⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠋⠉⠉⠉⠉⠉⠛⠒⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⣇⣀⣤⣴⠶⠶⠶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡇⠀⠀⣰⣿⣭⣤⣤⣤⣤⣀⣀⣀⠉⠉⠻⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡀⢸⢸⠷⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⠶⢦⣌⡻⣦⡀⠀⠀⠀⠀⠀⣼⣁⡴⢶⣿⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠽⠿⠈⠀⠀⠀⠀⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⡀⠀⠀⢀⣼⠋⠀⣠⣾⣁⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣶⡞⠃⠀⠀⣛⡽⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣶⠒⠚⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡴⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠲⢶⣤⡀⠀⠀⠀⢠⡟⢀⡾⢱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢺⠏⠀⠀⣠⡴⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣳⡀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⢿⢦⠀⠀⣼⠀⡼⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⡼⠀⢀⡞⠁⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠱⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⢈⣿⡇⠀⡇⠀⡇⢸⠃⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⡇⣠⠏⠀⢀⣀⣠⠤⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠻⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣾⣷⡾⣼⠃⠀⡇⠀⡇⣿⠀⠀⠀⠀⠀⢀⣴⠟⠓⢦⣄⠀⠀⠀⣧⠏⠀⠚⠋⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀
⠀⢀⡴⡏⢹⣿⣟⠁⠀⠀⢻⡀⡇⣿⠀⠀⠀⣀⣀⣾⣁⣀⡀⠀⠀⠀⠀⠀⣿⠀⣀⠀⣠⣤⣶⣦⣤⣈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀
⣰⠏⣠⣗⣼⣿⣿⡄⠀⠀⠈⢷⣇⢸⡆⠀⠀⢸⣿⡟⣿⣿⣿⣆⠀⠀⠀⠀⠉⠀⠙⣿⡟⣿⣿⠿⡟⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀
⡏⠀⣇⢿⣯⣿⣿⠇⠀⠀⠀⠀⠻⣦⣧⠀⠀⠞⣿⠀⠿⢷⣦⣿⡇⠀⠀⠀⠀⠀⠀⡟⠀⠿⠿⢿⣿⣾⠝⣷⠻⣦⡀⠀⠀⠀⠀⠀⠀⣿⠴⢦⣤⣠⡏⠀⠀⠀⠀⠀⠀
⣷⡄⠉⠙⣿⣾⣿⠉⠉⠙⢲⣄⠀⠀⢹⣇⠀⠀⣿⠀⣤⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠀⢀⣀⣀⣿⣿⣷⣿⠀⠈⡿⣦⡀⠀⠀⠀⢸⠇⢀⣤⡌⢿⠀⠀⠀⠀⠀⠀⠀
⠈⠳⠦⢤⣿⣿⣿⡗⠒⢦⠀⣻⠀⠀⠀⢻⡄⠀⣿⠠⣈⡻⠿⠟⠁⢀⡀⠀⠀⠀⠀⠘⢄⠈⠿⣿⣿⣿⣿⠏⠀⢠⡇⠀⠉⠀⠀⠀⡿⣰⣏⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣿⣿⡇⠀⣸⢠⡟⠀⠀⠀⢸⢻⣄⣿⠀⠉⠋⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠈⠳⠤⣈⣩⣽⠿⠃⠀⣸⠇⠀⠀⠀⠀⣼⣻⠁⠉⠁⣰⡟⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⢀⠀⠙⠋⢀⣴⡿⠋⠀⠀⠀⠀⢸⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡏⠀⠀⠀⢀⡼⠽⠃⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣿⢻⠿⡇⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠸⡆⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢠⣾⣇⣀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⢸⣼⣷⡇⠀⠘⠀⣀⡀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢀⣼⣿⣿⣿⡻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣼⠋⣼⣷⡀⢀⣼⣹⡇⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⣸⢩⡿⠷⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠇⢀⣴⣿⠏⠁⠀⣿⣧⠀⠽⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣴⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⢿⡾⠀⠀⠀⠉⠉⢻⡟⡷⠶⠶⢶⣶⣾⡟⢋⣽⢃⣴⣿⣿⣿⣿⣷⣶⣿⠃⠀⠀⢨⣿⣆⣠⣤⣤⣤⡄⠀⠀⠀
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣇⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠘⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⠟⠑⠀⣠⣶⣿⣿⠛⠋⣻⣿⣻⡇⠀⠀⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⣠⡾⠉⡟⠶⣄⠀⠀⢀⣴⣾⢿⣖⡂⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡶⠟⣛⡽⠟⠁⢀⣴⠋⠈⠻⣆⠀⠀⠀
⠀⠀⠀⠈⠙⢿⣿⣿⣿⠟⠀⠈⠙⠲⣄⡀⢀⡾⠋⠀⠀⣇⠀⠀⠀⣠⣾⠟⠁⠀⠙⢿⣅⡀⠀⠈⠙⢿⣿⣿⠿⠿⠛⠋⠁⢹⡆⣬⠉⠀⠀⢀⡾⠁⠀⠀⠀⠘⣧⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠻⣧⣀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⢹⣄⣀⣼⡟⠁⠀⠀⠀⠀⠀⠙⢷⣶⣀⣀⠈⢛⣙⣷⣤⡀⠀⠀⢸⣿⡜⡆⠀⢀⣼⠁⠀⠀⠀⠀⠀⠈⢧⡀