⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⢿⠟⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⡜⠿⣶⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠋⠉⠙⣿⠀⢀⣴⣾⡿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⡾⠃⢠⣾⣿⠋⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠙⠛⠻⣿⠛⢛⠁⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⠀⠀⠀⠀⣿⡇⢸⣦⣤⣴⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣶⣶⣾⡿⠁⠘⠻⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣝⠚⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡆⠩⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣀⡤⠤⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣜⣿⠿⣛⣼⣿⣿⠀⠀⠀⣼⣿⣿⣿⢟⠷⢬⣨⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⢉⠻⢷⣾⢿⣿⠀⢴⣾⣿⣿⣿⣷⣥⣾⣿⡿⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⡄⠸⡟⠘⠿⣤⢾⡿⢧⣤⣽⣿⣻⠟⠋⠛⠚⢼⢷⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢧⠀⢇⡆⢠⣺⡋⢀⢸⣭⣏⡟⣿⣽⡆⠈⠂⣨⣟⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠦⣜⣿⣼⣿⡃⢸⣾⣶⣿⣯⣽⣿⠇⠀⣰⣻⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡇⡆⡿⣷⣿⣿⣿⣿⣖⠀⡟⣼⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣽⡇⢸⣿⠇⠀⠈⢿⡄⡿⠈⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢸⣿⠀⠀⠀⢸⢸⡇⠀⠸⣿⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇⢸⣿⠀⠀⠀⠈⣿⡇⠀⠀⢻⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠈⡿⠀⠀⠀⠀⡯⡿⠀⠀⢰⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⡆⠀⠀⢀⣷⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡇⠀⡇⣳⠀⠀⣼⢃⣤⣶⣶⣶⣿⣶⣶⡶⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠯⠼⠶⠞⠒⢛⠿⠯⣿⣿⣿⣿⠿⣿⣿⡿⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀