⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⡦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⢀⡤⠒⠒⠢⣄⡀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣼⠁⣀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠙⢷⣷⠋⠉⢳⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣶⣾⣶⡀⢂⠘⣇⠂⠀⣨⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⢛⣿⣏⣈⣷⣜⠁⠈⠑⡄⢀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣴⢻⢿⠿⡛⠲⡀⠀⠒⣵⠋⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⢸⡧⡀⠀⠈⡄⠀⠀⠀⠸⠧⠤⣄⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⡏⠀⠈⠀⠴⠃⠀⠀⠀⠀⠐⢯⡁⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣤⣞⡁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢀⡼⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡴⠞⠋⠁⠀⠀⠀⠈⠙⠲⠞⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡽⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣴⠋⠀⠀⠀⣀⠤⠒⠉⠑⠲⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀
⠀⡼⠁⠀⠀⣠⠎⠁⠀⠀⠀⡠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⢿⣿⣿⠇⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣄⣀⡰⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀
⢸⡇⠀⠀⡴⠁⠀⠀⠀⠀⠮⣤⣤⡴⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠘⣿⡟⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢠⣤⡾⠟⠛⠉⠉⢻⡛⠻⠷⣶⣤⠄⠀⠀⠀⣿⠏⠀⠀
⣼⠁⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠸⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠘⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⡟⡇⣤⣶⣦⣄⠀⢳⠀⠀⠀⣿⢇⠀⠀⠀⠾⠟⠋⣿⠃⠀⠀⠀
⢹⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⣇⢳⡹⣿⣿⣿⠀⢸⠀⠀⠀⢸⠋⠀⠀⠀⠀⠠⠾⠯⠤⠤⢴⡄
⠈⡇⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠟⠛⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠑⢮⣉⣀⡴⠋⠀⡠⠮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠞
⠀⠘⣄⣰⢿⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⡏⠁⢀⣤⣶⣶⣯⢇⠀⠀⠀⠀⠀⠀⣀⣀⠣⣀⣀⣀⣀⣀⣴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠞
⠀⠀⠀⠙⢧⣄⣉⠀⠀⣀⣠⠴⢿⣠⣾⠀⠀⠀⠀⠀⢀⣀⣴⡟⠁⢱⡀⢻⣿⣿⣿⢸⢧⠀⠀⡴⣪⣽⣿⣿⡍⠀⠀⠈⠉⠉⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿
⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠀⠀⠈⠁⠘⣇⠀⠀⠀⠀⢀⣸⣿⠁⠀⠀⠳⣄⠉⠛⢁⡼⠀⢨⢦⠏⠸⣿⣿⡿⣋⠀⠀⠀⠀⢀⣠⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠸⠿⣷⣄⣀⣀⠈⠉⠉⠁⣀⡤⠟⠈⠀⠀⠀⣠⠾⢋⣛⣿⠿⠿⠽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡶⠶⠾⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⢀⠄⠀⠀⠀⠀⠀⠉⠉⠉⠒⠋⠁⢴⣦⣤⣴⠶⡿⠗⠞⠛⠛⠁⠀⠈⣿⣿⠃⠀⠀⠀⠀⠀⠀⣠⣴⠿⠿⢿⡅⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣖⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠁⠀⠀⠀⢸⡄⠀⠀⠀ ⣸⠋⠀⠀⠀⠀⠀⢀⡾⠟⠁⠀⠀⠀⠙⣦⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢢⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣄⣀⠀⠀⠈⠁⠀⢀⣴⠏⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠋⢙⠒⠤⣄⠠⣤⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠛⠋⠁⠀⠀⣀⣴⣾⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣾⠯⠒⠉⠀⠀⠀⠀⠐⠠⣙⢮⣵⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠖⠉⠁⣸⣿⡇⠀⠀⢀⠍⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀
⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣳⡌⠙⠒⣶⠁⣀⣠⣤⣤⣤⣤⡤⠤⠤⠤⣤⠴⢶⣶⡶⠒⠛⠛⠉⠁⣠⣾⣿⣿⠃⠀⠒⢫⠀⢸⠀⠀⠀⠀⢿⠀⠀
⠀⠀⣾⣿⠀⣀⠄⠆⠀⠀⠀⠤⢄⡀⠀⠀⠀⢹⡇⠀⠀⠷⠞⠋⠉⣿⠿⠟⠋⠁⠀⠀⠀⠘⣿⣿⣶⣤⣤⣤⣶⣶⣿⣿⣿⡿⠋⠀⠈⠻⡏⠀⠺⣆⠀⠀⠀⢸⡄⠀