⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠘⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠘⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡇⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⠃⣼⠀⢻⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣷⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⢰⠋⡇⠈⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⡞⠀⢹⠀⢹⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⢹⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⡇⠀⢸⠀⢸⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡆⢸⠸⡄⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⢰⠁⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⡇⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⢸⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⢳⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢸⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢸⡀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⡀⣇⠀⠀⠀⠀⠀⢻⠏⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⢿⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⣇⢸⡀⠀⠀⠀⠀⢸⢀⡤⠞⢱⠀⠈⠉⠒⠦⣄⠀⣾⠀⠀⠀⢹⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⡆⡇⠀⠀⠀⢀⡼⠋⠀⠀⠸⠀⠀⠀⠀⠀⠈⠻⣿⠀⠀⠀⢸⡄⠀⠀⠀⠈⣽⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠈⣧⡇⠀⠀⢀⡏⠀⠀⢀⠴⣒⣉⣙⠲⣄⠀⠀⠀⢸⠀⠀⠀⠀⣷⡆⠀⠀⢰⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢸⡇⠀⠀⢸⠀⢀⡴⡩⠚⢁⣀⡈⠙⠦⣑⢦⠀⠸⡄⠀⠀⠀⢹⡇⠀⢀⣿⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⡏⠀⡠⠋⢠⣾⢋⣠⠾⠋⠀⠛⢷⣄⡈⢳⣳⡀⠳⡀⠀⠀⢰⡅⢀⣾⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣠⠛⠋⠀⠀⣿⡵⠋⢁⣠⠤⠤⣄⣀⠉⠛⢶⡿⠇⠀⠈⠲⢄⡼⢀⣘⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⡷⠃⠀⠀⣀⣠⡾⢀⡴⠋⣠⠀⠀⠀⠉⠓⢦⡀⠱⣄⢰⣄⠀⠀⠀⠀⠙⢇⣀⠀⢀⣀⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠙⠁⢀⣤⣶⣿⣿⢋⡴⢋⡴⢺⠧⡀⠀⠀⣹⠀⢰⠉⢦⣈⠻⣿⣿⣶⣶⣄⡀⠀⠙⠳⠿⠿⣿⡟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣤⣶⣿⣿⣿⠻⣡⢏⠴⠋⠀⣿⠀⠈⠲⣄⣿⠀⢸⣾⢸⠈⠳⣌⠻⣟⣩⣽⣿⣦⣄⡀⠀⣠⣿⡿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣿⣿⣿⠿⢋⡼⢁⣾⠴⢲⣾⢹⢀⠃⠀⢀⣿⡐⢻⣿⢻⡗⢲⠌⠳⣄⠙⠿⣿⣿⣿⣿⣿⠿⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠶⠞⣛⠯⢀⡴⡟⢻⣹⡏⡜⣼⡏⢸⣸⡆⠀⡟⡏⡇⢸⢿⣿⢧⢸⡀⠀⣈⡷⣄⠀⠉⠉⠉⢉⣷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣴⣭⣥⣶⣿⡇⣿⢸⣿⣷⣷⣿⣇⠀⣿⢷⡀⣧⡇⠸⣿⣽⣿⣼⣶⢷⣼⣼⡇⢸⣿⣷⣶⣷⣿⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣿⣿⣿⣿⣿⣏⡇⣿⣾⡟⣿⣿⣿⣿⠀⠘⠈⠻⠟⠁⠀⠹⣯⣿⣿⣿⢨⡏⡟⡴⢸⣿⣿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡁⠿⠿⠿⠟⠋⠀⠀⠰⠄⠀⠀⠀⠀⠉⠙⠉⡷⠛⠲⣷⣷⢾⠻⠿⢿⣿⠿⠛⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⣿⣿⣏⣿⢧⡠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣾⢉⠉⢻⡗⠂⠠⡽⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣽⢻⠁⢸⠀⢹⢶⡤⣄⣀⠐⠲⢶⣛⣓⣲⠖⠂⣀⣠⣤⠖⠉⢸⢸⠀⢸⣿⡄⠀⠘⢾⣦⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⡼⠁⢸⠀⠘⡆⢸⠀⢙⡷⢮⣉⣹⠓⠒⠒⠚⣏⣩⡷⠛⠹⡄⠀⢸⢸⠀⢸⡟⣿⣄⠀⠀⠈⠳⣄⠀