⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠤⢄⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠅⠀⠀⠀⠀⠀⠀⠀⠉⣷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣃⡂⠀⠀⣀⣄⣤⣄⡀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦⣾⣿⣿⡟⢿⣿⡓⣼⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣄⢻⣿⠸⣿⣼⣿⣧⢸⣿⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡷⡇⢀⠙⠿⡿⠿⠋⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣌⣡⣾⣇⣈⣙⣷⣶⣶⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣹⣿⣿⣛⣀⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣷⠟⢃⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣤⣶⣿⡿⣟⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⡛⣧⣛⣾⡏⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣴⣛⢶⣯⢿⣿⡀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⣿⢧⡿⣹⣞⣿⣿⠷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢯⣷⣛⡾⣽⣿⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣟⣾⣽⣻⣿⠇⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⣷⣾⡏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣹⣿⣿⣿⡿⠯⣿⣿⣿⡿⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣾⠃⢸⣿⣿⠀⠀⣿⢿⡿⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢫⣿⠃⠀⢸⠿⣿⠀⠀⢹⠞⣧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⢡⡿⠁⠀⠀⠸⣿⣿⡀⠀⢸⣾⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⠋⢸⡟⠁⠀⠀⠀⠀⣿⣿⡇⠀⠘⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⣰⠃⣲⡿⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⢿⣿⠄⠀⠀
⠀⠀⠀⢀⣴⢇⣾⡿⠁⠀⠀⠀⠀⠀⠀⠸⡿⣷⠀⠀⢸⣿⡇⠀⠀
⠀⠀⣠⣾⣻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡀⢀⣾⣿⣧⠀⠀
⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⣀⣤⠤⠆⢰⣿⣿⣿⣿⡟⠁⠹⣿⡄⠀
⠙⠿⢿⣿⡏⠀⠀⠀⢼⣻⣛⢉⣴⣶⠾⠟⠋⢹⣏⣤⣄⣄⣝⣧⠀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠐⠾⠿⢵⠧⠿⠿⠛⠀