⠏⠉⠉⠛⠏⢙⣿⡷⠓⠾⢻⣟⡓⠒⠚⢛⡿⠚⠉⠉⢽⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⠀⠀⣰⠀⠀⠉⢧⣍⠀⣠⣤⣼⠟⠉⠀⠁⢀⣀⣨⡿⠎⢿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣧⣦⣘⣶⡶⢤⣀⠚⠿⠟⠋⣀⣠⠤⠖⠋⢉⡽⣰⠃⣠⣾⣿⠟⢋⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⢿⣿⣿⣿⣦⣈⣉⣛⣋⣉⣉⣀⡤⠔⠶⣋⠔⣡⣾⢿⠟⢁⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣇⠀⠿⣏⣀⠉⠉⠉⢁⣀⣠⠴⠚⠁⣠⢜⡵⣋⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣤⣀⡈⠉⠉⠉⠉⢁⣀⣤⣶⣿⣿⠿⠚⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣻⣿⣿⣿⣿⣛⣛⣋⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⡶⠶⠶⢶⠶⠶⠶⢶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⢟⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⢍⠉⠃⠀⠀⠀⢀⠄⠒⠒⠂⢀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⣺⣯⣶⠄⢀⠤⠄⠂⠀⣀⠀⠀⠔⠃⠀⠐⠤⡀⠐⠄⠀⢀⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡝⠟⠉⡀⠎⠉⣶⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢢⠀⠀⢀⡈⢹⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣫⡞⠀⢼⠀⢀⡀⣷⡀⠀⢄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠘⡇⠊⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⣿⣾⣦⣼⣶⣤⣽⣿⣿⣶⣾⣷⣤⣿⣿⣦⣄⣀⣀⣤⣄⡀⢀⣀⣁⡀⠀⠀⠁⠀⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣝⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⣿⣿⣿⣿⣿⡿⠿⠶⣶⣦⣴⢀⣸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠳⣭⣿⣥⣝⣿⣷⣶⣿⣿⣿⣿⣁⡀⠀⣀⡀⢠⣿⣿⣿⣾⣿⡿⠿⣿⣫⣶⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠉⠀⠀⢸⠿⢿⣿⣷⣿⣏⠉⢻⡟⣿⣇⠉⠋⠀⠀⡟⠃⣼⠟⠉⣹⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣥⣤⣤⣤⣤⣤⣤⣤⣬⡉⢿⡙⢿⣆⠀⠁⣿⣿⠀⠀⠀⢠⡇⢰⠏⢀⣾⣿⠟⣡⣾⣿⠁⠀⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⠲⣝⠆⠙⢧⠀⣿⣿⠀⠀⠀⠈⡇⠀⣠⡿⢋⡴⡚⠱⠂⠀⠀⠀⠀⠘⠻⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣭⣙⡛⠂⠁⠀⠀⢰⣿⣿⠀⠀⠀⠀⢱⡐⠋⠀⠑⠊⠁⠔⢛⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣭⣽⣛⣛⠟⠃⠀⠀⢀⣿⣿⣇⠀⠀⠀⠀⠀⢧⠀⠀⠀⠴⠒⢛⣛⣻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⣾⣿⣿⣿⡄⠔⠒⢂⣀⠜⠆⡀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠠⠁⡀⠀⠀⠈⠺⣿⠟⠛⠻⣿⣦⣴⣈⡀⠀⢀⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣖⣁⣀⣀⣀⣈⣙⢿⠶⣶⣀⣀⣠⡤⠈⠛⠉⠙⠛⢿⣿⣁⣙⣒⣲⣷⣶⣶⣀⣾⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⣛⣟⣹⢛⣟⣻⡿⣻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢠⠂⠁⠀⡂⠀⠑⢄⠀⠀⠀⡀⠊⠀⢸⠀⠁⠢⡀⠀⠀⢀⠔⠉⠀⡇⠈⠑⢄
⠀⠀⠀⠀⠀⣃⣀⣀⡀⡆⡀⡀⣀⡄⠀⠐⠀⠀⠀⢸⠀⠀⠀⢠⠀⠀⡂⠀⠀⠀⠃⠀⠀⠀⡆
⠀⠀⠀⠀⠀⡄⠀⠀⠀⡇⠁⠁⠁⠃⠀⠨⠀⠀⠀⢸⠀⠀⠀⠸⠀⠀⠅⠀⠀⠀⡄⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠈⠦⡀⠀⡇⠀⡠⠊⠀⠀⠀⠣⢀⠀⢸⠀⢀⠄⠁⠀⠀⠈⠄⡀⠀⡇⠀⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡠⠂⠀⡇⠀⠂⠀⠀⠀⠀⠠⠔⠀⢹⠀⠐⠄⠀⠀⠀⠀⡠⠂⠀⠁⠀⠂⢄
⠀⠀⠀⠀⠀⠌⠀⠀⢀⣇⠀⠀⠈⠄⠀⠰⠁⠀⠠⠸⠠⠀⠀⢡⠀⠀⡈⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠈⡇⠃⠓⠣⡤⠃⠃⠃⡛⠀⢛⠀⠘⢃⢀⢀⠃⠀⢘⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠐⢄⠀⠀⡇⠀⢀⠐⠀⠀⠀⢆⠀⠀⢸⠀⠀⡠⠂⠀⠀⠐⢄⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠂⠇⠀⠁⠀⠀⠀⠀⠀⠈⠐⠘⠐⠈⠀⠀⠀⠀⠀⠀⠁⠂⠂⠂⠁
⠀⠀⠀⠀⠀⠀⢀⠄⠀⡆⠂⢄⠀⠀⠀⠀⠀⡠⠀⣲⠀⠠⡀⠀⠀⠀⠀⢀⠤⠀⠖⠂⠄
⠀⠀⠀⠀⠀⡐⠁⠀⠀⠇⠀⠀⠑⡀⠀⢀⠂⠀⠀⢸⠀⠀⠈⠂⠀⠀⠐⠁⢀⠀⡄⢀⠀⠐⡄
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠶⠀⠦⠶⠴⠰⢸⠰⠰⠰⠸⠀⠀⡇⠀⠰⠀⠀⠰⠄⠀⠄
⠀⠀⠀⠀⠀⠡⠀⠀⠀⡆⠀⠀⠠⠁⠀⠘⠀⠀⠀⢸⠀⠀⠀⠌⠀⠀⠠⡀⠀⠂⠒⠒⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠈⠂⠀⡇⠀⠂⠁⠀⠀⠀⠈⠐⠀⠼⠀⠐⠁⠀⠀⠀⠀⠈⠂⠀⠄⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠊⠀⠀⡇⠀⠈⠢⠀⠀⠀⠔⠁⢀⢰⢀⠀⠑⠄⠀⠀⠠⠊⠀⠀⠀⠀⠈⠠⡀
⠀⠀⠀⠀⠀⡇⠀⣀⠀⠀⠀⡀⠀⡅⠀⠰⠀⢠⠁⠀⠀⢰⡀⠈⠀⠀⡆⠀⠀⠀⡄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢂⠀⠀⠀⡄⠀⠀⠀⠂⠀⠘⡀⠈⠀⢠⡀⠌⠀⠰⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠄⡀⡇⢀⠄⠂⠀⠀⠀⠀⠠⠀⠈⠀⠠⠐⠁⠀⠀⠀⠑⠄⡀⠀⢀⠠⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠀⠠⠀⠁⠀⠀⠀⠀⠀⠐⢈⠐⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡠⠂⠀⡀⠔⠈⠀⠀⠀⠄⠀⠒⢀⠒⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠢⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⡠⠊⠀⠀⠈⠀⠠⠀⠀⠀⠀⠄⠐⠂⢀⠀⠀⠀⠄⢀⠀⠀⠢⠀⠀⠀⠀⠈⠢⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠠⠀⠀⠐⠀⢀⠄⠂⠀⡀⠀⠀⠀⢈⠀⠀⠀⠀⡀⠀⠀⢄⠀⠐⢄⠀⠠⠀⠐⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠌⠀⠐⠀⠀⠀⠀⠔⠁⠀⠐⠀⠀⣀⣤⣤⣤⣤⣤⣄⡀⠀⠐⠀⠀⠑⠄⠀⠢⠀⠐⠀⠈⠄⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠔⠀⢀⣴⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣄⠀⠐⠄⠀⢂⠀⠡⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠂⠀⠈⠀⢠⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣽⣿⣧⠀⠈⠀⠀⠂⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠀⠈⠀⠈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠀⠈⠀⠸⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⢸⣿⣿⣯⣿⣿⣯⠀⠀⠀⢨⣿⣿⣯⣿⣿⣿⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢰⠀⢠⠀⢀⠀⠀⠀⠈⣿⣿⣿⣿⣻⣿⣶⡤⣴⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⠀⢠⠀⢠⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠄⠀⢂⠀⠘⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡟⠀⢀⠀⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠈⠄⠀⠠⡀⠈⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⠿⠋⠀⡠⠂⢀⠈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢂⠀⠠⡀⠀⠄⠀⠀⡀⠈⠂⢀⠀⠉⠙⠛⢛⠛⠛⠉⠀⠀⠀⠊⠀⡠⠀⠀⠄⠀⡠⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢄⠀⠀⠀⠈⠀⠄⡀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⡀⠄⠈⠀⠀⠀⢀⠔⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⢄⠀⠑⢄⠀⠑⠀⠀⠀⠁⠂⠀⠀⠈⠀⠀⠀⠂⠁⠀⠀⠐⠁⢀⠔⠁⢀⠄⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⡀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠐⠂⠈⠀⠀⠀⠂⠀⡀⠄⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⢈⠀⠀⠐⠂⠀⠀⢀⠠⠐⠈⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⣀⠀⢀⠀⠀⢀⡞⠁
⠀⠀⠉⠂⢸⣦⣀⣈⣠⠖⠀⠀⢀⡀⠀⠀⢀⡀⡀⠀⢀
⠀⠀⠀⠀⢠⠁⠉⠀⢇⣀⡀⠉⠉⡁⠔⢺⠼⠒⠀⠑⢮⠱
⠒⠒⢂⣴⣏⣀⢀⣴⠛⡅⡄⣆⠧⠐⠈⠀⠀⠀⠀⠀⢘⢈⡀
⠀⠈⠉⠀⡀⠘⡿⠸⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠾⠶⠶⠤⣤⣤⣀
⡤⠞⠁⡼⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡀⠀⠀⠀⠀⠀⣀⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⠿⠛⠛⠛⠛⠛⠛⠛⠿⣿⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠁⢚⠥⠒⠀⠢⣀⠀⠀⣀⠀⠀⡈⠀⠀⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⡰⠃⠀⠀⠀⠀⠈⢣⠊⠀⠀⠀⠈⠲⡀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⢰⠃⠀⠀⠀⣠⡄⠀⠀⡇⣀⡀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⣭⡿⠀⠀⡗⣼⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠛⠁⠀⢠⡇⠈⠁⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⣠⠋⠙⢄⡀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠊⠁⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠒⠖⠢⠤⢄⣀
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠄⠀⠀⠀⠀⠉⡗
⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢀⠠⠠⢤⡤⠤⡀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⢸⠀⢀⡀⢐⠈⠀⣃⠀⢀⡁⡁⣐⣀⣀⣀⣳⣄⡀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⣤⣤⣀⣀⣀⣤⣤⠤⠶⠚⠋⠁

⠀⠀⠀⠀⢀⡴⠋⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠙⢦⡀
⠀⠀⢀⡴⠋⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠙⢦⡀
⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦
⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⡤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠖⠛⠛⠉⠉⠉⠉⠙⠛⠒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠁⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣀⡴⠖⠋⠉⠁⠀⠀⠀⠀⠈⠉⠓⠲⢤⣀⠀⠀⠈⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡴⠛⠁⠀⢀⣠⠴⠖⠒⠒⠒⠒⠲⠤⣄⡀⠀⠉⠳⣄⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣴⠋⠀⠀⡠⠞⠉⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠙⠳⣄⠀⠈⠳⡄⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⡼⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⢠⠏⢳⡀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠙⣆⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣸⠁⠀⣰⠃⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠹⡄⠀⠸⡄⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡇⠀⢀⡏⠀⣀⣀⣠⡤⠤⠴⠛⠀⠀⠀⠀⠙⠒⠒⠶⠦⢤⣤⠀⢳⠀⠀⢇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⢸⠁⠀⠙⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⠀⠀⢸⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠸⡇⠀⠸⡆⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢸⠀⠀⣸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢧⠀⠀⢧⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⡏⠀⢀⡏⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠘⣆⠀⠈⢧⡀⠀⠀⠀⡿⠀⠀⢀⣤⠦⣄⡀⠀⠀⣇⠀⠀⢀⡞⠀⠀⡼⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠘⣦⠀⠈⠳⣄⠀⠀⣧⡴⠚⠉⠀⠀⠀⠉⠓⠢⢿⢀⡴⠋⠀⢀⡾⠁⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠈⠳⣄⠀⠈⠙⠦⣅⣀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⢀⡴⠋⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠓⢦⣀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⢀⣠⠶⠋⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠈⠉⠓⠲⠤⠤⠤⠤⠤⠴⠒⠚⠉⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣓⣲⣶⣤⣤⣤⣤⣶⣖⣚⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡤⠖⠛⠛⠓⠶⣄⠀⠀⠀⠀⢀⣀⣀⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀⣠⠴⠚⠛⠛⠲⢦⡀⠀⠀⠀⠀⢀⡴⠖⠛⠛⠓⠦⣄
⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⡯⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⠁⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡯⠀⠀⠀⠀⡄⠀⠀⠀⢨⡇
⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠘⣇⠀⠀⠀⠠⠀⠀⠀⠀⣼⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠸⠦⠤⠄⠀⠠⠤⠤⠇⠀⠀⠀⠘⢧⣄⠀⠐⠀⢀⣠⠞⠁⠀⠀⠈⠳⣄⡀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠶⠶⣤⡀
⠀⠀⠀⠀⠀⣴⠋⠁⠀⠂⠀⠉⢳⡄⠀⠀⢀⡼⠉⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⢸⡇⡀⠀⢀⣀⠀⠀⡀⣻⠀⠀⢸⠁⠀⠀⠀⢀⠀⠀⠀⠀⣷⠀⠀⣀⣀⠀⠀⣠⡀⠀⢀⣀⣀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠁⠀⠀⠀⡽⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠉⠁⠀⠀⠈⠁⠀⠀⠈⠉⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠙⢦⣀⠀⠂⢀⣠⠞⠁⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠖⠒⠋⠁
⠀⠀⠀⠀⠀⠀⢀⣠⡤⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⡤⡤⣤⣀
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠉⢳⡄⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡾⠀⠀⠀⢀⣀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⣿⠀⠀⠈⠀⠀⠈⠀⠀⢈⡇⠀⠈⠛⠀⠀⠀⠛⠁⠀⠀⠙⠁⠀⠸⡇⠀⠀⠀⠈⠀⠀⠀⠀⢸⠀⠀⣟⠀⠀⠀⠙⠛⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠈⠙⠶⠤⠤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠶⠛⠁⠀⠀⠀⠀⠈⠙⠶⠤⠤⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣴⠞⠉⠀⠀⠈⠙⠲⡄⠀⠀⠀⣠⠞⠉⠁⠀⠈⠉⠳⣄⠀⠀⠀⢀⡴⠋⠉⠹⠏⠉⠛⢦⡀⠀⠀⠀⡴⠞⠉⠁⠀⠉⠙⠲⡄
⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡿⠒⠀⠀⠀⠀⠀⠀⠚⢿⠀⠀⣗⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢷⡀⠀⠀⢀⠀⠀⠀⢠⠟⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠈⠳⢤⣄⣀⣤⠴⠋⠀⠀⠀⠀⠈⠳⢦⣤⣀⣠⡤⠞⠁⠀⠀⠀⠀⠙⠦⣤⣼⣧⣤⠖⠋⠀⠀⠀⠀⠈⠳⢤⣄⣀⣤⠴⠋


⣿⢿⠿⠿⡿⢟⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣟⣛⣻⣿⣿⣻⣿⣿⣟⣿⣻

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



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⡠⠊⠀⠀⢀⠀⠀⠀⠀⡀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢤⠴⢤⣤⠈⢘
⠀⢠⠊⠀⠀⠀⠀⢎⣹⡁⠀⠰⣉⡇⠀⠀⠙⡄⠐⢄⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠄⢠⡐⢈⢀⡼⠒⠒⠞⠡⠀⢨⠰⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⢸⠀⠀⠀⢠⣀⠈⠀⢠⢄⡀⠁⠀⢠⣀⠀⡇⠀⢆⠑⠠⡀⠀⢄⡀⣉⣰⠀⠀⣤⠀⠠⠉⠉⡠⠤⠂⠂⠦⣀⠘⠢⣄⠗⡀⠀⠀⠀⠀⠀⠀⠀⠨⠉
⠀⢸⠀⠀⠈⠧⠚⠀⠀⠹⠔⠃⠀⠈⠳⠒⠀⡇⠀⠀⢀⠀⠀⠳⠋⠻⡍⢹⠀⢨⣑⠃⠀⠠⢋⠄⠀⠀⠀⠈⠂⠙⡄⠘⣎⠘⡄⠀⠀⠀⠀⠀⠀⠈⠀⠰
⠀⢸⢀⡔⢤⠀⠀⣰⠲⡆⠀⢀⡖⠢⠀⠀⠀⡗⢺⠙⠿⠥⠆⠀⠁⣰⠇⣸⠀⢙⡋⠀⠀⡆⡔⠉⢀⠀⠀⠀⠚⡇⢐⠀⠉⠙⠃⠠⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢸⠀⠙⠉⠀⠀⠈⠋⠁⠀⠀⠙⠉⠀⠀⠀⡷⠾⣀⣐⡤⠄⠀⡥⠸⡤⢼⠀⠫⢁⠀⠈⢅⠐⠀⠀⠀⠀⠈⢀⠃⡈⢀⣠⢤⠂⠘⠀⠀⠀⠀⠀⠐⠀⠠
⠀⢸⠀⠀⠠⢏⣲⠀⠀⢼⣑⡆⠀⠠⣟⣲⠀⡇⠀⠠⠂⠂⢀⠔⡡⢸⡃⢸⠀⠘⡯⠁⠀⠈⠢⢄⠀⠄⠀⠐⡩⠎⠁⡰⠅⡸⠁⠀⠀⠀⠀⠀⠀⠀⠒⠤
⠀⢸⠀⠀⠀⠉⠀⢀⣀⡈⠁⠀⣄⣀⠈⠀⠀⡇⠀⢀⡥⠊⠁⠀⠑⠉⡶⢬⠀⠁⡂⠤⠀⠖⢦⡈⠈⠉⠉⠉⡀⣴⠋⢩⠆⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠
⠀⠈⠢⡀⠀⠀⠀⠣⠼⠄⠀⠘⡤⠇⠀⢀⡴⠁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠢⠤⢍⡉⠉⣦⡀⠀⡄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢚
⠀⠀⠀⠈⠢⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⡄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠟⠛⠉⠉⠁⠈⠉⠉⠛⠻⢿⡿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⢀⣠⣤⣶⣶⣶⣶⣤⣄⠀⣠⣿⣬⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⢀⣴⣿⣿⠿⠛⠛⠛⠛⠿⣿⣯⢟⠟⠁⠹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⢀⣾⣿⠟⠁⠀⣀⣤⣤⡀⣠⠞⠹⣿⣷⡀⠀⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⢸⣿⡟⠀⠀⣾⣿⡿⣿⣿⣷⠀⠀⢻⣿⡇⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢻⣿⣇⠀⠀⣿⣿⣦⣵⣿⣿⠀⠀⣸⣿⡟⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠘⣿⣿⣄⠀⠈⠛⠿⠿⠛⠁⠀⣠⣿⣿⠃⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠘⢿⣿⣷⣤⣀⣀⣀⣀⣤⣾⣿⡿⠃⠀⢠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⡀⠀⠙⠻⠿⣿⣿⣿⣿⠿⠟⠋⠀⢀⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⡛⠋⠉⠛⡲⠤⣄⡀⠀⠀⢀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢻⠁⠀⠰⠁⠀⣀⠊⠀⠀⣀⠉⠶⢄⡈⠑⠤⠞⠁⠀⠹⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⣠⠞⠛⠉⠉⠙⠲⢤⣀⠀⠀⠄⠙⠲⢤⠀⡤⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠟⡄⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⡳⢦⣀⣀⣾⠀⣳⡄⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⠋⠉⠉⡟⠀⠡⢀⡾⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠤⣤⠈⠍⢁⣸⠇⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣻⠹⣄⡀⠀⠀⠙⠦⠤⠞⠁⠀⠈⢳⡤⢄⡀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠋⠀⠀⢀⣀⢸
⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⠀⢻⣀⠀⠉⠓⠶⠤⠤⠤⠤⠤⠴⠒⢫⠇⠀⠈⠓⢦⣄⠀⠀⠀⠸⠖⠋⠙⢦⣀⡟⠈⠛
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣤⣀⣀⣀⣀⣠⣤⠴⠋⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃
⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠈⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠋

⠀⠀⠀⠀⠀⢠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠸⠀⠹⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢠⠀⠰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇
⠀⠀⠀⠰⠀⢘⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇
⠀⠀⠀⢸⡀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⠀⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠄
⠀⠀⠀⠀⢃⡘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠂
⠀⠀⠀⠀⠀⠈⠻⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠄⣀⠀⠀⠀⠤⠄⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠂⠤⠀⣀⡀⠤⢤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⡀⠠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⣴⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⢉⢄⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠂⠀⠀⠉⠉⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⣀⠁⣼⠋⠁⠀⠙⠉⢘⣧⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠸⡆⠈⠘⢠⢤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⣈⠁⠀⠀⠀⠀⢀⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⢸⠉⢀⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠂⠀⢤⠜⠉
⠀⠀⠀⠀⠀⡀⠀⢃⣀⢱⠀⠀⠠⣴⡿⠁⠀⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠒⠀⢰⠃
⠀⠀⠀⠀⠀⣨⠶⣿⣧⣌⣁⡘⢛⣋⡤⠟⣷⢚⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡗⠂⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡭⠬⠍⠛⠀⠁⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠾⠀⠀⠀⠷⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⢀⣀⠈⡠⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠐⢁⠂⠀⡀⠀⠀⡀⣡⠾⠁⠀⠊⢠⡀⠀⡂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠠⠃⠆⠀⢀⡜⠂⣰⡾⠃⠘⠀⠀⠀⠀⡆⠀⢰⠀⠀⠀⠀⠀⠐⠁⠀⠒⠒⣶⠆⠀⠀⠀⠀⠀⠀⠂⠀⠀⠒⠶⢶⠶⡖⠀⠀⠞
⠀⠀⢀⠒⠀⠀⡄⠀⠀⢼⠽⠛⠃⠀⠀⠀⠀⠀⠀⣁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⢁⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠣⣔⠀⠀⠀⠀⠀⠲⠀⠀⢀⡰⠁⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣼⠆⠁⠈⢆⠀⠀⠀⡠⠀⠤⠰⠞
⠀⠀⠀⠀⠐⠤⡀⠀⠑⠦⠬⣤⠀⡀⠠⠆⠉⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡓⢤⡴⡀⢉⡄⠀⡘
⠀⠀⠀⠀⠀⠀⠉⠀⠠⢄⣀⣄⠀⣀⣀⣼⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠀⠁⠋⠀⠈⠉⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⣰⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠉⠛⠻⢿⣿⣿⠟⠀⣠⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠈⠁⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠋⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⠆⠀⣠⣾⡿⠋⢀⣴⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠁⠀⠀⣠⣾⣿⣿⡿⠟⠛⠋⠙⠛⠛⠁⣠⣾⡿⠋⠀⠀⠈⢿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠁⠀⠀⣰⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⢀⣴⣆⠀⠀⠈⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢠⣿⣿⣿⠁⠀⠀⣰⣾⣿⣿⣿⣿⠋⠀⠀⣿⣿⣿⡄⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣏⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣹⣿⣿⡇⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠘⣿⣿⣿⡀⠀⠀⠹⢿⣿⣿⡿⠋⠀⠀⢀⣿⣿⣿⠃⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠏⠀⠀⢀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⡀⠀⠀⠙⢿⣿⣿⣷⣦⣤⣄⣠⣤⣴⣾⣿⣿⣿⠋⠀⠀⢀⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣄⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⣠⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⢀⣤⣾⣿⣷⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣦⣤⣀⣀⣀⣀⣀⣀⣤⣴⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⡆⠀⠀⠀⣀⠀⠀⠀⠀⠀⣤⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠘⠛⠁⠀⠀⠀⠉⠀⠀⠀⠀⠂⢨⡏⠀⣴⣆⣤
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⡿⠈⢁⡼⠉⣡⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠤⠄
⠀⠀⠀⠀⢀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠲⠀⡸⠃⢠⠞⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⢨⠖⠀⠀⠀⠀⠈⠁⢆⠀⢀
⠀⠀⠀⠀⠀⠐⢆⣀⡠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠺⢆⠛⡀⠀⠁⠀⠁⠊⠀⠀⠀⠀⠀⠀⠀⠠⢠⠄⠈⢀⠀⠀⠀⣶⣂⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠲⠘⠀⠀⠈⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⡀⠀⣀⠂
⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠒⠒⢤
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠒
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠁⢤⣀⢀⡀⠀⠀⠀⠀⣠⠤⠔⠃⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣷⡆⠀⠀⣇
⠀⠀⠀⠀⠀⠉⠉⠁⢶⡟⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⢀⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠴⣶⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⠀⠈⠀⠀⠀⠀⠈⠒⠲⠄⠀⠀⢄⠀⠀⠀⠀⠁⠀⠀⠛⠋⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣸⠃⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠠⣤⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠠⠄⣠⢄⠀⠄⣀⠴⠖⠒⠣⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢰⡏⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⡈⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠀⠉⠉
⠀⠀⠀⠀⠀⣶⣡⣼⣤⣧⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⢀⣀
⠀⠀⠀⠀⠀⠁⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠋⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢂⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠤⢀⠀⠁⠀⠀⠀⠀⠀⣷⣾⣿⠆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⢻⢈⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠀⠀⠀⡄⠐⠀⠀⠀⠉⠛⠉
⠀⠀⠀⠀⠀⣤⠀⡄⠁⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠀⠀⠁
⠀⣀⠀⠀⠀⠀⠑⠀⡀⢂⡀⠀⢀⠂⣀⣄⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⢀⠀⡀⢀⣠⠤
⠘⢋⡙⠉⠉⢀⠀⠘⠻⠟⡹⠧⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠁⠀⠀⠁⠂⠀⣀⠀⠀⠀⠀⠀⠐⠚⠀⠖⠈⠁⠀⠀⠀⠀⠀⠙⠰
⠀⠼⢃⠠⠁⠀⠀⣠⠁⠈⠃⠀⠀⠄⠀⠒⡤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠂⡀⠀⢈⠀⣴⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⡀⠀⠀⠀⣄⡀⠀⡀⠀⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠈⠛⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠋⠀⠘⠋⠀⠀⠀⠈⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢠⠀⣴⡆
⡆⠀⠀⠀⠀⡷⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠤⢈⣡⠔⠘⠋⠀⠉⠓⠤⠴⣀⢄⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠞⠉⠁⢠⣶⡄⠀⠀⠀⢠⡄⠈⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⢀
⠀⠀⠈⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠚⠀⠀⠀⠠⢀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠘⢢⣄⢠⠀⠀⡄⠶⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠘⠣⠀⠀⠀⠀⠀⠢
⣤⣤⣤⣤⣤⣤⣤⣤⣥⣬⣷⣶⣶⣦⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⢀⣠⠖⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠈⠳⠤⠋⢀⡀⠘⣆⣠⣤⠤⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢸⠀⡴⣄⠀⡴⠋⡇⢀⣀⣤⡄⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢉⡀⡇⠈⠛⠁⠀⠙⠉⠰⠯⢤⣄⡉⠙⠒⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢰⠈⠁⠀⣀⢠⠀⡀⠀⢠⠖⢋⣩⠤⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠈⣣⠀⠀⢻⣛⠛⡇⠀⠈⠙⢮⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠮⢤⣘⣛⡳⠤⠤⡼⠨⢠⠇⠺⠿⣝⢛⣁⣘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢑⡏⠀⣾⣛⣛⣛⣋⣁⣙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠈⡸⠃⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⣤⠚⠁⠈⠙⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢶⣏⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣆
⠀⠀⠀⠀⠀⠀⣰⠟⠁⣠⡤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣶⡛⣷⠀⠀⢻⡆
⠀⠀⠀⠀⠀⣼⠏⠀⡴⠋⠀⢀⣿⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠈⢻⡄⠀⠀⠈⣷
⠀⠀⠀⠀⢸⡟⠀⣸⠃⠀⢰⣿⣿⣀⣠⡄⣠⣴⣿⣇⠀⠀⠀⠀⢸⣷⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠈⠉⣿⠁⢹⠻⢿⡿⠟⠀⠀⠀⠀⣸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⣷⠀⢻⣄⠀⠀⠀⣰⡏⠀⢸⡀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠹⣦⠀⠉⠛⠓⠛⣋⣀⣀⠘⣷⡀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠉⠉⠹⡷⠈⠛⠷⠶⡶⠟⠋⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣶⣤⣤⣄⣀⣀⣀⣀⣠⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁
⣿⣿⣿⣿⣛⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣻⣿⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣀⣀⣀⡀
⠀⠈⢿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⢠⣞⠉⠙⣷⡌⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⠿⡿⠿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⢻⣶⣶⠟⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡶⡶⠾⢿⡿⠲⣶⡶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣹⡇⣀⣿⡇⡀⣷⡇⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣵⠁⠨⣭⣷⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣶⣾⡟⠷⣏⢳⣠⣵⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢽⣂⣴⣿⣿⣿⣿⣿⡄⠈⢹⣿⣿⣿⣿⣿⣿⡆⡰⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣏⠙⢿⡿⠛⠛⠈⢣⠀⠀⡟⡜⠘⢿⣿⡿⠋⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡄⠀⠈⠑⢤⣤⣿⣶⣶⣾⣄⡤⠞⠉⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣺⣿⣿⣷⣤⣀⣠⣿⡟⢣⡀⢨⣟⣿⣷⣤⣶⣿⣿⣿⣙⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⣿⣿⣷⡞⠚⢻⣿⡅⠻⡷⡯⠋⣼⣿⡟⠛⢛⣿⣿⣿⠓⠃⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣷⢀⡼⢿⣿⣦⣤⡜⣊⡿⠋⢑⠢⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣿⣿⠛⠁⠀⠀⢈⣛⡟⠛⠛⡆⠀⢹⣷⢮⣛⣿⡋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡾⠯⢧⣄⣐⡢⢶⣖⣸⡀⣰⣆⣹⡄⠀⣩⣷⣷⠟⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢷⢿⣿⣯⣷⣿⣿⣿⣷⣤⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⡏⠾⠙⡟⠻⠁⢨⣽
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣉⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠙⠷⡄⠀⢷⡀⠀⠀⠚⠁⢀⡠
⠀⠀⠀⠀⠀⠀⢸⡟⣦⣤⠤⣶⠏⠀⠀⢀⣠⣤⣄⠀⠀⣀⡠⡄⢰⢂⡲⠂⣤⡀
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠰⣧⣀⣀⡀⠉⠉⠀⣠⠴⠊⣩⠰⠓⠉⠉⠁⠻⡤⠙⡆
⠴⠶⠶⠆⢀⣴⠃⠀⠀⢀⣴⡾⣏⢉⡅⡤⢲⡉⣥⠔⠋⠁⠀⠀⠀⠀⠀⠀⡦⠘⡇
⠀⠀⢠⠶⠛⠛⠛⢻⣆⡟⣹⠂⠖⠰⠆⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠚⣇
⠀⠀⢀⡀⠀⢠⠄⠀⣿⠁⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡶⠾⠿⠛⠛⠛⠛⠛⠿⠿⢶⣶⣄
⣠⡶⠋⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⣶⣆⣀⣀⣀⣀⣀⣀⣠⣶⣦⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⣶⣿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠉⠉⠙⢿⡿⠶⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠁⠀⠟⣡⠤⠐⠂⠤⣀⠀⠀⠀⠀⠀⣀⡀⠀⠉⠀⠀⠈⠙⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠈⠳⡄⣠⠖⠉⠀⠀⠈⠒⢄⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠟⠁⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠹⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⣷⢀⣠⡀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼⣹⣿⠀⠀⠀⣿⢨⣹⣧⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⠟⠀⠀⠀⡾⠈⠿⠇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⡴⠋⠈⠳⣄⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⣤⠴⠋⠀⠀⠀⠀⠈⠙⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠚⠉⠛⠙⠛⠲⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⣀⢀⠀⢀⡀⠀⠠⠄⠀⠀⠉⢻⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣀⡠⢤⡀⠀⣀⣀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡀⠶⠀⠰⠀⠈⠋⡤⠈⠓⢀⡀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣀⣠⣌⣤⣥⣀⣄⣤⣤⣤⣤⣥⠤⡤⠼⠤⠤⠴⠦⠤⠼⠶⢶⡄⠀⠀⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⡴⠶⠞⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠰⣄⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⠀⢠⠀⠀⠀⠀⠀⢠⠀⠈⠀⠀⠀⠠⠀⣦⣠⠔⠀⡀⠀⠘⠆⠉⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡛⠀⠼⠀⠀⠤⠀⠸⠛⢀⡀⠀⠁⠀⠀⠔⣈⠁⠀⠀⠀⠠⢖⣀⣰⠜⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠁⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠂⡀⠀⠉⠈⢱⣌⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠒⠒⠰⢿⠠⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⢴⣛⣓⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡄⣸⣷⢸⣇⠷
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⣬⠍⠀⠀⠈⠀⠀⠀⠆⠒⠋⠀⠂⠰⡤⠴⢚⡁⢰⠀⠩⢾⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠐⣏⠀⠀⠀⠓⣚⠁⠙⠂⢑⣂⠀⢁⠀⢤⠴⢖⣼⣌⡐⠆⢠⣿⡿⠿⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠁⠠⣿⡈⢉⡳⢬⢟⣻⢿⡿⢿⡿⣶⢶⡿⢿⣿⣿⣶⠀⢿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⣀⣨⣿⠖⠙⣿⣷⠟⠷⠾⣰⠄⠸⣿⣿⠛⠷⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡧⠒⠒⣧⡇⢤⣌⣼⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡷⢳⢶⡦⠁⣀⡌⠙⡿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⡗⡎⢈⣷⠘⡄⣠⣿⣩⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢢⣿⣿⢹⠀⣅⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⠻⠃⠺⠂⠀⠀⠉⠉⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡀⠀⢀⠀⠀⠀⠀⢀⣀⣠⡀⠀⠀⠘⣠⣤⣀⠀⠀⠉⠀⢀
⠀⠀⠀⠀⠤⠤⠴⠤⠴⠾⠿⠧⠴⠌⠛⠓⠲⠷⠾⣿⣟⡡⠞⠒⢚⣾⣿⣿⣶⣆⣀⣛⣛⣺⣷⣶⣶⣶⣶⣤⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉
⣿⣿⠛⠛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⣶⣶⣼⣧⡙⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣷⣍⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠄⠒⠒⠠⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠓⢬⡳⢄⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣑⢦⡀⣠⠖⠁⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣍⠣⣀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠑⢮⡳⢾⣿⣿⣿⣿⠿⠛⠛⠋⠉⠛⠛⠻⢿⣿⣿⣿⣷⣄⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⣰⣿⣦⣙⢿⡋⠀⢀⣤⣴⣶⣶⣶⣤⣄⠀⠈⠻⣿⣿⣿⣷⡀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣰⣿⣿⣿⠏⠓⣍⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠘⢿⣿⣿⣷⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣿⣿⣿⡏⠀⢰⣿⣷⣮⡛⢏⣁⣀⡉⠻⣿⣿⣿⣧⠀⠘⣿⣿⣿⡇⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⠁⠀⣿⣿⣿⡟⠉⣦⣙⢿⣿⡆⢸⣿⣿⣿⡆⠀⣿⣿⣿⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸⣿⣿⣿⡆⠀⢻⣿⣿⣷⡀⠻⣿⣿⡿⠁⣸⣿⣿⣿⠁⠀⣿⣿⣿⡿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣿⣿⣿⣷⠀⠈⢿⣿⣿⣿⣦⣤⣤⣤⣾⣿⣿⣿⠏⠀⣰⣿⣿⣿⠇⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠘⣿⣿⣿⣷⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣴⣿⣿⣿⡟⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠘⢿⣿⣿⣿⣦⣄⡀⠈⠉⠉⠉⠉⠉⠀⣀⣴⣾⣿⣿⣿⠏⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣶⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⡦⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠁⠀⠀⠈⠉⠉⢻⣿⣿⡏⠁⠀⠀⠀⠀⠈⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠃