⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠒⠒⠒⠒⠂⠀⠐⠒⠒⠒⠒⠦⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣍⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⣤⠞⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⢀⡠⠞⠉⠀⠀⠀⢀⡀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣠⠞⣵⠋⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⡾⢡⡞⠁⠀⠀⠀⢠⣿⣿⣿⣧⡀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢀⡴⠃⠀⣠⡞⠁⠀⠀⠀⠀⠀⣰⠏⢠⡟⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣆⠀⢸⡇⠀⣀⣤⣤⣤⡀⢸⠀⠹⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⡾⠁⠀⣴⠏⠀⠀⠀⠀⠀⠀⡴⠃⠀⣾⠁⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⣿⣿⡇⢸⡆⠀⣷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⡾⠁⠀⣼⠃⠀⠀⠀⠀⠀⠀⡼⠁⢀⣼⠇⠀⠀⠀⢰⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⡇⠀⢸⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⡾⠁⠀⡼⠃⠀⠀⠀⠀⠀⠀⣼⠃⣰⠟⣿⠀⠀⠀⠀⣿⠘⠿⠿⢿⡿⠛⠛⠉⠉⣻⣿⣿⣿⣿⣿⣿⠏⠀⢸⠃⠀⠘⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡾⠁⠀⣼⠃⠀⢀⡶⠀⠀⠀⣸⣏⠞⠁⠀⡇⢠⡀⠀⢰⡟⠀⠀⠀⡾⠀⠀⠀⠀⢀⡿⣾⣿⣿⣿⣿⣟⡆⠀⡿⠀⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡾⠁⠀⢰⠇⠀⢀⣾⠁⠀⠀⢰⣿⠏⠀⠀⠀⢧⠀⠻⣄⢸⡇⠀⠀⣸⠃⠀⠀⠀⢀⡾⣹⣿⠁⠻⡿⠋⡼⠀⣸⠃⠀⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⢀⡏⠀⠀⣼⠃⠀⠀⢀⣿⠋⠀⠀⠀⣠⣄⠀⠀⠘⢿⣇⠀⠀⡿⠀⠀⠀⢀⡼⣡⡿⠃⠀⠀⠀⣴⠃⣰⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⣸⠁⠀⢸⡏⠀⠀⠀⣼⠃⠀⠀⠀⠀⠻⣿⣷⡄⠀⠀⠙⢷⣄⠇⠀⠀⠀⣾⣵⡿⠁⠀⠀⢀⣼⢏⣴⠃⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⣴⡏⠀⠀⣿⠃⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⡀⠀⠀⠈⠀⠀⠀⠀⠉⠋⣀⣀⣤⣤⣿⣿⠟⣿⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠴⠚⠁⠀⠀⣠⣾⣿⡇⠀⢠⣿⠀⠀⠀⣼⠁⠀⠀⠀⣀⣤⣤⣤⣤⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣀⣤⡁⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⢡⣿⡇⠀⢸⡏⠀⠀⠀⣿⠀⠀⠀⠘⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠿⠛⠁⠀⣿⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠚⠛⠉⠁⠀⣠⣿⣿⡇⠀⣸⡇⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡁⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡇⠀⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⢀⣼⣿⡏⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡇⠀⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⢀⣾⣿⣿⠃⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡇⠀⠀⠸⣿⣄⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣷⠀⠀⠀⣿⣿⣦⡀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠁⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⣿⠀⢸⣿⡄⠀⠀⢻⣿⣿⣿⣦⡀⠸⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⢠⡞⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣦⡀⠈⠈⠙⠻⠿⠿⠋⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⠃⢀⣴⠋⣧⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⣿⢿⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⡿⢁⣴⣿⡇⠀⠸⡆⠘⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⡟⢀⣿⡟⠀⢷⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣇⠀⠀⢻⡀⠘⣆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣦⠀⠀⠀⠀⣼⠇⢸⣿⡇⠀⠘⣧⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⣹⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⠀⠀⠘⣿⣄⠸⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠿⠿⠿⠷⠀⠀⠼⠿⠀⠾⠿⠀⠀⠀⠹⠆⠀⠻⠈⠻⠿⠿⠿⠿⠿⠟⠉⠀⠀⠀⠀⠴⠿⠿⠿⠻⠿⠿⠏⠸⠿⠿⠿⠿⠇⠀⠀⠿⠘⠧⠹⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀