⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢿⡹⣖⣻⣳⢯⡿⣿⣿⣿⣿⣿⣿⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⢠⣰⣾⣿⣿⣿⣿⣿⢿⣻⣽⣛⢿⣳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡟⣯⢞⣧⢻⡜⢧⣻⢯⣟⡿⣿⣿⣿⣿⣿⣿⣷⡀ ⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⢿⡽⣯⢷⣫⡝⣶⡹⣎⡟⡿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⣧⠿⣜⢯⢞⣣⢟⣣⢏⡿⣞⣿⣻⣯⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣟⣿⢿⣻⢇⣧⢻⡜⣧⣟⡼⣣⢟⡿⣿⣄⠀⠀⠀⠀⠀⣠⣿⣿⣻⢼⣻⢟⡼⣻⡜⢿⣘⠿⣸⣻⣼⣻⢿⣻⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣷⡿⣽⣛⢮⡻⣴⢫⡞⣵⣫⣿⣿⣯⣿⣽⣻⣷⣄⣠⣤⣼⣿⣿⣳⣯⣿⣳⢯⣳⢧⣛⢧⣏⢯⣓⢧⣿⣽⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⣻⡜⣧⣛⢶⣹⢞⡿⣿⣿⣿⣷⣿⠻⣿⣏⢿⣿⣷⣿⣿⣷⣟⣯⡗⣯⢞⡳⣎⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃ ⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣟⣯⡝⡧⣝⡲⣭⢫⠷⣯⣿⣳⣯⣿⣿⢎⡟⣼⢏⣮⢻⣿⣿⢿⡽⣞⣧⣟⣮⡟⡻⣜⢎⡷⢯⣟⣿⣿⣿⣿⣿⣧⡄⠀ ⠀⠀⠀⠀⠀⡠⣿⣿⣿⣿⣿⣿⢾⣳⡟⡵⣭⠳⣍⡻⡜⣭⢟⣿⣾⣿⣿⣮⡽⣾⣾⣾⣿⣿⡿⣯⡿⣽⢾⡙⠶⣭⢳⡭⡞⣽⣻⢾⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣳⣟⡳⣜⡻⣜⡳⢽⣩⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢣⡟⣛⢮⢧⡳⣝⢾⣽⣻⣯⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣾⢷⣏⢷⣣⠻⣴⢫⠧⣝⣞⣳⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣯⢳⡭⢻⡜⣎⢷⣚⣟⡾⣽⣿⣿⣿⣿⣿⣿⠱⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣟⡿⣞⡧⣏⠷⣙⢮⣝⣦⡿⣿⣿⣿⣿⣿⣿⠃⠀⢻⣿⣻⣟⡿⣿⡷⢧⣝⣧⡹⢎⡳⣞⡾⣽⡿⣿⣿⣿⣿⣿⡟⠈⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣻⣽⣳⣭⠾⠟⠛⠉⢠⣾⣿⣟⡿⣽⣿⠃⠀⠀⠀⢿⣳⡽⣚⢷⡻⣆⠈⠙⠛⠻⠵⣯⣽⣷⣿⣿⣿⣿⣿⣿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⣠⣿⣟⢾⡽⣻⢿⡏⠀⠀⠀⠀⠈⢷⡽⣩⠶⣹⡹⣧⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⢳⢮⡻⡼⢯⡟⠀⠀⠀⠀⠀⠀⠸⣗⢧⡛⣴⢳⡹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣎⡏⡶⡹⣍⣿⠁⠀⠀⠀⠀⠀⠀⠀⢻⡮⣝⢲⣣⢳⡭⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡓⣧⠽⣜⢳⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡭⢳⢎⡳⣼⣹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣹⣎⠷⣎⢧⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣹⣎⡷⣧⣻⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣞⣧⣟⣻⢮⡷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣳⢯⣟⡷⣯⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣯⣷⢿⣽⢯⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⣿⣟⣿⣿⣽⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣯⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀