⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⢸⣿⣿⡜⢯⣷⡌⡻⣿⣿⣿⣆⢈⠻⠿⢿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢳⣿⣿⣿⣿⣿⣿⡜⣿⣿⣧⢀⢻⣷⠰⠈⢿⣿⣿⣧⢣⠉⠑⠪⢙⠿⠿⠿⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⡇⡞⣿⣿⣿⣿⣿⣿⡇⣿⣿⡏⡄⣧⠹⡇⠧⠈⢻⣿⣿⡇⢧⢢⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⢃⢿⣿⣿⣿⣿⣿⣷⣿⣿⠇⢃⣡⣤⡹⠐⣿⣀⢻⣿⣿⢸⡎⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⣿⠘⡸⣿⣿⣿⣿⣿⣿⣿⡿⣰⣿⣿⢟⡷⠈⠋⠃⠎⢿⣿⡏⣿⠀⠘⢆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢹⣿⣿⡐⢡⢹⣿⣿⣿⣿⡏⣿⢣⣿⣿⡑⠁⠔⠀⠉⠉⠢⡘⣿⡇⣿⡇⠀⡀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣿⣿⣇⠇⢣⢻⣿⣿⣿⡇⢇⣾⣿⣿⡆⢸⣤⡀⠚⢂⠀⢡⢿⡇⣿⡇⠀⢿⠀⠀⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠹⣿⣿⡘⣆⢣⠻⣿⣿⢈⣾⣿⣿⣿⣶⣸⣏⢀⣬⣋⡼⣠⢸⢹⣿⡇⢠⣼⠙⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠁⠹⣿⣇⠹⡃⠃⠙⡇⠘⢿⣿⣿⣿⣿⣿⣏⣓⣉⣭⣴⣿⠘⢸⣿⠁⠘⠋⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠈⢿⣇⠂⣷⠄⠐⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⢸⡏⠀⢀⣠⣴⣾⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠙⠆⠈⠢⠲⠥⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⣸⠁⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠄⠃⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡏⠹⣿⣿⡿⠫⠊⠀⠀⠀⣶⠀⢻⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⢋⠀⠀⠀⠀⢀⣼⣿⡆⠈⣿⣿⣿⡟⣱⡷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣁⡀⠨⣛⠿⠶⠄⢀⣠⣾⣿⣿⣷⠀⢹⣿⡟⣴⠈⢃⣶⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⣿⣿⡿⠀⡀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠻⣿⣿⢀⠙⠻⠿⣿⣿⣿⣿⣿⣿⡇⠁⣿⠟⡀⠈⣧⢰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠴⠮⣥⠻⢧⣤⣄⣀⡉⢩⣭⣍⣃⣀⣩⠎⢀⣼⠉⣼⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⣛⠓⢒⣒⣢⡭⢁⡈⠿⠿⠟⠹⠛⠁⠀⠀⠀⠰⠃⠂⠀⠀⠀