⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⠀⡄⠀⠀⣠⠀⡄⡤⢀⢤⠤⢠⠀⠀⠀⠀⡀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠀⠀⠀ ⣿⣿⣿⣀⣀⣀⣀⣀⡀⡀⡀⡀⡀⠀⠀⠀⠀⣇⣜⢻⠀⠀⠀⡇⣸⣀⣀⣁⠟⣿⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣻⢯⠈⠀⣀⣿⠀⠀⠀ ⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⡜⠻⠀⠀⡇⢸⠀⠁⡿⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⢧⠈⠀⣿⠀⠀⠀ ⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⡜⠸⠀⡇⢸⠁⡿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣹⢻⠀⣿⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣟⠘⡄⢁⡿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡏⠸⣿⠀⠀⠀ ⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⠘⡟⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⢿⣿⠀⠀⠀ ⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢿⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⠿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀ ⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀ ⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀ ⣾⣄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀ ⢿⠀⡆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⠀⠀⠀ ⣿⠀⠀⣷⠙⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢰⣿⠀⠀⠀ ⣿⠒⠐⡄⣿⠳⠈⢄⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣠⠄⣿⠀⠀⠀ ⣿⠀⠀⠀⡀⢾⣝⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⢀⠀⠀⣿⠀⠀⠀ ⣿⠀⠀⠀⠃⢸⡄⣷⣿⢮⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡶⢸⠀⠀⠀⠀⣿⠀⠀⠀ ⣿⠦⠶⠶⡦⢲⠓⡛⢿⣜⠦⡙⢤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⠉⠀⠀⠀⠀⠀⠀⠁⠋⠚⡴⣠⢤⠤⢣⠛⠛⠛⠛⣿⠀⠀⠀ ⣿⠀⠀⠀⠀⠏⣿⣾⣠⣄⢷⠈⠄⠢⠀⡀⣀⣤⠯⠿⠿⠾⠶⠷⣶⣶⣶⣴⣥⢮⠿⠶⣤⣠⣇⢸⠀⠀⠀⠀⠀⡇⢸⠋⠃⡿⣿⠀⠀⠀ ⣿⠀⠀⠀⠇⣿⣰⠀⠀⠀⠀⣄⢦⠙⠈⠀⠁⡞⣠⠀⣄⣿⠙⣼⣆⠙⠀⣦⠘⢠⣄⠹⠀⠀⡇⢸⠀⠀⠀⠀⠀⡇⢸⡿⣿⣿⣿⠀⠀⠀ ⣿⠛⠛⠛⣿⣹⠀⠀⠀⠀⠀⠀⠀⠀⣄⢦⡿⠙⠉⠋⡖⣳⣦⡽⠀⣄⠹⠀⣮⠘⠁⣆⢹⠀⡦⢻⠛⠛⠛⠛⠛⡿⣶⣶⣤⣶⣿⠀⠀⠀ ⣿⣿⡀⣿⢿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⠀⠀⠀⡀⢹⣆⠸⠀⣾⠀⠀⣆⡘⢻⣴⠀⠀⣿⢸⠀⠀⠇⡧⣿⠀⠀⠀⠀⣿⠀⠀⠀ ⣿⣂⠻⣄⢷⣛⣝⠾⠘⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⡄⠘⣧⠈⢁⢸⠀⠀⢸⡏⠀⠀⠀⣷⢸⠀⠀⡿⡿⣿⠀⠀⠀⠀⣿⠀⠀⠀ ⣿⣷⠒⠒⡶⢻⡁⣿⠿⠓⠉⠀⠀⠀⠀⠁⠉⣇⠈⠀⠀⠀⠀⢀⠀⢸⡀⢸⠃⠜⢯⣻⠛⠛⠛⡾⢶⠶⣶⣶⣶⣷⠙⠉⠉⠉⣿⠀⠀⠀ ⣿⠀⠀⠀⠀⣧⠀⡀⣄⢦⠳⣛⣉⢍⠤⠀⡀⣁⢻⠈⠀⠀⠀⠁⠟⢡⡞⢀⠋⡵⣠⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⠀⠀⠀ ⣿⠀⠀⠀⠀⡇⢸⠘⠀⠀⡇⢸⠀⣀⣤⠥⠯⡿⣼⣥⡌⠲⠀⣀⠃⣹⠞⣴⢀⡇⢸⠀⠀⠀⡟⢸⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⠀⠀⠀ ⣿⠉⠉⠉⠉⣿⢾⠒⠒⠒⡖⢻⠉⠁⡞⣾⢠⢀⠛⠴⢤⠲⠙⠈⣷⣿⠙⠉⠋⡞⢶⠶⠶⠶⡶⢿⠛⠙⠉⠉⠉⡏⣿⣿⣿⣿⣿⠀⠀⠀ ⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⡁⢋⡿⢹⢩⠈⠀⡀⢤⠦⠓⡍⢻⠀⣄⡳⣮⠹⠸⠀⠀⠀⠀⠀⡏⣿⣿⣿⣾⣷⣿⠀⠀⠁⠁⣿⠀⠀⠀ ⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣾⢿⠀⠀⠀⠀⡀⣠⠀⠀⡀⢨⣇⢿⠖⠻⠁⠞⣤⣁⣌⣦⣿⢻⠀⣿⠘⠀⡇⠇⣿⠀⠀⠀ ⣿⣿⣿⣿⣿⢸⠀⠀⠀⠁⠉⣿⣿⢀⣿⣿⢿⣰⠁⡟⣿⢾⠻⠙⠈⠀⠀⢡⠀⣿⠀⣇⣿⢀⡿⣿⣿⠘⣇⣿⠘⡇⢶⠷⠘⣇⣿⠀⠀⠀ ⣿⣀⣀⣀⣀⣿⣿⣿⣿⣿⣦⢹⣇⠳⡈⣀⢀⠀⡇⣿⣿⢻⡟⣿⠿⠛⠈⡿⡏⣼⠁⡈⣦⢻⡈⣭⣬⠉⡿⢉⠛⠛⠿⡿⣿⣿⣿⠀⠀⠀ ⣿⠀⠀⠀⠁⣿⣿⣿⣿⣿⠹⣆⡻⢻⣌⢤⠀⠙⠈⣄⣶⣶⣶⣠⣷⣾⡿⢯⣽⠋⡿⣿⠿⡿⣿⣿⣿⣥⣿⣵⣛⡛⣷⣿⣿⣿⣿⠀⠀⠀ ⣿⠀⠀⠃⡾⣷⣿⣿⣿⣿⣿⢿⡙⣄⣷⠻⠈⡀⣤⠷⠾⠒⠀⠁⠋⣿⣾⣠⢁⡟⣿⣿⣿⣿⣶⣿⣿⣽⣄⢿⡄⢹⠀⣷⣿⣿⣿⠀⠀⠀ ⣿⠿⠿⣿⠀⡇⣾⣿⣠⣀⣀⣄⣤⣼⡤⣧⣾⠧⠿⢶⠶⠶⠴⣤⣿⣿⣿⣿⣿⢉⠉⠉⠋⣿⠈⡆⣾⣶⠀⡇⣿⣿⠘⡄⣿⣷⣿⠀⠀⠀ ⣿⣿⣿⣸⠀⡟⣭⣿⠉⣄⣤⣤⣷⣿⣤⣽⠄⡙⢳⠈⡦⣷⣿⠀⣷⣿⣿⣿⣿⣹⣁⣉⣉⡏⢸⠀⢿⠿⠸⠀⣿⣠⢉⠉⢻⠟⣿⠀⠀⠀ ⣿⢻⠛⠙⠉⣉⣏⣾⣤⣤⣦⢱⠃⣾⣶⣷⠉⣇⣿⣶⠿⡿⣿⠈⡇⣿⣿⣿⣿⣼⣀⣁⣉⣉⢿⠛⣟⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⣿⠟⣿⢿⡿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀