⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠒⠋⠉⠉⠉⠉⠉⠉⠉⠓⠲⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀
⠀⠀⠀⡼⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀
⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠒⠚⢻⣆⣠⣍⣉⣉⣉⣉⣙⢲⠀⣠⢤⣀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀
⠀⠀⢷⡀⠀⢀⣠⠴⣶⣠⣷⡴⠶⡟⠛⠛⢻⣿⠁⠀⠈⠉⢹⠉⠙⠓⢷⣤⣈⠙⠦⡄⠀⠀⠀⣸⠇⠀⠀
⠀⠀⠀⠙⠲⣯⡶⠚⢩⣏⣀⣀⡞⠀⢀⡀⠈⡿⣤⠤⠤⢤⣌⣧⠀⠀⠀⠳⣌⠙⠻⣷⣟⣦⣀⠏⠀⠀⠀
⠀⠀⠀⢠⠞⠁⠀⢴⣿⠋⠰⠿⠒⠋⢉⠉⠙⠛⠃⠀⠀⠈⠻⠭⠤⠖⠦⢤⣜⠦⣄⣘⣮⡙⢿⡀⠀⠀⠀
⠀⢀⣴⢿⡖⠚⠓⠚⠁⠀⠀⠀⣠⡴⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣮⡙⠻⠋⠻⣿⡆⠉⠲⣄⡀
⠈⠯⣄⣰⡇⠀⠀⠀⠀⢀⡴⠿⠭⠤⢤⣘⣆⠀⠀⠀⠀⠀⠀⣠⣖⡭⠤⠤⠞⠳⣦⡀⠀⠈⠓⢲⣖⠚⠁
⠀⠀⠀⣼⠁⠀⢀⡠⢾⡏⠀⠀⠀⠠⣄⣀⣹⣆⠀⠀⣠⡤⠞⣁⣀⡤⠀⠀⣀⡀⢿⠙⠲⣄⠀⠀⢿⡀⠀
⠀⠀⣸⠃⣠⡾⠁⠀⢸⡇⢹⠙⡟⠛⠒⠒⢶⠹⠶⠞⠉⠀⠀⡶⠲⠞⠋⠉⢹⠙⢸⠀⠀⠈⠙⣤⣈⡇⠀
⠀⠰⠷⠚⡗⠀⠀⠀⠘⡇⢸⠒⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡧⠜⠀⠀⠀⢸⠀⣸⡀⠀⠀⠀⢻⠈⠁⠀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⡀⢇⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢀⠎⠀⣿⠀⠀⠀⠀⠸⣇⠀⠀
⠀⠀⢀⡾⠀⣠⢦⠀⠀⠀⢳⡀⠉⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠈⠁⢀⡼⠃⠀⠀⣤⠀⠀⠹⣦⠀
⠀⠀⣼⠥⠞⡏⠀⢳⣦⣄⣀⣳⡀⠀⠀⠀⠀⠀⢀⡀⢀⠄⠀⠀⠀⠀⠀⣠⣞⡀⣀⡤⣾⠉⠳⢄⣀⠹⣆
⠀⠀⠀⠀⠀⢣⣶⠭⢬⣷⡙⣻⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡿⢛⡿⠿⣦⣸⡀⠀⠀⠈⠙⠛
⠀⠀⠀⠀⣠⠞⠁⠀⠀⢹⡿⠋⠸⣿⣍⡛⠉⢙⣿⢿⣶⡞⠛⢉⣭⡟⠛⠺⣍⠀⠀⠀⠙⢧⣄⠀⠀⠀⠀
⠀⠀⢀⣼⠋⠀⢀⣤⣚⠻⣄⠀⠀⡿⠀⠙⠓⢻⢺⣀⡽⡟⠚⠉⠀⢹⡀⠀⡼⢛⣹⡇⠀⠀⠘⢷⡀⠀⠀
⠀⢠⠞⠀⠀⣠⡿⠛⠉⠳⡌⢷⢀⡇⠀⠀⠀⢸⡀⣉⡇⣿⠀⠀⠀⠘⣇⡜⡰⠃⠈⠻⢶⣄⡀⠀⠱⡀⠀
⠀⡏⣀⣤⡾⠋⠀⠀⠀⣠⡼⡞⣻⠀⠀⠀⠀⢘⡇⠧⡄⢹⠀⠀⠀⠀⢿⡳⠷⣦⡀⠀⠀⠈⠻⣯⠉⠻⠀
⠘⠋⠁⣞⠀⠀⠀⢀⡴⣿⠖⠛⠳⣤⣄⡀⠀⠈⡇⡴⠃⣸⢀⣀⣤⣴⡞⠓⠒⢾⠿⢷⣤⡀⠀⢹⡇⠀⠀
⠀⠀⠀⠛⠦⠴⠾⠋⠀⣸⣷⣶⣊⢉⡽⠛⠛⢻⠛⢻⡟⠛⡟⠉⠱⢄⢈⣱⡶⣯⡀⠀⠈⠉⠛⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠉⠉⠛⠒⠲⠷⠶⠾⠷⠶⠾⠖⠚⠋⠉⠀⠀⠈⠙⠶⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⣀⠈⠳⣄⡀⠀⠀⠀
⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⣀⣤⣤⣤⣄⣀⠈⠀⠀⠀⠀⠀⠀⣠⠞⣿⠿⠞⠛⢧⣭⠿⣟⡿⠽⠆⠀⠀
⠀⠀⠀⠀⢯⣻⣤⣀⣀⣤⣾⣹⠿⠦⠼⢿⣉⣿⣦⣄⣀⣠⣤⠛⣟⣽⠁⠀⠀⠀⠀⢸⡦⠈⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⠼⠛⠿⢻⡟⠁⠀⠀⠀⠀⢸⡇⠑⠋⠹⠜⠁⠉⢻⣿⠀⠀⠀