⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⢠⠏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣿⡀⠀⠀⠀⣿⢴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⡿⣷⠀⠀⢀⠇⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢹⠀⡇⢿⡆⠀⢸⠀⡎⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠸⣿⠀⢸⠀⣧⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢧⠀⣿⠀⢹⠀⢳⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⠀⣿⡀⢸⠀⠸⢸⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⣆⣁⡇⠀⡇⣾⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠹⣿⡇⣀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢡⣿⣯⠻⣟⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠹⣿⡏⡁⠉⠙⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢹⣧⡀⠀⢸⣇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡤⠤⣸⣿⣽⣦⢸⣿⠛⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⠀⢨⣷⣯⡭⣻⣣⡿⠻⡟⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⡀⠀⠈⠹⣾⣿⡿⠛⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⣿⠁⠀⠀⠐⢿⣍⡿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⡿⠀⠀⠀⠀⠳⠤⠤⠞⠁⠀⣿⢣⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠙⢦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⣠⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠱⣄⠀⠀⠀
⠀⠀⠀⢀⡾⠁⠀⠀⣠⠔⢁⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠈⢣⡀⠀
⠀⠀⠀⣞⣀⣀⣀⣼⠁⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣤⣤⣷⡄
⠀⠀⠀⣿⣷⢿⠿⢿⣺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠦⠟⠋⢹⣯⣷
⠀⠀⢰⢻⡿⠻⠀⢠⡭⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⡖⢀⣀⣛⣹
⠀⠀⠸⡄⠈⠀⣠⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢞⣽⡿⠃
⠀⠀⠀⢹⡶⣤⣙⣧⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠀⠀
⠀⠀⠀⠈⢣⠀⠈⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣦⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢣⡀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡛⢷⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠱⢤⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠴⠒⠚⠉⠀⠈⣵⣶⠇⠀⠀⠀
⠀⣰⣾⠽⠯⢙⣿⣉⠉⠉⠃⠀⢉⣶⣾⠏⠉⠉⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠋⠀⠀⠀⠀⠀
⠸⣏⠀⣠⠞⠉⠉⠈⣛⡷⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠓⠛⠦⠴⢖⡛⡁⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀