⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⣿⣿⠆⠀
⠀⣀⣀⣿⣇⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀
⠀⠛⢻⣿⠛⠛⢻⣿⠀⠀⠀⠀⠀⣶⡟⠉⠀⠀⠀⠀
⠀⠀⣼⡏⠀⠀⢸⣿⣤⣤⣤⣤⣤⣿⣧⣤⣤⣤⣤⠀
⠀⢠⣿⠁⠀⠀⣿⡏⠉⠉⠉⠉⠉⣿⡏⠉⠉⠉⠉⠀
⠀⠾⡿⢷⣦⣼⡿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣽⣿⣷⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀
⠀⠀⣠⣾⠟⠁⠈⠻⠃⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀
⠀⠹⠟⠁⠀⠀⠀⠀⠀⠀⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀
⠀⢀⣀⣀⣀⣀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀
⠀⢸⡟⠛⠛⣿⣤⣤⣿⣧⣤⣤⣤⣤⣼⣿⣤⣤⣤⠀
⠀⢸⡇⠀⠀⣿⠉⠉⣿⡏⠉⠀⣀⡀⠀⠀⠀⣤⠀⠀
⠀⢸⡇⠀⠀⣿⠀⠀⣿⡇⠀⠀⢹⣇⠀⠀⢸⣿⠀⠀
⠀⢸⡇⠀⠀⣿⣀⣠⣿⣿⠿⠃⢸⣿⠀⠀⢸⡟⠀⠀
⠀⢸⣧⣤⣤⣿⠛⠛⣿⡇⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀
⠀⢸⡏⠉⠉⠉⠀⠀⣿⡇⠀⠀⠀⣿⡇⢠⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣀⣀⣋⣁⣈⣋⣀⣀⠀
⠀⠀⠀⠀⠀⠀⠸⠿⠿⠃⠀⠛⠛⠛⠛⠛⠛⠛⠛⠀
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀
⠀⢀⣀⣀⣸⣿⣀⣀⣀⣀⣀⣀⣀⣸⣿⣀⣀⣀⠀⠀
⠀⠘⠛⠛⢻⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⠛⠛⠛⠀⠀
⠀⠀⠀⠀⢸⣿⣤⣤⣤⣤⣤⣤⣤⣼⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠉⠉⠉⢹⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀
⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀
⠀⠀⠀⣀⣤⣶⡿⠟⠀⠀⠀⠐⠻⢷⣦⣤⣀⠀⠀⠀
⠀⠺⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣤⣤⣤⣤⣤⣤⣤⣿⣧⣤⣤⣤⣤⣤⣤⣤⡄⠀
⠀⢸⣿⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣿⡇⠀
⠀⠶⠶⠶⣾⡷⠶⠶⠶⣿⡷⠶⠶⠶⢾⡿⠶⠶⠶⠀
⠀⠀⠀⠀⠿⠷⠶⠶⠶⠿⠷⠶⠶⠶⠾⠇⠀⠀⠀⠀
⠀⠀⠀⢰⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⡆⠀⠀⠀
⠀⠀⠀⢸⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡇⠀⠀⠀
⠀⠀⠀⢸⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⡇⠀⠀⠀
⠀⠀⠀⠈⣉⣩⣭⡯⠍⠉⠉⠩⢿⣭⣍⣉⡁⠀⠀⠀
⠀⠰⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀
⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⣿⡇⠀⠀⠀
⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀
⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀
⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀
⠀⠀⠀⢸⣿⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⣾⡿⠀⠀⠀
⠀⠀⠀⢸⣿⠀⠀⠀⠀⢻⣷⡄⠀⠀⢀⣿⡇⠀⠀⠀
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠛⠋⠀⠀⣸⡿⠀⠀⠀⠀
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀
⠀⠀⠀⢸⣿⠀⣀⣤⣶⡄⠀⠀⣠⣿⣯⡀⠀⠀⠀⠀
⠀⣀⣠⣼⣿⠿⠛⠋⠁⠀⣀⣼⡿⠛⠻⣿⣦⡀⠀⠀
⠀⠛⠛⠉⠀⠀⠀⣀⣤⣾⠿⠋⠀⠀⠀⠈⠻⣿⣄⠀
⠀⠀⠀⠀⠀⠀⠻⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡟⠛⠛⠛⢻⣿⠀⠀⣿⡟⠛⠛⠛⠛⣿⡇⠀
⠀⠀⣿⡷⠶⠶⠶⢾⣿⠀⠀⣿⡷⠶⠶⠶⠶⣿⡇⠀
⠀⠀⣿⣧⣤⣤⣤⣼⣿⠀⠀⣿⣧⣤⣤⣤⣤⣿⡇⠀
⠀⠀⣿⡇⠀⣀⣰⠟⢀⣀⣀⣴⠏⣀⠀⠀⠀⣿⡇⠀
⠀⠀⣿⡇⠀⠈⢳⣶⣋⠀⠙⢷⡶⢋⡀⠀⠀⣿⡇⠀
⠀⠀⣿⡇⠰⠶⠾⠷⠾⣷⠶⠿⠶⠶⢿⡄⠀⣿⡇⠀
⠀⠀⣿⡇⠀⢸⡇⠀⣿⡇⢸⡇⠀⢸⡇⠀⠀⣿⡇⠀
⠀⠀⣿⡇⠀⠘⠛⢛⣿⠁⢸⡟⠛⠛⠃⠀⠀⣿⡇⠀
⠀⠀⠿⠇⠀⠀⠺⠛⠁⠀⠸⠇⠀⠀⠈⠿⠿⠟⠁⠀