⠀⠀⠀⠀⠀⠀⣀⣄⠶⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⢀⡠⣴⣾⢿⣷⣺⣾⣫⣽⣓⣒⠫⢽⡲⢤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⢀⣴⣶⣫⣾⣿⣿⣟⣿⣿⡿⠰⣶⣭⣽⣿⣦⢿⣟⣻⠒⠒⠉⣁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⡉⠛⠉⠘⠛⠻⢿⣟⢻⠟⠯⠤⠤⣤⡼⣏⠈⠛⠷⡞⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⣬⠙⣉⣽⡿⢿⠁⢸⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠊⠉⠀⠀⢢⠀⢺⡄⠀⠀⡌⠓⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠈⠀⠀⠇⢀⡴⠁⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢻⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡟⣽⠁⢠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣸⡏⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠏⠀⡿⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣰⠀⠀⠘⡇⡾⣷⢈⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⣫⢄⣠⠀⣧⢀⠀⠀⣸⡆⠀⢰⣀⠀⠀⡸⠀⠀⠀⣿⠂⠀⢰⢳⢳⢹⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠘⠓⢲⡟⡼⠀⣠⠃⠱⡀⠘⢇⠀⠀⡇⠀⠀⣰⣹⢀⣰⣿⣧⠃⡾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⠘⠼⠛⡆⣴⢶⣶⣾⠧⣠⠃⣀⠔⢛⢿⡽⠉⢸⢣⣾⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⢧⡄⢀⠿⣌⠊⠊⠙⠀⠚⠋⠁⠀⠀⠉⠀⢠⠟⡌⠈⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⢯⠏⠀⡞⢀⠞⢦⣀⠀⠀⠀⣀⡠⠄⠀⣀⠴⡁⠀⢱⠀⢿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡜⡱⠃⠀⡜⡰⠁⡰⢁⠄⠐⡶⢆⢢⢀⡖⣾⡏⠀⠈⢣⡈⡇⠈⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣞⡞⠀⢠⠎⠰⠁⢰⠁⠈⠳⢴⡇⠈⢻⣹⠋⢸⣷⠐⠀⠀⢣⠸⡄⠘⣿⡀⠀⠀⠀⠀ ⠀⠀⣰⣿⠏⠀⣠⠃⢠⠃⠀⡜⠀⠀⠀⠹⠁⠀⢸⠸⡀⠈⣯⡃⠀⠀⠘⡆⠱⡀⠸⣵⡀⠀⠀⠀ ⠀⣰⡿⡏⠀⡰⠁⢀⠏⠀⢀⠇⠀⠀⠀⢠⣄⣀⣸⠀⣇⣀⣼⠁⠀⠀⠀⢡⠀⢳⠀⠹⣷⠀⠀⠀ ⢰⡟⠙⠀⡼⠁⡜⣼⠀⠀⡜⠀⠀⠀⠀⢨⣉⢹⠛⠛⢛⢉⣩⡆⠀⠀⠀⠈⡆⠀⢇⠀⢿⣇⠀⠀ ⣿⠁⡇⢠⠃⠀⢠⢿⣇⢰⠁⠀⠀⠀⠀⣿⣿⣿⣷⣶⣿⣿⣿⡏⠀⠀⠀⠀⢱⠀⢸⡀⢸⢸⡀⠀ ⡏⡄⣃⠐⠀⠀⢸⡘⣎⡇⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢇⠀⡇⡞⠈⡇⠀ ⡇⠁⣯⠆⡀⠀⢸⠛⢻⡄⠀⠠⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⡼⢀⡷⠇⠐⡇⠛ ⠹⡀⡇⡄⣷⣄⢿⣶⣿⣧⣀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣸⣸⠀⠀⠀⢰⠁⠀ ⠀⠙⢶⡀⡗⠈⠾⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠀⢀⡴⠻⠄⠀ ⠀⠀⠀⠘⢿⠀⠀⠀⠀⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠧⣿⣿⣿⣿⠇⡙⡠⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣍⡝⠀⠁⠀⢩⡿⠈⠉⢻⠀⠀⠀⠷⢣⡝⠃⠀⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⡜⠀⠀⠀⠘⡆⠄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢰⠁⠀⠀⠀⠦⡇⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠘⠀⠀⠀⠀⠀⠃⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣀⣀⢀⡆⠀⠀⠀⠀⠀⣦⣀⢀⣴⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⣿⣟⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠻⢟⡿⠿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀