⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠞⠛⠉⠉⠉⠉⠉⠉⠛⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠯⠴⠒⠚⠓⠲⢤⡀⣍⠒⠦⠤⣄⣀⣀⠤⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⠖⠲⣦⠀⠀⢀⡾⠃⠱⣾⢿⣳⣦⡕⠢⢽⣂⠉⠒⠒⠒⠀⢔⣒⠉⠑⠦⡀⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⢁⣴⣦⣘⢧⣀⡾⠁⠀⠀⠈⢯⢿⡿⣿⣇⠀⠈⠉⠉⠉⠉⢉⡩⠥⣒⠒⠲⣄⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠇⣼⡟⠋⢻⣧⡾⠁⢜⠤⠤⠤⢤⣤⣜⡉⣿⢷⠀⠀⠀⠀⠈⣡⡴⣿⣿⣻⣷⣶⢸⡇⣠⡤⠶⠶⣤⠀ ⠀⠀⠀⢀⡟⢰⣿⡀⢿⣇⡿⠁⢠⣶⢽⠞⢩⣽⣿⣿⣿⣆⠀⠀⠀⠀⠐⢋⣙⣙⣛⠛⠛⠋⠉⠈⡟⣁⣤⣤⣤⠈⡇ ⠀⠀⠀⠈⢷⣀⢻⣿⡶⠛⠀⠀⠉⢸⣼⠀⢻⣿⣿⣭⡇⣿⠀⠀⠀⣴⣾⣿⣾⣿⡟⠿⣦⣀⠀⠈⣿⢋⣁⡈⣿⠁⡇ ⠀⠀⠀⢀⣠⡿⠟⠁⠀⠀⠀⠀⠀⠘⢿⣦⣀⠉⢉⣉⣼⠫⠭⣉⢹⣿⠸⣿⣟⣿⡞⠀⢠⠀⠀⠀⠘⣿⣿⠃⣿⢆⡇ ⠀⠀⣰⠟⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⡽⠿⢿⡿⠛⠁⠀⠀⠀⠘⣿⡄⠈⠉⠁⠀⣰⡿⠀⠀⠀⠀⠈⢧⡜⢉⡾⠁ ⠀⣼⠏⠀⠀⣠⣤⣌⠧⣄⣀⣠⣤⣴⣇⢀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣶⣶⠿⠟⠁⠀⠀⠀⠀⠀⠀⠳⡍⠀⠀ ⢰⡏⠀⢀⣾⣿⣿⡟⠿⡿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀ ⣿⠀⠀⢸⣿⣿⣿⣧⠀⣸⠿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣥⢶⣲⣴⣾⣶⡄⠀⠀⢻⡀ ⣿⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠰⣿⣍⠿⣿⣿⣿⣧⡀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⣸⣿⣿⡟⠀⠀⢸⡇ ⣧⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦⣴⡟⠁⠑⢢⣍⡉⠁⠙⠛⠛⢿⣿⣿⣿⣿⠿⢛⣡⡾⠁⠈⠃⣠⣿⣿⣿⡇⠀⠀⢸⡇ ⣿⠀⠀⠀⠈⢿⣿⣿⢿⣿⣿⣿⣤⣀⢀⣾⠏⠉⠓⠦⣤⣤⡤⠬⠭⢥⣶⠚⠉⠙⣿⠀⢀⣿⣿⣿⣿⣿⠀⠀⠀⣾⠁ ⢹⡆⠀⠀⠀⠈⣿⣇⠎⢀⠞⠉⢹⣿⣿⣿⣦⣤⣀⣀⣿⡏⠀⠀⠀⠘⣧⣀⣠⣴⣿⣿⣿⣟⠛⣿⣿⠃⠀⠀⣸⡟⠀ ⠀⢻⡄⠀⠀⠀⠙⢿⡄⡞⠀⣰⣿⣿⣇⣀⣼⡿⠿⠿⠿⠿⣶⣶⠀⣸⣿⠛⠛⢻⣿⠉⢻⠉⢁⣿⠃⠀⠀⣰⡟⠀⠀ ⠀⠀⢿⡄⠀⠀⠀⠀⠙⠛⠒⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢄⣀⢸⣿⠀⠀⢀⡼⠃⠀⢀⣴⠏⠀⠀⠀ ⠀⠀⠀⠻⣆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠉⠀⢀⣴⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⠿⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⣭⡤⠤⠀⠀⢀⡀⠀⠀⣀⣀⣠⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠾⠟⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀