⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⢻⡆⠀⠀⠀⠀⠻⣦⡿⢰⡟⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⢿⡆⢀⣤⣤⣤⣿⠃⣿⠁⠀⠀⢠⣿⠀⢀⣠⣤⠶⠶⠶⡶⣤⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣌⣿⣿⣿⣿⣿⣿⣾⣿⣶⣶⡶⢾⣿⡶⠟⠉⠀⠀⠀⠀⠀⠈⢻⣏⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣿⣿⡿⠛⠋⠀⠀⠀⠀⠈⠙⠻⢿⣅⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣿⣿⣧⣤⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⣠⣴⠿⣯⠉⠉⠉⠉⢉⣽⠟⠀⠀⠀⠀⣀⣠⣤⡴⠶⠶⢦⣿⣷⣶⠟⠋⠉⠉⢉⣀⣠⣤⣤⣶⣾⣛⣛⣛⣷⡄⠀⠀⠀⠀
⠀⢀⣴⠟⠉⠉⠀⠀⠹⣇⠀⠀⣠⡟⠁⠀⢀⣠⡶⠟⠋⠉⠀⣀⣀⣠⣤⣤⣿⣿⣷⣴⠶⢟⣻⣿⠿⣻⣿⣿⣿⣿⠛⠟⠻⠳⣦⠀⠀⠀
⡾⠛⠁⠀⠀⠀⠀⠀⢸⡇⠀⣼⠏⠀⠀⠀⠛⠉⠀⣠⣤⡶⢟⣿⡿⠿⠟⠛⠛⣛⣿⣿⣿⣛⣩⡴⠟⢻⣿⣿⣿⣿⣿⣆⣀⣼⡟⠀⠀⠀
⣷⠀⠀⠀⠀⠀⠀⠀⢿⣇⣰⣿⠀⠀⠀⠀⢀⣴⠟⠉⣡⡾⠛⠁⣀⣤⣶⣾⣿⣯⣉⠁⢉⣿⠉⠀⠀⣿⣿⣿⣿⠿⠿⠛⣹⡿⠀⠀⠀⠀
⠸⣧⠀⠀⠀⠀⠀⠀⠀⢹⡏⠛⠀⠀⠀⠀⠛⣡⡶⠟⢋⣤⡶⠛⢫⣿⣿⣿⣿⣿⣿⣷⠾⣿⠟⠛⠛⠛⠉⠁⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⠀⠘⠿⠿⠟⠿⠷⣤⣤⣼⣿⣿⣿⢿⣟⣫⣥⠾⠋⠀⢠⣄⣀⣀⣠⣴⠶⠿⢯⡀⠀⠀⠀⠀⠀
⠀⢿⡄⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⡶⠾⠿⠿⠿⠟⠛⢋⣽⠟⠀⠀⠀⠈⠉⠙⠛⠋⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀
⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣷⡄⠀⠀
⠀⠀⣿⡆⠀⣀⣠⣤⡀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠶⠟⠋⢉⣼⠇⠀⠀
⠀⠀⠸⣷⡾⠋⠁⠘⣷⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⠶⠛⠛⠛⠋⠉⣀⣀⣤⣴⠞⢻⣿⠀⠀⠀
⠀⠀⣼⠏⠀⠀⠀⠀⣿⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⢠⡾⠟⠉⠉⠉⠉⣉⣉⣉⣉⣩⣤⣤⡴⠶⠾⠿⠛⠛⠛⠉⣉⣁⣤⣴⠾⠃⠀⠀⠀
⠀⢸⡏⣠⣄⣠⡀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⡅⠀⠲⠛⠛⠛⠛⠋⠉⠉⣉⣀⣤⣤⣴⣶⠶⠶⠶⠞⠛⢛⣿⣏⠻⣦⡀⠀⠀⠀
⠀⠈⣻⡟⢸⣿⣥⣴⠏⠀⠀⢠⡿⠀⠀⠀⠀⠀⣀⠈⠻⠷⠶⠶⠶⠶⠶⠶⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢻⣆⠘⢷⣄⠀⠀
⠀⣰⡟⢀⣾⡏⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠙⠷⢶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⠙⢷⡄⠻⣦⡀
⢰⡟⢀⣾⢻⡇⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠈⠻⣦⡈⢷
⡿⢠⡿⠃⢸⡇⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⡾⠛⠻⠷⢿⡇⠀⠀⠀⠀⠀⠀⠈⠻⣦
⣳⠟⠁⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣀⣀⣀⠀⢀⣤⣶⠶⠶⣶⣶⡶⣶⡿⣯⣉⢩⡿⠋⠀⠀⠀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠏⠀⠀⠀⠸⣿⠶⢦⣤⠶⠶⠾⢛⣿⠟⠛⠋⠉⠛⠛⠛⠉⠻⣦⣰⡟⢻⣦⣿⣦⣬⣿⣿⢵⣶⣶⣟⣻⡋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣸⣇⢀⣀⣀⣀⣤⣤⣴⣶⡶⠾⣿⣿⣿⠀⠀⢻⣶⣶⠄⢺⣿⠿⠿⠿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣽⣭⣭⣽⣟⢻⡟⢻⣿⣯⣭⣤⣤⣤⣄⠰⣿⣿⡿⠿⣦⣀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⣿⠉⠛⠛⠛⠛⢸⡧⠙⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠙⠁⠀⣀⣀⣠⣤⣶⠾⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀