⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠴⡆⠐⣶⠒⠐⢶⠆⢀⣤⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⡉⣿⠀⠀⣷⠴⡇⠀⣿⠀⠀⢸⢀⠸⣦⡚⠀⣿⠑⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠹⣦⣀⡽⠤⠴⠁⠙⠲⠶⠋⠸⢤⣸⢇⣰⠏⠻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠉⠉⠙⢿⡛⠓⠶⠶⠤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠉⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠴⠖⣻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⣀⣤⠶⠟⠛⠛⠋⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣴⢟⣩⢤⡄⢀⡴⢫⣿⡼⠗⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢿⢯⣶⡾⠧⣾⣿⡿⠧⢤⣤⣤⣀⣀⣀⠀⠀⢠⡾⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⠟⠀⠀⠘⠋⢠⡖⠚⠉⠀⠀⠀⠀⠀⣼⣿⣭⣭⣿⡋⣠⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⣭⡉⠉⠉⠉⠉⠉⠉⠀⠘⢧⡀⣠⣤⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣉⣡⣭⣽⡟⢙⣽⣄⣀⢻⡄⢀⣀⣀⣤⡤⠴⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡷⠀⠀⠀⠀⠀⠀⠀⠈⢿⡩⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠙⠛⠻⠳⣆⣹⡿⣟⠉⠉⠁⠀⠀⠀⠀⢹⡄⠀⠀⡶⠢⡴⠉⢦ ⠀⠀⠀⠀⡀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣦⣤⡀⠀⠀⣿⡟⢀⣿⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⣳⠶⠷⣖⢿ ⢷⠶⢶⠒⢳⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠻⣏⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣴⣷⣿⠃⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⡄⠀⠀⠈⡟ ⢩⠖⠋⠛⠋⡄⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⣿⡶⣽⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢱⣿⣷⢦⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢀⡯⠏⠛⣟⠇ ⠘⣦⠶⣖⠛⢇⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢀⡼⣇⠀⠙⢷⣤⡙⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⢾⣏⣫⣾⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣸⡀⠀⠀⢨⠃ ⠀⠱⠤⠋⣑⣹⡄⠀⠀⠈⢷⡀⠀⠀⠀⢀⡾⠷⠿⣦⡀⠀⠙⠷⣝⣦⡀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠈⠉⠙⠓⠾⢦⣤⣀⡀⠀⠀⢀⣼⠇⢀⠛⢝⠓⠚⠋⠀ ⠀⠀⢷⠛⠉⠀⣸⠀⠀⠀⠈⢳⡀⠀⢠⡞⠁⠀⠀⠈⠻⢶⣄⡀⠈⠉⠱⣦⡀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢛⡿⠟⠁⢀⣾⡛⠛⠛⢶⠁⠀ ⠀⠀⠈⠳⠴⠾⣫⡾⠄⠀⠀⠀⢻⣤⡟⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣤⣷⣽⣋⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⣎⠀⠀⠀⢳⠀⠀⠀ ⠀⠀⠀⠀⢠⡟⠉⠀⢀⣦⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⣠⠗⣝⢷⣤⠴⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠳⠤⢚⣽⠖⠓⢦⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⣷⠀⢀⡶⠤⣤⣀⣀⣀⣠⡴⠟⠁⠀⠀⠀⢀⡐⠻⢦⣋⠁⡷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⢼⣿⠦⡀⠀⠈⠉⠛⠛⠛⠓⠒⠒⠒⠒⠚⠃⠀⠀⠀⢸⣄⡾⠁⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⡴⣍⢹⣆⣀⣉⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢖⣣⠞⢳⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠏⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀