⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⢋⡾⢫⡾⠋⣀⣿⣽⣿⣿⣿⣿⣿⣈⠻⣦⡹⣆⠹⣆⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⣼⣷⣿⡷⠛⠉⢡⡾⠷⠀⠶⠆⠈⠉⠻⢿⣿⣽⡇⣿⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢦⣄⣀⠀⠀⣿⢸⣡⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣸⢰⡇⠀⠀⣀⣤⡶⣶⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢻⣽⣿⣷⣾⣾⣿⣅⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣽⣷⣾⣿⣿⠇⣼⠟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⡉⠛⠛⣻⢿⡿⠁⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠘⣮⢻⡝⠛⢛⣁⣼⠏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣹⢯⡿⠁⢀⡾⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠴⠙⣦⠀⠘⣧⢻⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣰⣿⢟⡶⢀⣾⠁⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣇⠐⣿⠷⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⣉⣉⣠⣾⣧⣾⡏⠀⠀⢀⣿⣇⠀⠀⠀⣿⠀⢀⡿⢷⡀⣀⠀⠀⣿⣦⣹⣦⣄⣉⣙⣿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣡⡴⠟⣫⡍⠁⠀⣼⡟⠁⢻⡄⠀⠀⢹⡄⣼⠃⠈⢻⣿⣆⠀⠈⣯⣛⠷⣤⣈⣿⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠉⢛⣿⠟⠉⣀⢀⣾⣟⣛⣻⣿⣿⣷⡀⠈⣷⡟⣛⣛⣿⣻⣿⣷⣀⠀⠙⠻⣿⠋⠉⢻⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢁⣀⣴⢟⣁⣴⣾⡿⢿⢿⣿⣿⣿⣿⡿⠻⣿⣦⢹⡞⢻⣿⣿⣿⣿⣿⠿⣿⣶⣤⣈⢳⣤⣀⠙⣧⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠈⢉⣿⣿⣿⣿⣿⠀⣼⡆⠙⠛⠛⠛⠀⠀⠙⠟⠿⣿⡌⠛⠛⠛⠁⣼⡀⢸⣿⣿⣿⣿⣯⠉⠀⠈⠻⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡞⠁⣠⣀⣴⣿⣿⣿⣿⣿⣿⡄⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣰⣿⡇⢸⢿⣿⣿⣿⣿⣶⣤⣀⡀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⢸⣽⣿⣿⣿⣿⣧⠀⡇⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣿⢁⡿⢸⢿⣿⣿⣟⡇⠀⠉⠉⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⣹⡏⢹⣆⢿⡀⠈⠳⣦⣀⠀⠀⠀⠀⠀⣠⡴⠛⠁⣸⢇⣼⢡⣿⣆⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡿⢿⡇⡆⠹⣾⣧⡴⣶⣿⣽⣷⣦⣤⣴⣿⣽⣷⣶⣾⣿⣾⠃⢸⣿⡟⢷⣽⣿⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣸⣷⢸⣇⢻⡀⣿⠛⡇⠃⠈⠉⠉⠉⠉⠉⠉⠉⢀⣿⣿⢻⡇⢀⣿⣿⠀⢸⣏⣩⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢘⣿⠘⣷⢹⣤⣿⣤⣄⣀⠀⠀⠀⠀⢀⣀⣼⣧⣯⣸⣣⣾⣿⣿⡆⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠿⣧⠘⣿⣿⡏⣠⣼⣿⣿⡟⣻⣿⣿⣿⣦⡀⢿⣿⠿⢫⡿⢿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠘⣧⡸⣿⣴⣿⣿⣟⣹⣟⣿⣿⣉⣿⣿⣿⣼⣷⣴⡿⠁⠀⠀⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣅⣠⣽⠀⢛⣷⣼⣿⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣼⡟⢸⣏⣿⡿⢿⣟⣂⣶⣆⣨⣿⣿⣿⣿⡃⢿⣇⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⢠⡀⣸⣿⠀⣾⠙⣿⣿⡾⢛⣻⣭⣍⡻⣾⣿⣿⠟⣧⠘⣿⡄⢀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⡄⠀⠀⠀⠀⠘⣷⣿⠇⢰⠇⠀⠙⠷⢶⠿⠷⠶⠿⢿⡿⠞⠋⠀⢹⡄⢻⣿⡾⠀⠀⠀⠀⠀⢠⣾⣿⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠻⣿⣷⣶⣤⣀⠀⣰⣿⡟⠀⠛⠀⠀⠀⠀⠘⠶⣤⣧⣤⠾⠷⠀⠀⠀⠀⣧⠈⣿⣿⣄⠀⢠⣴⣶⣿⣿⠟⣻⣦⠀