Chicken ASCII Art

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⡤⢮⢄⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡧⠖⢋⠁⡀⠀⠈⠈⠱⢢⢆⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠙⠱⢦⢄⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⠴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠳⣦⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⡀⠄⠀⠁⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠐⠠⢀⠈⠐⠢⢄⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠤⠂⠁⠀⠀⢰⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢰⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠻⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂⠄⡀⠙⡇⠄⡀⢰⣶⣤⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡇⠀⠀⠀⠉⠃⠀⠀⠉⠛⠿⡇⠀⠇⠀⠀⠀⠀⠀⠀⣤⣦⠀⠀⠀⢠⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠑⠂⡄⡀⠀⠀⠀⠀⠀⠢⢄⠀⠀⠄⠁⠀⠀⠀⠀⠀⠿⠛⠀⢠⣶⠟⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⣶⡯⠀⣠⠀⠀⠀⣠⠜⠋⠀⠀⢀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⠤⠞⢻⣋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠏⠈⠑⠢⢄⣴⡞⠉⠀⠀⡀⢀⣼⠉⠐⠠⢀⠀⠀⠀⠀⢀⠠⠴⢪⢅⡴⠴⠋⠽⡃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠁⠘⠁⠀⠀⢰⣿⠚⡃⢸⠀⡀⠔⠈⠛⠐⠒⠮⠑⣀⡼⠚⣿⡿⠀⠀⠀⡴⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠀⢀⡠⠖⡉⠰⠀⢠⣾⠃⠠⠄⠈⠀⣀⠤⠒⠉⠉⠀⠀⢹⣏⠀⢀⣼⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢋⠠⢂⠁⠀⠀⠛⡇⠌⠒⠬⠔⢋⡡⠀⠀⠀⠀⠀⠀⣸⡿⠛⢋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠈⠒⡤⡔⠊⠀⠠⢤⡇⠀⠀⠀⠈⠁⠀⠀⠄⢂⣤⣴⣾⠛⡇⠀⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠀⠁⠊⠄⡠⠜⠒⠣⢄⠠⠑⠀⠀⣀⠽⢦⣀⠀⠀⢀⡠⠔⠊⢹⢸⣿⣿⣀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠄⣷⣤⣀⠀⠈⠑⠢⢄⡀⣀⠤⠒⠉⠀⠀⢸⣿⣷⠖⠉⠙⠢⢀⢸⣸⣿⣿⣿⡗⠢⢄⠀⠀⠀⠀ ⠀⠀⡀⢀⢀⡨⠿⣿⡀⠉⠂⠄⣀⡀⢸⠀⠀⡀⠄⡆⠀⢸⡿⠋⠀⠀⠀⠀⢀⣹⣿⣿⡿⣋⠵⠔⡉⢈⣴⡀⠀ ⠀⠠⣷⠛⢓⡤⠀⠀⠁⠢⢄⡀⣼⣿⣾⠀⠀⡇⠀⠧⠔⢺⠁⠀⠀⠐⠊⣠⣾⣿⣿⣟⠉⠑⠢⢄⡀⠉⢺⠆⠀ ⠀⠀⠀⠙⠣⢄⠀⠀⠀⠀⡀⠈⠙⠻⢿⠠⠔⠀⠀⠀⢀⣼⡀⠀⠀⢀⣴⣿⣿⠟⢡⠄⠃⠀⢀⠠⠐⡏⠀⠀⠀ ⠀⢨⠂⠄⡀⠀⠈⠑⠒⠍⡈⠑⠒⠊⢹⠀⠀⠀⢠⣆⣱⣆⣭⢋⣴⣿⣿⠟⠁⠀⢀⡨⢴⠊⠹⠀⠀⡇⠈⡀⠀ ⠀⠸⢄⡀⠀⠁⠀⠄⠀⠀⡇⠀⣀⠤⢺⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠟⣁⡠⠔⠊⠁⠀⣸⠀⠀⠀⢀⡇⠠⠄⠀ ⠀⠀⠆⠈⠑⠢⣄⡀⠀⠁⡟⠉⠀⢀⣼⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⠁⠀⠀⠀⠐⠁⠀⢀⠰⠀⠈⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣷⣦⣷⣴⡮⢁⢸⠀⠀⠀⠈⡟⠋⢹⠿⣿⠟⢸⠃⠁⠀⠀⡠⠀⠀⠀⠀⠀⠀⡄⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⠀⢸⠀⠀⠀⠀⠁⠀⢸⠀⠐⠀⢸⠀⠀⠆⠁⡇⢀⠀⠐⠈⠀⠀⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡛⠋⠀⠀⢸⠂⠀⠆⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⡶⠀⠉⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠈⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⡀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠀⠁⠁⠺⠦⠀⠀⠀⢀⡠⠔⠚⠀⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⡀⡇⠀⠀⠀⢸⠀⠀⠀⢸⣀⡤⠔⠈⡿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠂⢄⠀⢸⠀⡠⠄⠊⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⣻⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⡀⠀⢈⠸⢀⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠂⠓⣄⠀⠈⠉⠀⢠⡔⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠫⢄⡀⠤⠀⠄⡀⠈⠒⠤⣀⡠⠔⠒⠤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠑⡢⢄⡀⡡⠆⠀⠀⠀⠀⠶⣉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠈⠓⠠⢐⡈⢑⣢⠔⠊⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣟⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣷⣦⡀⠀⠀⠀ ⠀⠀⣠⣶⡿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣴⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀ ⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡁⣽⣖ ⡇⠀⠀⢠⣶⣶⣖⣖⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⠰⣿⠛⠆⠐⢆⠀⠃⢠⣤⣤⣤⣤⣴⣦⣦⣤⣬⠁⢸⠙ ⡇⠀⣀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣾⠀⠀⠀⢈⠀⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⢘ ⡇⠀⡏⢸⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⡏⣿⠀⠀⠀⢸⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⢸ ⡇⠠⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⣿⠀⠀⠀⠈⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣸ ⡇⠈⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⣿⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⠿⣿⣿⣿⣿⡄⢸⠭ ⡇⠀⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁⣿⠀⠀⠀⠀⠀⡗⢸⣿⣟⣿⣶⣶⣿⣿⣿⣿⠂⢸⢰ ⡇⠀⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⣤⣴⣋⠀⠀⠀⠀⠀⢀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⣿⠀⠀⠀⡀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⠨ ⡇⠀⡇⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⢀⠀⠀⠀⠀⣀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⣿⠀⠀⠀⠅⠀⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⢐ ⡇⠀⡇⠐⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⣏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢨⠈ ⡇⠀⡇⠀⡟⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡗⠀⣿⠀⠀⠀⡆⠀⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⢀ ⡇⠀⡇⠀⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠛⠛⢿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢀⣿⠀⠀⠀⡇⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡍⢠ ⡇⠀⡇⠀⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣾⣿⠈⠀⠀⡇⠀⣯⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⠀ ⠇⠀⠇⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⠂⡄⠀⡇⢰⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡁⠀ ⠀⠀⠀⠀⠳⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⠛⠛⡛⢛⢛⣛⣛⣛⣻⣿⣟⣛⣛⣛⣛⣃⡻⣿⠀⠃⣴⡇⢨⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠉⠉⠉⡉⠉⠓⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠤⠤⣇⡀⠐⡈⢄⣁⣂⣄⡡⠈⠄⠠⢈⠙⢦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣞⣤⡴⠤⠬⢷⣡⣰⣞⣉⣀⡈⠙⣦⠈⡐⢀⠂⡄⡘⢦⡀⠀⠀⠀ ⠀⠀⠀⢀⡔⢧⣈⢁⡴⠒⠛⠄⠸⡆⠚⠂⠉⢙⡟⠋⠙⡉⢉⠉⡉⠛⠹⣄⠀⠀ ⠀⢀⡴⠃⠀⠄⡈⠙⣧⡀⣌⡄⠁⡉⠓⢒⣚⠋⠚⡙⠓⡀⢂⠐⡀⠂⠄⠹⡆⠀ ⠀⡼⠀⠠⠁⢂⣾⡭⢤⡭⢥⠴⠶⠶⠓⠚⠉⡉⠄⠐⠠⠐⢀⠂⠠⢁⠈⠄⢳⠀ ⠀⡇⠠⠁⠌⡀⠙⣆⠀⠄⠂⠠⠀⠄⠂⡁⠂⠄⡈⠄⢁⠂⠄⡈⠐⠠⢈⠐⢸⡀ ⠀⡇⠄⡁⠂⣤⠷⠛⠠⠈⠄⠡⠈⠄⡁⠐⡈⠠⠐⢈⠠⡆⠐⡀⢁⠂⠄⣺⢸⠄ ⠀⢹⡀⠐⡈⣧⠀⠂⡁⠂⣌⠠⠁⡐⠀⢥⡀⢁⠂⠄⠂⣧⠐⢀⠂⡐⢠⡟⣸⠀ ⠀⠀⠳⣄⠐⡙⢦⣅⣀⣢⡼⣄⠐⡀⠡⣸⠇⠀⠂⠌⠐⠈⠳⠦⠴⠴⠋⣰⠇⠀ ⠀⠀⠀⠈⢓⣦⣄⠀⡉⠀⠄⡈⠛⠛⠋⠁⠄⠡⢈⠐⢈⠐⡀⢂⠐⢠⡱⠃⠀⠀ ⠀⠀⣠⡞⡯⢞⡭⣟⠷⣾⡴⣤⣦⣔⣈⣴⣬⡴⣤⣬⣀⡐⢀⣢⠼⠊⠀⠀⠀⠀ ⠀⠀⠘⠯⣵⣫⣞⣜⣯⣖⡽⠵⣿⢫⢟⡼⡲⣝⣣⠯⣝⡻⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠷⠮⠷⡽⠶⠭⠾⠓⠛⠋⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀ ⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⡀⡁⠁⢆⠹⣄⠀⠀ ⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠡⠀⠈⠀⠀⠀⠀⠠⢐⠁⠐⠘⡎⡀ ⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠒⠀⠀⠀⠀⡀⠐⠀⠈⠀⠀⠀⡀⠄⢹⠀ ⢠⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⣀⠤⢆⡁⠀⠀⠈⡇ ⢸⡇⠀⠀⠀⠀⢀⠄⠁⢀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢣⠀⠀⠀⡇ ⠈⡇⠀⠀⠀⠀⠓⠐⠀⡤⠈⠀⠀⠀⠀⠀⠀⠀⠀⡈⡀⣀⠀⠀⠀⠀⠀⢰⠇ ⠀⢹⡀⠀⠀⠀⠀⠀⠀⠑⠐⠀⠂⠀⠁⠈⠀⠀⠠⠀⠀⠀⠈⠹⠀⠀⠀⡼⠀ ⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠄⠁⠀⠀⡼⠁⠀ ⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠐⠀⠀⠀⣠⠞⠁⠀⠀ ⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⢅⠀⢀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣀⣀⣀⠀⣀⣡⣄⣠⠤⠗⡋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣶⠞⠋⢉⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠿⠿⠿⢿⣿⣶⣤⣀⠉⣻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣄⣀⣀⣀⣀⣙⣿⠿⠿⠿⢿⣿⣦⣤⣄⠈⠛⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡏⠹⢿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠻⣿⣿⣷⣦⣴⣿⣷⣄⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠀⣀⡼⠿⠛⠁⢀⣤⣤⣤⠀⠀⠀⠀⠀⠈⠉⠛⣿⡿⢿⣿⣿⣿⡿⣿⣷⡄⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⡿⠋⠁⠀⠀⡉⠀⠀⣠⣶⠿⠛⠁⠉⢷⣄⡀⠀⠀⠀⠀⠀⠈⣷⣶⣽⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⣠⣿⡿⠃⠠⣄⣀⣠⡼⠃⣠⣾⠋⠁⠀⠀⠀⢀⡸⠛⠻⣶⣄⡀⠀⠀⢀⠀⠿⠿⠷⣿⣿⣿⣿⡀⠀ ⠀⠀⠀⣰⣿⡿⠻⡆⠀⠉⠉⠁⠀⣴⡉⠁⠀⠀⠀⠀⠀⣸⣿⣦⣤⣬⣿⣿⣶⣿⡿⠀⢠⣶⣦⣾⡿⣿⣿⡇⠀ ⠀⢀⣾⣿⠋⠀⢀⣼⠁⠀⠀⠀⣴⡿⠟⠋⠀⠀⠀⣀⡀⠋⠙⠏⠉⠙⠛⢿⣿⣧⣀⣴⣿⣿⣿⣯⣤⣿⣿⡇⠀ ⢰⣿⡟⡇⠀⠀⠘⠁⠀⠀⠀⣸⣿⠃⠀⠀⠀⢠⣾⡟⠃⠀⠀⠀⣠⣦⣴⣿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡇⠀ ⣾⣿⡄⠀⣴⡆⠀⢠⡄⢠⡾⠟⢛⣀⡄⠀⢠⣿⣿⣦⣤⣴⣦⣾⣿⣿⡿⢡⣾⣿⣿⠁⢀⣿⣿⣿⣿⣿⣿⣇⠀ ⢸⣿⣧⣀⢻⡇⠀⠀⠀⠉⠀⢰⡿⠿⣿⣶⣿⠋⣸⣿⣿⠟⢿⣙⣿⣿⡿⠋⠙⠿⣿⣿⡟⣿⣿⣷⣿⣿⣿⣿⣦ ⢸⣿⡏⠻⣿⣧⠀⠀⣠⠀⣴⣿⠁⢠⣿⡟⢁⣾⣿⡏⠀⣀⣼⣿⣿⡟⠀⠀⢀⣀⠈⢹⣿⣿⣿⣿⣿⣿⣿⠏⠀ ⢸⣿⡇⠀⠀⠀⠀⢰⣇⣀⣿⣟⣠⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀ ⠈⢿⣧⡀⠀⠀⠀⠀⠁⢸⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⢀⣀⣾⣿⠏⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠻⣿⠀⠀⢀⠀⣰⣿⣿⡿⠿⠟⠃⠀⢀⣾⡆⠀⢘⣿⣿⣿⠃⠀⠀⠀⠀⠘⣿⠻⣿⣿⣿⣿⣿⣿⣷⠀⠀ ⠀⠀⢀⣿⣷⡆⠀⢰⣿⣿⠏⠀⠀⠀⠀⠀⠺⠟⠁⠀⢸⣿⠟⠻⣿⠀⠀⠀⠀⠀⣸⣧⢹⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⢸⣿⣿⠁⣀⣿⣿⣯⠀⠀⢠⡄⠀⠀⠠⠀⠀⠀⠀⠙⠀⠀⢸⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀ ⠀⠀⠀⠉⠻⣾⣿⣿⣿⣇⣀⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⣀⡀⢀⣛⣸⣿⣿⣿⣿⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⡿⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣟⠀⣸⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣧⣸⣿⣏⠀⠀⠹⠿⠿⠿⡷⠀⠀⠀⠀⢸⠋⠉⠉⠉⠙⠿⡿⣉⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣷⠙⢿⣷⣄⠀⠀⢀⠀⢰⡄⠀⣰⡿⠃⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠙⢿⣷⣶⣿⣷⣤⣁⣴⣿⠃⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠈⣿⠿⠿⣿⣿⣿⣿⣿⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠛⠤⣤⡆⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣄⠀⠀⠈⠇⠀⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣶⣶⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠐⣶⣶⠀⠀⠀⢙⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣧⢀⣀⠀⣈⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣇⣠⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⣿⣿⣷⡿⠛⠉⣿⣿⣿⣿⠋⢙⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⡿⠉⠀⠀⠀⠸⣿⠋⠛⠿⢿⣷⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣶⣾⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠀⠈⠁⠀⠘⠛⠋⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣻⠿⣶⡄⣰⡿⠿⣿⠿⢿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⠚⠉⠶⣈⠀⠃⠚⠘⠇⠋⠨⠌⠠⠀⠇⠉⠟⣏⣏⢄⠓⢏⡹⠁⣾⠙⠹⠰⣽⠿⠣⠁⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⣀⡀⢀⡀⡀⠀⣀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣌⣿⣧⣿⣿⣿⣾⣶⣉⣀⣠⣅⣦⣿⣷⣳⣿⣞⣄⣾⣿⣿⣿⣿⣿⣿⣷⣤⣶⣽⣄⣦⣿⣷⣿⣿⣿⣿⣷⣧⣻⣿⣟⣯⣿⣿⣿⣿⣽⣿⣿⣷⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢞⠫⣔⡺⣿⢀⠀⠁⠏⡿⠿⡼⠰⠊⡷⢱⣺⣾⢼⠡⢛⣿⣶⣿⣿⣿⠻⣹⠍⣯⣽⡿⠟⡽⣉⣿⣴⣡⠄⠤⣷⡿⣿⣿⢶⣿⣿⣿⣿⣿⣹⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠷⣛⣯⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿ ⣾⢳⣽⠯⢾⠔⠤⡿⣿⣿⣠⢈⠁⢀⠀⡿⠄⢀⠃⣿⣰⠀⠀⠀⠁⣯⣿⣼⠘⣇⣿⣯⣿⣮⣠⢀⡤⢖⠷⡿⣿⣷⣿⣶⡿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣻⣿⣽⢾⣿⣿⣿⣿⣿⣿⣞⣽⣿⣯⣾⣟⣞⡿⣽⢿⣿⣷⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿ ⠊⡕⢫⡟⠛⠉⠀⡇⣿⢡⠀⠀⠙⠈⣿⣿⢹⠀⣷⣼⠀⠋⠛⠛⡄⢫⣵⡞⣤⢻⡟⢹⠀⠀⠀⠀⠃⠚⠃⠛⠛⣾⣤⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣽⣾⣷⣿⣿⣿⣾⡟⣯⡏⣿⣿⣾⣿⣿⣿⣿⣿⣽⢻⣿⣿⣿⣿⣾⡟⣿ ⣶⡶⣲⣿⣿⣫⢯⡍⣿⣳⠉⡞⣟⢶⣿⣿⣿⠿⡿⣿⡿⣞⣡⢚⢬⡻⡴⠀⠄⠪⡄⣏⣸⣤⠏⠾⣫⡖⣠⣉⠛⠟⡴⣿⣯⣽⣿⣿⣿⣿⣿⣿⣻⣿⣿⣾⣿⢿⣿⣟⣿⣿⣽⣾⡟⣱⣺⣷⢟⣻⣶⢿⣿⡿⣷⣟⡾⣿⣿⣿⣿⣿⣿⠿⣻⣿⢿⣷ ⢫⠽⡧⣯⣿⣠⢀⡓⣿⣿⣿⣄⣽⠍⣿⣿⣿⣿⣿⢽⣫⡑⢼⠫⢟⡼⠀⠀⡭⢈⡅⣿⢈⠇⣿⢀⢁⠟⣿⣛⣘⣛⣗⣏⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣻⣿⣿⣷⣟⣯⡞⢿⡿⡟⣯⣻⢶⡿⢿⡿⢯⣿⣟⡾⣿⡿⣿⣿⣻⢿⣫⣿ ⢿⡻⢿⣿⣹⠂⠄⡿⣿⣻⣤⣩⣷⣿⣿⣽⣿⣧⣿⣿⠿⣻⣟⣿⣿⣿⠿⣿⣿⣿⡿⣽⣤⣤⢦⠛⣿⣿⣿⣿⣏⡿⣴⣫⣛⣿⡿⢿⣿⣿⣿⣿⣿⡿⣟⣯⣾⠻⣷⣋⣷⣽⡿⣽⠻⣟⢿⣾⣻⣷⣯⣿⣿⣿⣷⣯⣽⣚⢿⣿⣿⣯⣽⣾⣟⣿⣞⣿ ⣿⣿⣿⣿⣿⣤⣡⣧⣿⣴⣀⠀⠃⣿⣿⣿⡭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⢈⠀⠀⠋⣨⠋⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣷⡷⣟⣽⣿⣽⢿⣫⢿⣿⡿⣟⣯⣿⣿⣾⣻⣟⣿⢿⡾⣟⣧⡾⣟⣼⣷⣟⣧ ⣾⣿⣷⣮⣿⣹⡘⢄⡀⠤⠈⠁⡟⣿⣿⣿⣿⣾⣧⣔⢠⡟⣿⣿⣿⣿⣿⣿⣿⢹⠀⠁⠉⠉⠉⡈⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣿⣽⣯⣿⣾⢿⣷⣾⣏⣽⣿⣟⣯⡿⣟⢯⣿⡿⢏⣾⣽⣯⢿⣰⣛⡾⣟ ⢟⣹⠷⣍⡶⣼⠋⠙⠛⡛⢿⣿⣶⣿⣿⣻⢞⢡⣠⡑⡏⣿⣿⣾⣾⣾⣀⢧⣿⣿⣆⣿⣻⣴⠦⠙⠀⡀⣤⣷⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣳⣿⣷⣽⢾⣿⣯⢷⣯⣷⣿⣿⢿⣯⡾⣿⣯⣿⣿⣍⡭⢭⣯⡷⣟⣿⣻⡷⡿⣿⣿ ⠈⣀⢆⡷⠂⢀⣻⣀⣐⣤⣤⣷⠿⣿⣿⣿⢿⣏⠼⡿⣿⣾⣿⢼⢠⢀⠀⣇⢀⡄⢸⡐⡄⢸⠀⣄⣳⢟⠛⡛⡽⣦⣿⣿⣿⣿⣿⡵⢿⣾⣿⣯⣷⣿⠿⣻⣽⣾⡟⣿⡿⢾⣽⣯⣻⣿⣾⣙⣯⣿⣿⣟⣯⣿⣏⡼⣡⣟⣿⣳⡽⣻⢿⣽⡾⣽⣟⣿ ⠶⣳⠿⡟⢵⡼⢤⠻⠘⠣⠴⡚⣞⣧⣿⣿⣿⡿⢸⡄⣿⢈⣾⢸⠄⠘⠁⡍⠈⠀⠀⠀⠀⠀⠈⣻⠀⡴⣦⠽⡀⣷⠻⣥⣿⣿⣿⣿⣻⣿⣾⣿⣿⣳⣿⣽⣻⣿⢯⣽⡿⣯⣿⢿⣿⢿⣿⣿⣟⢾⣽⣿⣻⣷⢿⣿⣿⣻⣿⣿⣟⣿⣾⣿⣿⣷⡾⣿ ⠠⡀⡀⣘⣿⣿⢿⣧⣿⣾⠙⠾⢟⢫⣿⠿⠛⢧⢻⠈⡇⠘⢀⢠⠀⣆⡿⣿⠀⠀⠿⠈⠀⠟⢸⣞⢷⢺⠑⡃⢮⠐⣀⢳⡛⣭⣷⣿⣿⣿⣿⢿⣻⣿⣽⣻⣿⢿⣽⣾⣿⣿⣿⣯⣟⣿⣷⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣟⡽⠿⣿⣿⡿⣾⣿⣟ ⢿⠻⠻⠟⣿⣿⢳⣬⣥⢦⠉⣤⣷⣔⣿⣿⣾⣽⣦⣌⠴⢦⠲⠙⠈⠀⡄⣹⠘⠘⣷⢸⠀⡇⣮⠐⡀⢧⡆⣿⠛⠓⠈⡇⠚⣷⣭⣾⡿⣿⣿⣾⢿⣿⡿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣽⢿⣯⡷⣟⣮⡿⢟⣿⢿⣿⢿⣿ ⣧⣟⣿⣿⣽⣾⡻⢄⡙⠿⣻⠘⡍⠡⣿⣯⢿⣉⠠⢃⠄⠀⠛⣶⢘⠀⠀⣯⢚⢿⡄⢿⠀⡆⢌⠃⠀⡀⠹⣈⣇⡹⢈⡁⢈⡀⣄⢦⣧⣿⣿⢿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣟⣿⣿⣾⣿⣿⣯⣿⣿⣿⣿⣿⣾⣿⣿⡷⣿⢿⣻⣷⣿⣿⣿⣿⣿ ⣤⣞⣷⣶⣻⣵⢲⣍⡿⣿⣿⣛⠝⠩⣷⠘⣇⣼⣦⠦⣛⡴⣨⠀⠀⠀⠀⡄⢱⡄⢠⡃⢸⠀⢠⠀⢘⠀⠀⠀⡀⢧⠉⡆⢀⠈⢄⠻⠀⣧⣻⣿⣿⣾⣿⣿⣶⢿⣿⣿⣿⣿⣳⣿⣟⣾⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿ ⠡⠘⣋⠏⣻⣽⢮⡟⣿⣻⣵⢢⠃⡹⡿⢸⣦⢷⠻⠟⢲⠙⡀⠤⠀⠀⠀⠀⡄⠳⠀⠀⢆⠐⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⡆⣝⡲⣿⣻⣿⣿⢿⣿⣿⢇⣿⣯⣿⣷⣿⣯⣿⣿⣷⣿⣿⣿⣿⣽⣿⣿⣿⣽⣿⣿⣿⣻⣿⣿⣿⣿⣷⣿⣿⣿ ⡂⡕⣾⣾⣶⣾⣵⣠⣉⣤⡽⣦⣿⡿⣿⣿⣔⠧⡢⣍⢾⣠⣦⣉⠄⠲⠙⠀⠀⡄⠌⠘⠆⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠳⣏⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿ ⢿⠻⢏⣘⠐⣷⠣⣌⡛⢯⢰⡦⣿⣿⣿⣿⠀⢋⣼⣩⠛⡟⣿⢿⠻⠛⠙⠉⠀⠀⢃⠌⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⣬⣷⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢶⣏⣼⣄⡒⣑⢾⣏⡿⣭⡿⣴⣙⣜⣈⣷⣿⣿⣶⣈⣐⣁⣶⣿⣿⣿⣿⣿⣿⠿⠻⢛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⡇⣿⣿⣾⣿⡟⣿⡿⣛⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢻⢐⡀⣄⠒⡃⢯⣞⠿⣿⢹⠈⡄⠿⡏⠸⣠⣦⢿⡟⠛⣱⠾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣡⠰⣈⠱⣞⠄⣩⣖⣉⣶⣿⣿⣿⢓⡿⣙⣠⡾⣀⠒⠙⠩⠟⣿⣿⣿⣷⣿⣙⣏⣿⣿⣿⣿⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⡐⠊⢅⡠⢀⡍⡘⢢⡵⠚⠡⣀⣤⣤⠴⡈⠁⢆⠜⠉⠈⣅⣿⣿⣻⡽⣻⣟⣳⣽⡿⣿⣿⣵⣾⣾⢷⠙⠀⠀⠀⠀⢰⠀⠀⠀⣇⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⣸⠐⠠⠀⠄⡙⢶⡨⠐⡁⢆⠷⣿⣿⡟⠛⢹⠿⣟⢾⣿⢯⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣾⣿⠨⠁⠀⠀⠀⢀⡟⣿⣾⣿⣿⢛⡟⣿⣽⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⠀⠟⡀⡿⠘⡄⡄⣿⢻⢠⡿⣿⣿⣿⢿⣧⣿⣟⣿⣿⢿⣻⣿⡼⣿⣟⡿⣿⣼⣿⣻⣿⣼⢿⣿⣿⣿⣟⢿⠻⠀⠀⠀⠀⣼⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢻⠷⠿⣿⣧⢍⠀⢂⣝⡱⠿⣿⣽⣻⢿⣿⣶⣿⢿⣿⢿⣿⣿⣽⣿⢾⣽⣿⡿⣟⣻⣽⣻⣿⣿⣯⣿⣿⣷⣿⣟⢿⠻⠙⠉⡆⣾⢡⠟⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⣿⣿⣿⣾⢻⡽⠟⢯⡜⡛⣧⣿⣿⣽⢶⡀⠱⢂⠀⣟⡽⣻⢿⣽⣻⣿⣽⡿⣽⣻⣿⣷⣯⣽⢾⣿⣻⣿⣿⡿⣿⡿⣿⣿⣿⣿⢿⡿⢧⣿⣿⣿⣿⣾⣿⢿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣜⢾⣫⣵⣞⣍⣮⣿⣿⣿⣾⣭⣿⣿⡾⡱⣞⠉⢱⡬⠟⣯⣟⡾⣟⣯⣟⣯⣿⣻⣷⣟⣿⣿⣾⣽⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣭⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢿⣫⠿⣛⢷⣟⣿⣿⢷⢊⡱⣵⣎⣿⠜⢯⡳⣟⢿⣮⣟⣽⢾⣻⣽⣿⢯⣿⣾⣻⢷⣿⣯⣿⣟⣻⣿⣷⣾⣿⣿⣽⣿⣾⣿⣿⣟⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢿⣿⡿⣿⡿⣿⣿⣻⣜⡙⠧⢏⣻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣻⣿⣿⡿⣿⣿⣯⣟⣿⣿⣏⣿⣻⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠖⠒⠒⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠁⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⡀⡀⣠⣤⣴⣶⣿⠦⠤⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡒⢾⠀⠀⠀⠀⠀⠀⠀⢀⣷⣿⠟⠋⢉⣀⡠⠤⠤⢄⣉⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡀⠠⣄⣠⣾⣥⣄⠹⣼⠀⠀⠀⠀⠀⠀⣤⣾⠟⢁⡤⠚⠉⣀⣠⠤⠤⠤⢤⣉⡻⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⣿⣷⡿⠋⠁⣈⣻⣧⡏⣆⠀⠀⠀⣠⣾⡿⠁⣰⠋⢀⡴⢋⣡⣤⣶⣶⣶⣦⣤⣙⣮⣳⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⡿⠀⣰⡿⣿⡁⠈⣇⡿⣾⣶⣿⣿⡿⠁⣰⠁⣰⣿⣾⠿⠛⢉⣉⣠⣀⣉⠙⢻⣿⣿⣷⣟⣡⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢰⡏⣼⣿⣿⣿⣿⢷⣈⠉⠉⠉⠀⣰⠃⢠⣿⣿⠁⢀⣴⠟⣁⣤⡞⠉⢻⣆⠙⢿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠸⣧⠹⣿⡿⠛⠉⠀⢈⣙⢦⣠⠴⠃⠀⢸⡿⠃⠀⣼⠁⣾⣿⣿⣷⣶⡞⢹⡆⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢘⣷⠁⠀⠀⠀⠀⠀⠹⠄⠙⢦⡀⠀⠸⡇⠀⠀⢻⡄⢿⣿⣿⣿⣿⠇⢨⠇⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⢹⡀⠀⠈⠿⣦⡉⠛⠛⢁⡠⠋⠀⢀⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢀ ⠀⠀⠀⠶⠦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⢿⣗⡲⣦⣄⣀⡀⠀⠀⢀⣠⢶⡟⣧⠀⠳⡀⠀⠀⠈⠉⠉⠉⠉⠀⠀⢀⡾⢹⠀⠀⠀⠀⠀⠀⢀⡀⢠⡇⠀⠀⠀⠀ ⠀⠀⢀⡞⠁⠀⠐⠊⠉⢩⠳⠤⣄⡀⠀⠀⢀⡤⠚⠉⠀⠸⣿⠙⣿⣿⠁⢋⣽⠿⢁⣴⠟⠀⠈⢷⡀⠘⠲⢄⣀⠀⠀⠀⣀⣠⠖⠋⢠⣿⡀⠀⠀⠀⢀⡔⣡⣹⡎⡇⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⢄⠀⠀⠀⠁⠀⢀⡴⠙⣦⠖⠁⠀⠀⠀⠀⢀⣿⠀⣏⣿⠷⠋⣁⡴⢫⡟⠀⠀⠀⠀⠙⢦⣀⠀⠈⠉⠉⠉⠁⠀⣀⣴⣏⢸⠁⠀⠀⢰⢋⣾⢣⣿⢰⠀⢠⡣⠀⠀ ⠀⠀⠀⠀⠀⠈⠁⠀⣀⣀⡀⠈⢀⠞⠁⠀⠀⠀⠀⠀⠀⢨⣿⣦⣤⣤⣶⣯⣥⣶⡟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣶⣶⣶⣶⠶⢟⡟⠁⢻⣼⠀⠀⢰⠋⣼⢃⣿⡇⠀⢀⢯⠇⠀⠠ ⠀⠀⠀⣀⡤⠖⠚⠉⠁⠀⠉⢲⠏⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣃⣿⡿⠿⣶⢿⠁⢀⠏⢰⡟⢨⡏⡷⠀⡞⡞⠀⠀⠀ ⠀⠀⢠⣖⠻⡶⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡍⢹⡿⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢿⣿⡇⠠⣿⡼⡄⣸⠀⣾⠃⡾⢳⠇⣸⣹⠁⡼⠀⠀ ⠀⠀⠒⢠⡉⡳⢵⣄⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⣀⣼⣿⡿⠙⢦⣴⣿⡅⠊⣻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣯⠞⠙⡇⡇⡷⣴⣟⣸⡇⠀⢠⣧⡏⣼⠃⠀⠀ ⠀⠀⣈⣒⡺⠥⠤⠛⣆⠀⢀⣠⣿⣿⣷⣶⣶⣿⣿⠿⣿⠤⠞⢻⡿⠉⢷⡒⠹⣆⢻⣷⣄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠏⢩⣿⣷⣄⣉⣏⣟⠟⠻⣿⣄⣤⣼⠾⢶⣧⠀⠀⠀ ⠀⠀⠠⠤⠭⠭⣍⠉⠘⣤⢟⣵⠟⢻⣿⣏⡿⠋⣁⣤⣾⡀⠀⣾⠇⢳⢀⣿⡖⡺⠻⣿⣿⣷⣦⣀⡐⣶⣾⣿⣿⣿⣿⣯⣦⣿⡟⠁⢹⠹⡇⢷⡀⢀⣬⡛⠉⠛⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣈⣹⣡⡴⣾⣿⠋⠉⣽⡟⠀⢧⡀⠙⠀⢈⡿⡟⣟⠁⠀⡿⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠛⣿⠀⣾⣄⠙⣴⣿⣇⠀⠀⠟⣇⡆⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⡿⠋⣏⣽⠟⠁⣼⡟⢹⡄⠰⡟⠀⠀⣴⣻⣖⠞⠁⣿⠡⡌⢦⣄⣀⣠⡿⢻⡿⡿⣧⡁⠙⢁⣴⢿⣿⣿⣦⣩⣾⡟⣏⡍⠻⡎⢹⡭⠶⣄⠉⠫⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⢀⣽⣨⣬⣾⣿⡇⠀⣰⡟⠐⡆⣷⣤⡤⠴⢋⣧⠃⢿⠀⠐⡿⠀⢹⣴⣿⣧⠼⠁⢸⣟⢳⡛⣿⣿⣯⠁⠀⢻⣏⢿⣿⣿⣿⣿⣿⣧⣤⠾⡿⢦⠈⣷⣦⣄⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⡍⣰⡿⠁⡉⢷⠂⢿⠀⢀⣷⣫⢿⡇⠀⢸⡏⠘⡎⢧⡀⠁⢒⠾⢹⡇⠸⣆⠀⠘⢻⣠⣷⢿⣿⢿⣷⣦⡄⣛⣮⣿⠁⠙⣷⢸⣿⣿⣧⣽⣦⠴⠟⠛⠚⠳⠆⠀⠀ ⠀⢀⣾⣿⣿⣤⠛⣀⣠⣵⡿⣿⢺⠲⢉⣯⠇⢄⢧⠞⣲⠁⠀⣸⣿⣹⢻⡀⠀⠘⡇⠀⠹⣵⣦⣴⡟⠀⠈⣿⡴⣭⣿⣿⣿⣿⣿⣷⣷⣾⣾⣿⠿⠋⠉⠙⠿⢿⠟⠺⠾⣧⣄⠀ ⠀⠘⣿⣿⡿⣿⣿⣿⠿⢹⣻⢹⣍⠄⣼⡏⢰⢸⡈⣷⣧⠠⠞⠁⡏⡇⢦⣷⡄⠀⠁⢡⣴⠏⢻⣏⣝⢦⣀⡌⠛⣎⢿⣿⣿⣿⣿⣿⣿⣿⡟⡁⣀⠀⣠⠀⣤⣿⣀⡀⠀⠀⠈⠀ ⠀⣼⣿⣿⣿⣿⣿⣣⠀⣿⢇⠈⢧⣀⡟⠀⢸⣬⣾⠇⢻⡀⠀⢀⣿⢁⢀⢫⣯⣷⣾⣹⠃⢀⢸⢫⠘⣞⣿⣿⣧⡛⡌⠿⣏⣳⣿⣿⣿⣿⠿⠟⠛⠻⢿⣿⠋⠘⠽⡯⠭⠬⡏⠉ ⢠⣿⣿⣿⣿⣿⣿⣧⡐⡿⡜⣼⣼⣿⣷⡿⠋⢸⡾⡄⠈⢿⣄⠀⢿⠸⣼⣼⣻⠫⠘⢿⣤⣾⠘⠈⠀⣼⣿⣿⣿⣿⣿⣤⣶⣿⣿⣿⣿⣿⠐⠲⢤⣀⠒⣿⢠⡾⡄⡼⣃⡴⠃⠀ ⢼⣿⣿⣿⣿⣿⡿⣟⣿⣿⢿⡿⢿⡿⠿⣧⡀⠀⠃⢳⢀⣾⣿⣷⣷⣔⠋⠉⠸⠹⡄⢸⣿⣿⣲⣶⣞⠉⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠠⣀⣾⡿⠷⣷⡿⠛⠋⠁⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠋⠈⢨⡇⠀⠈⢇⣲⣶⡾⠿⠙⠛⡏⠀⠛⣶⣄⣀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣧⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣳⢤⣘⠙⠳⣶⣦⣄⣔

⠀⠀⠀⠀⠀⠀⠁⠋⠛⠛⠛⠛⠛⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠟⡷⣯⣷⣟⣾⣻⢿⣷⣞⣻⣷⠿⠛⠈⠀⠉⠟⠿⣽⣿⣟⡷⣽⢿⣯⣽⣿⢾⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠃⣿⣞⣿⣿⣽⢿⣯⣽⡿⣿⣿⣿⣷⢯⣿⣯⡿⣟⣯⢿⣷⣟⡿⣿⣿⡾⣽⡿⣷⣽⣿⣷⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣾⣽⣾⣿⣯⡷⢿⣯⢷⣻⣽⡾⣽⣻⢷⣾⣟⣿⢾⣻⣿⢯⣽⣻⢾⣽⣾⣟⣿⡷⣻⣷⣿⠸⠀⠀⠀⠀⠀⠀ ⠃⠚⣿⣿⣟⣯⢾⣽⣾⡿⣟⣿⡿⣞⣿⣯⣞⣿⣷⣿⣷⣿⣻⢿⣻⣽⢾⣿⣯⣟⣽⣿⣾⡿⣳⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⣿⣼⣦⣿⣟⣯⢷⣾⣿⡷⣯⢷⣻⣿⣳⣿⣾⣿⣿⣟⣻⢿⣷⣯⢷⣻⢾⣽⣻⣿⣳⣿⣿⢩⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⣦⢿⠙⡈⣄⣦⣷⣷⣟⣯⣳⣿⢯⣻⣽⢿⣯⣷⣞⣿⣽⡿⣯⣞⣿⡽⣾⣻⢷⣻⣿⣾⢠⠀⡀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⣶⣿⠛⠉⡅⣿⣽⣾⣿⢳⣿⣿⣽⣿⣯⣷⣿⣯⡟⣽⣿⣯⢻⣽⣿⣿⣿⣾⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣷⣿⡿⣿⣟⣻⣷⢿⣷⡽⣿⣯⡷⣽⡾⣿⣿⣟⡿⣾⣷⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠞⡤⣀⠀⠉⡀⣄⣦⣿⡿⣳⣽⢾⣿⣯⡽⣾⣻⣿⣼⢀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢈⠀⠁⡼⣀⠀⠀⠻⡀⣷⣽⣻⣷⢿⣯⣳⣿⣞⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣆⣸⣀⢺⠛⠛⠍⣦⣼⡏⣾⣻⣿⡿⣿⣿⡿⣟⣯⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣆⣹⣿⣿⣿⣿⢻⣿⣾⣟⣿⣼⢀⠛⡀⣿⡿⣞⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⠿⣿⣿⣿⣴⣧⣿⢯⣷⣟⣿⠛⠟⢿⠿⣿⣻⣽⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣼⢀⠀⡇⣿⣯⣳⣿⣿⣿⣿⣿⣿⣿⣽⡿⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⣿⣿⣾⠀⠀⠀⡇⣿⣯⣿⣿⣿⣯⣷⣟⣯⣷⣿⢿⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⠿⠿⡿⣿⣿⢯⣿⣿⣾⣷⣿⡿⣿⣶⢿⣻⣷⣿⠿⠻⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣦⣷⣿⣿⣿⣿⣿⢷⣿⣿⣿⢿⠀⣇⣿⣿⠹⡀⣷⣿⣿⣿⣿⣿⣿⣿⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⣿⣹⠀⡁⣿⣿⣬⠈⡇⣿⢸⡀⣄⣤⣶⣿⣿⣴⣯⠶⠓⠛⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⣟⣿⣿⣿⣴⠀⡟⣿⣿⢲⡠⡟⣿⢠⠀⠀⠀⠀⡀⣧⡼⢂⡝⣀⣉⣈⣧⠸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⣟⢯⣿⣿⠿⡻⣽⣿⣻⠛⡿⣿⣸⠀⠀⠀⠀⠀⠀⡆⢿⠁⡼⣀⣀⣀⣄⢧⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣾⣽⡿⣳⣿⣽⣾⣿⣯⣷⣿⣾⣿⣾⠀⠀⠀⠀⠀⠀⠀⡇⣸⠃⣼⡠⣀⣄⠦⣿⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣽⣿⣷⣯⣿⡿⣞⣿⣯⣟⣷⡾⣟⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⣧⣌⢦⠛⠟⡿⠿⣴⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣼⣟⡼⢿⣧⡟⣧⣿⢿⣿⡿⣿⣿⣿⢠⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⠀⡄⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⣽⡾⡽⢾⣟⣳⡽⣳⣻⣷⣽⣟⣯⢯⣟⣧⢾⠙⠀⠁⠋⣿⠙⠉⠀⠀⠀⢹⠀⠀⣏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣻⢷⣳⣟⢳⣻⣳⣽⡟⣳⣿⡽⢯⢷⣫⣽⣞⣿⡀⣀⣦⣿⣠⣇⠸⠀⠀⣄⠤⡤⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⡿⣻⣿⡟⣳⡽⢾⣳⡽⣳⣿⡼⣻⡾⣝⡾⣟⣼⠀⠀⠁⢢⠋⡿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⠀⡄⣿⡟⣭⣻⣳⣿⣳⣼⢻⣾⣛⣿⣰⠀⠀⠀⡀⣄⣶⣿⣿⣾⣤⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⠙⠀⡀⢦⣷⡟⣯⣻⢷⣮⢻⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⢿⠛⠉⠉⣻⣝⡿⣟⣾⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠉⡀⠀⣄⠶⡙⣈⣆⠲⡙⠧⠟⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⠿⠛⠈⠀⣄⠦⠑⠀⢆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢳⡰⣀⣤⢴⡂⣔⣦⣶⢿⠻⠉⠀⣗⠲⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣶⠻⣝⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣆⣿⣿⣿⣿⢹⡀⠀⠀⠁⠀⠈⠀⠀⠀⠀⡜⠣⠀⣆⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⠹⠀⠀⡄⠀⢀⠀⠈⠀⠀⠀⠀⠣⠀⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡆⣿⣿⣿⣿⣧⠘⠀⠀⠀⠈⠀⠀⠁⠀⠀⠻⡜⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣤⣤⣤⣤⣤⣀ ⠀⠀⣧⣿⣿⣿⠉⣧⠉⠈⠀⢀⠀⢀⡄⠹⠀⣣⢰⠂⠄⣿⣿⣤⣦⣀⣀⠀⠁⠋⠛⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⠀⣇⣎⠘⠀⠀⠀⠀⣆⢹⠀⠡⢸⠀⣷⣿⢸⠀⠀⠁⠟⣴⣠⠀⠀⡀⣧⠻⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⣿⣿⣿⢸⠙⣄⠀⠀⠀⠀⠀⠀⣆⢻⠀⢹⠃⡇⣿⣻⠀⠀⡗⢺⠀⠀⠀⠀⠀⠀⣷⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣆⣿⣿⣿⠂⡀⠲⠀⠀⠀⠀⠀⠀⡇⣼⢸⣄⣿⢸⣿⣾⠅⢳⣏⢸⠀⠐⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⣿⣿⡿⠀⠀⢠⠀⠀⠀⠀⠠⠀⢹⣿⠀⣿⢻⣿⢼⠅⣿⣴⢀⢄⡙⠗⠈⢀⠸⡿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡧⣿⣿⣿⠘⠀⠀⠀⣄⠠⡘⢠⡆⣿⣿⠀⣇⣿⣿⢻⡾⢠⠙⠈⠦⠘⢄⣄⠠⢶⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣧⣿⣿⢻⠀⠀⠀⠁⠍⢯⠟⠿⣿⣿⠿⣿⣿⣿⣿⢀⠀⠀⡄⠱⡀⢥⠿⠛⠞⣤⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣴⣤⣥⣯⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⢨⢠⠀⠀⠀⢾⡀⠀⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡧⣿⣿⢰⠀⠀⠀⡄⣶⣿⣿⣿⣿⣿⣿⣼⢀⣢⢌⠸⠀⠀⢸⠀⠉⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⣾⣞⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣷⠹⠈⠀⡇⢰⡐⡄⢲⢏⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢠⠀⠀⠀⠀⠀⡀⣑⣬⣿⣿⣜⢀⠀⠀⠁⡴⠀⠛⠀⢏⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠈⠋⣼⢪⢴⠀⠀⠀⠃⣰⠀⠞⢣⡿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⣿⠀⠀⠀⠀⠀⠀⡝⢞⣠⠞⠠⠀⠀⠀⠀⣸⠁⡴⢏⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⣿⢀⠀⠀⠀⠀⠀⠂⣀⠦⡀⠀⠀⠀⠀⠉⠆⢶⢋⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡆⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠞⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠒⠟⠿⣵⣟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡿⢰⠀⡏⣼⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡎⣯⢀⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⢰⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠞⢠⠃⡿⣿⢿⠿⠛⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⢔⡤⠀⠋⣾⣀⣀⣤⣤⣶⣶⣿⣿⣿⠿⠿⠛⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⠀⠀⠏⣿⢠⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣤⣦⣶⣿⣿⣿⢿⠿⠻⠛⠉⠈⠀⠏⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣾⠁⠐⡇⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣄⣤⣶⣶⣿⣿⣿⣿⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢻⡰⠀⡁⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⣏⣾⠀⠀⡁⣿⢿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡁⣾⢠⠀⠂⡿⣿⣿⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠂⣿⣰⠀⠇⣿⣿⣧⣿⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⣰⠁⠟⣿⣿⢣⣼⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠋⡴⢩⠟⣿⣿⣾⢇⣤⡏⣧⣏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠊⠖⡶⣷⣿⢂⣵⢋⣿⠔⢀⡎⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⠤⣀⢀⠉⠚⠄⣠⠋⠟⣴⣫⡰⠀⠋⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠉⠋⠒⠤⣴⣩⠛⡴⢀⠀⠊⢳⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣀⢀⠁⠋⠟⡢⣪⣠⠀⠀⠀⠋⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠋⠔⡠⣊⡠⢀⠀⠀⠀⠀⢉⡔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠊⠒⠲⠐⠆⠐⡽⠲⠶⠤⠠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⠀⠀⠀⠀⠧⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠀⠀⠀⠗⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠈⠁⡟⣿⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⣿⣿⣿⠻⣿⣿⢻⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⠻⠛⠿⠛⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀ ⠀⠄⠀⠀⠀⠀⠀⠀⠁⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀ ⠇⡇⠈⠀⠀⠀⠁⠟⡿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣾⣀⣧⣿⣿⣿⣷⣾⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⠸ ⡄⣿⢻⠀⠀⠀⡄⣿⣿⣿⣿⣝⣷⣿⣿⣿⣿⣿⣿⠿⡿⣶⣷⢿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢿ ⠀⣧⣿⠹⠀⠀⠇⣿⣿⣷⣿⣿⡿⣿⣿⣿⣿⣿⣿⣾⣠⠰⡀⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡀⣷⣿⢿⠙⠀⣿⣿⢻⣽⣿⣿⣻⢛⡔⣤⣦⢀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼ ⠀⠀⠀⣆⣷⣹⣮⣷⣿⣭⣭⣭⢋⡚⢴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣯⣿⣯⣿⣿⣿⣿⣿⢠ ⠀⠀⠀⠀⠀⣄⣦⠶⡲⣶⣒⢒⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣟⢿⣿⣿⣿⣿⣿⣿⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣯⣿⣿⣿⣿⣿⣸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⠙⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⣟⣿⣻⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣯⣿⣿⣿⣿⣿⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣆⣴⣻⣷⣞⣨⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⢀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠁⠝⣿⣾⣿⣾⣿⣾⣷⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠋⣫⡾⣻⣿⣟⣯⢧⣎⢻⣹⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠊⠛⡿⣿⢾⠯⠚⠈ ⠀⠀⠀⠀⠀⠇⢷⢫⣿⣶⣛⢮⣱⣿⢞⣟⡽⡾⣟⠛⠛⠛⠟⠟⠿⠿⣻⣿⣿⣿⢿⣿⡿⣷⣾⣟⣧⣞⣿⣟ ⠀⠀⠀⠀⠀⡇⡏⣏⡲⣽⡷⣏⣿⣣⣽⣿⡶⣟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣷⣾⣟⣷⣯⣳⣼⣛⢧⣥⠾⣿ ⠀⠀⠀⠀⠁⡿⡿⣿⣷⣯⡱⣞⡯⣶⣝⡳⣏⣶⣟⣿⣾⣿⣾⣳⢷⣬⣻⣽⣫⢷⣮⣾⣹⢻⣬⢛⢳⣦⡝⣿ ⠀⠀⠀⠀⡧⣯⣿⡿⣿⣦⢚⢱⢭⡼⡓⠲⣈⣿⣏⢽⣮⣽⣛⢥⡹⣌⠳⣌⡞⢷⣽⢞⣫⠷⣎⠑⡸⢯⡷⣿ ⠀⠀⠀⠀⡄⡾⢿⣯⢲⢭⡌⠐⠁⣊⡑⢫⣟⢁⣯⡑⢿⣎⡙⣢⠵⣌⡹⢦⣁⡼⣎⡷⣌⠲⣍⡲⡙⢞⣠⠀ ⠀⠀⠀⠀⠀⢣⢯⣯⣿⣻⣝⠦⣄⠏⠳⢒⠈⡂⢁⣩⠑⠜⡡⢞⡡⣜⠉⢧⡐⡜⢋⢂⠗⠫⢝⣾⣴⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⣿⣿⣿⠾⣙⣹⢳⢋⣀⠖⡈⢀⠁⠋⠠⡜⠡⡴⢊⡡⢌⠚⡡⠵⠊⣥⠞⡤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⣿⢿⣯⣝⡲⢽⣁⡘⠣⠆⡉⣱⡜⢊⡑⣊⣐⢤⡒⢎⡙⢲⡩⢖⡠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⠛⠿⡿⣿⣿⣞⡹⢿⣂⡰⠃⢙⡮⣙⣷⠞⣙⠷⢋⣰⣇⠌⢭⡧⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⡟⣿⣿⣿⣿⣿⣞⣽⣛⣦⢼⡻⢎⡳⢦⡲⢸⣵⡜⡻⠞⣃⠳⢉⢟⣽⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡸⡿⣿⣾⣿⣼⣻⢵⣎⡳⢸⣏⠶⢎⣓⠬⢷⡆⡏⣅⠳⣍⣹⠶⠻⣚⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⣧⢻⣷⣛⣶⣎⡱⡌⡔⣎⢦⣬⣳⢖⡜⢫⣥⣈⣽⠮⣱⡟⢪⡜⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⣲⣬⣷⡽⢫⢳⡈⠁⡌⠐⢩⢦⠹⣣⢞⣩⠶⣌⡹⣾⣘⡶⢧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠦⣑⢮⠹⠏⡋⠔⡪⢖⠤⠓⢫⠒⣉⣽⢎⠳⣜⡏⢀⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⣿⡿⢿⣿⡿⢚⢩⣡⠦⠞⣯⢺⡷⢎⢧⡓⣌⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠋⠛⠽⢿⣿⣿⣿⣿⢿⢮⣙⡚⣝⢧⣋⣤⢳⣈⢉⠳⠙⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣫⣿⢽⣾⣿⣷⣿⣿⣷⣿⣽⣎⡷⣜⣋⢡⡾⣗⢧⣬⡙⠖⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣽⢿⣯⣞⣱⣾⣟⣻⣳⢦⡸⢍⣴⣭⢂⠸⠖⣊⠴⣚⣱⡽⢮⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢧⡾⢋⣵⡮⠞⠳⣆⣬⢳⢽⠂⣤⠚⢥⡒⢨⠄⣉⣋⡖⣞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠦⣞⣳⡽⢳⣍⠢⢊⢐⡀⡏⠐⣄⠒⢣⡆⠐⢢⡖⣏⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢤⠦⣾⡟⠣⢮⢒⣹⣄⠡⡆⠀⠄⠠⢉⣊⠔⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣄⣑⢯⡙⠻⡙⢚⠹⠉⢋⠖⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠚⢉⣙⠻⠟⢏⠙⠲⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠉⢀⡒⠊⢽⠁⡢⠑⠤⢀⠄⠀⣹ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠚⠉⠁⡤⠠⢈⡨⠃⠢⡀⢄⠆⡇⢀⠄⢄⠤⢄⣳ ⠀⠀⢀⡠⠔⠒⣉⢉⣀⠀⡴⢄⡁⠜⢱⠪⡑⠄⢅⣆⠀⡀⠘⠀⠅⠂⠀⠀⢸⠁ ⠀⢠⣿⢄⠒⠬⢂⠔⠂⢺⠀⠢⡑⠴⢈⠀⢈⣰⠂⠀⠈⠂⠀⠁⠀⠀⠀⡠⠃⠀ ⣠⠊⠉⢂⠢⣀⠸⠈⠆⢚⡰⠒⠨⠒⢓⡐⠑⠒⠂⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀ ⣇⠤⠀⢀⡓⢠⠖⠒⠒⠈⠡⠈⠑⠊⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠁⠀⠀⠀⠀⠀ ⠙⢆⣀⢈⡔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⠳⣄⣀⠀⠀⣀⣀⡠⠤⠖⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠂⠓⠝⠭⠻⠛⠞⠬⠿⠯⠿⠛⠛⠤⠧⠻⠛⠈⠁⠚⠒⠒⠓⠛⠉⠉⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⣟⠀⠁⣧⣿⣽⠧⠂⣿⣿⣿⢻⠪⣟⣿⣿⢋⡛⣹⣘⡊⣗⣿⣿⢼⡺⣿⣿⣿⣿⣿⣿⢿⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣆⡵⣱⣦⣧⣿⠉⠇⣿⣿⣿⣽⣯⣿⣾⣧⣿⣿⢹⣀⢉⡿⣿⣿⣸⣯⣾⣷⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⢮⡿⣿⣹⣷⣿⣿⣩⣿⣾⡼⠀⠀⣿⣿⣤⣄⣿⣿⣾⣫⠟⣿⡾⣥⣾⣶⣤⣠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣾⢳⠚⣷⣿⣿⣾⣠⠀⠀⠀⡄⣷⢿⠒⣗⣿⣿⣿⣿⣶⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣹⢀⣏⡟⣿⣿⣿⠀⠀⠀⠀⠀⠇⣃⢠⠀⠇⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠴⢀⡂⣧⣿⣿⣿⢸⠀⠀⠀⠀⡇⠺⠀⡔⢞⣷⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⢀⠀⠗⡄⣿⣿⣿⢸⠀⠀⠀⠀⣿⢠⠀⡀⠀⡃⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡉⠌⠄⠀⢄⣿⣿⣿⢸⠀⠀⠀⠀⣺⠀⠀⠧⠿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠪⠀⠁⡏⣿⣿⣿⢸⠀⠀⠀⠀⢷⢹⠉⠉⢏⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣿⣌⡅⣾⣿⣿⣿⢸⠀⠀⠀⠀⡎⣴⣠⣇⣿⣿⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡾⠿⠷⣿⣿⣿⢿⠈⠀⠀⠁⡾⢿⠿⢾⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣭⢀⠀⠀⢀⣿⣿⣿⢹⠀⠀⡿⣴⣄⡐⢒⡿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠼⡀⢁⢠⠉⡿⣿⣿⣿⠀⠀⣿⠐⠀⠀⢀⡊⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠚⠛⠚⠓⠛⠈⠀⣾⢑⠟⡿⡿⡿⣿⣿⣿⣿⠀⠀⣿⣻⠝⠊⠓⠥⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡎⢹⣾⣠⡇⣽⣇⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⢿⡻⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⠧⢂⠁⡷⡠⡟⣷⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢁⢪⠨⠀⠈⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠜⢦⣤⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡟⣣⠤⠁⢸⢁⣟⣿⣷⣿⣿⣿⣿⣿⣴⡤⣠⣄⣤⣤⣧⣷⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⣋⢟⢿⡟⠿⣾⢀⠀⡄⣯⣾⣽⢗⢀⠀⠀⠀⠀⠀⠀⠁⠊⡟⣫⣿⣿⣿⣿⣽⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡿⣄⣥⣷⣷⣿⣿⠘⠀⠇⣿⢹⡻⡟⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣢⠀⠀⠊⣷⣿⣿⢸⠀⣿⣿⣄⣝⣷⠀⠀⠀⠀⠀⠀⡈⠐⣵⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⡺⣖⣦⢿⠻⠈⠀⠀⠀ ⣸⢲⠀⠠⣧⣿⣿⣿⢸⠇⣿⣾⣓⣿⣗⠀⠀⡀⠀⠀⠀⢀⡂⡷⡋⡿⣿⣿⣿⣿⣿⣿⠘⠀⡜⣤⣤⢿⡿⣿⢸⠀⠀⠀ ⢡⠃⠀⠂⠂⣿⣿⣿⢠⡇⣿⢺⢴⣣⣞⠈⠀⠀⠀⠀⠀⠀⠀⠊⡋⣿⣿⣿⣿⣿⣿⣿⢸⠃⣤⢦⠻⡟⣿⣿⢿⠻⠈⠀ ⡄⠑⠫⠑⡇⣿⣿⣻⠈⡀⣿⠅⢔⠨⠙⢸⠀⠀⠀⠀⠀⠀⠀⡀⣤⣾⣿⣿⣿⣿⣿⣿⠋⢯⠻⠙⡟⣷⣾⣿⣽⣯⣿⠹ ⠀⠁⠊⣤⣦⣵⣷⣿⣿⠻⣿⡹⠁⠈⠑⣗⠀⠀⠀⠀⠀⠀⠋⠛⠛⣿⣿⣿⣿⣿⣿⣾⢆⡶⣿⣿⣿⢵⡿⣯⣿⡿⣿⣿ ⠀⡀⡸⠁⠀⠁⠎⣖⣿⣿⣿⣿⡹⢃⠁⣈⢣⠀⠀⠀⠀⠁⣮⣷⣿⣿⣿⣿⣿⣿⣿⢠⠋⡟⣿⣿⣿⣿⣨⣌⣠⣏⣷⣼ ⠀⠀⡆⣳⠘⡀⣄⢂⣯⣿⣿⣿⡿⡘⠀⠑⢁⠹⠀⠀⠀⠁⠿⡿⣿⣿⣿⣿⣿⣿⢻⡿⣿⣿⣿⣿⣿⣿⣿⠻⠙⠾⣠⠀ ⠀⠀⠀⢣⠓⠀⡀⠁⣖⣷⣿⣿⣿⣿⠀⠐⣹⣋⢻⠙⠈⠁⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣇⣿⣿⣿⣿⣿⣿⣼⢀⠀⠀ ⠀⠀⠀⠀⢢⠍⠰⠄⠀⣩⣿⣿⣿⣿⢿⢻⡶⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣯⣿⣿⣿⣾⣠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⣲⣭⣎⣗⣯⢙⠩⣿⣿⣿⢿⣷⣀⠀⠀⣿⣿⣿⡓⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣾⣠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢶⣏⣿⣰⣮⢎⣁⠉⠛⠓⡿⣿⢩⠑⡛⣿⣿⣿⣿⣝⣶⣠⠤⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣾⡗⣾⣠⣖⣤⣆⣾⣿⣿⣄⣾⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⣭⣦⢙⠁⠰⡾⡴⠀⡧⣿⡀⠀⡇⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠊⢁⣄⠎⣷⡟⢋⠉⠋⡟⣻⠟⡿⢻⣝⣟⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣗⣺⠣⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠛⡟⡌⠈⠀⣍⣯⣿⣿⣿⣴⡝⣿⣿⣿⣿⣿⢹⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣻⣷⢰⡀⣤⣧⣷⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣿⣿⣿⣿⣼⠽⠗⠸⠈⠀⠀⠀⡝⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⠀⡀⢤⠿⡿⢯⠿⠿⣿⣿⣿⣼⣠⠀⡀⣤⣤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣇⣿⣿⣿⣿⣿⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

ִֶָ𓂃 ࣪˖ ִֶָ🐣་༘࿐

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

⠀⠀⠀⠀⠀⠀⠄⠈⠈⠀⠁⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⣠⣫⡟⠛⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠁⠀⠀⠀⠀⠀⢀⡃⢸⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠁⠀⠀⠀⠀⠀⠀⡁⡃⣎⠀⠀⠀⠀⡘⡆⠀⠀⠀⠀⠀⠀ ⠠⠀⠀⡀⠐⠀⠀⠀⠀⠀⡃⣇⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀ ⠀⠀⣐⠁⢄⠀⠀⠀⠀⠁⡃⢆⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀ ⠀⠠⠢⡅⠀⠀⠀⠀⠀⠂⠅⡃⡀⠀⠀⠀⠀⡻⠄⠀⠀⠀⠀⠀ ⢀⠉⢂⠁⠀⠀⠀⠀⠀⢔⢁⠃⡀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀ ⠆⠌⡘⠀⠀⠀⠀⠀⠀⢜⢸⠀⠠⠀⠀⠀⠀⡶⡂⠀⠀⠀⠀⠀ ⡂⢠⠃⠀⣀⣠⣤⣀⣀⢭⢸⠀⠀⠅⠀⠀⠀⡯⠂⠀⠀⠀⠀⠀ ⠁⠀⢠⢯⡿⠋⠁⠹⠽⡿⣾⣧⡀⠑⢀⡀⠤⡏⣧⡄⠤⡀⠀⠀ ⠀⠀⢸⡇⡅⠀⠀⠀⢠⠃⠀⠉⢋⣷⠁⡠⣢⡯⠀⠉⠉⠲⡀⠀ ⠀⠀⢘⡷⠀⠀⠀⠀⠀⠀⠀⠀⣐⡧⡟⠁⠁⠂⠀⠀⠀⠀⠫⡀ ⠀⠀⠈⣿⣄⣀⡀⠀⠀⠀⠀⢀⢲⣽⠇⠀⡃⠀⠀⠀⠀⠀⠨⡅ ⠀⠀⠀⠑⢇⡉⠉⠋⠋⠶⢖⣒⣣⡳⡀⡌⠀⠀⠀⠀⠀⠀⢨⡃ ⠀⠀⠀⠀⠀⠁⠙⠓⠒⠂⠊⠿⣟⣪⠕⣧⡀⣀⠀⡄⠀⢀⡗⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠛⠍⠭⠝⠉⠀⠀