⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢠⣾⣿⣿⣿⣿⣿⣿⠿⠿⢷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡏⣴⣶⣝⣿⣿⣿⣏⣴⣤⡹⣧⣿⣿⡿⢿⣿⣿⣿⣇⣾⣷⡌⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠃⠻⠿⠟⠿⡿⠿⠛⠿⠿⠁⠹⡟⢸⣿⣿⢿⣿⣿⡇⠛⠛⢁⠀⠀⣀⠀⠀⠀⠀⠀ ⠀⠀⢾⠃⠀⠐⠀⡎⠁⢦⠊⠑⡄⠀⢠⣄⣉⠈⠙⠋⡠⠂⠤⠊⠉⢶⠀⠀⠀⠙⢢⡀⠀⠀⠀ ⠀⠸⡸⠀⠀⢠⡀⠑⠒⠁⠳⠐⢡⢮⠁⠈⠢⣇⠀⠀⢣⣠⠎⠑⠒⠋⠀⠀⠀⠀⠈⠫⣆⠀⠀ ⠀⢀⣴⣄⠀⠈⢎⡆⠀⠀⠀⠀⢈⡮⡢⢄⣀⢱⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃⠀⠱⢣⠀ ⠀⣿⠀⠢⡕⢀⠘⡰⠀⠀⠀⠀⡱⠇⢀⡡⠂⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠦⣀⢫⡆ ⢠⠑⠀⠀⠈⠐⠂⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠒⠒⠃ ⠈⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡼⠀⠀⠀ ⠀⢃⢇⡀⠀⢀⣀⣀⡀⠀⢀⣀⡀⠀⠀⡠⡓⡁⠀⠀⣀⣀⠀⠀⢀⣀⣀⠀⠀⠠⣣⠃⠀⠀⠀ ⡠⠄⠣⠬⠢⣿⣿⣿⣷⠴⣿⣿⣿⡷⠦⠊⠙⠨⢦⣾⣿⣿⣷⢰⣿⣿⣿⡷⠒⠛⢠⣤⠀⠀⠀ ⠀⠈⠉⠁⠈⠑⠓⠒⠓⠒⠚⠛⠓⠒⠒⠒⠒⠒⠂⠒⠛⠛⠓⠒⠓⠈⠐⠀⠈⠉⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠟⠉⠻⣦⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⣄⠀⠀⣀⣀⡀⠀⠀⠀⣿⠀⠀⠀⠈⠛⠃⠀⠉⢿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡅⠀⠹⣦⡾⠉⠉⢻⣧⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢀⡀⠀⣿⠀⢀⠀⠀⣿⠀⠀⠀⢻⣆⠀⠀⢀⣀⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢠⡿⠀⡸⡇⠀⣿⠀⠀⠀⠀⠈⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢸⡇⠸⣇⠀⣷⠃⢸⡟⠐⠀⠀⠀⠀⠀⣨⡶⠷⣦⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠁⠈⠁⠀⠉⢠⣿⠂⠀⠀⠀⠀⢠⡾⠉⠀⠀⣸⣷⠟⠋⠙⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⢠⡟⠉⣴⡇⢠⡿⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣾⠁⢸⡟⢀⣾⠃⣰⡿⠀⣸⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⢀⡀⠀⣴⡄⠀⠀⣤⡄⠀⠀⠀⣀⡽⠞⠃⠀⠈⠐⠸⠃⢰⡿⠁⣰⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣧⠀⠀⢀⡆⠈⠀⠀⠀⠉⠀⠈⣹⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠙⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀ ⣠⡞⠛⠉⠉⠉⠉⢛⡏⠙⠓⠲⠶⠶⠦⠶⠶⢺⣇⠀⠀⠚⠓⠀⢠⣄⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⢻⣄⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠈⢄⠈⢳⡄⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀ ⠀⠙⠓⠦⣤⣀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠓⠲⢦⣄⣀⠀⠈⠉⠉⣀⣤⡾⣧⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠉⠉⠉⠛⠛⠉⠉⠀⠀⠈⠉⠓⠦⣄⡀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀ ⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠐ ⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡟⠁⠀ ⠀⠀⠀⠀⢸⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⢨⡏⠉⠙⠛⠓⢲⡖⠒⠒⢲⡞⠛⠛⠛⠉⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⢿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⢠⣿⠁⠀⠀⠈⢿⡄⠀⠀⠀⣸⠏⠛⠲⠶⢾⡓⠒⠲⠞⠋⢡⣧⡾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠷⢤⠴⠟⠁⠀⠀⠀⠀⠈⠛⢦⣤⡴⠟⠀⠀⠀⠀⠈⠻⢶⣤⣀⣤⠾⠋⠀⠀⠀⠀⠀⠀