⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣶⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⢀⠠⠠⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠄⣰⣿⠿⠻⠟⠻⢻⣿⣿⠂⠀⠀⠀⠀⠀⡆⢀⠠⠀⠀⠀⡄⡀⢘⡀⠀⠀⠀⠀⡭
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡅⢂⠀⠀⠀⠀⠀⠀⠀⣿⡗⠀⠀⢀⣀⣤⠿⣿⡄⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⡇⡇⠸⡿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠇⢸⣟⣯⣿⣿⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⣥⡶⣾⡅⠀⠀⠃⡇⠐⡄⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠈⠉⣥⣼⣏⠉⠀⣿⡇⠀⠀⠀⠀⠀⣿⠐⠒⡇⠀⢠⣴⣧⣀⣇⣀⣠⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢨⠦⣱⠶⠍⢈⢻⡇⠀⠀⠀⠀⡰⢻⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⡇⠀⢠⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡢⣠⣤⣦⠵⠛⡌⡇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⢨
⠀⠀⠀⠀⢀⣀⣀⣀⠘⠀⠀⠀⠀⢤⣤⡀⡄⡀⡀⢒⡒⢶⡦⠈⣀⣠⣷⣄⡉⠍⢱⣾⡇⣏⣩⣵⡲⡦⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠁⢸⠰
⡇⠂⠴⢰⠤⢂⣍⣇⠡⡒⠨⠒⠉⠠⠼⠤⠥⠑⠊⠁⠈⢈⣡⣴⣾⣿⣿⣿⣿⣾⣿⣿⡇⣿⢺⠿⣿⣶⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡
⢧⠀⠇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣉⣉⠚⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆
⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠸⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⣯⣉⠙⠛⠤⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢎
⠘⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣏⣉⣛⠈⡒⠂⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀⢸⠀⠀⡗⡌
⠀⣇⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣥⣭⣠⣁⠆⡀⠀⣹⣿⡆⠀⠀⠀⠀⠀⢸⠀⠀⡗⡌
⠀⢸⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣶⣿⣿⣿⡄⠀⠀⠀⠀⢸⠀⢀⡯⡐
⠀⠸⡆⠘⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⡇⠥
⠀⠀⣇⠀⡆⠀⠀⠰⣵⠂⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣰⠹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⢡⢃
⠀⠀⢹⠀⢀⠀⠀⠀⠀⠓⠀⡇⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⡇⢸⣶⣿⣿⣿⣿⣿⣶⣶⣶⡆⠀⢸⠰⣈
⠀⠀⢸⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⢸⠰⢡
⠀⠀⠈⡇⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣷⣸⢻⣏⣋⣭⣩⣩⣭⣩⣿⠁⠁⣽⠘⡤
⠀⠀⠀⣷⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣋⢔⠿⣟⣿⣯⣽⣿⣟⣄⠀⣿⠐⢢
⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣷⣕⣺⣿⣿⣿⣿⣿⠂⠀⡏⡌⢥
⢄⣀⢵⡘⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⣿⣿⣿⣿⢸⠀⠀⡇⡜⠤
⠀⠀⠀⣂⣧⠤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣟⣭⣱⣹⣯⠀⠀⡧⡘⢆
⠂⠀⠊⢠⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠛⣹⣧⡤⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⡂⠀⣧⠑⡎
⠀⠀⡠⠊⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣡⡴⣿⡃⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠁⠉⠋⠀⠀⠀⠀⢈⡇⢣⠜
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠳⠿⣄⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠇⠀⠄⠁⠀⠀⠀⠀⠀⠀⢸⡇⢣⢚
⠒⠒⠒⠒⠒⠛⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠐⡄⠂⠀⠀⠂⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠛⠛⡟⠛⠛⠛⠂⠁⠀⠂⠀⠠⠤⠤⠤⠤⡼⢈⢇⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣌⣎⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡐⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣈⣘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣇⠌⠀⣀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⠢⠤⣾⣿⡋⡄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⣄⡀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⡠⠔⠁⣸⣿⣿⣿⣿⣏⡆⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠑⣤⢂⢆⡰⢀⠤⡀⡄⢀⣰
⠀⠀⢀⠄⠀⢀⠜⠀⣿⣿⣿⣿⣷⠏⠀⠀⠀⠀⠀⠀⢠⣿⣿⢇⣐⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣭⡞⣬⣓⢮⡱⣜⢦⡽
⠀⠀⠀⠀⠠⠂⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡵⣯⢾⡽⣽⢾⡽
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣿⣽⣯⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣾⣿⣿