⠀⠀⠀⠀⠀⣠⣾⠟⣍⣯⡛⣟⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⢤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⡿⣱⣩⣯⠟⣯⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢯⣱⠾⣧⣿⢵⣳⡀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣷⣞⡾⣮⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣯⣻⡯⣿⡽⣿⠾⣳⣃⠀⠀⠀ ⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣞⣿⣾⣿⣽⣻⣿⡝⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⣛⡿⣿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡷⣾⡷⣟⣿⠕⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣱⣿⣽⢯⣏⣾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣿⣿⣿⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⡤⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⡎⠂⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣁⣐⡣⠀⣀⠀⢠⠀ ⠀⠀⢻⣿⣶⡱⡣⣿⣿⡷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣵⣶⣦⡍⣰⣌⠀ ⠀⠀⠀⡟⡶⡢⣛⢿⣿⢞⡥⣗⣯⢷⣦⣤⣀⣀⣀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⢶⣸⣿⣿⡳⣾⡽⡷⢼⠑⠀ ⠀⠀⠀⣿⣿⢳⣧⡏⣷⠈⠀⠘⢪⢻⣾⣽⡟⣿⣿⣿⣿⣷⣶⣿⣿⣶⣶⣴⣶⣤⣤⣶⣾⣿⣿⡟⣯⢳⣽⣯⣾⣿⣿⢳⡞⣯⠛⡆⠀⠀ ⠀⠀⢠⣿⠍⠿⣿⣿⣾⣷⢶⣤⣬⣠⢧⣞⣭⣛⣟⡻⣟⢿⣽⣿⣿⣿⣟⣯⢿⣽⡿⣿⢿⢯⣳⢿⣹⣮⢳⣛⣾⣿⣿⢗⣟⡭⢃⠃⠀⠀ ⠀⢀⣞⣩⢇⣢⠄⡌⠟⠻⠿⣿⣾⣯⣿⣞⡷⣯⣞⣵⣻⡞⣾⣿⣿⣿⡞⡼⣏⡾⣝⣳⢯⣏⢷⣛⢿⢯⣛⣉⠘⣿⣿⣾⢯⣗⢶⡄⡦⡀ ⡐⠽⣿⣽⡿⣽⡀⠀⡈⠀⠀⠀⠈⠉⠛⠻⠿⠷⣿⣞⣷⣻⣽⣿⣿⣿⣽⣻⣭⢟⡽⣎⣺⠼⡗⠾⠝⠋⠊⠉⠀⠘⣿⣿⣿⡾⡽⡟⣯⠷ ⣏⣿⣻⣭⣻⣯⡃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⡏⠁⠉⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣟⠿⣿⢧⡛ ⠸⣶⣮⡅⣋⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⠫⠙⠐⠒ ⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀