⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⢤⣔⣲⠤⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⢤⣒⣲⠮⠽⠝⠒⠒⠊⠉⢉⣀⣀⠉⠉⠐⠒⠒⠫⠭⠷⣒⣒⡦⠤⢤⡀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣴⣒⠮⠭⠝⠙⠒⠋⠉⢉⣀⣀⣤⣤⣤⢶⣶⡶⣟⡿⣯⣟⡿⣿⣻⢿⣶⣶⡶⣤⣤⣤⣀⣀⡉⠉⠑⠒⠛⠩⠭⠶⣒⣦⣤
⠀⠀⣁⣠⣤⣤⣴⡶⣶⢿⣿⣻⣟⣿⣯⣟⣾⡽⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠷⠿⢿⣷⣯⣟⣿⣻⢿⣻⡿⣶⢶⡶⣤⣤⣄⣀
⠀⠀⣿⢯⣷⣻⣷⣻⡯⠿⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⢽⣯⣿⢯⡿⣽⣻
⠀⠀⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢛⣿⣿⣿⣖⣦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣽
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣾⣿⣯⣿⣿⣿⣺⣿⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠷⣌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠈⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣧⣿⣿⣿⣿⠻⢤⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⡀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣟⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠻⣿⣿⣶⣾⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⡙⠉⡀⠀⠀⠀⠀⢀⠔⢂⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣶⣦⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢷⠉⠉⠀⠀⠀⠀⢠⡏⣠⠏⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣿⡇⣿⡏⠻⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡃⡼⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠘⠋⠁⣿⡇⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣷⣝⢧⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠈⢳⣝⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⠀
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠈⠛⢾⣻⣿⣿⣿⣿⣻⣿⣿⣿⣦⠀⠀⠀⢀⡿⣿⠇⠀⠀⠀⠀⠀⢠⡟⠀
⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣤⣞⣵⠟⠀⠀⠀⠀⠀⠀⣸⠃⠀
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣮⡿⣷⣿⣿⣿⣿⣯⡿⣿⣟⣯⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀
⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣳⣿⣿⣿⣿⣿⡿⠃⣏⡟⢋⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣼⣿⣿⣿⡿⠋⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⡾⠿⠿⠧⠷⢾⣿⣧⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡄⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⡆⠀⠀
⠀⠀⠀⠀⢠⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⣀⣴⡿⠋⠁⢀⣀⣀⡀⠀⠀⣀⡀⠀⠀⣴⠏⠀⠀⠐⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⢾⣄⡈⠙⠄⠀⣠⣼⡿⠋⠀⠀⠰⡭⠌⢩⡟⠉⠉⠀⠀⢀⣼⠃⠀⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⣤⡍⠛⠷⡆⠀⠛⠛⠉⠀⢠⣤⠀⠀⢲⡿⠒⠁⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠈⢧⣀⣀⡰⠃⠀⠀⠀⠀⠀⠘⢄⣀⣠⠟⠁⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⠀⠀⣀⣴⠟⠋⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀