⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⠀⢀⣤⢤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡀⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠵⠋⣩⡎⢒⣚⣓⣓⡚⣭⢳⣶⣦⢄⠴⢒⡘⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢺⣿⣷⣽⣭⡽⠿⠷⠶⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡤⣝⠼⢻⣥⢒⣒⣒⣪⣲⣾⡿⣟⣕⢅⣋⠵⠎⣽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠻⣿⣿⣧⡻⠷⠶⠤⠤⣍⣙⣛⡶⣦⣤⣀⠀⠀⣀⣀⢜⠵⡵⣯⣖⣿⣾⣿⣿⣿⣿⣿⣿⣿⣮⣯⣯⣲⣷⠛⣽⣲⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠛⢿⣿⣆⠀⠀⠀⠀⠀⠉⠉⠛⠚⠽⠟⠷⣿⣽⣷⣧⢝⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡻⡆⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠘⣿⣿⣿⣿⣿⣿⣿⣯⠋⠁⢻⣿⣿⠁⠀⢹⢷⠳⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣟⣛⣿⣿⣤⣤⣼⣿⣿⠦⣤⣾⡎⣞⣵⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣟⢷⢮⣻⢿⣟⣿⣿⣁⣄⣿⠋⢺⣷⣬⣿⣟⣛⠳⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⠀⠀⢠⢤⣀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⣿⠧⠙⣿⣹⢋⢻⡟⣿⠀⠀⠀⠀⠈⠉⠉⠛⠠⠀⠉⠙⠛⠧⣤⣀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣴⣾⣾⡿⣷⡀⢀⣠⢄⣤⠄⢸⣿⣇⣿⡀⠀⠀⠈⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⣉⠿⣿⣿⣶⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣽⣧⢟⢱⣾⣱⢏⣾⣭⢩⡻⣮⣰⠠⣀⢸⠿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣽⣴⣵⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣻⣷⢷⣽⣷⣮⣯⣟⣸⡷⢞⣽⠟⣈⣻⢿⣶⣿⣾⡶⣴⣿⣷⣀⢄⣀⣀⣀⣀⣤⣤⣤⣶⣶⡾⠿⠟⠛⠛⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣕⣛⡵⢿⣿⣯⡙⠚⠛⠛⠋⣧⣿⣷⣿⣿⣭⡛⢛⢿⣟⣯⣿⣿⢹⣾⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣷⣄⠈⠉⠛⠛⠲⠶⠿⢿⣿⣿⣿⣿⣯⣍⣡⣼⣏⢾⣿⣇⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠈⠛⠿⣿⣶⣤⣤⣤⣴⣶⣿⣿⣿⣿⣯⡉⠛⠋⣡⣿⠗⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣦⡀⠀⠀⠉⠙⠛⠛⠛⢛⣿⣿⣿⣿⣏⠛⠿⠿⠟⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠈⠻⠿⣿⣶⣶⣶⣶⣶⠿⠿⣿⣿⣿⣿⠿⢷⣦⣴⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⢷⣦⣀⡀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣷⣄⣀⣀⣠⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣄⠈⠙⠛⠛⠛⠛⠛⠋⣹⣿⣿⣿⣿⣿⡉⠛⠿⠿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀