⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠿⠟⠻⠛⠛⠛⠻⠶⣦⣄⣠⣠⣄⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⣀⣶⠿⠛⠉⢁⣠⣥⣌⡛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡿⠋⢀⠠⠀⠄⠠⣀⡤⡴⠶⣶⣿⠋⡀⠌⠀⡈⠁⠈⠙⢿⡆⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠏⠁⡐⠀⠄⢂⣰⡷⢋⡑⢄⠡⣼⠇⡐⢀⠂⠀⠀⠀⠀⠀⢈⡿⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⡿⠟⠁⣀⡐⡤⢒⢎⡹⣌⣷⣂⠒⠞⠡⣿⣷⣄⡢⢌⠣⠄⡀⢀⢀⣸⠟⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣾⡟⠋⠀⠀⠀⣀⣄⠲⡜⢢⡱⣌⢳⣊⠵⣟⠻⣷⡌⢠⠣⢼⣿⣿⣿⣮⣷⣬⣐⣉⣘⣠⣶⡿⠿⢷⢶⣤⣤⣄⣀⡀⠀
⠀⠀⠀⠀⠀⢿⣿⡰⣀⢤⠶⡙⠦⣌⢳⡼⣱⠶⠧⠳⠎⠷⠚⠛⠛⠛⠛⠒⠛⠛⠛⡛⠟⠻⠿⠿⢿⢻⠻⡝⢲⠂⠄⠀⠀⠈⠉⣙⣿⠆
⠀⠀⠀⠀⠀⠹⣿⣷⡿⣞⣳⣽⠳⠍⣣⣴⣵⡶⣷⠿⣿⣶⣿⣶⣶⣶⣦⣦⣤⣤⣄⣄⣀⢁⠀⡀⠀⠀⠁⠀⠀⡀⢀⣠⣤⣶⡾⠛⠉⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⢡⣴⣿⠿⣙⢦⡙⢦⣻⣿⣏⣶⣿⣿⣯⣝⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣭⣿⡟⠀⠀⠀⠀
⠀⠀⠀⣠⣴⠿⠛⣋⣍⡴⣾⢿⡹⢎⡳⣩⠲⣍⣷⣹⣿⣾⠛⢠⠈⠛⣿⣿⣍⠙⠛⠛⠛⠏⠁⠉⠙⢋⣌⡡⣙⣿⣿⣿⣿⠁⠀⠀⠀⠀
⠀⢠⣾⠟⢁⣶⣿⣟⡯⣝⡞⣣⠝⣎⠵⣡⣛⡬⣷⡽⣿⠱⢾⠃⠀⢸⣿⣿⣿⠀⠀⠀⡀⠄⡴⢢⢦⣼⣿⡷⠀⢻⣿⡟⣿⣧⠀⠀⠀⠀
⠀⢸⣿⡄⢺⣿⡿⣜⡱⢮⡱⢣⠞⡜⢮⡱⢮⡵⣻⣿⣿⠁⠀⡀⠀⠈⢿⡿⠏⠀⠀⠄⢀⠃⠄⡐⢈⠸⡿⠃⠀⢸⣿⣟⣬⢻⣷⠀⠀⠀
⠀⠈⠙⢿⣿⣿⢳⣌⠳⣧⡹⢡⣛⡜⣣⢕⣻⢖⡹⣷⡀⠀⠿⡷⠇⠈⠀⠀⠀⠀⠠⠀⠀⠾⡴⣴⢦⡟⠃⢀⠐⢨⣿⡿⢼⣿⠛⠃⠀⠀
⠀⠀⠀⢾⣿⢧⣿⣬⣻⣷⣍⣳⣿⣏⠶⣬⣿⣮⣵⡿⠡⠀⠄⢀⠐⠈⠀⠄⣐⣦⣦⣤⢤⣠⣄⣤⣌⡿⠂⠀⠠⣼⣿⣟⠦⣿⠀⠀⠀⠀
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠷⠧⠧⠬⢄⣀⠈⠀⠀⠀⠀⠀⠈⠈⢁⠈⠀⠀⢀⣠⣼⣿⣿⣿⣿⣼⡟⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠻⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣀⣄⣠⡀⠀⠈⠱⣦⣐⠠⡀⢄⠠⣈⢂⣍⣶⣿⣿⠟⣿⣿⡿⠛⠿⠿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠉⠉⠀⣿⡿⠟⠋⢉⠈⠙⠛⢛⠳⠶⣽⣿⣟⣿⣞⣷⣻⣿⣿⡷⢿⣿⣂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠓⠫⠶⣤⣄⡘⢦⡩⠞⠤⡀⠸⣿⣯⣟⣿⣿⡇⠸⢧⠀⣉⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢃⠠⢀⠀⡀⠀⠀⠘⣷⣼⣯⣧⡴⣤⣥⢿⣏⡻⢭⢿⣷⣼⣾⡗⠋⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡉⢰⢂⠐⢠⣠⠀⠀⣿⣿⡟⣮⢳⣳⢎⡷⣜⡳⣏⡾⣜⣿⣿⣿⠀⠐⣆⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣽⣆⣨⣿⣷⣌⣴⣿⢷⣫⡽⢯⢿⣟⣾⣭⣷⣯⣷⢻⢿⣿⣿⣧⣿⣏⣴⣻⠏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⣠⣿⠿⣛⠛⢶⢻⡿⣾⣽⣿⣿⣿⣿⡾⢿⠻⠿⣷⣎⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣧⣿⣶⣳⣾⣽⣿⣿⣿⣿⣿⣼⣶⣽⣶⣧⣿⡟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀ ⠀⠀⠀
⠀⠀⠀⠀⠀