⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠛⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠛⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡄⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣧⠀⢀⣄⡀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣧⠀⢀⡀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⡀⠘⡏⠛⢦⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣇⢸⡏⠳⣄⠀⢺⡿⣦⡀⣀⣤⡶⠾⠛⠛⠻⡄⠙⠀⣸⡄⠈⠳⡄⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡄⢳⡀⢈⣷⠀⠻⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠉⠳⢤⣻⡀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣧⠀⣷⠟⠁⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢺⣯⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⡏⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀ ⠀⠀⠀⣸⡇⠀⢺⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⢀⣠⣿⢿⡁⠀⠀⢻⣶⣤⣄⣀⣤⣴⡿⠂⠀⠀⠀⠀⠀⠀⢴⣦⣀⠀⠀⠀⢀⣠⣴⡛⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⢸⣍⠙⠓⠉⠀⠀⣸⡆⠈⠉⠉⣻⡄⠀⠀⠀⣶⠦⣤⣄⠀⠀⠉⠙⣿⠛⠛⠉⠁⣠⡇⠀⠀⠀⠀⣤⣿⣧⠀⠀⠀⠀ ⠀⠙⢷⣦⡀⠀⢹⡇⠀⠀⠀⣰⠿⠁⠀⠀⠀⠛⢶⠛⠁⠀⠀⠀⠰⣟⡀⠀⠀⠰⣇⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀ ⠀⠀⠀⠘⢧⣀⡞⠋⠀⠀⠰⡇⠀⠀⠀⠀⠀⣴⠿⠦⠀⠀⠀⠀⠀⣸⠇⠀⠀⢀⡿⠃⠀⠀⢀⣀⣀⣼⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢧⣀⠠⢤⡾⠛⠀⠀⠀⠀⠀⠀⠀⠀⡞⠛⠳⢦⡈⣧⠀⠀⠀⠘⢦⡀⠀⣠⡾⠛⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⢾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠹⣎⣆⠀⢀⣢⣼⡷⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡿⠶⠦⣤⡀⠀⠀⠀⢹⣄⠀⠀⠀⠈⢻⡿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⢀⡆⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠹⣮⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣶⠿⢷⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣀⣤⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣤⣤⡾⠋⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⢀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⠖⠛⠋⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⣠⡾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣰⠾⠁⠀⣀⣤⠾⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡦⠶⠾⣛⣁⣤⠶⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣤⣤⣤⡤⠤⠤⠤⣤⣤⣄⣀⠀⢾⡶⠶⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡾⠻⢶⠶⣤⣄⠀⠀⠀⢀⣀⣀⡀⠀⠀⣀⣀⣀⣤⣤⣤⠤⠤⣤⣤⣤⠄⠀ ⠀⠀⡇⠀⠀⠉⠢⣈⠛⠛⠛⠉⠉⠉⠉⠛⠋⠉⠉⠀⠀⢀⠠⠔⠊⢉⡼⠋⠀⠀ ⠀⠀⣇⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⣠⠟⠁⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀ ⠀⢀⡟⠢⢀⡀⠀⠀⣀⠠⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⢀⡇⠀⠀⠀⠀⠀ ⠀⡾⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠞⠁⠀⠀⠀⠀⠀ ⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⣾⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⠀⠀⠀⠀⠈⢫⠋⣿⡖⢦⠀⠀⠀⢀⡴⣿⢙⡏⢉⡏⠀⠀⠀⠀⠀⠀⠀ ⠘⢷⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠓⢣⠀⠀⡞⠓⠚⠊⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⠇⠀⢀⠔⠁⠀⠀⠀⠙⢦⡀⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⣗⡜⠀⡠⠃⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠈⠐⠤⢀⣀⣉⣉⠦⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢹⡄ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢷ ⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸ ⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢸ ⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢠ ⠀⠀⠀⢻⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸ ⠀⠀⠀⠘⣧⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⢹⡀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢠⡏ ⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢱⡦⣤⣀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣾⠁ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣀⡆⠀⠀⠀⠀⢀⡟⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⣧⣀⣾⣤⡤⠞⠁⠀⠀⠀⠀⠙⣦⣄⣰⣧⣬⣿⠟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠒⠀⠈⠓⠠⠐⠢⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠠⠤⠀⠀⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠤⠒⠒⠒⠠⣀⠀ ⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣ ⣔⠀⠤⠄⣀⣀⠀⠀⠀⠀⠀⠀⣠⡂⠀⠀⠀⠲⣄⣀⠀⠀⠀⠀⢀⡤⠒⠈⠀ ⠀⠀⠀⠀⠀⠌⠀⠀⠀⢠⠖⣁⡀⠈⠀⠀⠀⡌⢠⣄⠑⡄⠀⠀⠉⠂⠀⠀⠀ ⠀⠀⠀⠀⡜⠀⠀⠀⢠⠃⢸⣿⣽⠀⠀⠀⠀⠇⢿⣷⠇⠘⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠉⢉⡔⠀⠀⠀⠈⢆⠁⠀⢀⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠑⠒⠉⠀⢀⡴⣀⠀⠀⠉⠐⠁⠀⠀⠀⡀⠀⠀⠀ ⠒⠒⠒⠂⠘⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠒⠀⠠⠤⠃⠤⠠⠄ ⠀⠀⠀⠀⠀⢘⣤⠌⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠁⠒⠤⡴⢁⣀⠀⠀⠀ ⠀⠀⠒⠂⠈⠀⠀⠱⡴⠉⠑⠉⡵⠂⠀⠀⠀⡔⢲⠒⠖⠒⠊⠀⠀⠀⠉⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠣⠴⢇⡠⠅⠘⠉⠉⠁⢄⣀⣠⣀⠄⠀⠀⠀⠀⠀⠀⠀
⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀ ⣿⠈⠉⠛⠒⠲⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠚⠋⠉⠀⣷ ⢻⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣲⣤⣤⠴⠶⠶⠶⠶⠤⢤⣄⣀⡀⠀⠀⣀⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⣿ ⢸⡀⠀⠀⠀⠀⠀⢀⣠⣶⣻⡿⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠾⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏ ⢸⡇⠀⠀⠀⠀⠀⠟⠁⢿⣯⢴⡟⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁ ⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣼⣧⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀ ⠀⠸⣧⠀⠐⡖⠀⠀⠀⠀⠀⠻⠞⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡼⠃⠀⠀ ⠀⠀⠘⢧⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢠⡾⠁⠀⠀⠀ ⠀⠀⠀⣼⢃⣾⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⢀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡴⠋⠀⠀⠀⠀⠀ ⠀⠀⠺⠛⡿⣧⣤⣤⣶⣿⡿⢿⣶⣸⣿⣶⡇⢸⣆⡿⢶⣭⣓⡦⢤⣀⣀⠀⠀⠀⠀⠙⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⢁⣿⢿⠛⠉⠁⠀⢸⣿⣿⣿⣿⣿⣾⣿⠁⠀⠀⠉⠛⠿⢶⣮⣭⣽⠀⠀⠰⣿⠧⠀⠀⠀⠀⠀ ⠀⠀⣸⠃⣹⡇⢸⡀⠀⠀⠀⣸⣿⢿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⣷⠀⣿⡄⠀⠀⢻⡄⠀⠀⠀⠀⠀ ⠀⢰⡏⠀⠈⣧⠈⣷⡀⠀⣠⣿⢿⠸⠿⠿⠿⠿⣿⡄⠀⠀⠀⠀⠀⢰⡇⠀⡿⠧⠀⠀⢸⣇⠀⠀⠀⠀⠀ ⠀⠘⢧⡀⠀⠙⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⡀⢀⣀⣴⢏⡤⢾⡇⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠆⠀⠀⠀⠀⠈⠉⠉⠉⠁⠈⢳⡞⠁⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⣠⣤⣾⣧⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⣀⣀⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠓⠒⠲⠶⠶⠒⠒⠒⠚⠋⠉⢉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠛⡓⠒⠒⠲⠶⠶⠶⠶⠶⠒⠒⠺⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣹⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⡴⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⠲⢄⡀⠀⠀⠀⠀⠀⡏⠒⠤⡀⠀⠀⠀⠀⠀⠀ ⠀⠘⡄⣀⠙⣦⠀⠀⣀⣰⡣⢸⠢⡈⠢⡀⠀⠀⠀⠀ ⠀⠀⠸⡰⡰⠈⠉⠉⠀⠀⠀⠈⠑⠰⡀⠘⡄⠀⠀⠀ ⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀ ⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀ ⢀⣾⡀⢳⢤⣀⠤⠀⠀⠀⢠⣀⣀⡀⠔⠀⠀⣸⠀⠀ ⠘⢦⡀⡎⠀⡼⠁⠀⢻⠃⠀⠸⡄⠀⡅⠀⠈⢽⠀⠀ ⠀⠀⠙⠤⣰⠃⠀⠀⠁⡖⠒⢼⡀⠐⣄⠤⠋⠁⠀⠀ ⠀⠀⠀⠀⢀⡝⠒⡆⠀⠘⡄⠀⠻⣫⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠊⣀⡼⠀⠀⠀⠈⠢⢀⡠⠃⠀⠀⡰⠊⢱ ⠀⠀⠀⠀⠉⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⡠⠊⣠⠔⠁ ⠀⠀⠀⠀⠀⢸⠀⢤⠤⠤⠤⢤⠄⡯⠓⠋⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡠⠇⠀⠀⠀⠈⢆⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⢀⡟⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠁⢻⣄⠀⠀⠀⣸⠃⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡟⠀⠀⠙⢻⢷⠶⣋⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠁⠀⠀⠐⠁⣰⠀⣄⠑⠆⠀⠈⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣲⠖⠀⣠⣎⡟⠀⢧⣱⠤⣄⠫⠤⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⠀⠙⣳⡟⠐⢶⠆⠉⣭⣁⣀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣦⢒⠕⡟⠀⢀⠞⠦⡀⠑⠌⠒⢠⣽⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠉⡠⠘⢳⣮⣀⣀⠀⠀⠀⣀⣀⣠⣷⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⡠⠐⠁⠀⣸⠏⠉⠉⠉⠉⠀⠀⠀⠈⠳⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠉⠙⠳⢦⡀⠀ ⠀⠀⠀⣀⡽⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⣠⡼⠷⣄⠀⠀⠀⠹⡆ ⠀⠀⡾⠁⠀⢀⡏⠉⠉⠉⠛⡿⠀⠀⢸⣏⣹⢿⡏⠉⠉⣹⠃⠀⠘⢷⠀⠀⠀⢹ ⠀⠀⠛⠦⠴⠋⠀⠀⠀⠀⠘⣧⣀⣀⡼⠉⠁⠈⠛⠒⠚⠁⠀⠀⠀⢸⡇⠀⠀⡼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠀⠀⢰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠖⠚⠋⠁⠀⠀⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⢀⣀⣠⡴⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠂⠐⠐⠐⠀⠒⠒⠐⠒⠀⠀⠀⠘⠙⠓⠛⠓⠛⠓⠙⠀⠀⠀⠀
⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣴⣶⣄⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠇⠈⣾⡜⣿⡌⣇⢰⡇⢠⣷⣄⡄⢀⣤⣄⣏⠀⠀⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣻⣿⣿⣿⣿⠿⣝⢏⠋⣿⡄⣶⣿⣿⣻⣧⣿⣿⣧⣾⣿⣿⣿⣿⣿⣯⣿⢸⣿⡏⢭⢇⣽⢿⣿⣿⣿⣿⡥⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡝⠻⢿⠿⡝⢳⣄⣸⢦⢿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⡟⣿⣯⠀⣩⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣽⣿⢶⣶⡊⣀⢻⡿⣿⣿⣿⣿⣻⣿⣿⢻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⢾⡵⢋⠰⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠜⠉⠉⣻⡿⢫⣻⣷⣿⣿⢿⣿⡿⣿⣿⣿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣿⡟⢸⣧⣿⢟⣵⣿⠾⢏⣀⣀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡾⣣⣴⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡏⣸⣿⣿⣿⣿⣿⣿⣯⣿⡿⠿⠿⡭⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡿⣽⣻⣷⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣠⠽⣋⣿⣿⣿⣿⣿⣿⣿⣶⣿⢿⣾⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣽⡏⠛⢻⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⠗⠛⣺⣿⣿⣿⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣧⠙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⡙⠋⢀⣠⣿⣿⣿⣿⣿⡇⠀⠀⠀⢼⣿⣿⣿⣯⠀⠘⢿⠆⢀⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣙⢿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣯⣟⣯⣽⣿⣿⣿⣿⠟⠂⠀⠀⠀⠀⠛⣿⣿⣾⣷⣶⡶⣶⣿⣷⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⡿⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣇⡈⠙⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠛⠉⠑⠲⣤⣄⠀⣀⣤⣴⠆⠈⠻⣿⣿⣿⣿⣿⣿⣏⣻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⢽⣓⠶⣬⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⡉⠁⠁⠀⠀⠀⠀⠀⠘⢳⠞⠃⠀⠀⠀⠀⠈⠻⢯⡛⠛⠛⠛⠋⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⠃⠀⠈⠩⣓⣶⠾⢿⣿⣏⣭⣭⣭⣿⠟⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠓⢦⣄⠀⠀⠀⠀⠀⠐⣟⣿⡯⠭⣝⣛⡿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣼⡿⠛⢋⣽⣿⠟⠀⠀⠀⢀⡤⠖⠋⠀⠀⠀⠀⠀⠈⢷⡄⠀⢀⠀⠸⢦⣀⢉⡙⠛⡦⠟⠁⠀⠀⢄⡀⠀⠀⠀⠀⠀ ⠀⠃⠀⠂⠀⠀⠀⠀⢀⠉⠠⠤⠞⠉⠋⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⢈⢧⠳⣳⣌⠙⠻⠟⠃⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠸⠷⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠈⢑⣆⠀⠀ ⠀⠀⠀⠀⠀⣠⡶⠀⠀⢠⠎⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡈⠳⣦⠀⠙⠷⣄ ⠀⠀⠀⣠⡾⠁⠀⢀⡴⠋⠀⡴⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢢⡀⠙⠲⣌⠲⣌⡳⡾⢿⣄ ⠀⠀⠀⠀⠀⠀⣠⢏⠀⠀⡴⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⠉⠲⣄⠙⢦⡀⢘⣧⡙⣷⡀⠑⠌ ⠀⠀⠀⠀⠀⠚⣡⣁⣀⣾⡁⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⢄⡀⠈⠑⢦⣜⣿⣌⣻⡾⢽⣻⣎⣗⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣧⣤⡄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣶⣦⣧⡙⢯⡉⢳⣬⣿⡟⠙⠃⠀ ⠀⠀⠀⠀⢸⠽⢿⣿⣿⣿⣾⣿⣡⣴⣤⣄⠀⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢮⡻⣶⣽⣾⣿⡉⠁⠀⠀⠀ ⠀⠀⠀⢀⣤⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣋⣀⡤⠀⢰⠀⣀⣦⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡟⠉⠀⠀⠀⠀⠀ ⠀⢀⣠⠚⠀⠀⠀⠀⠀⣀⡀⠉⠛⠿⡿⢿⣥⣀⡀⣻⡞⠋⠠⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣦⡀⠀⢠⣤⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⡜⣦⡄⢸⣮⣿⡿⠋⠀⠀⠀⠀⠤⣄⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣼⣿⣿⡿⠷⠤⣤⣤⣄⣠⣄⣀⣀⣀⠀⠀⠀ ⡏⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢁⣨⠷⠛⠋⠉⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢧⡀⠀⠀⠀⠀⠀⠙⣣⣠⡴⠖⠉⠀⠀⠀⠀⠀⠈⡆⠚⠁⠀⠀⠀⠀⠀⠀⠀⣾⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣤⠆⠀⣠⡼⠀⠀⠀⣿⡴⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠛⠓⠒⠛⠋⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠶⠒⠒⠛⠋⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠓⠒⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠛⢻⣴⠖⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⡥⠒⠚⣻⣤⠄⣶⣒⣿⣆⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡏⠀⠐⠒⣿⠏⢠⣼⣟⢙⣯⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣀⠀⠉⠉⠓⠲⠒⠛⠉⠙⠿⣿⣟⣻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀ ⣸⣹⡟⠙⣿⣲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠒⠒⠲⠖⠚⢓⣶⣾⣿⠟⠃⠀⡟⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀ ⣿⣿⡀⠀⠉⠙⠛⢿⣿⣷⣦⣤⣀⣀⠀⣀⣀⣀⣀⣀⣀⠀⣠⠀⣠⣾⣿⡿⠛⠁⠀⠀⢰⣷⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀ ⣧⢹⡁⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⡍⠉⠁⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⡟⠐⠀⠀⠀⠀⠈⣿⣿⡗⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀ ⣿⣿⣷⡄⠀⠀⢀⣤⣶⣷⣶⣶⣾⣥⣄⡀⢠⠀⠀⢀⣤⠀⣀⣹⣿⣿⣦⣤⠀⡀⣠⣤⣀⣿⣿⡧⠬⠷⢄⡀⠀⠀⠀⠀⠀⠀⠘⡄⠀ ⠸⣯⣿⣷⣄⢲⣾⣿⣯⣭⣉⣉⣹⣿⣿⣷⣼⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⠿⣶⣿⣿⣼⣿⣿⡿⠀⠀⠀⠀⠈⠑⠢⣄⠀⠀⠀⠀⠙⠀ ⠀⠙⣿⣟⣙⣿⣿⣇⠀⠈⠻⠿⠿⢋⣽⣿⠟⢠⣬⣿⣿⣯⡀⠈⠻⠿⠃⠀⣸⣿⣿⣿⡿⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⣫ ⠀⣴⠉⢴⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⡟⠁⠀⠈⣿⣁⠉⠻⢿⣷⠶⠶⠶⣾⣿⣿⣿⡍⡁⠈⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠉⠀ ⠰⡟⠀⠙⠿⣿⣝⣿⣿⣿⣿⣿⠋⠁⠀⠀⡴⠋⠀⠈⢦⠀⠀⠙⣿⣀⣩⡿⠿⢯⠏⠙⠁⠀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡆⠀ ⠀⠳⣦⠀⠀⠈⠉⠉⢩⣿⣿⣏⠀⠀⠀⢰⣇⠀⠀⠀⢨⡆⠀⠀⢸⡏⠉⠉⠉⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⡷⢦⡀⠀⠀⠀⠙⢻⣿⣦⣀⠀⠀⢷⣔⡤⢄⣸⡇⢠⣤⡾⠟⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀ ⠀⠀⣾⠃⠀⠈⠓⠤⣀⠀⠀⠀⠉⠉⠁⠀⠀⠉⠛⠛⠋⠀⠀⠀⠠⠒⠋⠀⢀⡠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠀⠀⠀⡇⠀ ⠀⠐⣿⡂⠀⠀⠀⠀⠀⠉⠙⠒⠒⠢⠤⠤⠤⠠⠤⠤⠤⠤⠄⠒⠒⠒⠊⠉⠁⠨⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⡇⠀ ⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡿⠀⢠⠃⠀ ⠀⠀⢹⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⡜⠀⠀ ⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢻⠃⠀⢸⠁⠀⠀ ⠀⠀⠀⠀⠻⠗⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠟⠀⠀⠀⠀⣠⠎⠀⠀⢀⣰⣿⠇⠀⠀⢀⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⣼⠏⠀⢀⣞⡿⠛⠁⠀⠀⠀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡟⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⡯⠀⠀⠀⠀⠀⢸⣿⠀⠀⣼⠉⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⠛⠲⠦⣤⡴⠦⣄⡀⠀⣀⡴⠟⠛⠉⠁⠀⠀⠀⠀⠀⣠⣿⡏⣢⣼⢿⣄⡀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⠀⠀⠀⠀⠀⠉⢱⡏⠉⠙⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠁⠀⠀⢹⡏⠀⠀⠀⡰⠀⣸⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⢀⠼⠃⠀⠤⠚⠁⡰⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⣿⣦⣤⣤⣤⠀⢰⡾⠁⠀⠀⠀⢸⡀⢰⠀⢀⣀⡀⣀⣴⣿⡏⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠉⠉⠋⣳⠎⠀⠀⠀⠀⠀⢸⣿⡾⡿⠿⠿⠿⠿⣿⣿⠀⠀⠀⠀⠈⠳⢄⣀⡀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠓⠤⣄⣀⣀⣀⡠⠞⠁⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢤⣀⡀⠀⢀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠒⠒⠚⠹⣄⣀⣀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠒⠒⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠒⠒⠚⠛⠓⠒⠒⠤⣀⠀⠀ ⠀⠀⠀⠀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄ ⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠼ ⠀⢀⡜⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠊⠉⠀⠀ ⠀⠈⠉⠉⠀⠀⠀⠀⠉⠉⢘⠇⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠙⢲⡀⠀⠀⠀⠀⢠⠎⠉⠉⠑⢦⡀⠀⠀⠀⠀⠀⢾⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢠⠞⢀⣠⣤⣄⠀⠀⣷⠀⠀⠀⠀⡼⠀⣰⣶⣦⡄⠙⣆⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢠⠏⠀⣾⣿⣯⣽⡆⠀⡏⠀⠀⠀⠀⣇⠀⣿⣿⣾⣷⠀⠘⡆⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⢯⠀⠀⠹⣿⣿⡿⠃⡸⠁⠀⠀⠀⠀⠸⡄⠙⠿⠿⠃⠀⠀⢻⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⠴⠊⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠙⠲⠤⠴⠊⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠯⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠉⠉⠁⠒⠉⠉⠹⡍⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠦⣴⠗⠒⠤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠽⢤⠀⠀⠀⠀⠀⠀⠲⠄⣀⡀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠼⢶⡋⠀⠀⠀⢀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣲⠞⠓⠲⠶⢄⡀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠖⠊⠑⠋⠀⠀⠀⠙⢦⣀⡴⠋⠉⡟⠉⠉⡷⠚⢳⠀⠀⠀⠀⠀⣠⠖⢲⠖⠒⣤⠖⢢⠞⠁⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣰⠃⠀⣰⠃⠀⣸⠒⠒⠢⠤⢤⡇⠀⡎⠀⣸⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠖⠙⠤⠴⠛⠦⠴⠃⠀⠀⠀⠀⠀⠣⣤⣧⣠⣧⣀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡖⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣧⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⣄⣿⠀⢠⣄⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣆⢠⢤⡀⠈⣳⣄⠀⠀⢀⣀⣤⡿⡝⠧⠘⡌⠱⣄⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡄⢆⠘⣦⠘⠏⠓⠊⠉⠁⠀⠀⠁⡀⠀⠛⠢⣜⣆⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⣸⠞⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀ ⠀⠀⠀⢰⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀ ⠀⠀⣤⡿⠀⠸⣆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⢸⠀⠀⠀⠀ ⠠⡾⠿⠗⠀⠀⣹⠛⠓⠺⣟⠉⠀⢀⣄⣀⡀⠈⠛⢶⡦⠴⠒⠋⡧⠀⠀⠀⣀⣾⡀⠀⠀⠀ ⠀⠙⠶⣄⠀⢸⡁⠀⠀⣶⠏⠀⠀⠘⢳⠛⠁⠀⠀⠸⣇⠀⠀⢾⡀⠀⠀⠀⢀⣼⠃⠀⠀⠀ ⠀⠀⠀⠙⢦⡏⠁⠀⣸⣇⠀⠀⠀⠀⠛⠃⣤⣄⡀⢠⠏⠀⠀⣼⠃⠀⠀⣠⡴⠞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠶⣽⡏⠀⠀⠀⠀⠀⠀⠸⡇⠀⠙⢮⣦⠀⠀⣈⣧⡴⠚⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⠶⠤⣄⠀⠀⠀⢧⡀⠀⠀⠻⡷⢿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⢠⠇⠀⠀⠀⠀⠳⡄⠀⠀⠈⠲⢻⡄⠀⠀⠀⠀⠀⠀⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠘⠢⣀⡀⣀⡼⠁⠀⠀⠀⠀⣰⠞⠉⢹⡇ ⠀⠀⠀⠀⠀⠀⠘⠶⠖⠋⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠀⠀⠀⠀⣠⠞⠁⠀⣠⠾⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢀⣠⠾⠋⣀⡤⠞⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣹⣉⡭⠾⠒⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣹⠋⠉⠁⠀⠀⠉⠹⡍⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣠⠏⠀⠀⠀⠀⠀⠀⠀⢻⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⣲⠀⠀ ⠀⠀⠘⢿⢆⠀⠈⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⣠⣾⠇⠀⠀ ⠀⠀⠀⠈⢻⡳⣄⠀⠀⠀⠈⠙⠢⢄⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⣠⢞⡵⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢬⠳⣄⠀⠀⠀⠀⠀⠉⠓⠒⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠒⠋⠀⠀⠀⠀⠀⢀⠜⣡⠞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⣎⣧⡀⠀⣄⣹⠛⠂⠀⠀⠀⠀⠀⢀⡀⢠⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢛⣀⣽⠉⠀⠀⠀⠀⠀⠀⢠⡟⢻⠋⠙⡾⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡏⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⢙⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡜⢹⣟⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⡿⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡇⠀⠿⠁⠀⠀⢷⠦⠤⣀⣀⠀⠀⠀⠀⢰⠀⠀⣤⠀⠀⠀⠀⢀⣀⡤⠤⢶⠃⠀⠀⠿⠃⢘⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠘⢧⡀⠙⠉⣙⡶⠀⠀⣸⠀⠀⢻⠀⠀⢰⣏⠉⠛⢀⡴⠋⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠱⣄⠀⠀⠈⠉⠉⠁⠀⠀⣰⠇⠀⠀⠘⢧⡀⠀⠈⠉⠉⠉⠀⠀⢀⡶⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠑⠦⣄⡀⠀⣠⠴⠋⢁⣤⢤⠤⣤⣀⠙⠲⣄⡀⠀⣀⠤⠚⠁⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⣀⣀⣩⣟⣧⡄⠀⠈⠛⢻⡟⠟⠋⠀⠀⡤⣿⣏⣁⣀⡀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠁⠀⠀⢀⡠⠖⠊⠉⠁⣀⣼⡬⠟⠂⢀⡠⠖⣛⣙⠲⢤⡀⠀⠒⠤⣿⣀⠀⠉⠙⠲⢤⣀⠀⠀⠈⢳⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⠞⠀⠀⠀⠖⠉⠀⠀⢀⠴⠊⠁⠀⠳⣄⣰⠋⠀⠈⠁⠀⠉⠀⠙⢦⣀⠜⠁⠀⠉⠲⣄⠀⠀⠈⠳⠄⠀⠀⠙⣆⠀⠀⠀ ⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠂⠀⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀ ⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀ ⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⣆⠠⠤⣤⠤⠤⠤⠤⠤⠤⠀⠤⣔⠒⢀⡨⠛⢵⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡄⡠⠃⠀⠀⠀⠀⠈⠆⠀⠀⠂⠀⠀⠀⠀⠀⠀⠱⣸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢧⢀⣀⣀⣀⣒⣀⣀⡲⠀⠀⣂⣀⣀⣒⣂⣀⣀⡀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢫⣍⡻⢟⣉⠽⠳⣖⣲⠞⠫⣁⡛⢋⣠⠜⠁⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠋⠁⠀⢀⡡⠚⠓⢄⡀⠀⠀⠁⠁⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⢄⠏⠀⠐⠀⠀⠸⠂⡄⠀⠀⠀⠀⡼⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠑⢄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⡴⠋⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠊⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠈⢆ ⠀⢀⠤⠐⠒⠉⠉⡇⡠⠤⣇⠀⠀⠀⠀⠀⡿⠀⠀⠀⢻⠀⠀⠀⠀⢰⡡⠒⢄⡸ ⡰⠁⠀⣀⣄⣀⡀⢹⣱⡞⡜⡄⠀⠀⠀⠀⡇⠁⠀⠊⢠⠀⠀⠀⢀⠏⠰⡲⣮⣷ ⢇⠀⠀⠀⠀⠈⢹⠉⠚⠒⢣⠼⣀⠀⠀⠀⡐⠉⠉⠉⠹⡀⠀⠀⡀⢯⣳⠊⠀⠀ ⠈⠢⢀⣀⣀⠤⠃⠀⠀⠀⠳⠧⠄⠬⠤⠔⠁⠀⠀⠀⠀⠑⠂⠀⠓⠊⠀⠀⠀⠀
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⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣄ ⢽⠀⠈⠉⠉⠒⠦⢤⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠋⠉⠀⠀⢸ ⢸⠀⠀⠀⠀⠀⢀⣠⣴⡿⠋⠉⠉⠉⠉⠉⠑⠒⠦⢤⡖⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⢸⡄⠀⠀⠀⠰⠋⢿⣯⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⢠⡇ ⠀⣧⠀⠀⠀⠀⠀⠀⢰⡇⣼⣧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀ ⠀⠹⣆⢈⡇⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡞⠀⠀ ⠀⠀⢈⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣰⠋⠀⠀⠀ ⠀⠀⠾⣾⣃⣀⣤⣶⣿⣤⢰⣦⣴⢰⣠⢯⣕⡢⣄⣀⠀⠀⠀⠀⠻⡅⠀⠀⠀⠀ ⠀⠀⢠⢃⡿⡟⠋⠁⠀⣿⣾⣿⣿⣾⡟⠀⠈⠙⠛⠿⣮⣭⡆⠀⢰⡿⠄⠀⠀⠀ ⠀⢀⡏⠸⡇⣧⠀⠀⢠⣿⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⡷⠀⡧⠀⠀⣷⠀⠀⠀⠀ ⠀⢾⡀⠀⠇⠘⠧⠤⠞⠛⠘⠉⠙⠉⢻⡄⠀⠀⠀⣰⠃⣸⠋⠀⠀⢻⠀⠀⠀⠀ ⠀⠀⠳⣄⠀⠀⠀⠀⠀⠠⢶⣤⠀⠀⠀⠉⠓⠒⠚⠑⢯⠿⠀⠀⣰⠋⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⠀⠀⠀⣄⣴⣄⣀⣄⡀⠀⠀⠀⠀⠀⢸⣀⡴⠊⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣯⣉⣉⣉⣉⣉⣉⣁⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢺⣧⠶⠂⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⠀⠀⠀ ⠀⠀⠀⢸⣤⡀⠉⠙⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠉⠁⡤⡾⠀⠀⠀ ⠀⠀⠀⠀⢻⡿⣄⠀⠀⠀⠈⠙⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠚⠉⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣮⠳⣄⠀⠀⠀⠀⠀⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠁⠀⠀⠀⠀⣠⡾⢣⡞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⡈⠳⣄⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣤⠤⠖⠒⠒⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠛⠓⠒⠲⠦⢤⣤⠴⠛⠉⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡝⢷⡀⠀⠀⠀⠀⢠⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠿⣆⠀⠀⣤⣼⡇⠙⠁⠀⠀⠀⠀⠀⠀⠀⢰⡀⢠⣦⡀⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟⠇⢀⣹⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⢿⡟⠁⠻⡾⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠻⣯⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⡄⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢷⡦⢿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⣧⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⣿⠾⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⢸⣿⡯⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⠀⠀⠛⠃⠀⠀⠀⢸⣏⠙⠒⣶⣤⣄⡀⠀⠀⠀⠀⢸⠁⠀⠀⣿⠀⠀⠀⠀⠀⣀⣤⣴⠖⠛⢉⡟⠃⠀⠀⠐⠛⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠆⠀⠀⠀⠻⣆⡀⠘⠃⠈⣙⣷⠄⠀⠀⣸⠀⠀⠀⢻⠀⠀⠀⣶⣏⠉⠈⠛⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠈⢦⡀⠀⠀⠈⠙⠓⠒⠚⠉⠀⠀⠀⣠⡟⠀⠀⠀⠸⣧⡀⠀⠀⠉⠙⠒⠒⠛⠁⠀⠀⠀⣤⡔⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠉⠻⠦⣄⡀⣀⡴⠛⠁⠀⣰⢾⡛⣛⢛⣳⣦⡄⠀⠙⠳⣄⢀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⠛⠶⣤⠀⠀⠈⠉⠻⣿⠹⠛⠉⠀⠀⠠⡴⠾⢻⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⣠⡴⠖⠛⠉⠉⠉⢹⣏⣽⣷⡦⠀⠀⣀⣴⠖⠛⠳⢦⣄⡀⠀⠠⣧⣭⣍⣟⠉⠉⠉⠙⠒⠦⣄⡀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⣠⠴⠚⠉⢻⡄⠀⠀⣠⠞⠉⠴⠒⠒⠒⠲⠈⠙⢦⡀⠀⠀⣼⠋⠙⠲⣤⡀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠙⠦⠤⣧⣀⡀⠀⠀⠀⠀⠀⠀⣀⣨⡷⠤⠞⠁⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀ ⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠒⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀ ⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀ ⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀ ⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⢀⡴⠛⢦⡀⠀⠀⠀⠀⣀⣠⠤⠤⠖⠒⠒⠲⠀⠀⠀⠀⠀⠀⢠⠟⣆⠀⠀⠀⠀ ⡼⠀⠀⠀⢹⣄⡤⠒⠋⠁⠀⠀⠀⠒⠛⠉⠉⠉⠙⠓⠒⠦⣄⡾⠀⠸⡄⠀⠀⠀ ⣇⠀⢠⠔⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠙⢦⡀⢳⠀⠀⠀ ⠸⣴⠃⠀⠀⠀⠀⠀⠀⠀⢀⡴⣚⠛⡆⠀⠀⠀⠀⣞⠉⠾⣆⠀⠀⠙⢮⣇⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠉⠀⢹⠀⠀⠀⠀⠸⡄⠀⠈⢧⠀⠀⢠⡟⣆⠀ ⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⢀⣸⠁⠀⠀⠀⠀⠹⠤⠤⠼⠃⠀⠈⠀⠘⡆ ⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠆⢳ ⢻⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠘⢯⣩⠏⠀⠀⠀⠀⣀⡘⠉⠀⠀⠀⢸ ⢸⠀⠀⠀⠀⠀⠀⠠⠤⢤⠀⠁⠀⠀⠀⣀⣀⣏⠀⠀⠀⠀⠀⣌⠉⠉⠉⠓⠀⢸ ⠈⣇⠀⠀⠀⠀⠀⠐⠒⠋⠀⠀⣠⠞⠉⠁⠀⠈⠙⠦⣄⠀⠀⠈⠙⠢⡄⠀⠀⡜ ⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠹⣠⠞⠁ ⠀⠀⠀⠉⠳⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⢤⣀⣀⣀⣀⣀⣀⣠⠤⠴⠒⠋⠁⠀⠀⠀⢠⡦⠀
⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀ ⠀⠀⠳⣄⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠈⡠⡞⠀⠀ ⠀⠀⠀⠑⢕⢄⠀⠀⠁⠢⠤⠒⠒⠒⠒⠒⠒⠒⠒⠠⠔⠊⠀⠀⡠⠪⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠱⡧⠐⡾⠉⠀⠀⠀⡰⡴⢄⢦⠀⠀⠀⠀⠀⠀⢴⠕⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠛⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠉⣏⠀⢤⣀⡀⠀⠀⠀⡀⢀⠀⠀⠀⢀⣀⣠⠀⢹⠏⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡄⠀⢄⠈⠢⠙⠩⠆⢀⠇⠈⡄⠰⠬⠙⠔⠁⠀⠀⢀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠈⠒⠤⣀⣀⠔⢪⣤⢤⣈⠢⢄⢀⠠⠐⠁⠀⠸⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⠜⠀⢀⡠⠄⠒⣺⡻⠆⣀⠬⠯⣁⠀⠝⣓⠒⠠⠄⡀⠀⠱⡀⠀⠀⠀ ⠀⠀⡠⠃⠀⠐⠁⢀⠔⠉⠈⠢⠬⢀⣉⣈⣁⠵⠔⠁⠈⠢⡀⠈⠑⠀⠈⢆⠀⠀ ⠀⡰⠁⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⢢⠀ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
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⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠔⠆ ⡄⠀⠀⣀⣴⢗⠈⠉⠉⠀⠂⠤⡀⠀⠀⠀⠀⡄ ⢇⠀⠀⠁⢳⣇⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁ ⠘⢤⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⡐⠁⠀ ⠀⡷⣧⣤⠾⣤⠂⣴⡴⠷⣤⢀⣀⠀⢫⠀⠀⠀ ⢠⠡⡏⡀⢀⣿⣶⣿⡇⠀⠀⢈⢹⠄⠸⡀⠀⠀ ⠐⡀⠃⠑⠊⢁⡀⠈⠑⠄⠠⢮⡤⠀⡠⠃⠀⠀ ⠀⠈⠑⢄⠀⠒⠣⠀⠄⠀⠀⣀⠇⠊⠀⠀⠀⠀ ⠀⠀⠀⢀⣹⣐⣒⣒⣀⣉⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢘⡩⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⣼⡇⠀⠈⠓⠦⣉⠛⠻⢷⣦⣄⣀⣀⣠⣤⣤⣴⣶⣶⣦⣤⣄⣀⣤⣤⣤⣶⠶⠿⠿⠟⠛⠛⠛⠛⠛⠛⣛⣻⠿⢛⣿⡿⠁⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠉⠓⢦⡀⠉⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠉⠉⠀⣠⣿⠋⠀⠀⠀⠀ ⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⡀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⡏⠙⢦⣀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⡏⠀⠀⠀⠈⠉⠓⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡙⡷⠒⣶⣶⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣖⢲⣶⠖⠋⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡁⠀⠿⠿⠇⢹⢣⡀⠀⠀⠀⠀⢠⢿⠹⠿⠿⢠⡿⠀⠀⣾⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠿⠾⢷⠀⠀⠀⠀⡿⠞⠓⠒⠒⠋⠀⠀⠀⠈⠻⢷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢸⠃⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⡆⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣼⠀⠀⠀⠀⣰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣿⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⡀⠀⠀⠀⠀⠀⠀⣀⣠⣷⠊⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⠛⠉⠁⠀⣈⣧⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠘⣿⡀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢻⡇ ⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻ ⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢠⣿ ⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⣾⡇ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⣤⣤⣤⣤⣤⣤⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⠀⠀⠀⠀⠀⢠⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠈⠉⠉⠉⠉⠉⠁⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⠷⣾⡟⠀⠀⢀⣤⠀⠀⠀⢠⣾⡏⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⠀⠀⠀⢠⣤⠀⠀⣶⣦⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣤⣤⣼⡿⠷⠶⠿⢟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣻⢷⣦⣤⣿⣿⣿⢾⣿⣛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⠀⠀⣀⣀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠁⠀⡐⠁⠀⠈⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣤⠶⠋⠉⠙⢳⠄⠀⠐⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠞⠀⠀⢀⠄⠀⠠⠄⠈⠑⢧⡀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡰⠁⠀⡀⡬⢳⣶⡄⡐⣿⣿⠍⠁⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠸⢧⠼⡑⡁⡽⠾⡛⠀⠀⣸⠖⠒⠢⡄⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠁⠀⢹⠙⢗⢗⠀⠈⡟⠀⠀⠀⠘⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⡌⠀⠀⢹⠀⠀⡇⠀⣴⡄⠀⠀⡧⠤⠀⠀⠤⣄⣀⠀⠀⠀ ⠀⠀⠀⡸⠀⣰⡁⠀⠀⠈⡄⠀⣧⢰⠃⠹⡄⠀⣇⣀⡀⠀⠀⠀⠑⢦⡀⠀ ⠀⠠⠏⠠⠜⠒⠀⠀⠒⠺⠃⠀⠫⠿⠀⠀⠘⠴⠁⠀⠈⠳⠄⠀⠀⠀⠹⠄
⠀⠀⢰⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠀⠀⠀⢰⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠈⢧⡀⢀⣠⠤⢾⣇⣤⣤⣄⣀⣤⣤⣠⣷⠦⢤⣀⠀⣠⠏⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⢸⡀⠀⠀⢀⣤⣼⢯⠉⠉⠀⠀⠀⠈⠉⠁⠉⠋⠁⠈⠉⠀⠀⠀⠈⠉⠹⢻⣤⡄⠀⠀⠀⣼⠀⠀ ⠀⠀⢸⣿⣤⣾⠿⠋⠃⠀⠀⠀⠀⠀⢀⣠⠀⣀⡄⠐⣄⡀⢠⣀⠀⠀⠀⠀⠀⠀⠋⠻⢿⣦⣾⡟⠀⠀ ⠀⠀⠈⣿⣿⠓⠀⠀⠀⠀⠀⠀⣠⡐⣾⣧⣾⡿⢀⣇⠹⣷⣬⣿⡄⣠⠀⠀⠀⠀⠀⠀⠘⣹⣿⡇⠀⠀ ⠀⠀⠀⣿⣿⠁⠀⠀⣄⣀⣤⣤⣿⣿⣿⣿⣿⡇⠘⠹⠄⣿⣿⣿⣿⣿⣧⣤⣄⣀⡴⠀⠀⢹⣿⡇⠀⠀ ⠀⠀⠀⡿⠀⠀⠀⣠⣿⣿⠉⠀⡏⠙⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡟⠉⡇⠈⢹⣿⣤⡀⠀⠀⠹⡇⠀⠀ ⠀⠀⢰⠁⠀⠠⢾⣿⣿⣿⣷⣄⣃⣠⣿⣿⠏⠀⠀⠀⠀⠈⢿⣿⣧⣀⣃⣴⣿⣿⣿⣿⠦⠀⠀⢳⠀⠀ ⠀⠀⡏⠀⢰⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣠⣶⣶⣦⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢠⠀⠘⡇⠀ ⠀⢸⠃⠀⡏⠀⠈⢙⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠻⡟⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣟⠉⠀⠈⡦⠀⢷⠀ ⠀⢸⠀⣠⠏⠀⢀⡼⠆⠙⠛⢛⡏⠀⠀⠀⣠⠔⠋⠉⠓⢤⡀⠀⠀⠘⡟⠛⠛⠁⠾⣄⠀⠈⢧⠀⢸⠀ ⢀⡏⠀⠘⡄⠐⣳⣀⣀⠀⠀⠉⡶⠀⢀⡜⣡⣜⣠⢦⣰⣦⡙⡄⠀⠰⡎⠁⠀⢀⣀⣸⡓⠀⡜⠀⠘⣆ ⠈⢳⡀⠀⠀⠀⠉⠘⠹⢶⣈⣉⣁⠾⠋⠀⠘⠹⠁⠀⠹⠛⠀⠘⠻⣄⣉⣉⣰⠿⠙⠉⠁⠀⠀⠀⣰⠋ ⠀⠀⠓⠦⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠞⠁⠀
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⠀⠙⠫⡙⠫⣍⠑⠒⣲⡶⠤⠖⠒⠒⠒⠒⠒⠒⠒⠒⠦⠶⣖⡒⠂⣉⠍⢛⡭⠋ ⠀⠀⠀⠈⢦⠀⣱⠋⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠉⣿⠁⡰⠃⠀⠀ ⠀⠀⠀⠀⠀⢳⡏⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠸⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⢀⣀⣀⠀⠀⠀⢠⠁⠆⠀⠀⠀⣀⣀⡀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡞⠀⠈⠹⣝⠿⢿⡻⠓⠄⠀⠠⠒⢯⡻⠿⣋⠟⠉⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⠀⠀⠀⠈⠺⣃⢠⠤⣚⣻⣛⡦⣄⣑⠓⠀⠀⠀⠀⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢧⣦⡀⠀⡡⠒⠑⠉⠀⣀⠀⠉⠊⠑⠌⠀⠀⣠⢶⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣹⠐⠢⠤⢀⣀⣈⠀⢉⣀⣀⠠⠤⠒⢹⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀ ⠀⠀⢠⠶⠚⠑⣺⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣷⠊⠑⠲⣄⠀ ⠀⠀⡟⠀⠀⠀⢿⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⢰⠎⠀⠀⠀⣽⠀⠀⠀⢸⠀ ⠀⠀⢹⡄⠀⠀⠘⣆⠀⠀⠀⣸⠀⠀⠀⢸⠀⠀⠀⢼⠀⠀⠀⢠⠏⠀⠀⢀⡞⠀ ⢀⣴⣏⣹⠶⢢⠄⠈⠂⢀⡤⣯⣄⠀⠀⣸⠀⠀⢀⢼⢤⡀⠀⠋⠀⢔⠶⣯⡀⠀ ⠊⡞⠺⣆⣀⠁⠀⠀⠀⡏⡜⢠⠃⠀⠀⣿⡀⠀⠈⠆⢱⢸⡄⠀⠀⠈⡆⣸⡽⠀ ⠀⣿⣀⠀⠉⠉⠉⠩⠿⠛⠳⠾⠶⠶⣶⣯⣗⡒⠒⠓⠚⠉⠉⠉⠉⠉⠉⠀⠀⠀ ⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣼⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠢⢝⣆⠤⢐⣦⣤⡤⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡠⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡜⠀⠱⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣀⢠⡤⢀⠎⠀⡗⠉⠀⠇⠀⠀⠀⠀⠀⠀ ⡜⠋⠙⡑⠢⣀⠀⠀⠀⠠⠃⠊⠐⢓⣒⣥⣆⡀⡇⡐⠢⢸⠀⠀⠀⠀⠀⠀ ⣧⠃⠀⠘⡄⠀⢈⡉⠰⠁⠀⠀⠀⠀⠀⢀⣀⠈⠙⠶⡶⣰⠀⠀⠀⠀⠀⠀ ⢹⡆⠊⠀⠈⡤⢀⡀⠃⠀⢞⠳⡀⠀⠀⣦⢟⣀⠀⠀⠘⢾⠀⠀⠀⠀⠀⠀ ⠀⢻⡄⠀⠁⣴⢈⠂⠀⠀⣠⡥⡀⠀⠀⠀⡞⣧⢝⠆⠀⠀⠑⠢⠤⡄⠀⠀ ⠀⠀⠙⠶⡮⡎⡜⠀⠀⣜⠙⡗⡹⠀⠀⠀⢔⠒⠋⠀⠀⠀⠀⠀⡔⠁⠀⠀ ⠀⠀⠀⠀⠑⡿⠁⠀⠀⠀⠈⠁⠀⢠⣶⣶⣿⠀⠘⢦⠀⠀⠀⠈⠀⣶⠀⠀ ⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⢠⠣⠤⢀⡉⠻⡋⣃⠠⢍⠇⠀⢀⡠⠊⡘⠀⠀ ⠀⠀⠀⠳⡒⠂⠀⠀⠀⠀⠸⡄⢁⠀⣨⠜⠁⠒⢌⠬⢒⠟⠉⢀⠔⠁⠀⠀ ⠀⠀⠀⠀⠈⡰⠆⠀⠀⢀⣀⣈⡀⠐⠁⠀⡠⠂⠁⠰⠓⠈⣩⡛⠓⣢⡀⠀ ⠀⠀⠀⠀⠘⠓⠲⣆⠀⠀⡩⠆⠀⠉⣂⠈⢤⡀⠀⠀⠀⠈⠓⢞⠫⢌⣢⡀ ⠀⠀⠀⠀⠀⣠⡾⠋⠀⠈⠉⣝⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣀⠼⠃ ⠀⠀⠀⠀⠀⠛⢳⠋⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀ ⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⡏⣧⣦⣄⣤⣤⣠⣤⢒⣲⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠘⣻⢻⢯⣦⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣹⢿⡿⠀⠀⠀⠀⠀ ⠀⢈⣟⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣯⣿⣿⣷⣥⡘⠀⠀⠀⠀⠀ ⢰⡟⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠁⢫⣿⣿⣿⠷⣾⣷⣆⠀⠀⠀⠀ ⠐⣷⢹⣿⣿⣿⣷⣮⣴⣿⣿⠇⠀⠘⢿⣧⣽⣴⣿⣿⣿⠀⠀⠀⠀ ⠀⣏⡻⣿⣿⣿⣿⣿⣿⠟⠃⠤⡀⡠⠌⠿⣿⣿⣟⡟⠘⠀⠀⠀⠀ ⠀⠃⠙⠿⠿⣿⡿⣿⠀⠀⢀⠠⠚⠢⡀⠀⢈⠶⢶⣶⠆⠀⠀⠀⠀ ⠀⠀⠀⢀⠄⠑⠊⠁⠀⠀⠁⠀⠀⠀⠈⢠⣶⠧⠓⠂⠀⠈⠢⡀⠀ ⠀⠀⡠⠂⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⣨⡂ ⠀⠀⠀⣚⣠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⢈⠀⢕⣔⣴⣯⣢⠁ ⠀⠀⠸⠿⣿⣷⣤⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣾⡟⠁⠀ ⢀⡔⠁⠀⠠⢙⡻⢢⣅⡷⠊⠀⠀⠀⠀⢦⣀⣤⣤⠀⠀⠉⠀⠀⠀ ⠈⠀⠀⠠⡀⡀⠜⠚⠉⡀⠔⠀⠀⢀⡄⠀⠟⠉⠀⠀⠉⠉⠉⠀⠀ ⠈⠁⠀⠈⠁⠀⠀⠀⠀⠑⠆⠴⠠⠄⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠉⡲⣄⣀⠀⠀⣀⡠⢊⠉⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠔⠠⡉⠀⠀⠀⠀⠀⠈⡡⠔⠠⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠖⡺⠀⠀⠀⠀⠀⠀⡗⠲⠀⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⢀⠀⢀⠖⠁⠈⠐⠊⠀⣤⠖⠒⠒⢦⣄⠈⠐⠊⠀⠈⠢⡀⠀⡠⠀ ⠀⠀⠀⠀⠤⠤⢭⠃⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⢱⠡⠤⠤ ⠀⠀⠀⠀⠀⠤⠚⡄⠀⠀⠀⡀⠤⠒⠂⠀⠉⠉⠀⠒⠂⠤⢀⠀⠀⠀⣸⠒⠤⢀ ⠀⠀⠀⠀⠀⠀⠀⠘⢄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⡔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡍⠉⠉⠉⠉⡏⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡇⠀⠀⠀⠀⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⢰⠁⠀⠃⠀⠀⠀⠀⢸⠀⢸⠔⠢⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠤⠞⢁⡔⠈⡙⠀⢸⠀⠀⠀⠀⠀⠈⡄⠀⡏⠑⢦⠈⠢⢄⡀⠀ ⠀⠀⠀⠀⢸⣁⢴⡄⢸⡁⢠⠃⠀⡆⠀⠀⠀⠀⠀⠀⢃⠀⢸⠀⢸⡆⣰⡦⣈⡆ ⠀⠀⠀⣀⠀⠉⠉⠈⠚⠀⡜⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠈⠛⠁⠉⠁⠀ ⢠⠂⠁⠀⠈⢂⠀⠀⠀⢀⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⢇⠀⡀⢀⠀⠸⠀⠀⠀⢸⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠉⠀⠈⠆⠀⠣⠀⠀⢀⡆⠀⠀⢃⠀⠀⠀⠀⠀⢀⠌⠀⠀⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠢⣀⠈⠉⢀⣧⠀⠀⢄⠈⠀⠀⠀⠈⢁⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⣠⠝⠉⠙⠫⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠇⠀⡰⠁⠀⠀⠀⠀⠘⡄⠀⠮⠀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⢱⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⡝⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣄⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⠶⠾⠿⠛⠛⠛⠛⠛⠿⠷⠶⣶⣤⣤⣀⡀⠀⠀ ⠙⣶⡶⠶⠶⠚⠛⠛⠛⠉⠉⠉⢉⣭⡿⠛⠉⠉⠉⠀⠀⠀⠉⠉⠉⡩⠿⠛⠉⠉⠀⠀⠀⢀⣀⣀⣤⣤⠤⠤⣤⣤⣀⣀⠀⠉⣉⣻⣷⡤ ⠀⠈⢿⣦⢄⡀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡖⠋⠉⠁⠀⠀⠀⠀⠀⢀⡤⠞⣡⣴⠿⠛⠉⠀⠀ ⠀⠀⠀⠻⣧⡙⢶⣄⣀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡀⠀⠀⠀⣀⡶⢋⣴⡾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢷⡌⢷⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⢀⡴⠋⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠁⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⣿⣸⣏⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠉⠙⠢⣄⠀⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠋⠉⠉⠉⠙⠳⣦⣾⣽⣭⡽⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠈⠑⢤⣀⡸⢀⠀⠀⢀⣀⣠⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⢿⡟⠛⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⠛⣶⢦⣄⠀⣿⠁⢸⡏⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⠏⠸⡄⣿⣦⣈⡟⢻⠀⢸⡇⠛⠒⢲⡟⠛⣿⣿⠛⠉⠉⢻⣿⡿⠛⢻⠛⠛⢺⠇⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡄⠀⠹⣌⣻⣿⢷⡏⠀⢀⣧⠀⠀⠀⢷⡀⠙⣿⣷⣶⣾⣿⡿⠁⣠⠏⠀⢠⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠙⣩⠞⠻⣯⠽⠛⣦⡀⠀⠈⢷⣄⡀⠉⠛⠛⢉⣠⠴⠋⢀⣴⠋⠀⠀⣀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣿⡶⠴⠚⠁⠀⠀⢛⡶⠟⠆⠙⠳⢤⣄⣉⠛⠛⠛⠛⢉⣁⣤⠶⠋⠀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⣀⣠⠜⠹⣄⠀⠀⠀⠀⠀⠉⠉⠛⠓⠚⠉⠁⠀⣀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⢿⣿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠟⠛⠋⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⣄⠀⡶⠀⠀⢀⠀⠀⠀⣠⡴⠶⠦⣄⡈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠘⢷⠃⠀⠀⢸⠀⠀⣼⠃⠀⠀⢀⡼⠁⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢶⣿⣠⣶⣿⣄⠀⢀⣸⣄⢰⠃⣀⣠⣽⠿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣴⣁⣼⡏⣼⠀⡜⢳⣾⣿⣭⣿⣶⣾⡯⠁⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠧⣯⣽⠟⡋⠁⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣫⡴⠊⠁⠀⢀⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⢀⣤⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣡⡟⣡⡴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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