⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡾⢚⣋⣻⣿⣤⡖⠶⣮⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣵⣶⣾⣿⣿⠟⣿⣏⣠⣟⣿⣽⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣻⣿⣿⣿⣿⡟⠋⠁⠀⠘⠯⣿⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠋⢁⠀⡀⠀⠀⠀⠀⠈⠀⠹⣿⣿⣿⣿⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠀⠀⠀⢾⠂⠴⠃⠀⠀⠀⠀⠿⣿⣿⣿⣯⡆⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣺⣤⣤⣤⡀⠈⠀⠀⠬⣇⣂⡂⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⠗⠋⠀⠀⠈⠝⡻⠷⠂⢃⢸⡿⣿⡟⠻⠷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠠⣜⣼⣿⣶⣿⣿⣶⠀⠀⣿⣿⣿⣻⣦⣀⢸⢾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⠀⠀⠛⠿⢿⣿⠿⠛⠁⠀⠀⢻⣿⣿⣿⣿⣿⡟⡀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡟⠀⠀⠀⠀⠀⣠⢊⣀⢠⡀⠳⡼⣇⠙⠋⠉⠀⠀⢀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢿⣿⢀⡀⠀⠀⣀⡤⠚⢾⣿⣇⡴⠿⣿⣿⠂⠀⠀⢀⠀⠀⢸⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⣸⣿⡇⣵⡄⢈⡀⡤⢠⠤⠉⢹⣦⣜⣤⡀⠘⠆⠀⠀⠺⣦⣿⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠻⣷⣇⠈⠂⠈⣰⠿⠟⠛⢻⠂⠑⠺⢿⣯⡄⠈⠂⠀⠀⣼⣷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⢱⠋⣿⠀⠀⠀⠁⠀⠀⠀⡤⠛⠞⠀⠀⠀⠙⠆⠀⠀⣺⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣨⣿⢿⠇⢠⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⠙⢦⣦⡀⠆⠀⠀⠀⠀⠀⠀⠀⣠⢤⢡⡾⡿⠛⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣯⡑⠀⠙⠳⢤⣄⣀⣀⣀⡀⠀⠐⡹⣇⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠉⠑⠆⠀⠀⠀⠘⠀⢻⣿⣤⡀⡀⠀⠉⠹⠻⡿⠿⠛⠙⠙⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣷⣄⠀⠀⠀⠀⠃⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⠿⣦⣄⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣷⣄⠂⠐⠂⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣄⣸⡽⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⠆⠈⢭⡓⡶⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠃⠀⣿⡧⢀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⣿⣇⣆⣽⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣺⣿⡧⠀⠀⠀⠀⠀⠀⠠⣤⣼⣱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⡠⣀⣿⣭⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⡘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠹⣽⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣆⡹⡄⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⢐⢢⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠨⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣤⣴⡋⠏⠙⢛⠦⡀⠀⠀⠀⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠄⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⡿⠴⣧⢰⣀⠀⢄⠊⡆⠀⠀⠀⠈⣿⣆⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⢸ ⠀⠀⠀⣢⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⡟⠸⣸⣿⣿⣷⣿⡔⢱⠀⠀⠀⠀⢿⣿⣧⠀⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⢸ ⠀⠀⠘⠁⠀⣿⣷⢥⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡦⣻⣀⣿⣿⣿⣿⣿⣿⡞⠁⠁⠀⣠⢤⣿⣿⣶⣌⠀⠐⠀⢡⠀⠀⠀⠀⠀⠀⠀⠸⣷⣷⣾ ⠀⠀⢀⡒⢠⣿⣟⣆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢻⣿⣿⣿⣿⣿⣿⣿⡇⢀⢁⣼⣿⣀⣀⠈⠉⠙⣻⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⡀⢻⣿⣿ ⠀⠀⢀⡆⢸⣿⣿⣏⠁⢈⠀⠀⠀⠀⠀⠀⡀⠀⡿⡄⣽⠙⣿⣿⠿⠋⠀⣐⣠⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠲⢤⣀⣁⠜⠀⣿⣿⣿ ⠀⢠⠈⠀⣸⣿⣿⣿⣦⡈⣄⠀⣠⠀⠀⠀⢀⢸⠀⠏⢾⡇⢉⣾⣤⣰⣶⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣿⣿⣿⢿ ⠀⠊⢠⠅⠟⣿⣻⣿⣷⣙⣯⣿⡆⡂⢁⠐⢏⣠⣀⡀⣒⣿⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠉⠀⠀⢸ ⢀⠀⢣⢸⣷⣶⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣾⣿⣿⣿⣿⡿⠿⠏⠉⠁⠀⠀⠀⠀⢠⣀⣀⣀⣀⣀⣤⣀⣤⣤⣅⣈⣹⣅⣄⣄⣀⣀⣀⣀⣤⣼ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿