⠀⠀⠀⠀⣺⣿⣿⣄⣀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⢻⣹⣿⣿⣿⡄⠀⣼⣿⣿⣿⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⡇⠈⠛⠛⣿⣿⣟⠛⠛⠓⢹⣿⣿⣿⣿⣾⣿⣿⣿⣿⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⠿⠿⢿⣿⣿⡇⠀⠀⠀⣿⣿⡧⠀⠀⠘⣿⣿⣿⠟⣿⣿⠟⣿⣿⣿⠀⣿⣿⣿⣄⣀⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⡀⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿⣿⠀⠀⠀⣹⣿⣿⡆⠈⠃⠀⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠋⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⠀⠉⠉⠉⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠁⠈⠉⠀⠈⠉⠈⠉⠙⠋⠉⠀⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⣿⣿⡿⢿⡟⣿⢻⡟⣿⢻⡟⣿⢻⡟⣿⢻⡟⡿⢿⢿⡻⣟⢿⡻⣟⢿⡻⣟⢿⡻⣟⢿⡻⣟⢿⡻⣟⠿⡿⢿⠿⣿⣿⣿ ⢻⣿⣽⢳⣽⡎⣷⢹⡎⣷⢹⡎⣷⢹⡎⣷⢹⡝⣮⢳⡝⣮⢳⡝⣮⢳⡝⣮⢳⡝⣮⢳⡝⣮⢳⡝⣮⢻⣵⢫⡟⣼⣿⣿ ⢸⡿⢧⣏⢷⡹⣎⢷⡹⣎⢷⡹⣎⠷⣹⢎⡷⣹⢎⡷⡹⣞⠰⡓⡬⢣⠱⢎⠥⡓⡜⣆⠳⣌⢣⢓⡜⡢⢕⢪⢷⣻⣿⡿ ⢸⣿⢧⣛⢮⡳⣝⡎⣷⣙⢮⡵⢫⣝⣣⢏⡾⢥⡻⣜⡳⣭⢣⢱⡡⢇⢫⠜⡬⣑⠎⡴⢣⠜⣢⠍⢶⡉⣎⢎⡷⣻⣿⡇ ⠸⣿⢧⣏⢷⡹⢶⣹⣶⠿⣾⣽⣷⡾⣵⣿⣼⣷⣿⣾⣵⣿⣾⣧⣿⣮⣷⠿⣶⠽⡾⠵⣯⢾⡶⣿⣧⢜⡰⢎⡷⣻⣿⡇ ⠀⣿⡳⣎⢷⣹⢣⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢊⡴⢫⡞⣽⣿⠁ ⠀⣿⡷⣹⢎⡷⡹⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣌⠲⣏⡽⣻⣿⠀ ⠀⢻⡿⣥⢻⡼⣙⢯⣷⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣾⠏⡴⣙⢮⣓⣿⣿⠀ ⠀⢸⣿⡜⣧⣛⡭⣞⣿⠀⠀⠀⠀⠀⢸⡿⣜⣣⠟⣼⢣⣛⠤⡓⡜⢢⠓⡜⢢⠓⣬⢉⠞⣌⢻⡅⣞⠱⣌⡳⣭⣻⡟⠀ ⠀⢸⣷⡝⡶⢭⢶⡹⣿⠀⠀⠀⠀⠀⠸⣿⣮⢵⡻⣜⢧⣏⠲⣭⣘⡥⢫⡜⣡⢏⡴⣉⢞⡴⣻⣴⡏⠶⣘⢷⣳⣿⡇⠀ ⠀⠈⣿⡝⡾⣙⢮⡳⢿⡇⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣌⠣⣝⡾⣽⣿⠇⠀ ⠀⠀⣿⣝⡳⣝⢮⣝⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠢⡝⢮⡝⣿⣿⠀⠀ ⠀⠀⢻⣷⡹⣎⢷⢪⡽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⡧⡓⢬⣳⢛⣯⣿⠀⠀ ⠀⠀⢸⡷⣝⢮⡏⢷⢺⡽⣿⣿⣶⣷⣾⡟⡿⣟⢿⡻⣟⢿⡛⣟⢻⠳⡟⣶⣿⠀⠀⠀⠀⠀⣼⡗⡩⢖⡭⣏⣿⡿⠀⠀ ⠀⠀⢸⣿⢭⢶⣹⣋⠷⣿⠛⠛⠛⠛⠛⢿⡷⣭⠞⣵⢫⢶⠱⣌⠲⣉⠖⣱⡟⠀⠀⠀⠀⠀⣿⡱⢱⢪⢷⣩⣿⡇⠀⠀ ⠀⠀⠘⣿⣏⢮⣓⢮⣛⣿⡀⠀⠀⠀⠀⢸⣿⣜⡻⡜⡯⣞⠱⡌⢇⡣⢞⣹⡇⠀⠀⠀⠀⠀⣿⠜⣡⠞⣧⢻⣿⡇⠀⠀ ⠀⠀⠀⣿⣎⢷⡹⣎⠷⣻⡇⠀⠀⠀⠀⠈⠿⣷⣽⣳⣽⣸⡑⢮⣱⣼⣿⠿⠃⠀⠀⠀⠀⢰⣿⣉⠦⣻⣜⣻⣿⠁⠀⠀ ⠀⠀⢠⣿⣟⡼⣣⢟⣻⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠘⡤⢧⣜⣻⣿⠀⠀⠀ ⠀⠀⢸⢻⣟⢶⡹⣎⡗⢯⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⡇⣏⠜⣧⢻⣼⣿⠀⠀⠀ ⠀⠀⠈⢸⣟⢮⡳⣝⡺⢧⡻⢿⡶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡶⢾⠟⡳⢌⠻⣜⢧⣻⡟⠀⠀⠀ ⠀⠀⠀⢸⣯⢷⡹⣎⢷⡫⣵⢫⡞⡵⣫⠟⣽⣻⢶⣦⣤⣤⣠⣤⡶⢶⠿⡛⢏⡙⢦⡙⢦⡙⢦⡍⢳⡝⣮⣽⡇⠀⠀⠀ ⠀⠀⠀⠈⣿⣧⣛⡼⢣⡟⣼⢣⢟⡱⢧⣛⠶⣭⢞⡼⢭⣫⢍⠳⣌⠣⢎⡱⡩⡜⢦⡙⢦⣙⠲⣌⣧⢻⣼⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⢿⣷⣧⣏⢷⡹⣎⡽⢮⡝⣧⢏⡿⣜⢧⣏⠷⣳⢌⠳⣌⢣⡝⣰⢵⣩⢶⡹⢶⣩⢟⡼⣲⣯⣾⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠾⣷⣯⣞⣵⢫⢶⡹⣎⡞⣭⢳⢎⡳⣎⢷⣩⢗⣫⣎⣷⣯⣷⠿⠾⠛⠛⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⣷⣿⣼⡹⣎⠷⣽⡾⠷⠿⠛⠋⠉⢁⠀⠀⠀⠀⣀⢀⣀⣠⠄⠀⠀⠀