⠀⠀⠘⢦⡀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⢀⣀⣴⡒⠛⠭⣑⣒⠊⠷⢖⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣄⠀⠀⠀⠈⢦⡀⠀⢠⡶⢫⢋⢯⢿⠻⡉⠓⠲⣛⣲⡖⠮⣷⣝⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⡤⣺⡟⡵⢻⢸⢸⠀⢇⠹⡉⢑⡢⠸⣍⠒⠤⣙⣆⠳⣿⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⡄⣠⢋⣜⡟⡼⣱⢻⢸⢸⠀⠘⡄⡯⠗⠺⠥⡀⠙⡢⣄⡙⠦⡙⢟⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣹⢃⡾⡼⢰⢣⠇⡞⢸⠸⡄⠀⣇⠇⠐⠤⠤⣀⡀⠙⢮⡙⠷⣾⣎⠻⡒⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠃⡜⣧⠇⡏⡼⢠⠇⢸⢰⡇⢀⣿⣲⡼⢭⡉⠑⢯⡲⡄⠱⡀⠘⢮⠳⣾⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠻⢽⣲⢤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡞⡼⡟⣻⢸⠀⡇⡞⢀⡷⢳⣇⣸⣳⡒⠧⣄⡈⢢⡀⠙⢮⣆⠱⡀⠈⢧⠹⣧⠩⣛⠷⣤⡀⠀⠀⠀⠀⠀⣀⣤⠤⢤⣠⠋⠑⠦⠤⣅⡀⠀⠀⠉⠛⠿⣶⣤⣀ ⠀⠀⠀⠀⠀⠀⢰⢣⠃⡇⣿⡎⠀⣷⠃⢀⣤⠻⣟⠛⠁⠉⢢⣦⡙⢦⡙⡄⠀⢻⣆⢳⡀⡞⢀⢿⠀⠈⢻⣮⡻⡿⠶⣽⡟⠉⠁⣀⡀⠀⣸⠀⠀⠀⠀⠀⠙⠢⣤⣀⡀⠀⠀⠉⠛ ⠀⠀⠀⠀⠀⠀⢸⢼⠀⢹⣜⣧⡀⣾⠿⠃⢠⣤⣽⣆⠀⠀⠀⢱⣹⢄⠙⡼⣇⠀⣏⣆⠱⣝⢦⣀⠀⢰⡀⢳⣿⣼⠓⢦⣍⢆⠀⠸⡷⠀⡇⠀⠀⠀⠀⠀⠀⠈⠙⠒⠭⢝⡒⠒⠢ ⠀⠀⠀⠀⠀⠀⠸⣿⠠⡈⡎⣏⡏⠉⠻⢦⣻⣿⡯⣹⡶⢃⣴⣟⣧⢤⣷⡼⣿⣦⡘⣌⢦⡈⠓⢬⠏⠁⠑⢤⡹⣌⠀⢸⠈⢾⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠦⠀⢠⠟⣦⢷⠃⡘⢿⠀⠀⣰⠿⡟⣵⢙⣿⠟⢝⣵⣿⣿⢃⣽⣿⡳⡑⢬⡣⣝⡦⢌⣓⡦⠤⢄⣉⣛⡷⠺⡏⠈⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠱⠶⣷⠾⢻⢸⡇⡇⡎⢯⠛⣛⣿⣮⣹⡿⣻⣇⠈⢹⣿⢿⠊⡀⠹⡷⡝⢄⠈⠱⡝⢷⣄⢦⢄⣀⣤⠞⣀⠀⣷⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⢱⢳⢳⠘⢿⣛⣿⣿⡯⣷⠿⠿⣄⠟⠙⠛⢇⢧⡄⠹⣼⢾⣷⣤⣌⠈⢿⡈⠢⣄⣸⣤⡟⠀⠸⣦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀ ⠀⠀⠀⠀⠄⠀⠀⠀⢠⡇⠈⢿⡎⢇⢮⣷⡉⢋⠔⠿⠀⠀⠙⠳⠴⠀⣨⣾⣿⣆⠘⢆⠙⢦⡘⢗⠦⣌⡓⠦⣔⡿⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠉⠉⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡆⡿⡇⣇⠀⢹⡌⠱⡻⣿⣦⣀⠒⠒⢦⣀⣠⣴⠿⠛⠈⣻⠷⢵⣦⡽⠂⠱⡜⡆⣠⢟⠽⠋⣧⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣭⠭⠷⢾⡶⠶⠲⠶⢤⣀ ⠀⠀⠀⠀⠀⢀⡼⠋⠀⡇⢻⣦⠘⣿⣄⠑⣽⣻⣌⢙⡶⣦⣍⣉⡁⠀⢀⣤⣷⠀⠀⠀⠀⠀⠀⠹⡧⠟⠁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠰⡇⢳⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠒⠋⠀⣀⣀⠘⠮⠏⢧⠘⣮⡳⣈⣻⡈⠫⣧⡿⠿⡟⣽⣿⡅⢸⠈⠙⠒⠒⢤⡀⠀⢰⠂⢠⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡜⣧⠈⣷⠀⠀ ⠀⠀⠀⠀⢀⠔⠋⠁⠈⢣⠀⠀⠈⣿⠚⠻⢚⢧⢳⣀⢸⡇⠀⢿⡟⠻⡟⠺⢤⣀⡀⠀⣀⣀⣐⡣⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠀⢳⠹⣷⣻⣇⠀ ⠀⠀⠀⢰⠃⠀⠀⠀⠀⠚⢲⠀⢀⡇⠀⠀⢸⠈⠛⠛⡏⠃⠀⠉⠁⠀⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢰⣶⠉⠀⢀⡠⣦⣀⣤⣿⡋⢿⡄ ⠀⠀⠀⠈⡃⠀⠀⠀⠀⠀⣸⠀⢸⠃⠀⠀⠸⡄⠀⠀⠹⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣼⡿⠾⠻⣿⠉⠹⡇⠘⣷ ⠀⠀⠀⠀⢧⡀⠀⠀⠀⡠⠃⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠳⡀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⠒⠐⠐⠀⠀⠀⢸⡟⠿⠇⠀⠀⠀⢻⡆⠀⢳⡀⠹ ⠗⠀⠀⠀⠀⠈⠙⠒⠊⠁⠀⠀⢺⠀⠀⠀⠀⢹⠀⠀⠀⠀⡇⠀⠀⢳⡀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡇⠀⠀⢀⣠⣼⡷⠚⠻⠿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠘⡆⠀⠀⠀⡇⠀⠀⣼⠙⣦⣌⠲⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢧⠀⠸⢿⣧⡾⢣⣤⣀⣤⡾ ⣠⣴⢶⡄⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢳⠀⠀⠀⠁⠀⢰⠇⠀⠈⠙⢷⣌⠓⢤⣀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢸⠀⠀⢠⢀⣤⡾⠟⠉⠀⠀