⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠿⠍⢿⣿⣤⣬⡙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠈⢻⣿⣿⣷⣄⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣄⣀⣾⣷⣄⠈⢿⣟⢿⣷⣌⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣮⡛⢿⣻⣿⣿⠇⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣾⣿⣿⣏⣈⣥⣤⣉⣉⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⡀⠈⠻⡿⠟⠋⠉⠀⠀⠀⠉⠙⠻⢿⣷⣾⣛⣛⡛⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⠉⠉⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡀⠹⣤⣤⣤⣤⣀⣀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⡄⣸⣷⠀⢸⡏⢿⣿⣿⣿⣿⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢰⣷⣿⣿⡀⢸⣇⠈⢻⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⠟⠋⠙⠛⣿⣿⡀⣄⠀⣠⣿⣿⣿⣿⡇⡸⣿⡆⠀⠙⠛⠀⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣫⣴⣶⣶⣶⣶⣶⡿⠇⢁⣴⣿⣿⣿⡿⣋⣾⠃⠘⣿⡆⠀⠀⠀⠀
⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⢠⣾⣿⣿⣿⣿⡿⣿⣿⢡⣴⣿⣿⣿⠿⢿⣿⣿⣿⣇⠀⠸⣿⡀⠀⠀
⠀⠀⠀⠀⠙⢦⣴⠀⠀⢠⣾⣿⣿⣿⣿⠿⠿⣻⡿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣅⠀⠈⠓⠀⢀⡟⠁⠙⢿⣿⠟⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⢻⣿⣿⣿⡆⠀⢹⡇⠀⠀
⠀⠀⠀⣀⡤⠞⠙⡇⢠⣿⣿⣿⣿⠉⠁⢠⣾⢏⣾⣿⣿⣿⣿⠛⢿⣿⣿⠏⠀⢉⣧⠀⠘⠀⢸⣷⣤⡀⠀⠉⠀⢀⡾⠋⠉⢿⣿⣿⣿⣿⡇⠀⢿⣿⣿⣷⠀⠈⣷⠄⠀
⠰⣶⡿⠉⠀⠀⠀⣧⣹⣿⣿⣿⣿⣶⡇⣿⣟⣿⣿⣿⣿⣿⣧⡀⠀⠉⠛⠀⢀⣾⣿⡆⠀⠀⠘⣿⣿⣿⠆⠀⠀⠈⠳⣤⡀⢸⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⢷⠀⢿⠀⠀
⠀⠹⣷⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣿⣿⣿⣿⣿⠈⠙⢦⡄⠀⠀⠛⢿⣿⣿⠀⠀⠀⣿⣿⠃⠀⢠⣷⣄⠀⠈⣻⣿⣿⣿⣿⣿⣿⣷⡤⣿⣿⣿⡾⡄⣸⡆⠀
⠀⠀⠈⠻⣦⣤⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣰⠟⠀⢀⣆⡀⠀⠉⣻⡇⠀⠀⠹⣷⣄⣠⣿⣥⣽⡷⠴⠟⠻⢿⣿⣿⢿⣿⣏⠁⢹⣿⣿⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠉⠛⠛⠛⣷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢀⣾⣿⣿⣦⣴⡿⠀⠀⠀⠀⠈⠻⠿⠛⠉⠁⠀⠀⠀⠀⠀⠉⠻⣦⠈⢙⠇⣿⣿⣿⡟⣰⣿⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠈⣿⣿⣿⣿⡉⣿⣿⣿⣿⣿⣿⣿⠟⠛⠚⠛⠙⠙⠙⠛⠃⠠⠄⠀⠘⠛⠂⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⡜⢸⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⢹⡄⣿⣿⣿⣿⣗⠛⠻⣿⡿⢻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡤⠖⡩⠂⠀⠀⠀⠀⠀⢀⡴⢃⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣼⡏⣼⣿⡸⣿⣿⣿⣿⣆⠘⠋⠀⠟⠁⠀⠀⠀⠀⠀⠐⠢⠤⠤⠤⠤⠖⠋⠁⠀⠉⠉⠁⠐⠊⠀⠀⠀⠀⠀⢀⠀⠈⢀⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣷⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣴⣾⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣦⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠶⠚⠉⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣦⠈⠻⣶⣴⣤⠤⠤⠤⣶⣤⣶⠶⣦⣠⣤⣴⠛⣿⣍⣉⣀⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠀⠻⠛⠁⠀⠀⢠⠾⠟⢿⡼⠉⠻⣌⠛⠛⠛⠛⠛⠻⠷⣄⠀⠀⠀⠙⠿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠠⠘⢋⣡⡀⠀⢙⡳⢂⡀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠈⠙⠿⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠀⢀⣤⣤⠶⠖⠒⠶⣄⠀⣹⣿⣴⡟⠁⠋⣡⠤⠤⠤⢶⣶⠟⢦⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠀⣴⣞⠙⣷⣤⣶⡖⠀⠈⠝⣿⣿⣿⣷⣤⠞⠁⢀⣄⠀⢿⣷⣦⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠀⠀⠀⠉⠛⠛⠟⠛⠉⠀⠀⣀⣾⣿⣿⣿⣿⣿⣷⣶⣿⣿⣷⣤⣈⠉⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀