⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠂⠈⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢈⣵⣦⣤⣀⣀⣀⣀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠠⣾⣿⣿⣿⣿⣿⣆⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠘⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠘⣿⣧⡀⠈⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⠃⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠈⢻⣷⣄⠉⠉⢻⡿⢿⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣰⠃⠀⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠙⢿⣿⣦⣌⣁⣾⡙⣆⠀⠀⠀⠀⠀
⠀⠀⢠⠇⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠸⡀⠈⠙⣿⠿⠟⠁⠘⢧⠀⠀⠀⠀
⣀⡴⡟⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⡀⠀⣆⠀⠀⠀⢹⡀⠀⠀⠀⡇⠀⠘⡌⣇⠀⠀⠀⢈⣧⠀⠀⠀
⡏⢸⠀⠀⢸⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⢷⠀⢹⣆⡀⠀⠀⢧⠀⠀⠀⠸⠀⠀⡇⠘⣆⠀⠀⠀⠋⢧⠀⠀
⠁⡿⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠐⡀⠀⠀⣇⠀⠀⠀⠀⠀⡼⠉⢧⢸⠃⠙⢦⣀⠘⡆⠀⠀⠀⠀⢀⡇⠀⠹⡄⠀⠀⠸⡈⣆⠀
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡇⠀⢀⣿⡀⠀⠀⠀⣼⠃⣀⣈⡟⠀⠀⠀⠈⠳⣷⠀⠀⢸⠀⣸⠀⠀⠀⢳⠀⠀⠀⢣⠘⠄
⠀⠀⠀⠀⡄⠀⢸⠀⠀⠀⣸⣷⡀⠀⢸⠇⠀⣼⠀⡇⠀⢀⡼⠓⠋⠁⣀⣀⡀⠀⠀⠀⠀⢸⡆⠀⡜⠀⡏⠀⠀⠀⠈⣧⠀⠀⠀⠀⣧
⠀⠀⠀⠀⡇⠀⢸⡆⠀⢠⠟⠁⠻⣆⣸⠀⣰⠃⢰⣧⠞⢋⡀⢒⣶⣿⣾⣷⣿⣿⣿⡛⠻⣿⠇⢀⡇⣸⠃⠀⠀⠀⠀⢹⡀⠀⠀⠀⠁
⠀⠀⡀⠀⡇⠀⡾⡇⢀⡞⠀⠀⠀⢨⡏⡰⠃⠀⠀⠀⠀⠀⠿⡿⠛⠉⢿⠋⠡⠥⠿⠉⣩⡇⡀⠸⢀⠇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀
⡇⠀⢷⠀⢰⢰⠇⣧⠞⠚⠉⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⠶⠚⠋⠉⠁⣅⡄⡞⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀
⡇⠀⠘⡄⢸⣼⠐⠁⣀⣰⣤⣤⣿⣿⣶⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠸⠁⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀
⠃⢦⠀⢳⡀⣧⣲⣾⣿⣿⡿⢿⣿⠖⢚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⠀⠈⣆⠀⢣⢸⣹⠟⠈⠳⣄⣤⢴⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀
⠀⠀⠘⣆⠈⢻⣇⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡇⠀⠀⠀
⠀⠀⠀⠈⠣⠀⢻⡤⠀⠊⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠖⠋⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢈⣿⡀⠀⠀⠀⠀⠐⠤⠤⠤⠤⠤⠴⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠳⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢠⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢸⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⢀⣀⣀⡤⣶⣛⣥⠞⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⡞⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠸⡹⡏⠉⢩⣏⢯⣿⣯⠥⠶⠾⠋⠁⠀⢸⠃⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣸⠃⠀⠀⠀⠀
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⣿⠃⠀⣞⣼⣿⠋⢿⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⡔
⡀⠀⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠋⣀⣼⣿⡿⠃⠀⠈⢧⡀⠀⣀⡤⠚⣁⣇⣀⠤⠖⠉⠀⠀⠀⠀⠀⢀⣼⣅⠀⠀⠀⣀⠋⠀
⢳⡀⢷⠈⠳⣤⣄⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠁⠀⠀⢀⣤