⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⣿⠁⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣰⡿⠁⠀⠀⣾⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀
⠀⢀⣼⣿⡇⠀⠀⣼⡟⠉⠉⠉⣿⡏⠉⠉⠉⣽⡏⠀
⢠⣿⠿⣿⡇⠀⠺⠟⠀⠀⠀⠀⣿⡇⠀⠀⡀⠿⠁⠀
⠀⠁⠀⣿⡇⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠹⣷⡀⠀⠀
⠀⠀⠀⣿⡇⠀⠀⢠⣿⠇⠀⠀⣿⡇⠀⠀⢻⣧⠀⠀
⠀⠀⠀⣿⡇⠀⢠⣾⠏⠀⠀⠀⣿⡇⠀⠀⠈⣿⡆⠀
⠀⠀⠀⣿⡇⠀⠈⠋⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠉⠀
⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⣿⣿⠆⠀
⠀⣀⣀⣿⣇⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀
⠀⠛⢻⣿⠛⠛⢻⣿⠀⠀⠀⠀⠀⣶⡟⠉⠀⠀⠀⠀
⠀⠀⣼⡏⠀⠀⢸⣿⣤⣤⣤⣤⣤⣿⣧⣤⣤⣤⣤⠀
⠀⢠⣿⠁⠀⠀⣿⡏⠉⠉⠉⠉⠉⣿⡏⠉⠉⠉⠉⠀
⠀⠾⡿⢷⣦⣼⡿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣽⣿⣷⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀
⠀⠀⣠⣾⠟⠁⠈⠻⠃⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀
⠀⠹⠟⠁⠀⠀⠀⠀⠀⠀⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣤⣤⣤⣤⣤⠀⣿⡿⠿⠿⢿⣿⠿⠿⠿⠿⠀⠀
⠀⢸⣿⠉⠉⢹⣿⠀⣿⣇⣀⣀⣸⣿⣀⣀⣀⡀⠀⠀
⠀⢸⣿⠀⠀⢸⣿⠀⣿⡏⠉⠉⢹⣿⠉⠉⠉⠁⠀⠀
⠀⢸⣿⠀⠀⢸⣿⠀⣿⡷⠶⠶⢾⣿⠶⠶⠶⠆⠀⠀
⠀⢸⣿⠀⠀⢸⣿⠀⣿⣇⣀⣀⣸⣿⣀⣀⣀⣀⡀⠀
⠀⢸⣿⣶⣶⣾⣿⠀⠛⠛⠛⠛⢛⠛⢛⡛⠛⢻⡇⠀
⠀⠸⠿⠀⠀⠀⠀⢰⡟⠀⢿⡄⠸⣧⠈⢿⣤⣿⡇⠀
⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⢸⡇⠀⠟⠀⠀⢀⣿⠇⠀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠻⠶⠾⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡄⠀⠀⠀⠀⠀⡀⠀⠀
⠀⠀⠀⠀⣰⡾⠿⢿⡏⠀⠘⣿⡄⠀⠙⢦⡀⢹⡄⠀
⠀⠀⣠⡶⠿⣧⠀⠀⢻⡄⠀⠸⣿⡀⠀⠀⡇⢰⠃⠀
⠀⣀⣿⡄⠀⠘⢷⡀⠀⠻⡄⠀⢹⣷⠀⠀⠃⣀⣀⣀
⢸⡟⠉⠙⢦⡀⠀⠻⣤⣤⡿⠒⠀⢻⣧⣤⣾⠛⠉⢻
⠘⢿⣄⠀⠈⠳⣤⡴⠟⠁⠀⠀⠀⠀⣻⡿⠁⠀⢠⣾
⠀⠀⠙⢷⣄⠀⠚⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⣰⡿⠁
⠈⢆⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀
⢦⣈⠛⠶⠤⠌⠻⣷⣄⡀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀