⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠒⠒⠶⣄⡤⠴⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠲⢶⣿⡀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠈⣟⣲⠶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⣙⣧⡤⠤⠶⠦⠒⠶⠤⣤⣀⣸⠞⠁⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⣻⡀⢀⡤⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀⠀⠀⣸⣇⡈⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⣨⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣸⠵⠛⠉⠛⢮⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⢳⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠞⠏⢹⡞⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠙⣦⠀⣠⣾⡀⠘⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⠀⠀⢠⡏⠀⢀⡖⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢿⡭⠈⠉⢳⣸⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠐⢲⡞⠀⠀⡼⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣄⠀⢀⠀⠀⢠⠈⢷⠀⠀⠀⡇⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⡷⢺⠃⠀⢠⡇⠀⠀⣸⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢤⠀⠘⡆⠘⡆⠀⠈⡆⠘⣇⠀⢠⠇⢸⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠟⠳⡿⠀⠀⢸⠀⠀⠀⣿⣧⠀⠀⠸⡄⠀⠀⠀⢰⠀⡇⣿⠈⣧⡀⠈⢧⠀⢳⠀⢧⠀⠀⢻⣠⠿⣶⢿⡖⢾⡇⠀⠀⠀⠀⠀ ⠀⠀⢀⡏⠀⠀⡇⠀⠀⣿⡆⠀⢸⣿⠹⡆⡆⠀⣇⠀⠀⠀⢸⢠⣇⡗⠋⣽⣻⣶⣄⢣⣸⡇⠈⠀⢠⠏⠀⢀⡿⡿⠓⠀⠹⣄⠀⠀⠀⠀ ⠀⠀⠀⢧⣀⣸⡇⠀⠀⣿⣷⠀⣿⣏⠓⢿⣷⡀⠸⡄⠀⠀⣾⣼⣿⢻⠍⣽⢀⣨⣿⣧⣻⣷⠀⠀⡿⠀⠀⠞⢸⢿⡀⠀⠀⠙⣆⠀⠀⠀ ⠀⠀⠀⢀⡽⢿⡇⠀⠀⣿⡇⣸⡏⠉⠉⣭⡹⣿⣆⣷⠀⢰⡿⢹⠃⣶⣿⣿⣿⣿⡏⠙⣿⣿⠀⠀⡇⠀⢀⣰⡟⠀⠱⣤⣀⡀⠹⣆⠀⠀ ⠀⠀⣰⠏⠀⣸⡇⠀⠀⢿⣿⣿⡿⣿⣿⣿⣷⣾⠯⠻⣧⣿⠁⠈⠘⠁⠸⣿⣿⣿⠃⣸⠇⣿⠀⢠⣇⣴⡋⢹⠁⢀⠀⠙⣌⢻⠳⣿⠀⠀ ⠀⢠⡏⠀⠼⢁⣇⠀⠀⣀⢻⣹⡀⢻⣿⣿⡇⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠉⠁⠐⠃⠀⣿⡆⠈⠁⣾⣷⢸⡄⠈⠳⢄⡈⠻⣧⡈⠀⠀ ⢀⣼⣀⡤⠴⣾⣿⠀⠀⢸⡘⣧⠙⠆⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⣰⠛⣿⡌⣿⣦⡀⣦⡉⠙⠺⣿⠶⣄ ⠋⠉⠀⠀⡴⣣⠻⣇⡀⠀⢧⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣼⠀⣰⠋⠀⣿⣧⢹⡏⠙⢻⡟⡷⢤⣈⡳⣄ ⠀⣀⣴⡾⢻⠏⠀⠹⣿⡄⠈⢿⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢠⣇⣼⡇⠀⠀⣿⠙⢿⣇⠀⠀⠳⢻⠀⠈⠉⠙ ⠛⠉⠁⣠⠏⠀⠀⠀⣹⣿⣦⡈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⠀⠀⣿⠀⠈⠻⣆⠀⠀⠘⡇⠀⠀⠀ ⠀⣠⠾⠁⢀⣠⣴⠾⣿⠉⠻⣿⡶⢿⣷⡄⠀⠀⠀⠀⠀⣴⣶⣦⣄⠀⠀⠀⠀⠀⠚⣵⣿⣿⣿⡇⠀⠀⣿⡇⠀⠀⠈⢦⠀⢀⢿⠀⠀⠀ ⠚⠓⠚⠋⠉⠀⠀⢠⣷⡇⢠⢸⡟⠀⢹⣿⣦⣄⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢀⣤⡾⢻⣿⣿⢻⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠘⡜⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⣻⠃⢸⢸⣇⠀⠈⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⣀⣴⣾⡿⠛⠀⣸⣿⢿⢸⠀⠀⠀⢸⣿⣇⡇⢀⠀⠀⠀⢻⢹⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⣿⣿⠀⠀⠳⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⡿⠻⣄⢰⠃⠹⣿⢸⠀⠀⠀⢸⣿⡼⣄⠸⡄⠀⠀⠈⣧⢳⡀ ⣀⣀⠀⠀⠀⠀⠀⢰⡇⠀⣸⣿⣿⠀⠀⠀⢸⣿⣿⣿⡻⣿⣿⠈⢿⣉⡞⠀⠀⢹⡏⠀⠀⣿⢸⠀⠀⠀⢸⣿⣷⣹⡄⢷⠀⠀⠀⢹⣮⠟ ⠀⠉⠉⠛⠒⠦⣤⣞⠀⢀⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⣧⡙⣿⠀⠈⢿⠃⠀⠀⠸⠇⠀⣰⣿⠈⠀⠀⠀⢸⣿⣿⣧⣷⣈⣷⣤⣠⡾⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠻⣾⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣏⢹⣜⢀⣀⣰⢷⣀⣀⣤⣖⣠⠟⡇⠀⠀⠀⠀⠸⡟⠛⡿⣿⣫⡄⣼⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡛⠿⡇⠀⠀⠀⣿⠁⠀⢸⡟⠛⠛⣻⡿⢿⣯⣉⠉⠉⠙⣧⡇⠀⠀⠀⠀⠀⣇⡼⡽⠧⣄⡴⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⢸⠀⠀⠸⣧⣴⣾⠏⠀⠀⢻⡝⠛⠳⠶⠟⡇⠀⠀⠀⠀⠀⣟⡹⠇⠀⣸⡇⠀⠀⠀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣿⣾⡇⠀⠀⠀⣸⠀⠀⠀⢀⣸⠇⠀⠀⠀⠈⣷⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻⡓⣆⣴⡿⠿⠛⠉⠉⠉⠀