⠀⠀⢀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄
⠀⠀⠀⠀⣶⡶⠶⠶⠶⢶⠶⠶⠶⠶⠶⠶⠶⡶⢶⠶⡶⠶⠶⠶⠶⠶⠶⠶⢶⠶⠶⠶⠶⢶⣶⠀⠀
⠀⠀⠸⠀⣿⠇⢰⠒⠒⠒⠛⠒⠒⠒⠒⡒⠒⠂⢂⠒⠀⠂⠀⠂⠒⠐⠒⠂⠀⠐⠀⠐⢦⠀⣿⠀⠀
⠀⠀⠸⠀⣿⠃⢘⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⠀⠀⠀⠀⠀⢀⣠⡶⠀⣿⠀⠀
⠀⠀⢸⠀⣿⠃⢸⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣼⣿⣿⣿⣧⠀⣿⠀⠀
⠀⠀⢸⠀⣿⡃⢸⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢡⠀⣿⠀⠀
⠀⢀⣸⣀⡿⣇⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⢰⠀⣿⠀⠀
⠀⢰⠀⣿⠀⢹⣼⣿⣿⣿⣿⣿⠉⣹⣿⣿⣿⠛⠛⠛⢛⣿⣿⣯⡀⢸⠀⠀⠀⠀⠀⠐⢲⣴⠛⡤⠂
⠀⢈⠀⣿⠀⢺⢹⣿⣿⢿⣿⣿⢸⣿⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠸⣿⠀⡃⠀
⠀⠀⠀⣿⠀⢻⠈⣿⣿⠀⢿⣿⠸⣿⣿⣿⣿⠇⢠⠀⢺⣿⣿⣿⡇⠠⠀⠀⠀⠀⠀⠀⠐⣿⠀⡅⠀
⠀⠈⠀⣿⠀⢹⠀⠘⣿⣷⣾⠻⡆⠛⠿⡿⠟⠀⠘⠓⡜⠿⠿⠟⠀⢐⠀⠀⠀⠀⠀⠀⠠⣿⠀⡆⠀
⠀⠈⠀⣿⠀⡺⠀⠀⠹⣿⣿⡀⠀⠀⢈⣀⠀⠀⠐⠚⠁⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⢀⣿⠀⠆⠀
⠀⠐⠀⣿⠀⡇⠀⠀⠀⢹⣿⣇⠀⠀⡿⣦⣑⣢⣄⡀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠇⠀
⠀⢀⠀⣿⠀⡇⠀⠀⠀⠈⣿⣿⡄⠀⠳⠭⣿⣿⡿⠇⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⡆⠀
⠀⠀⠀⣿⠀⢱⠀⠀⠀⠀⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⣀⣤⡾⣟⣲⠀⠀⠀⠀⠀⠀⠠⣿⠀⠆⠀
⠀⠈⠀⣿⠀⢸⠀⠀⠀⢸⣿⣿⣿⣿⣽⣻⢿⡒⠒⠚⠉⣽⣯⣳⣟⣁⣀⣀⣀⠀⠀⠀⠠⣿⠀⠇⠀
⠀⠐⠀⣿⠀⠀⠀⠀⠀⣸⣛⠻⢭⡙⡞⡽⢿⡷⣤⣀⡴⡿⣿⡝⣒⠲⣒⠲⡺⣆⠀⠆⢀⣿⠀⠇⠀
⠀⢸⠀⣿⠀⢸⠀⠀⣰⢣⢎⡙⢦⡹⣘⠜⡣⢿⡲⣉⢮⢱⢹⡗⣬⠓⣬⢳⠱⣹⣆⠀⢠⣿⠀⠇⠀
⠀⣸⠀⣿⡀⣸⠀⡼⡑⣎⠞⡌⢧⡑⢎⣳⡹⡜⣷⡩⢆⣋⠖⣯⠒⡍⣿⢢⡛⡴⢹⣇⢠⣿⠀⡇⠀
⠁⢸⣿⠀⡟⠁⡜⣡⠳⡜⢬⡙⢦⣙⣾⢇⡳⡜⣿⡘⢦⠍⡎⣧⠛⡴⢻⡧⡱⣍⡇⢸⣟⠈⠏⠀⠀
⠀⢸⣿⠀⣧⢞⡜⣡⠳⡜⢣⡜⣣⣾⢋⢮⠱⡜⣼⡙⢦⠛⡴⣇⡛⡴⣉⣷⡓⢦⡇⢸⡯⠀⠃⠀⠀
⠀⢰⣿⠀⣷⢩⡖⢡⣧⣭⡇⣼⣿⣿⡌⡎⡇⢳⢸⡍⢲⠙⢲⡆⢳⡌⣧⢻⡟⡆⡇⢸⡗⠀⠃⠀⠀
⠀⢸⣿⠀⣧⠫⣔⠫⣜⠦⣍⣷⣿⡷⡩⡟⡾⡜⢦⡹⢌⡳⣊⡼⣡⠞⡴⢊⡷⣩⡇⢸⡗⠀⡃⠀⠀
⠀⢸⣿⠀⠙⠓⠛⠛⠚⠛⠚⠛⠛⠓⠛⠛⠓⠛⠓⠛⠚⠓⠛⠒⠛⠛⠛⠛⠛⠛⠃⢸⡯⠀⡅⠀⠀
⡀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠀⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀