⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢤⣀⠰⠄⠀⣤⣢⣶⣿⣭⣤⣤⣿⣵⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣺⣵⣮⣿⣿⣿⣿⣮⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⡻⣿⣿⣯⡻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡴⣫⣾⣿⣿⣷⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡟⠿⣿⡻⣿⣻⣿⡿⣿⣯⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠐⣾⣿⣿⣿⣿⣿⣷⡹⣿⡆⠉⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡍⢿⣿⣿⣷⣦⣺⣿⣿⣯⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣷⣶⣬⣝⠏⡛⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⣿⣿⣿⣿⡿⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢹⣿⣿⣿⡏⠀⡴⠛⠛⠿⠛⠛⢢⡄⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠻⣿⣿⠀⠄⡀⠀⢀⣀⣉⣙⠦⣍⠀⠀⠠⠁⠀⢀⣤⣴⣶⣦⣄⠀⢉⡿⢿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⡿⣿⠀⠄⢀⣾⠿⣿⣿⢿⣿⠟⠃⠀⠀⠀⠙⣛⣿⣿⣿⣋⣛⠳⠂⠀⠀⠈⣇⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣇⣿⠀⠀⠀⠀⠟⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠂⠀⠀⠀⠠⢿⡧⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢱⡏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢯⠃⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⡀⠀⠀⡀⠀⣻⣦⡀⠀⠀⠀⢀⡀⠀⢸⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⣴⠟⠁⠲⠟⢯⣿⡾⠟⠋⠁⠈⠻⣆⠀⣠⣠⠀⠀⣾⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠺⠛⠁⣠⠖⠀⢀⣈⣀⣀⣀⡀⠀⣲⡄⠈⠀⠈⠁⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠿⠒⣛⠛⠛⠛⠛⣛⡛⠋⠉⠋⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠈⠹⠿⠶⠛⠋⠀⠀⠀⠀⠀⠀⢀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢳⡈⠙⢦⣄⡀⠤⣦⣤⡤⠶⠶⢾⣛⡯⠋⠀⢠⠞⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠙⠦⣀⠀⠉⠛⣿⣾⢿⣷⠾⠛⠉⠀⣠⠞⠁⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠁⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⢀⣿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣤⡴⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⠍⠳⠦⣤⣀⠀⠀⠀⠀⠀
⢀⣠⣴⣶⣿⣿⣁⣀⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⣿⡿⠋⠉⢷⡄⢠⢀⡉⡝⠳⠦⣄⣀