⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣿⣿⡿⣿⣿⣿⣿⢏⣼⠟⣟⢺⣭⡳⣍⠦⣽⡜⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⣿⣷⠜⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣟⡚⡤⡴⣞⡽⣤⠛⠃⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣷⢿⠳⠋⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⢛⣿⣿⣿⣿⣿⠟⡉⡋⣿⣇⡻⣭⠕⡿⣱⠙⣟⢦⣧⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⡿⡿⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠮⣿⡼⣯⣿⢸⣿⣻⣿⣧⣻⢹⣟⣮⡪⣿⣦⣧⣽⣥⣹⠃⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⣠⠃⠈⠁⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⢵⣿⣿⣏⢷⣿⣿⣦⡻⣾⡷⣻⣿⣿⣭⣯⠇⠀⠀⠀⠈⢧⡀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢻⠐⠒⡞⠀⠙⢿⣿⣷⡉⣡⣿⣿⣋⣸⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⣿⣿⡻⡷⠁⠀⠀⠀⠀⣿⢿⣿⣿⣿⣥⡧⣴⢯⡳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣬⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣲⣁⠃⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣽⣿⣿⣻⡌⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣛⣳⣛⣳⣿⢏⡿⠀⠀⠀⠀⠀⢀⣿⣿⣣⢹⠋⣤⣙⠷⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣿⣋⣉⣹⡏⡟⣿⠀⠀⠀⠀⠀⠀⣿⠾⣿⠿⠿⢯⣥⠈⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣏⣽⣐⣐⣀⠃⠀⠀⠀⠀⠀⠀⠀⢸⣶⢿⢹⣛⠟⡋⣿⢹⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣙⡱⣿⡶⣽⠀⠀⠀⠀⠀⠀⠀⢿⠟⣷⠾⣄⡐⠸⢉⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣩⣿⣿⣷⢹⠟⣇⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣛⢿⢽⣵⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⣫⠎⠂⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡛⣸⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⣿⢁⠀⠴⠁⣴⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢶⣶⣿⡿⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣾⣿⣭⣥⣀⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣾⢿⢿⡿⣄⣏⣼⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡤⠻⣶⣯⣿⣿⢀⡙⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⣧⣵⣮⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⡶⣝⡶⢼⣍⣥⣥⣤⡯⠿⠒⠍⣛⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⣭⠼⠟⠛⠿⠶⠶⠶⢶⡶⢶⣾