⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠧⣒⠦⠄⣀⡀⠈⢹⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠑⡴⡒⠚⠷⣶⣯⡁⠉⠙⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠂⠀⠀⠀⠀⠑⣚⢦⣄⡏⡀⠉⠀⠀⠀⠈⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⡞⠁⣄⠀⠈⠀⢀⠈⠛⢾⡿⣮⡻⡮⠱⠂⡀⢀⠀⠀⣘⣆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠄⠀⠀⠀⢰⡽⡄⠀⠘⡲⣀⠀⠀⠐⣔⠀⠹⣿⠱⣷⡤⠔⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢀⣤⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣠⠀⠀⠀⣾⢡⡇⠀⠀⢧⠈⣑⠤⡀⢸⣆⠀⢻⣆⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⡼⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠿⡷⡢⣀⣿⢼⠸⡀⢠⠘⡴⠁⢀⣿⣏⢻⠛⣾⠷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⠠⠤⠤⠦⠤⣄⣀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⣇⠘⢾⣿⣿⣾⡷⣫⣳⣿⢠⣾⡿⣹⣼⠸⡿⡆⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠠⢪⠗⣚⠛⠓⠂⠀⠤⠬⣙⠒⢥⡙⢦⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢹⣆⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠡⡿⠃⠀⣷⠇⢸⡀⠀⠠⠤⢒⣲⠖⢉⠉⢉⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣞⠛⣿⣮⡍⠴⣲⣄⡀⠀⠉⠒⠽⡽⡿⣆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠹⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⠁⠀⠀⢻⡶⡸⠁⠀⠀⣴⠟⠁⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣯⡉⠐⠓⠦⢄⣭⠋⢦⡀⠀⠀⠙⡷⢹⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⢀⡘⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⠙⣿⣷⡄⠀⠀⠀⠈⠑⢆⠹⡀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠑⠝⢿⣷⡽⢿⢧⠹⣧⣀⠀⣰⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠈⣿⡆⣺⣿⡞⡄⠀⠀⠀⠀⠀⢣⢳⠀⢠⡧⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠜⡇⣷⠱⠁⡹⠟⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⢠⠇⡟⢿⠟⣿⢰⢃⠀⠀⠀⠀⠀⣏⣷⡿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠊⢀⣷⡟⡿⠋⠀⠀⠀⠀⠀⠈⠀⠀⠸⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⢮⢣⠇⠈⢞⡏⢸⠈⡄⠀⠀⠀⠠⢿⡯⠖⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⣠⠊⠀⠀⠠⢴⡶⢗⡵⠋⠀⢀⣜⣰⣾⠀⠇⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠜⠁⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠉⠠⣴⣞⣡⠟⢻⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠖⠁⠀⠀⠀⢑⣄⣴⡡⠤⠤⠤⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⡀⠈⣼⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡎⠀⣄⠀⠀⢣⠀⠀⣧⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⣣⠀⠈⣇⠀⠘⡆⠀⢸⢱⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⣆⡧⡀⠀⠀⠀⠀⠀⠀⣞⣡⠞⠛⡆⠀⢸⡆⠀⢹⡁⠉⣮⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀