⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢠⡟⠀⠀⠀⠀⢠⡄⢠⡄⠀⠀⠀⠀⢻⠄⠀⠀⣷⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀ ⠀⠀⠀⡆⠀⠀⠀⠀⠀⢠⣏⠀⠀⠈⣷⠀⠀⠀⠀⣼⠃⠘⣧⠀⠀⠀⠀⣿⠀⠀⠀⣼⠂⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀ ⠀⠀⢧⡀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠘⢧⣀⠀⢀⢹⣤⣤⣟⣀⠀⣠⠾⠋⠀⠀⡼⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀ ⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠹⣧⣀⣀⡀⠉⣷⣿⣿⣿⣿⣿⣿⣿⣁⣠⣤⡶⠾⠃⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀ ⠀⠀⠀⠀⠈⢧⣤⣄⣀⠀⠀⠀⠈⠉⢉⣉⣛⣿⣿⣿⣿⣿⣿⣿⣿⠯⠥⣤⣤⣄⣀⣀⣤⣶⠞⠛⠉⠀⠀⠀⠀⠈⢆⠀⠀⠀
⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⠶⠚⠋⠉⠁⢀⣤⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠉⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀
⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡷⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀
⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠋⠁⢰⣿⣿⣿⣿⣿⢟⠀⣿⣿⣿⣿⣿⣿⣇⠀⠈⠙⠻⣶⣤⣤⣤⣤⣤⣤⣄⣼⠁⠀⠀⠀
⠀⠀⠀⠸⣧⡤⠶⠒⠒⠚⠻⠟⠋⠀⠀⢀⡠⢿⣿⣿⣿⣿ ⠾⠀⠟⣿⣿⣿⣿⣿⡟⠳⢤⣄⣀⠀⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀
⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠚⠉⠀⠘⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⡿⣧⠀⠀⠈⠉⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢀⣴⠞⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠘⠳⣤⡀⠀⠀⠈⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⢰⣿⠁⠀⠀⠀⠈⠙⠛⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠙⠿⣦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⠄⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⠀⠀⠀⠀⠀⠀⠠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀