⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡶⠾⠿⠾⠿⠶⠶⠾⠿⠿⣷⣶⣒⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠻⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠯⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⣀⣤⣤⣴⣶⣤⣴⣶⣶⣦⣶⣦⣄⣀⠀⠀⠀⠀⠐⠶⣤⣉⠻⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⣡⠶⠋⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣄⣀⡉⠳⣬⡻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⡾⠁⣀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠁⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⢠⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⣰⣿⠇⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⡤⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⢀⣠⣾⣿⠃⣷⠀⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⢀⢇⡔⢨⣯⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠀⣀⣠⣴⣾⣿⣿⡟⠁⢀⣿⡀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⣸⡾⠀⠈⡿⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⢶⣶⣿⣿⣿⡿⠿⠿⠛⠉⠀⠀⡞⠉⢇⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀
⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⡇⠀⢀⣤⠤⢤⡈⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠋⢁⣠⠤⠤⡄⠀⠀⠀⡇⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀
⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀⠀⠀⣷⢠⣿⠏⠀⠀⠙⠳⢤⣀⣀⣀⠤⠖⠒⠲⠦⣄⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠘⡆⠀⡼⠁⠀⠀⢸⡳⣄⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀
⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣹⡇⠀⠀⠀⠹⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⣀⢀⣠⠏⠀⠀⠀⠀⠀⠸⣄⡡⠀⠀⠀⠈⡇⠈⢆⠀⠀⠀⠀⠀⠀⠀⢱⡀
⣼⠃⠀⠀⠀⠀⠀⠀⠀⢸⡿⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣿⡀⠘⡇⠀⠀⠀⠀⠀⠀⠀⣇
⢸⠹⠀⠀⠀⠀⠀⠀⠀⡾⠁⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⣸
⠸⡄⠀⠀⠀⠀⠀⠀⠀⠸⡄⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⢰⠇⠀⠀⠀⠀⠀⠀⢀⠟
⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⣠⠏⠀⠀⠀⠀⠀⠀⠀⡜⠀
⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠈⢧⣈⠻⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀
⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⡙⠿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠛⣁⡴⠚⠁⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀
⠀⠀⠀⠀⠀⠱⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⣽⣛⠿⣿⣿⣷⣶⣶⣤⣄⣤⣤⣤⣀⣀⣀⣀⣤⣤⣤⣶⣶⣾⣿⣿⣟⣉⣥⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⣿⣿⣿⣟⣛⣿⣛⣛⣿⣿⣿⣿⡿⡟⠻⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣤⡤⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠦⠤⠤⠤⠠⣤⣀⣀⡀⣀⣠⡤⠄⠰⠶⠶⠤⠞⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀