⠀⡀⠂⠂⠀⠀⠀⠀⠀⠄⢀⡤⠠⠤⠤⠤⢤⡤⢤⡤⠤⠤⡤⠤⢤⣤⡤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢄⠀ ⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠒⡂⢠⠒⠉⠁⠀⠀⠉⡹⢝⠫⡉⡝⢹⢹⠉⠉⠀⠀⠀⠀⠀⣀⡠⠳⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡇ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠘⠓⠘⠃⠛⣒⠊⠛⠘⠒⠂⠀⠀⠀⠀⠀⢹⠎⠀⠀⠀⠀⠀⠀⠠⠤⢃⣀⠀⠀⡇ ⠀⡇⠀⠀⠀⠀⠀⡔⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢲⠊⠀⠙⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡇ ⠀⡇⠀⠀⢤⣒⠊⢀⠷⠦⠀⠀⠀⢀⣴⣀⠀⣀⠔⠉⠀⠀⠸⠄⠀⠘⠀⠀⠀⠈⠑⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇ ⠀⡇⠀⠀⠀⠈⠱⡞⠀⠀⠀⠀⠀⠙⠲⠉⡔⠁⠀⠀⠀⠀⠀⡀⡄⢀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⢠⡶⣄⡠⣤⠀⠀⠀⠀⠰⡃ ⠀⡏⠙⢆⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⡡⠟⠣⠄⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⢀⡧⠈⠀⣓⡆⠀⠀⠀⠀⠇ ⠀⡇⠀⠈⠀⠉⠉⠒⠒⠰⠤⢤⠀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠛⠲⣆⡟⠁⠀⠀⠀⠀⠀⡃ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠛⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⢀⡾⠶⠀⠀⠀⠉⠀⠀⠀⠀⠀⠰⣼⠄ ⠀⡏⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠘⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀⣤⡇⢸⠂ ⠀⡇⠀⠀⠀⠀⠀⠀⠖⠢⠤⣆⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡆⣸⡀ ⠀⡇⠀⠀⠀⠀⠠⡮⡅⠠⢀⠕⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠟⢹⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠧⠁⠀⠀⠀⠀⠰⠀⡀⠀⠀⠙⠒⠦⢤⣠⣀⣀⡤⠤⠒⠋⠀⠀⠀⠀⠀⠀⠀⣈⠓⠋⡏⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠒⡚⠀⠀⠀⠴⢻⢠⠎⠛⠀⠀⠀⣀⣀⡔⠒⢺⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢄⡀⠀⣀⡀⣠⡀⠀⠀⠀⠓⠑⠒⠀⠀⠀⠀⠈⠁⠀⠠⣒⡉⠉⠁⠀⠀⠀⢸⠀ ⠀⡆⠀⠀⢗⢲⠂⠀⠀⠀⠀⡔⠉⠉⢦⠀⠀⡜⠀⠀⠀⠹⠀⠽⣝⣳⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠲⠴⠦⢼⠀ ⠀⡄⠀⢠⠖⠉⠃⠀⠀⠀⢸⠂⠀⠀⠀⣇⠀⡇⠀⠀⢠⣾⡁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠆⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠨⡆⠀⠀⠀⢸⢠⠁⠀⠀⠀⢩⣿⡿⣟⣷⣶⣦⠀⠀⠀⠀⠀⢀⣶⣶⣾⣿⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠿⠀⠀⠀⠀⢰⢹⣿⡽⣞⣷⣿⢶⡾⣟⣿⣻⢾⡿⣷⣻⢾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣷⣿⣿⣟⡾⣯⢿⡽⣾⡽⣯⢿⡽⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣳⢯⡿⣽⢯⣟⣷⣻⣽⣞⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⠁⠀⡀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠸⣿⣯⡿⣝⣿⣽⢾⣽⢯⣿⣿⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⢱⡙⠉⢛⡆⠀⠀⠀⠀⠀⠈⠲⣤⢀⣀⡀⣀⣀⣀⣄⠴⠃⠀⠀⠈⢻⣿⣿⣯⣟⣿⣯⣿⣾⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣶⣄⣸⠀ ⢸⠀⢙⠎⡏⠀⠀⠀⣀⠀⠀⠀⢀⠯⡤⠤⠞⠣⠤⠤⠼⣀⠀⠀⠐⢾⡿⠿⢻⣿⠿⠿⣿⡟⣛⣷⡀⠀⢀⣠⠔⠲⢄⡾⢶⡛⠭⢯⣹⠀ ⢸⠓⠚⠒⠓⠒⠒⠊⠁⠉⠉⠋⠋⠈⠁⠀⡖⢒⠄⠀⠉⠁⠩⠉⠉⡏⠈⠀⠉⢡⡒⡢⠓⠃⠀⠀⡏⠉⣉⠔⠢⠤⡀⠉⠉⠉⠉⠛⢺⠀ ⢸⠀⠀⠀⣠⠤⠄⢲⡄⠀⠀⠀⠃⠄⠤⠈⠚⠂⠁⠤⠒⠀⠁⠀⠀⠑⠤⠚⠒⠒⠒⠒⠒⠒⠤⠞⠀⢘⠄⠯⠘⡌⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⡀⠀⢸⠂⡎⠑⢁⠬⠃⠀⠀⠀⢀⡠⠄⡀⠀⠀⠀⠀⠀⡖⣲⡑⢄⠀⠀⠀⠀⢀⠴⡒⠖⢢⠀⠀⠈⠊⠉⠂⠁⠀⠀⠀⠀⣠⠤⢼⠀ ⢸⡶⠲⡀⠀⠘⠒⠊⠀⠀⠀⠀⢘⠇⠴⠲⡈⠇⠀⠀⠀⡀⢙⣤⣊⣡⢀⡀⠀⠀⠈⠲⡈⢚⠀⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠰⠂⢾⠀ ⢸⡍⠃⣁⣀⣀⣀⣀⠀⠀⠀⠀⠉⠊⠢⠔⠁⠀⢀⢔⠽⠊⠁⠀⠀⠀⡉⠒⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠂⢺⠀ ⢸⠻⠛⠀⠀⠀⠀⠘⠛⠻⣄⡀⠀⣀⣀⣀⡤⠼⠟⡇⢀⣠⠀⢀⣠⣼⣛⣻⡼⡤⠤⠿⠛⠛⠛⠻⠧⠤⡤⢤⡤⠤⠤⠤⠤⠤⠤⠛⢻⠀ ⢸⣀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢀⣀⡉⣛⣩⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀ ⢸⠀⠀⠀⠀⠀⠈⠢⢀⡀⣀⠠⠤⠒⠒⠉⠉⠀⠀⠀⠀⠈⠳⠄⣀⣀⣀⠠⠤⠴⠒⠊⠉⠉⠉⠙⠒⠢⠤⠤⣀⣀⡀⠤⠄⠤⠒⠉⢸⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⡀⠀⠤⠤⠄⢀⣀⣀⣀⣀⠠⠀⠤⠔⠒⠊⠈⠉⠑⠒⠤⢀⣀⠀⠀⠀⠀⠀⡀⣀⠤⠄⠤⠤⠤⠠⢀⣀⣀⠀⠀⠀⠀⠀⣀⠠⠔⢺⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⢸⠀ ⢸⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⢻⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡏⢩⡡⣆⡶⠂⠀⠀⡖⠒⠋⡆⡄⠒⡲⣄⣒⡆⡖⠢⢄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠒⠂⠀⠀⠁⠀⠀⠋⠈⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠈⠙⠋⠛⠉⠓⠙⠋⠛⠙⠚⠓⠒⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠃⠀