⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣇⠀⠀⢸⢠⡤⠒⢉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠉⠛⢾⣮⠑⠢⠐⣋⡀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀
⠀⠀⠀⠀⠀⡠⢊⣴⡾⢆⠀⠀⠈⣿⠷⢤⡀⣔⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀
⠀⠀⣠⣶⡎⢠⣿⣿⣄⣀⣵⡦⣤⡿⠉⠉⠛⠓⠾⣗⠒⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀
⠀⢰⣿⣿⠁⣾⣧⣄⠙⢿⡟⠀⠘⣿⣄⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠉⢑⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀
⠀⢸⣿⣿⠀⡟⠙⣿⣷⠀⢻⢶⡔⠉⢿⣟⠒⢄⢀⠔⢉⡭⣭⣷⡀⡔⢁⠴⣶⣯⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀
⠀⢸⣿⣿⡀⢣⠀⢸⣿⡇⠘⠃⡇⡠⠃⠉⠢⡀⠙⢦⣿⣿⣿⣿⠏⢳⠿⠿⠿⣋⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀ ⠀
⠀⢸⣿⣿⣇⠘⣴⣿⣿⣷⡀⢀⠇⠑⢄⡀⠀⠈⡗⢄⠀⠀⠣⡤⠒⠁⠀⠀⠀⠀⠑⢄⠀⠀⠈⢆⡀⠀⠀⠀ ⠀
⠀⠘⡅⠹⡏⢆⠙⡟⠋⠉⠛⡅⠀⠀⠀⠈⠉⠉⠀⠀⠑⢄⣀⡸⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠈⠑⢄⠀ ⠀
⠀⠀⡇⢠⠃⠈⠢⡈⠢⣀⢀⡇⠀⠀⡠⠤⠤⡀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⡱⠀⠀⠀⠀⠀⠉ ⢆
⢎⣑⠁⠈⠊⠉⡢⠈⠢⢄⣙⠛⠢⠤⠧⢄⣀⣇⣀⡠⠔⣆⠀⠀⠀⠀⢠⠊⠀⠀⠀⢀⠀⢸⠀ ⡜
⡔⢁⢄⢸⡉⠉⠀⠀⠐⠉⠉⠉⠑⠢⠤⢄⣀⣀⣀⣀⣤⠔⠣⣼⣿⣿⣿⡆⠀⠀⠀⠸⡀⠀⡄⠀⠀⢇⢀⠏ ⠀
⠈⠁⠣⠜⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⠇⠈⠙⠃⠀⠀⠀⠀⠈⠉⡇⠀⠀⠈⢣⠀ ⠀
⠀⢴⣦⣰⣿⣿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢇ ⠀
⠀⠈⠻⣿⣿⡟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢀⠬ ⡆
⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢇⣀ ⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠔ ⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣇⠀⠀⢸⢠⡤⠒⢉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠉⠛⢾⣮⠑⠢⠐⣋⡀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠀⠀⠀⠀⠀⡠⢊⣴⡾⢆⠀⠀⠈⣿⠷⢤⡀⣔⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠀⠀⣠⣶⡎⢠⣿⣿⣄⣀⣵⡦⣤⡿⠉⠉⠛⠓⠾⣗⠒⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠀⢰⣿⣿⠁⣾⣧⣄⠙⢿⡟⠀⠘⣿⣄⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠉⢑⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠀⢸⣿⣿⠀⡟⠙⣿⣷⠀⢻⢶⡔⠉⢿⣟⠒⢄⢀⠔⢉⡭⣭⣷⡀⡔⢁⠴⣶⣯⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠀⢸⣿⣿⡀⢣⠀⢸⣿⡇⠘⠃⡇⡠⠃⠉⠢⡀⠙⢦⣿⣿⣿⣿⠏⢳⠿⠿⠿⣋⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀ ⠀ ⠀⢸⣿⣿⣇⠘⣴⣿⣿⣷⡀⢀⠇⠑⢄⡀⠀⠈⡗⢄⠀⠀⠣⡤⠒⠁⠀⠀⠀⠀⠑⢄⠀⠀⠈⢆⡀⠀⠀⠀ ⠀ ⠀⠘⡅⠹⡏⢆⠙⡟⠋⠉⠛⡅⠀⠀⠀⠈⠉⠉⠀⠀⠑⢄⣀⡸⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠈⠑⢄⠀ ⠀ ⠀⠀⡇⢠⠃⠈⠢⡈⠢⣀⢀⡇⠀⠀⡠⠤⠤⡀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⡱⠀⠀⠀⠀⠀⠉ ⢆ ⢎⣑⠁⠈⠊⠉⡢⠈⠢⢄⣙⠛⠢⠤⠧⢄⣀⣇⣀⡠⠔⣆⠀⠀⠀⠀⢠⠊⠀⠀⠀⢀⠀⢸⠀ ⡜ ⡔⢁⢄⢸⡉⠉⠀⠀⠐⠉⠉⠉⠑⠢⠤⢄⣀⣀⣀⣀⣤⠔⠣⣼⣿⣿⣿⡆⠀⠀⠀⠸⡀⠀⡄⠀⠀⢇⢀⠏ ⠀ ⠈⠁⠣⠜⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⠇⠈⠙⠃⠀⠀⠀⠀⠈⠉⡇⠀⠀⠈⢣⠀ ⠀ ⠀⢴⣦⣰⣿⣿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢇ ⠀ ⠀⠈⠻⣿⣿⡟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢀⠬ ⡆ ⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢇⣀ ⢼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠔ ⠁