⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⠿⠋⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣴⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡿⠂⠄⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠔⣿⣿⣿⣿⣿⠟⢿⣿⡀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣾⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠸⠀⢀⣲⡿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠐⣄⠀⣔⠀⡜⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠘⣧⢘⢗⠃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣾⣦⣶⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⣿⣿⠂⠑⢤⡤⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠉⣋⠀⠈⡧⢄⢿⣶⣷⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣢⣾⣿⣆⠀⠀⠀⠀⠀⡧⣎⢿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠁⠛⢹⣿⣿⣦⡀⠀⢀⡄⣿⣿⠷⠫⣿⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⢳⣢⣤⣿⣿⣿⡝⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⠀⠀⠀⠀⠘⠉⠉⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿⠁⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣟⡿⣿⡷⠈⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡶⣫⣶⣶⡁⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡿⢋⣤⣷⣨⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣾⣿⣿⡿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡹⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⢠⣶⣶⣶⣶⣴⣤⠙⡽⣿⣿⣿⡄⠀⠀⠀⠀⠀⢈⣿⣿⡤⣦⠀⠀⠀
⠀⠀⠀⠀⠀⣷⣟⣿⢿⣿⣿⡟⠀⢸⣿⣿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⢿⣿⣿⣿⣴⣧⠀⠀⠀⠀⢿⣿⣿⢀⠃⠀⠀
⠀⠀⠀⠀⠠⣿⢟⣿⣿⣿⣿⠀⠀⢸⣿⡿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠻⣿⣿⣿⣻⡗⠀⠀⠀⢿⣿⣿⣿⣷⠀⠀
⠀⠀⠀⠀⠡⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠹⣿⣿⣿⣿⡀⠀⠀⠀⢿⣿⣿⣿⠀⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⢰⠁⢐⣿⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠹⣿⣿⣿⣿⡀⠀⠀⠀⢻⣿⣿⢐⣀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⣨⣶⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠹⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⡟
⠀⠀⣸⡝⣿⡿⣿⣿⠟⠀⠘⢿⣿⡿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠹⣿⣿⣿⣿⣌⡆⠀⠈⠛⠿⠁
⠀⠀⡟⢳⠀⠀⠀⠀⠀⠀⠙⠿⠿⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⣿⣿⣿⣿⡇⠀⠀⠘⣦⠀
⠀⢰⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⠀⢿⣿⣿⣿⣨⠩⠂⠒⣽⣿⣟⠝⠂⠒⣉⣰⣿⣿⣿⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡄⠀⢿⠀⠀
⠀⣼⣿⣿⣽⠃⠀⠀⠀⠀⠀⠈⠀⠀⡏⣾⡄⠿⣿⣿⣿⣷⡶⢀⡀⠰⠐⡐⡠⣶⣿⣿⣿⣿⠃⡄⠀⠀⠀⠀⠀⡟⣿⣿⣿⠀⠀⠈⠁⠀
⠀⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢹⣿⣦⠙⣿⣿⣿⣿⣿⡅⣿⡀⣾⣿⣿⣿⣿⠟⣠⣿⠀⠀⠀⠀⠀⠀⠇⠙⠟⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠈⠁⠈⠛⠛⠋⠉⠉⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀
⠀⣿⣿⡿⠀⠀⠀⠀⠀⠰⠛⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀