⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣀⡀⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣴⣿⣿⠿⣫⣥⣄⠄⠄⠄⠄⠄⠄⠄⠄⠄
⠄⠄⠄⠄⠄⠄⠄⠄⠄⢀⠄⠄⠄⠾⢿⢟⣵⣾⣿⡿⠃⠄⠄⠄⠄⠄⠄⠄⠄⠄
⠄⠄⠄⠄⠄⠄⠄⠄⣰⡿⣀⣤⣴⣾⣿⡇⠙⠛⠁⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄
⠄⠄⠄⠄⠄⠄⣠⣾⣿⣿⣿⣿⣿⣿⣿⠁⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄
⠄⠄⠄⠄⠄⣴⣿⣿⠿⠛⠉⢩⣿⣿⡇⠄⠄⠄⠄⠄⠄⠄⠄⣀⣀⡀⠄⠄⠄⠄
⠄⠄⠄⠄⠈⠛⠉⠄⠄⠄⠄⢸⣿⣿⡇⠄⠄⠄⠄⠄⠄⢀⣼⡿⣫⣾⠆⠄⠄⠄
⠄⠄⠄⠄⢀⣶⣶⣶⣶⣶⣶⣿⣿⣿⠇⠄⠄⠄⣠⣎⣠⣴⣶⠎⠛⠁⠄⠄⠄⠄
⠄⠄⠄⠄⣾⣿⣿⣿⣿⠿⠿⠟⠛⠋⠄⠄⢀⣼⣿⠿⠛⣿⡟⠄⠄⠄⠄⠄⠄⠄
⠄⠄⠄⠄⠛⠉⠉⠄⠄⠄⠄⠄⠄⠄⠄⠄⠘⠉⠄⠄⢸⣿⡇⠄⠄⠄⠄⠄⠄⠄
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣼⣿⣿⣿⡿⠿⠃⠄⠄⠄⠄⠄⠄⠄
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠋⠉⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⢿⣿⣦⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣦⣍⠐⢼⣿⣿⣧⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣄⣿⣿⣿⣦⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣄⣒⣚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⡽⣿⠟⢃⣿⠟⡉⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢯⣭⣿⢹⡟⢶⣗⠀⢸⠇⢁⣠⠫⠟⣹⣿⣯⡭⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣄⠣⠁⠈⠓⠊⠐⠃⠀⠀⣰⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣽⠀⠀⠀⠀⠀⠀⠀⣿⣯⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣀⡀⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⣀⣀⣿⡿⠃⢢⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⡿⣷⡿⠿⣿⢿⡿⠩⢹⣿⡟⠉⠉⠉⢹⣿⢻⠛⠛⠻⢿⣿⣷⣿⣿⠉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢶⣿⣦⣿⣷⡇⢁⠚⡇⠐⢀⣿⣷⣤⣤⣤⣿⣧⣀⣠⣇⡰⢀⡿⣿⣿⣷⣾⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣵⡎⠹⣿⣿⣿⣁⣾⢻⣿⢻⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣾⣿⡿⠛⠛⢛⡟⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣞⣰⠞⣩⣿⣻⡇⢠⠃⠸⠉⠙⣿⣿⣿⣿⢈⡁⠤⠁⠌⢉⢙⣿⣐⣧⣤⣾⢇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢿⢋⡍⢇⠛⣿⣧⣼⣦⣴⣔⣠⣿⣿⣿⣯⣦⣤⣦⣤⣦⣄⣸⡻⢛⠋⠉⠻⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⣆⣷⣴⣶⠿⣿⡿⣿⢿⣿⣿⣿⣿⣿⢿⡿⢿⣿⢉⠉⣿⣿⣷⣾⣤⣭⡁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣾⣿⣿⣿⣿⠐⣉⣌⠇⠐⠁⡄⣿⣿⣿⠈⡠⢾⡇⠠⠠⣼⣽⡟⢣⠄⣹⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣉⠁⣿⣷⣿⡟⢿⡵⣾⣶⣦⣿⣿⣿⣴⣷⣾⣷⠖⡴⠿⣿⣿⠷⠚⢛⡻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⣿⣿⣿⣧⠐⡅⢘⠃⣿⣿⣿⣟⠿⡿⣿⣧⣈⠴⢃⠘⣻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⣿⠃⢸⣿⣶⣿⡿⡟⢉⣿⢿⣻⣼⣧⠂⠛⢿⣷⣟⣀⣥⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⡙⣿⣾⣿⣿⠿⢄⠉⣸⡿⠁⠉⠉⠟⢬⢛⢚⠻⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⣅⣙⣿⣧⣮⣬⣽⡟⠀⠀⠀⠀⢶⣶⣮⢧⢠⠙⣰⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣈⣽⣶⣿⣿⣷⣼⠟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢥⣏⢿⢯⣿⡟⠀⣿⣿⣿⣶⣄⣠⢈⠲⠟⣛⠏⣍⣏⠬⣄⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣃⣧⣿⣿⣿⣿⣿⣧⣒⣴⣦⣾⣶⣾⣶⣿⡇⠀⠀⠀