⠀⠀⠀⢀⠒⣜⣶⡶⠿⣅⣇⢿⣷⣝⣤⣥⡇⣮⡖⣶⢧⡛⡤⡤⡀⠀⠀⠀ ⠀⠀⡤⢧⣆⣷⣯⣇⣵⣿⣿⣻⣿⣷⣿⣿⣛⣿⣿⣏⣟⡟⣟⣦⡇⠀⠀⠀ ⠀⢀⣂⡍⡧⡏⣩⡟⣯⣿⣧⣵⣻⡡⢯⣾⣿⣋⣻⣷⣟⡯⣾⡍⣫⠄⠀⠒ ⠀⢀⡿⣲⢯⣍⡺⣿⣿⣿⡯⣼⣦⡾⠋⠉⢻⣦⣍⣯⠷⣯⣯⣷⠕⣥⡀⠀ ⠀⠊⡇⢛⣷⣏⣳⢳⣿⣿⣿⣱⣏⡀⢀⣤⣤⣷⡭⣺⡏⣭⣿⣿⠵⢕⢐⠀ ⠀⣫⡧⢌⡝⡉⣎⢸⣿⣿⣿⡛⠛⣻⣘⠛⠋⢹⣿⣷⣧⡫⣽⣝⣤⡋⠆⠀ ⠀⡃⣿⣡⢗⣿⣶⣿⣿⢿⣿⣷⣀⣿⣞⣀⢀⣽⣿⢹⡇⡷⣯⢥⣯⠊⠀⠀ ⠀⡏⡛⣟⡇⣔⣯⡿⣾⣿⣿⣿⣷⡛⠟⣡⣾⣿⣿⣽⣯⣟⣏⣝⣾⡕⠀⠀ ⠀⠈⠳⡭⡝⣿⣋⣶⣿⣿⣿⣿⡿⢿⡿⠋⠸⣿⣿⣿⡟⣷⡖⣭⡟⡃⠀⠀ ⠀⠀⠀⠀⢁⣤⣿⣻⣿⣿⣿⣟⣣⣾⠁⣆⣀⣈⡙⠿⠻⠽⠧⣈⠉⠀⠀⠀ ⠀⠀⠀⣰⡏⠁⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠄⠱⠀⠀⠀ ⠀⠀⠀⣿⣽⢓⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀ ⠀⠀⠀⣿⠟⢸⣧⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢠⣼⠀⠀⡇⠀⠀ ⠀⠀⠀⢿⡀⣼⣯⡀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⠀⣤⣌⢷⠀⠀⠇⠀⠀ ⠀⠀⠀⢸⣷⣿⣿⠇⠀⠀⠀⠀⣡⠀⢿⡼⣄⠀⠀⢖⣿⡽⢸⠀⢰⠀⠀⠀ ⠀⠀⠀⢸⣧⢫⣹⢶⣄⣀⣀⡴⠃⠀⠈⢿⣿⣢⣀⡀⠀⣠⡞⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⣷⠁⢹⣿⡺⢿⡋⠀⠀⠀⡇⠀⠙⠛⠿⠟⣻⣿⠀⠀⣸⠀⠀⠀ ⠀⠀⠀⢠⣿⡀⢸⡿⣇⠀⣿⠃⠀⠀⡇⠀⢠⠀⠀⢀⠇⣷⠀⡄⢏⠀⠀⠀ ⠀⠀⠀⣾⠃⠇⢸⡇⢿⡄⣷⡇⠀⠀⡇⠀⠀⠀⠀⣼⠀⣿⠀⠃⠘⡀⠀⠀ ⠀⠀⢰⡏⠀⠀⣸⢡⡾⠁⡏⢻⠀⠀⡇⠀⠀⠀⠀⠹⣄⢻⡇⠀⠀⢃⠀⠀ ⠀⠀⢸⠧⠀⢰⣿⠟⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⢺⣿⡀⠀⢸⠀⠀ ⠀⠀⣿⠆⢠⡟⢣⠞⠀⢸⣧⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠸⡄⠀ ⠀⢀⡏⢠⣟⠀⣸⡀⠀⠘⡼⣆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⡇⠀ ⠀⣸⠇⣾⡃⢀⢯⣷⡀⠀⢡⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢱⠀ ⢀⣿⢰⡟⠁⣿⠀⠻⣿⡄⠀⠁⠉⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠈⣧⠘⡆ ⢈⣿⢿⡇⠀⢸⠀⠀⠈⠛⢦⣴⡄⠀⠀⠀⢀⣴⢞⡿⠃⠀⠀⠀⠀⡿⠀⡇ ⢸⣿⠈⡇⠀⢸⡇⠀⠀⠀⠀⠹⣿⠶⠿⢴⡿⠃⣸⠁⠀⠀⠀⠀⢰⠁⠀⡇ ⢼⣻⣆⡇⠁⠀⣧⠀⠀⠀⠀⠀⠘⡆⢀⡏⡀⠀⠏⠀⠀⠀⠀⠀⢸⣠⣇⣧ ⠘⣿⣿⣷⠀⠀⢸⡀⠀⠀⠀⠀⠀⡇⢸⡇⠃⠀⠀⠀⠀⠀⠀⠀⣿⣾⣫⠋ ⠀⠈⢻⣿⣷⡀⠀⢧⠀⠀⠀⠀⠀⡇⠘⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠀

⠀⠋⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⣇⠘⡇⠀⠀⠀⠀⠀⢧⠀⡀⣷⣿⢻⠈⠀ ⠋⣫⣾⣿⠀⠀⠀⠀⠀⠀⠀⠃⡇⢸⡇⠀⠀⠀⠀⠀⡀⢸⠀⠀⣷⣿⣿⠘ ⣧⣇⣠⢸⠀⠀⠀⠀⠀⠏⠀⡀⡏⢀⡆⠘⠀⠀⠀⠀⠀⣧⠀⠁⡇⣆⣻⢼ ⡇⠀⠁⢰⠀⠀⠀⠀⠁⣸⠃⡿⢴⠿⠶⣿⠹⠀⠀⠀⠀⡇⢸⠀⡇⠈⣿⢸ ⡇⠀⡿⠀⠀⠀⠀⠃⡿⢞⣴⢀⠀⠀⠀⡄⣴⢦⠛⠈⠀⠀⢸⠀⡇⢿⣿⢈ ⡆⠘⣧⠈⠀⠀⠀⣤⢀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡄⣿⠻⠀⣿⠁⡟⢰⣿⢀ ⠀⢱⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠘⢡⠀⡀⣷⢯⢀⡃⣾⠇⣸⠀ ⠀⡇⠀⣇⠹⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣆⡼⠘⠀⡀⣸⠀⣟⢠⡏⢀⠀ ⠀⡄⠸⠀⣧⠹⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣧⢸⠀⠞⢣⡟⢠⠆⣿⠀⠀ ⠀⠀⢸⠀⡀⣿⢺⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠟⣿⢰⠀⠧⢸⠀⠀ ⠀⠀⢃⠀⠀⡇⢻⣄⠹⠀⠀⠀⠀⡇⠀⠀⢻⡏⠁⡾⢡⣸⠀⠀⡏⢰⠀⠀ ⠀⠀⡀⠘⠃⠀⣿⠀⣼⠀⠀⠀⠀⡇⠀⠀⡇⣷⡄⢿⡇⢸⠇⠃⣾⠀⠀⠀ ⠀⠀⠀⢏⡄⠀⣷⠇⢀⠀⠀⢠⠀⡇⠀⠀⠃⣿⠀⣇⡿⢸⡀⣿⢠⠀⠀⠀ ⠀⠀⠀⣸⠀⠀⣿⣻⠟⠿⠛⠙⠀⡇⠀⠀⠀⡋⢿⡺⣿⢹⠁⣷⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⡞⣠⠀⡀⣀⣢⣿⢿⠈⠀⠃⡴⣀⣀⣄⢶⣹⢫⣧⢸⠀⠀⠀ ⠀⠀⠀⢰⠀⢸⡽⣿⢖⠀⠀⣄⡼⢿⠀⣡⠀⠀⠀⠀⠇⣿⣿⣷⢸⠀⠀⠀ ⠀⠀⠇⠀⠀⢷⣌⣤⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⡀⣯⣼⡀⢿⠀⠀⠀ ⠀⠀⡇⠀⠀⣼⢠⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡆⣧⢸⠟⣿⠀⠀⠀ ⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⢓⣽⣿⠀⠀⠀ ⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠁⡏⣰⠀⠀⠀ ⠀⠀⠀⠉⣈⠧⠽⠻⠿⡙⣈⣀⣆⠁⣾⣣⣟⣿⣿⣿⣻⣿⣤⢁⠀⠀⠀⠀ ⠀⠀⡃⡟⣭⡖⣷⡟⣿⣿⣿⠸⠋⡿⢿⡿⣿⣿⣿⣿⣶⣋⣿⡝⡭⠳⠈⠀ ⠀⠀⡕⣾⣝⣏⣟⣯⣽⣿⣿⣾⣡⠟⡛⣷⣿⣿⣿⣾⡿⣯⣔⡇⣟⡛⡏⠀ ⠀⠀⠊⣯⢥⣯⡷⡇⢹⣿⣽⢀⣀⣞⣿⣀⣷⣿⢿⣿⣿⣶⣿⢗⣡⣿⡃⠀ ⠀⠆⡋⣤⣝⣽⡫⣧⣷⣿⢹⠋⠛⣘⣻⠛⡛⣿⣿⣿⢸⣎⡉⡝⢌⡧⣫⠀ ⠀⢐⢕⠵⣿⣿⣭⡏⣺⡭⣷⣤⣤⢀⡀⣏⣱⣿⣿⣿⢳⣳⣏⣷⢛⡇⠊⠀ ⠀⡀⣥⠕⣷⣯⣯⠷⣯⣍⣦⢻⠉⠋⡾⣦⣼⡯⣿⣿⣿⡺⣍⢯⣲⡿⢀⠀ ⠒⠀⠄⣫⡍⣾⡯⣟⣷⣻⣋⣿⣾⢯⡡⣻⣵⣧⣿⣯⡟⣩⡏⡧⡍⣂⢀⠀ ⠀⠀⠀⡇⣦⣟⡟⣟⣏⣿⣿⣛⣿⣿⣷⣿⣻⣿⣿⣵⣇⣯⣷⣆⢧⡤⠀⠀ ⠀⠀⠀⡀⡤⡤⡛⢧⣶⡖⣮⡇⣥⣤⣝⣷⢿⣇⣅⠿⡶⣶⣜⠒⢀⠀⠀⠀