⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣷⡦⢤⣤⣤⣤⠤⠤⣤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠿⠛⢭⢅⣀⠄⠈⠩⢄⠀⡀⢀⠉⠉⠲⣧⣄⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠉⠀⠈⠙⠛⢷⣶⣤⣔⠈⠀⠄⠠⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠛⠀⠀⠂⠀⠈⢀⠐⠀⠐⠈⠀⡀⠈⠻⣿⣿⣦⠐⣠⣿⣿⣿⣿⣿⡿⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢀⠀⠀⠀⠈⣀⠂⠀⠀⢂⠀⠀⠠⠐⠀⠘⠛⣿⣿⣿⣿⣿⣿⣳⡺⠀⠀⡜⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡸⠀⡀⠀⠀⠀⣐⣿⠟⠀⠀⠀⣼⠄⡀⠀⠀⠀⠀⠀⠻⣿⣿⢿⣿⣿⣿⠇⠀⠄⢲⢙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡇⣼⠇⠀⡀⢩⡾⣏⡀⠀⠀⠄⢸⠀⠈⠢⣀⣐⡤⠐⠀⢻⣿⣿⣿⣿⣿⡇⠀⠂⢸⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡇⡞⡅⠀⠀⣸⣆⣈⠣⠘⢆⠀⡼⢘⡛⠛⠛⠏⠀⢀⠠⠘⣿⣿⣿⣿⡏⠁⠀⠐⢸⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⡷⠉⡗⠀⠀⣿⢻⣿⣷⠀⠈⠂⠹⣴⣶⣶⣶⣦⡢⠀⠀⠄⣿⣿⣿⣿⡇⠀⠐⠀⠸⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⢧⡠⠀⡿⠸⠿⣿⠀⠀⠀⠀⢻⣿⣿⣿⡿⢷⠀⠡⠀⣿⣿⣿⣿⠁⠀⠠⠈⠐⠠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣗⠄⣇⢀⠉⠉⠀⠀⠀⠀⠐⠾⠿⠿⡇⢾⠠⠑⣸⣿⣿⣿⣿⠀⠀⠄⠐⠈⡀⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣿⣬⣀⠀⠀⢠⣄⠀⠀⠀⢠⠶⣁⣼⢀⢆⣿⣿⣿⠟⢹⠀⠀⡄⠆⠰⠁⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣹⡿⡿⣿⣷⣾⣿⣶⣶⣾⣿⣿⡛⡷⢈⣿⡿⠋⠁⠀⡟⠀⢀⠀⠀⡘⠀⡁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣕⡿⣿⡿⣀⡿⠛⠻⡟⣿⡿⣟⡷⠟⠘⠇⠀⠀⠀⡇⠀⠀⡀⠂⢀⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠋⢁⡿⡳⠚⡧⠤⣴⠿⢻⡕⠉⣇⡀⠀⠀⠀⠀⢸⠁⠀⠐⠀⠀⠄⠂⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⢸⣷⣇⡨⠀⠄⡏⠛⠃⡇⢀⡿⣇⠀⠀⠀⠀⣸⠀⠀⠂⠈⠀⡐⠀⡁⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠇⢀⣾⣿⣿⡟⠀⠀⢰⡿⣖⣺⣧⣴⣾⣿⡀⠀⠀⠀⣿⠀⠐⠀⠁⢀⢰⡄⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠟⢀⣾⡿⣟⣴⠀⠀⢀⣸⠗⠺⣴⣿⣿⣻⣿⣧⠀⠀⠀⣷⠀⠀⠀⠠⠀⠸⣽⣨⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⠤⢊⠴⠾⣋⣁⣼⣿⠉⠀⢀⢀⣿⠁⢠⣶⣿⣯⡿⣽⣿⣷⡀⠀⣿⠀⠄⠀⠀⠀⠀⠋⣷⢪⣧⠄⠀⠀⠀⠀⠀⠀⠀
⣰⣶⣆⣀⠾⠋⠀⣠⣿⢠⢠⣿⣿⠀⠀⠀⠄⢠⣾⣿⠰⠿⣧⣟⣾⣽⣳⣯⣿⣿⣧⣯⡄⢀⠀⠀⠀⠀⠄⠰⣧⡞⣿⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠙⢿⣷⣶⣶⣾⣿⣷⣧⣑⣛⢻⣿⣟⣾⡽⣷⣿⣿⣿⣿⣿⣦⣤⣅⢀⠠⠀⠄⠈⠑⠓⠿⣦⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣾⣷⣿⣾⣿⣿⣿⣶⣾⠛⠻⣿⣿⣾⣻⣿⣿⣿⣿⣿⣿⣾⣽⡷⣯⣿⣿⣿⣿⣿⣿⡧⡇⠁⢀⠠⠁⡀⠀⠀⠀⠘⠻⠤⡀⠀
⠻⣿⣿⣿⣿⡿⠿⠿⠟⠛⠋⠉⠉⠉⢹⣿⣳⣯⢷⣿⣿⣾⣿⣿⣷⣟⣾⣿⣻⣟⡾⣯⣿⣿⣿⠇⣿⣄⠠⢀⠰⢀⣁⣈⣐⣠⣀⣂⢈⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⣯⣿⣷⣿⣿⡟⢺⡻⣯⣿⣾⣿⣾⣽⣿⡿⢟⣿⠟⠛⠻⠾⠿⠟⠛⠃⠀⠀⠀⠀⢀⣧⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠟⠉⠀⠀⠑⠺⠭⠭⠭⠭⠭⠽⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀