⢃⣀⣠⡬⠧⠤⣤⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠙⣆⡤⠖⠊⠉⠉⠉⠉⠉⠉⠑⠚⠧⣀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠤⠤⠴⠀⠀⠈⢛⢷⣤⢄⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⢤⣄⡀⠀⠀⠀⠀⠀⢹⣄⠙⢮⣇⡞⠁⠀⠀⠀⠀⠀⠀⠰⡿⠀⠀⢀⣤⡄⠀⣷⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠷⠀⣀⣠⣀⠀⠀⠀⠉⠈⢿⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠿⣿⡿⠿⠈⠳⣄⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠒⠒⠒⣖⡒⠛⠤⢤⣹⡀⠀⠀ ⣀⡠⢄⣀⡀⠀⠀⠀⠸⢿⣿⣿⣾⠉⠹⣶⠀⠘⡇⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢇⢠⠴⠶⢤⡤⢖⣉⠟⠀⠀⠀⠀⠀⠀⡩⠭⠤⣀⠈⠙⠢⣄ ⠁⠀⠘⢮⣙⣦⡀⠀⠀⠀⠀⠉⠉⠀⠀⣀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇⢀⡴⠋⠀⢀⠴⠒⠙⠲⡄⠀⠀⢼⢡⣤⠀⠈⢳⠀⠀⠈ ⠀⠀⠀⠀⠂⠻⠽⣦⡀⠀⠀⢀⣀⣀⡞⠁⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⣷⠏⠀⠀⢰⠃⠀⠀⣶⠀⡽⠀⣀⣼⣶⡿⠤⢄⡸⠀⠀⠀ ⠀⠀⠲⣄⠀⠀⠀⠉⠿⠉⠋⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠃⠀⢠⡀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⢠⠇⠀⠀⠀⠸⡄⠀⠀⢀⡴⠁⠸⠿⠿⠛⠁⠀⠀⠉⢢⡀⠀ ⡄⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠊⠀⠀⠀⠉⠉⠀⠀⠀⠴⠁⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀ ⠱⣄⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⣠⣷⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⢀⣠⠤⢀⣀⣀⣀⣀⣀⡠⠴⠶⣦⡀⠀⠇ ⠀⠈⢳⣄⡀⢸⠁⠀⠀⣀⣤⠞⠉⠈⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣖⣒⣲⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣾⣭⠷⠾⠷⣶⡛⠒⠚⠀⠀⠀⢨⠇⠀⠀ ⠤⠤⠤⠁⠈⠛⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠫⠤⣄⠀⠀⠀⠀⠀⠀⢸⠃⠀⠈⠋⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠈⠓⣤⠀⢀⣴⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠛⢻⡄⢀⡠⠖⢊⡽⠋⠙⣦⣴⠖⠚⢧⡒⠤⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⠄⣀⣀⣀⠬⠷⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⡷⠋⠀⠀⠈⠀⠀⡴⠋⡇⠳⡀⠀⠑⠀⠙⢦⡜⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⠀⠀⠀⠀⠀⢈⣧⣀⣸⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢀⡴⠚⠯⢤⠀⠀⠀⠈⠉⠉⠑⠒⠲⠤⠤⢄⣀⣀⡀⠀⠀⠀⠀⢀⣀⠠⠔⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣾⠥⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠒⠀⠀⠀⠀ ⠓⠶⢤⣤⣤⡤⠤⠤⠴⠖⠚⢹⠋⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠘⣄⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀