⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣯⠫⠀⠀⣴⠿⢽⣷⣦⣄⠀⠀⠀⠐⠚⠛⢧⣿⣷⠀⠀⠀⠀
⠀⠀⠀⣐⣴⣯⣿⡿⠁⠀⠘⠁⠀⠀⠙⣷⢸⡷⣄⠀⠀⠀⠀⠀⣿⠸⣧⠀⠀⠀
⠀⠀⣴⣿⡀⣯⣿⠃⠀⠀⠀⠀⠀⠀⢰⣧⢿⡇⣧⣻⡀⠀⠀⢀⡟⣀⣿⣆⠀⠀
⠀⣼⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⣠⡏⡟⣾⡇⠃⢻⡇⠀⣰⣿⣿⣙⡚⢽⣆⠀
⣰⢟⣽⣿⣼⣹⣿⣿⣿⣦⣀⣀⣴⡃⣇⡗⣿⣷⣷⢽⣷⡿⡟⣿⣿⣟⣜⣾⣾⡂
⠘⣯⣟⣟⣻⣿⠼⠿⠿⣾⣿⣿⣾⣧⣿⠳⣡⡟⣸⣻⣿⣿⣷⣻⣿⣿⣿⣿⡟⠀
⠀⢹⣿⡿⣿⣟⣽⡄⠀⠀⠀⠉⠉⠛⠛⠾⠟⠛⠛⠉⠉⠉⠉⠁⣜⣽⢯⡟⠀⠀
⠀⠀⠋⢿⣿⣯⣾⣻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣮⣯⡟⠀⠀⠀
⠀⠀⠀⢈⣿⣞⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⡯⣳⣄⠀⠀
⠀⠀⠀⠈⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⢹⣿⣼⣟⠝⠀⠀
⠀⠀⠀⠀⠀⡿⢿⣿⠀⠚⢛⠳⠶⣶⡷⠂⠀⠸⢾⣿⠓⠛⠂⣾⡿⡟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⣇⠀⠹⡄⠀⠇⠀⠘⣿⡇⠀⢀⠈⣻⡿⠀⢀⠃⡏⠀⡧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠹⣂⡀⢇⠀⠈⠂⠴⠎⠀⠀⢸⠀⠈⠒⠔⠀⣸⣁⣼⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠺⠛⢻⡄⠀⠀⠀⠀⠀⠘⢼⠀⠀⠀⠀⢠⡏⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠤⠐⠚⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣿⢦⣄⠀⣠⣾⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡃⢀⡇⢳⠏⠙⡿⣸⡆⡘⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣦⣸⣿⡀⡆⣧⠁⣿⣇⣴⠜⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣾⡈⡇⡇⣿⡀⣟⡇⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡷⡌⠻⢷⣿⣿⡿⠟⢡⢾⣷⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⠖⠁⠀⢸⡇⢸⡇⠀⠐⠊⠍⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠇⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀