⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣶⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⢰⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⡷⢠⣿⣿⡏
⠀⠀⠀⠀⠀⣀⣿⣤⣿⣿⣷⣶⣤⣤⡤⠀⠀⣠⣿⢋⡾⣳⡟⣿⣿⠀
⠀⠀⠀⠀⣀⣡⡼⠶⠛⢿⣿⣿⣧⠀⠀⣀⣴⢟⣵⣟⣿⣿⣮⣿⠋⠀
⠀⠀⠀⠙⣿⠟⠿⠖⠀⣴⣿⣿⠟⣠⡾⣿⡵⣻⡿⢋⣥⡿⣻⡇⠀⠀
⠀⠀⠀⠀⠉⠀⢀⣴⣿⣿⡿⣫⣾⢫⣞⣷⣞⣩⣶⢿⣯⡾⡋⠀⠀⠀
⠀⠀⠀⠀⢠⣾⣿⢿⣿⠟⢠⣿⢡⣾⣿⢿⣋⢸⣿⢟⣻⡾⠁⠀⠀⠀
⠀⠀⠀⣰⣿⣿⠏⣾⣿⠀⣼⢏⣿⣿⣿⣿⡥⣼⣾⣟⣯⠄⠀⠀⠀⠀
⠀⠀⢀⣿⣿⣿⠀⣿⣿⣿⣿⣾⣿⣿⣿⡿⣰⣿⠿⡋⠁⠀⠀⠀⠀⠀
⠀⠀⠸⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⢿⣶⣮⣵⣚⡛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⣿⣿⣿⣦⡻⣿⣿⣿⡹⣷⣿⢿⣍⣉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⣿⣿⣿ ⣷⣿⣿⣿⣮⡻⣷⡝⢿⣷⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢩⣿⣛⡿⠿⣿⣿⣿⠈⢻⡄⠻⣿⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⣆⠈⠇⠀⢻⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠙⠁⠋⢻⣿⠙⠃⠘⠇⢸⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠘⣿⡅⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠰⢺⡿⠿⠿⠿⠶⢶⠀⠀⢶⣿⠿⠿⠿⠷⠶⡦⠀