⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣿⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀
⠀⢀⠂⠀⠀⡾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠀⠀⠀⡆⠀
⠀⣸⠀⠀⠀⡇⢻⡀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀⡼⠘⡄⠀⠀⣷⠀
⠀⣿⠀⠀⠀⡇⠀⠑⠦⣤⣄⠀⢠⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠘⡆⠀⣤⣤⠴⠚⠁⠀⡇⠀⠀⢿⡄
⢰⣿⠀⠀⠀⡇⠀⣠⠞⠉⠀⢀⡞⡇⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢰⠿⣄⠀⠈⠙⣦⠀⢀⠇⠀⠀⢸⡇
⢸⣿⠀⠀⠀⣧⢠⠃⠀⢀⡴⠋⠀⠸⣆⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⣠⠏⠀⠙⢦⣀⠀⠈⣆⣸⠀⠀⠀⣾⡇
⢸⣿⠀⠀⢰⢸⢸⠀⠀⠙⢦⡀⠀⠀⠈⡳⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⡴⠋⠀⠀⣿⡟⡇⠀⠀⣿⡇
⢸⣿⡀⠀⢸⠀⣿⡄⠀⠀⠀⠻⣄⠀⢰⠇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⡇⠀⢠⠞⠁⠀⠀⢀⣿⠁⡇⠀⠀⣿⡇
⢸⣿⣇⠀⢸⡄⢻⠹⢤⣀⠀⠀⠈⢧⣼⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⣧⡴⠋⠀⠀⣀⡤⠞⡿⠀⣷⠀⢸⣿⡇
⠘⣿⣿⠀⣿⣧⠈⣇⠀⠈⠳⣄⠀⠀⠻⡇⢸⣿⡆⠀⠀⠀⡰⠶⠦⠤⣀⠀⠀⠀⣀⡤⠴⠶⢦⠀⠀⠀⢠⣿⡇⢠⠟⠁⠀⣠⠞⠁⠀⣰⠃⣸⣿⠀⣾⣿⡇
⠀⣿⣿⣷⣿⣿⡄⠘⢦⣀⣀⠈⠳⡄⠀⠙⢺⣿⣷⡀⠀⢀⡇⠀⠀⠀⠈⠳⣀⡾⠁⠀⠀⠀⢸⡆⠀⠀⣼⣿⡇⠋⠀⢀⡞⠁⣀⣀⡴⠋⢀⣿⣿⣾⣿⣿⠀
⠀⠘⠻⣿⣿⣿⣿⣦⣀⠀⣿⣷⣄⠹⡆⠀⣼⣿⣿⣧⠀⢸⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣇⠀⣸⣿⣿⣷⡀⢠⡏⢠⣾⣿⡁⣀⣴⣿⣿⣿⣿⠟⠋⠀
⠀⠀⠀⠘⣿⣿⣿⡿⠛⠁⢻⣿⣿⣆⠹⣾⣿⣿⣿⣿⣧⣹⢇⡞⠒⢤⡀⠀⣿⠀⠀⣤⠖⢻⡜⡏⣼⣿⣿⣿⣿⣿⡞⢰⣿⣿⡟⠈⠙⢿⣿⣿⣿⠃⠀⠀⠀
⠀⠀⠀⢀⣿⣿⡟⠀⠀⠀⠀⠻⣿⣿⣆⠙⢿⣿⣿⣿⣿⣿⣼⠀⠀⠀⣧⢠⠋⣇⢸⠁⠀⠀⣳⣿⣿⣿⣿⣿⡿⠋⢰⣿⣿⡟⠀⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀
⠀⢠⣴⣾⣿⣿⠁⠀⠀⠀⠀⠀⡟⢿⣿⣆⠀⠙⠻⣿⣿⣿⣿⣷⣦⣤⢃⠏⠀⠹⡜⢦⣤⣾⣿⣿⣿⣿⠿⠋⠀⣰⣿⡿⢻⡀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣄⠀
⠀⠀⠉⠛⢿⣿⡆⠀⠀⠀⢀⡼⢻⣀⣼⣿⣷⣄⡀⠈⠙⠿⠿⣿⣿⣿⣿⣤⣀⣤⣿⣿⣿⣿⠿⠿⠛⠁⢀⣠⢼⣿⣿⣀⡞⢳⡀⠀⠀⠀⢀⣿⡿⠟⠉⠀⠀
⠀⠀⠀⠀⠀⠙⢿⡀⢀⡴⠋⠠⣴⣿⣿⣿⣿⣮⡉⢻⡙⠓⠒⠖⠲⢭⣿⣿⣿⣿⣿⡭⠗⠲⠖⠚⢋⡿⢉⣹⣿⣿⣿⣿⣷⡄⠙⢦⡄⠀⡾⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠙⣄⠀⠈⢿⣿⣿⣿⣿⠇⠀⠙⡦⠀⠀⣰⡿⢋⡿⣿⢿⡙⢿⣦⠀⠀⢰⠋⠀⠘⣿⣿⣿⣿⡿⠋⠀⣠⠞⠀⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⡟⣿⣿⣿⡀⠀⢸⠃⠀⢰⡟⢀⡞⡼⠉⢳⡻⡄⠹⡇⠀⠈⣇⠀⢀⣼⣿⣿⢿⡀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡇⠈⢻⣇⠹⣆⢘⠀⠀⠘⠀⡾⡼⠁⠀⠀⢳⣻⠀⠃⠀⠀⢸⢠⠞⢹⡿⠁⢸⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠹⣆⠈⢿⡀⠀⠀⢸⣽⠁⠀⠀⠀⠀⢷⣇⠀⠀⠀⡾⠃⢠⠟⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠳⠀⠀⣿⠃⠀⠀⠀⠀⠀⠘⣿⠀⠀⠞⠁⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀