⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣬⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠊⣰⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⢳⠈⢺⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡃⡁⡇⠀⠈⠛⢤⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⢀⠔⠋⠀⠀⢸⢼⡄⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⣀⡏⡇⠀⠀⠉⠢⠈⣖⣉⡉⠉⣹⢧⣀⣀⠤⠬⠭⢹⣋⠀⠀⠀⠀⡜⠈⠹⣄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠻⡁⠀⢧⠀⠀⢀⡤⠚⠉⠀⠀⠀⠘⡾⣷⡀⠀⠀⠀⠀⠈⢍⡒⢤⣰⠃⠀⠀⣼⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⢶⡃⠀⠈⣦⠞⠁⠀⢠⣮⣤⣴⣾⣿⣷⠹⣿⣿⣷⣿⣿⣶⣦⣷⣄⣈⡳⣄⠀⡬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣟⢀⡜⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣽⣧⠹⣿⣿⣿⣯⣵⣾⣿⣶⣲⠃⠈⢳⣳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠃⢸⠏⠀⠀⠀⢀⣿⣿⣿⠿⡿⢿⠿⠟⠛⢧⠙⢟⠉⠙⠛⠛⢻⠛⠻⡄⠀⢄⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡏⢀⠏⠀⠀⠀⠀⡜⠁⠀⠀⢠⡇⡜⠀⠀⠀⠀⠳⡌⢻⡀⠀⠀⠈⡆⠀⢸⡀⠈⠆⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠻⠀⡼⠀⠀⠀⠀⢰⠃⠀⠀⢠⠇⡇⣷⠀⣧⠀⠦⠀⢸⢦⡹⣄⠀⠀⢧⠀⠀⡇⠠⠘⡄⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢼⡇⢀⠇⠀⠀⠀⠀⢸⠀⠀⣾⣸⠀⡇⡿⡀⣿⡆⠀⠀⢸⡀⣷⢮⣦⡀⢸⡆⠀⢸⠀⠀⢱⡀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠀⢸⠀⠀⠀⠀⠀⠸⡆⢰⢹⡇⠀⢸⡇⢧⣷⣽⡄⠀⢸⣧⣻⣎⣿⡿⣾⣿⠀⢸⠀⠀⠀⢃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡍⠀⡇⢀⠀⠀⠀⠀⠀⣷⢼⠬⣧⣀⣈⣷⠘⢧⣹⢿⣄⠈⣏⢻⣞⣿⣷⣼⠿⡷⣦⣀⠀⠀⠘⠌⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⡆⠀⣇⠀⠀⠀⠀⡿⣼⠀⠀⠀⠀⠙⣍⠉⠃⠀⠉⠓⠾⣉⣙⣈⣈⠃⠀⣷⠃⠉⠓⡦⣄⡀⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⡇⠀⠘⣆⠀⠀⠀⣇⠙⠟⠛⣻⣿⡏⠉⠀⠀⠀⠀⠀⠈⠉⢛⣿⣟⡟⠋⢸⠆⠀⣠⠇⠀⠈⡏⠙⠒⠲⠦⠤⠄⠀⠀ ⠀⠀⠀⡇⠀⡷⡀⠀⠘⣆⠀⠀⢹⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⢸⠀⣠⠋⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⣧⠱⡄⠀⠈⢧⡀⠘⣇⠀⣴⡶⡢⠾⠂⠀⠀⠀⠀⠀⠀⠀⠺⠊⢴⡷⢴⣏⡴⠃⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢧⠀⢸⡀⠙⢄⠀⠀⠙⢦⣘⣆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⢾⡟⠀⠀⠀⡴⠃⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡀⠀⢳⡀⠈⠣⡀⠀⠈⢻⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⢠⠞⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⢃⠀⠀⠳⣄⠀⠈⢦⡀⠀⢧⣀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢀⡴⣾⠁⢀⡔⠁⢀⢾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⢸⡆⠀⠀⠈⡷⣦⡀⠙⢄⠘⣿⡝⠲⣤⣀⡀⠀⠀⠀⢀⣠⡴⠚⠁⣷⠇⡰⠋⣀⡴⠋⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡼⣡⢣⢷⠀⠀⢰⠀⡇⠈⠳⣄⠃⢹⣷⡿⠷⣄⣉⡉⠒⣊⡩⠿⣿⠀⠀⡟⣰⠕⣫⣾⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⡵⠁⡜⠘⠀⣀⡦⠴⠥⢤⠤⢾⠳⣜⡏⡷⣤⠶⠤⣍⣷⣣⡤⠴⢻⢳⣶⣧⢣⠾⠖⠛⠒⠤⣼⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡾⠋⢀⡜⠀⢠⠏⠁⠀⠀⠀⠈⣦⠎⠀⠘⢿⡇⢸⠀⢐⣺⣧⣿⣋⣀⣼⣀⣿⢰⢳⠀⠰⡄⠀⠀⠀⠙⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠎⠀⢠⠇⠀⠀⡄⠀⢀⠔⠃⠀⠀⢠⠟⡇⠈⡏⢡⣾⡿⠿⣿⡍⢹⡏⢹⡇⠈⠣⡀⡇⠀⠀⠀⠀⠘⡄⠉⠒⠒⠒⠢⣤⡶⠞ ⠞⠁⠀⠀⡸⠀⠀⠀⢸⣶⠋⢦⣀⣀⣴⡟⠀⢧⠀⡼⠼⣇⠀⠀⢀⠗⠛⣿⠘⣦⣀⠀⠈⢳⣄⠀⠀⠀⠀⢻⢿⣉⠉⠉⠉⠁⠀⠀