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⢠⣷⣶⡖⠒⠶⢤⣄⣀⢰⠏⢋⣷⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡧⠈⠁⠀⠀⣾⣷⣮⠉⠛⣺⣿⣿⢯⣳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢦⣄⣀⠀⠈⠛⠛⠁⠀⣿⣟⣿⣿⣿⠃⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⣝⠀⠀⠀⠀⠀⠀⠛⠿⠛⠉⠈⠙⠛⠛⠋⠉⠁⠉⠉⠉⠛⠛⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡇⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⣿⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠞⣿⠶⠶⠶⢾⠆⠀⢀⣷⣏⡀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣾⡇⠀⠀⢠⡇⠀⣠⢿⠃⠀⠉⠓⠦⣤⣀⡀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠛⠀⣀⣀⣾⣤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠈⢹⡍⠙⠛⣦⠀⠀⠀⠀⠀⠀⢀⡿⢴⡟⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠲⢶⣿⠿⠧⠴⠋⠀⠀⠀⠀⠀⠀⣴⣶⣖⣫⣉⣿⣶⡞⠉⠳⣄⠀⠀⣠⠴⠚⠓⠾⠧⣄⡀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣀⣤⣤⡴⠲⠖⠛⠓⡾⠋⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠓⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣄⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠭⠥⠤⠤⢤⣄⣀⡀⠉⠉⠉⠒⠒⠲⠦⠤⠤⢤⣄⣀⣀⡤⠤⠴⠋⠀⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠲⠤⢤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠐⠾⢴⠂⡓⡲⣛⠀⠀⡐⠛⠂⠀⠈⠗⢃⡀⠀⠈⠀⠀⠀⠁⢐

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠖⠒⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠒⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀ ⠀⠀⢀⣤⡖⠲⣏⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⠀⠀ ⠀⠀⠘⣿⣧⡖⡤⠍⣾⠿⠉⠻⠧⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀ ⠀⠀⠀⡸⠻⣿⣿⠟⠉⠀⠀⠀⠀⠸⢄⣀⠀⠀⠀⠀⠛⠆⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷ ⠀⠀⣴⠁⠀⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰ ⠀⠀⢹⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠈⢧⠀⠇⠀⠀⢰⡟⡦⣦⠀⢠⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢿⣯⡛⢷⠀⠀⠀⠀⠀⠙⢏⠀⠀⠀⠀⠈⢣⡘⣶⠞⠁⠀⣠⣿⣧⣾⣆⣧⠀⠀⠀⠀⠀⠀⢀⣨⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾ ⠀⠙⠻⣿⣦⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⢿⣿⠀⠀⢠⣟⣿⡿⠃⠈⡽⣄⠀⣀⣀⣴⣟⡋⢹⣦⠀⠀⠀⠀⠀⢀⣶⡶⢾⣿⠀⠀⢻ ⠀⠀⠀⠀⠉⠣⢬⣿⣶⠀⠐⣄⠀⠀⢀⡱⠀⣼⢛⢀⢰⡏⠉⣁⡠⠴⢊⣡⣶⣾⠛⠉⢀⣙⡿⠦⠽⠷⣄⣀⡀⣤⠈⠉⠀⢰⡇⠀⠠⣼ ⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⣙⠳⣤⣜⣧⡼⠻⣸⣾⣷⣷⠞⢃⠄⣰⣟⢿⣟⣹⠦⠖⠋⠁⠀⠀⠀⠀⠉⠑⠙⠧⠤⠤⠴⢿⢃⠀⢲⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠉⠙⠻⠥⠼⠧⠊⠙⠓⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠐⢤⣿⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡚⢁⣠⢶⡶⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡤⢶⢲⢺⡙⣤⣽⣿⡼⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⢩⣁⣦⠴⠶⠿⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢉⡠⠗⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⡡⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢄⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣉⣶⠴⠖⣤⠤⠽⠶⠦⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢛⠻⢝⡆⠀⠀⢿⠇⠀⣴⣰⠗ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠶⠖⠋⠚⠛⠿⠃⠀⠀⠀⢀⡴⣿⠙⣣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠘⠘⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⡀⠺⢬⡳⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠈⠳⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠼⠀⣠⡄⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⢤⣶⣒⣚⣋⣉⡉⠤⠤⠺⠟⣧⠀⠀⣀⣴⠾⢉⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣆⡻⢤⣀⣉⠓⠒⠒⠎⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣛⣻⡷⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠹⣷⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⣡⣶⠏⠉⠉⠉⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠈⣿⣿⢦⣀⣤⣤⡴⠶⠶⠶⠶⠶⠶⢺⠟⣺⣿⡃⠀⣠⣾⣶⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠐⢿⣶⣿⠟⠛⣰⡿⣿⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢀⣀⣼⡿⢧⢫⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⠇⠀⡟⢩⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠛⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠚⠓⠿⣏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡷⠖⠃⠀⠀⠀⢢⠀⠀⠀⢠⠃⠀⠀⠀⠀⢠⠀⣐⡆⠈⢧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⡿⠁⠀⢠⣶⣦⣦⠀⠀⠀⠀⠀⢀⣴⣿⣻⣅⠀⠀⠀⠟⠀⠀⢳⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⢋⡾⠀⣿⣁⠠⡄⣿⣿⡿⠻⣇⠀⠀⠀⠀⠓⢿⣿⣿⡟⡀⠀⠶⣀⣀⡀⡈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠰⡃⣾⠇⠀⡙⣷⠀⠀⠂⠋⠁⠀⡀⠀⠀⠀⠀⢀⣀⡀⠀⣀⡤⠖⠀⠀⠀⠈⢁⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣸⡏⠀⠀⣇⠻⣄⣀⠒⠂⣶⢿⠀⠀⠀⠀⠀⠀⢛⢿⣯⣁⣠⣤⣴⣶⣦⡄⣼⣿⣿⠀ ⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⢰⣯⡇⠀⠀⠘⢆⣈⣿⡤⣾⣥⣼⠀⠀⠀⠀⣼⢯⣿⡾⢿⠒⢠⡤⠊⠉⢁⣴⣿⣧⣽⡄ ⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣸⠀⠒⠛⢻⣷⣞⣯⢿⡘⣿⣿⣿⣾⡗⠀⣀⢭⣿⠓⠶⢄⣀⣠⣿⣿⣿⣈⠿⡇ ⠀⠀⠀⢰⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⢀⠴⠃⠈⠛⢿⣿⣀⠙⠛⣿⣅⣀⣀⣼⣷⡜⣷⣾⣿⣿⣿⣿⣿⡏⢸⠀⢹ ⠀⠀⠀⣸⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣫⠀⠀⠀⢠⠏⡿⣮⣿⡿⡭⢍⣡⣞⣁⣿⣿⣯⡹⣿⣻⣿⠝⠁⠁⠈⠀⣸ ⠀⠀⠀⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⢿⠀⢀⡏⠸⠀⠈⠉⠁⠉⠛⠿⣿⣿⣿⣿⣿⢷⣼⠋⠉⠀⠀⠀⠀⢰⠇ ⠀⠀⠀⢸⣿⢸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠈⣧⣿⡶⠀⠇⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣛⡆⡉⠙⠲⡀⠀⠀⢠⠟⠀ ⠀⠀⠀⢸⣿⣼⠀⡆⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡹⣷⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠼⢶⣿⠏⣴⣿⣿⣴⣿⣿⡾⠃⠀⠀ ⠀⠀⠀⠈⡟⣿⠘⣗⢤⢧⣤⠀⠀⠀⠀⠀⢀⠀⠀⠘⣝⡦⣄⠀⠛⣦⠀⠀⠀⠀⢧⣄⡀⢠⣌⣹⡷⠿⣿⠿⠿⠛⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡸⡄⡌⣾⡀⣏⠣⣤⡄⠀⠀⠘⣧⠆⠀⠘⢿⣮⣵⣦⣀⢀⠀⡀⠀⢀⣉⠉⢤⣽⡾⢓⠄⣿⣷⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡇⣷⢰⣇⣧⠈⠂⣜⠿⣆⠀⠀⠈⠀⠀⠀⠈⠻⣿⣟⡟⣿⣿⣭⣽⣿⣿⣽⣿⣿⡟⢾⣷⣽⠳⣽⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣹⢸⡏⣿⣿⣦⠀⠻⡄⣿⣄⡀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣾⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀ ⢀⣀⣠⣤⣾⣿⣿⠰⣿⡼⡝⣿⣦⣇⣿⣮⡁⠀⠀⠀⠀⠀⡀⢸⣿⣿⡟⣩⡯⡷⠚⠙⣛⡶⠦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠿⠿⠿⣿⠿⠿⡆⢈⣷⣧⣣⡃⢽⣽⡽⢷⣤⣠⣤⠘⣿⠿⠟⢻⣿⠿⣧⣙⣛⠛⠛⠓⠿⠖⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠛⠸⢧⣼⣾⣶⣿⣦⣀⣎⣹⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠾⠟⠓⠚⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⢀⣄⣠⣌⣙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣴⡚⠋⠉⠁⠈⠉⠑⠺⣦⡀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⢀⡠⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠉⠉⠉⠙⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠿⠦⠑⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠆⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠙⢶⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⣸⡇⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠇⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡖⠴⢤⡽⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣤⡴⡿⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⡷⠀⠀⠀⠒⠈⠉⡠⠄⠒⣲⠖⠁⣠⣣⢟⠦⡀⠀ ⠀⠀⠀⠀⢠⠞⠁⣠⠞⠉⠀⠀⡇⠀⠀⠀⠀⠀⢘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⢀⡠⠊⠁⠀⣠⠾⠛⠋⠉⠁⠀⠈⢣⠈⠣ ⠀⠀⠀⣰⠋⣠⠞⠁⠀⠀⠀⢸⠷⢶⣆⣀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀ ⠀⠀⣰⠃⢰⠃⠀⠀⠀⠀⠀⢸⡄⠈⠙⣿⡉⠉⠉⠉⠛⠳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡴⠊⡘⠛⠒⢲⣦⡀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⡟⠀⡏⠀⠀⠀⠀⠀⠀⣿⠀⣄⠠⡘⢿⣦⠀⠀⠀⠀⠈⠙⠳⣦⣶⡶⠂⡀⣠⣠⡦⠟⠻⠷⢴⣇⢠⣤⣙⢾⡷⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠙⣧⡟⢷⡵⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡋⠉⠘⢷⣤⣀⠀⢸⠙⠛⠃⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣧⢰⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⢸⡄⢆⢳⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠞⢳⠛⢿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⢣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⡦⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣋⣄⣀⡀⠀⠀⠀⠀⠀⠉⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣀⣀⡴⠓⠉⠉⠀⠉⠉⠻⢶⡀⠀⠀⠀⠀⠉⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠁⠀⠀⢀⠤⣀⠀⠀⠀⠀⠀⠀⠉⠛⠢⠄⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⠞⠁⠀⣀⣤⡀⠀⠀⠘⠊⢙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠋⣀⣀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠘⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⠓⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣸⣟⣄⠘⣯⠍⠍⣉⠒⠂⠤⡀⠀⢠⣾⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠙⣧⣀⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠐⢁⠎⠈⠉⠓⠒⠻⢦⡀⠉⠒⢄⡀⠀⠀⠉⠲⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⣣⠈⠙⠳⣄⠙⢦⡀⠀⠀⠀⠀ ⢀⠋⠀⠀⠀⠀⠀⠀⠀⠙⣄⣄⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣁⠀⠀⣀⣄⡲⢿⡀⠀⠀⠈⠳⣄⠹⣄⠀⠀⠀ ⡌⠀⠀⠀⠀⠀⣠⣶⣏⠉⠙⡌⢷⣼⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠋⠉⠉⠉⢉⡽⠉⠀⢸⡱⠀⠀⠀⠀⠈⡆⢹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣯⡵⢶⣴⢿⠛⠋⠉⣺⡶⣦⣤⣙⡿⠾⠋⠁⠀⠀⠀⠀⢼⡟⣻⣃⣴⢰⠇⠀⠀⠀⠀⠀⢻⠀⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⢀⡴⣿⣿⢠⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠋⠳⠏⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣧⢧⡼⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢻⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⡴⠋⠉⢉⠍⣉⡉⠉⠉⠉⠓⠲⠶⠤⣄⠀⠀⠀ ⠀⠀⢀⠎⠀⠪⠾⢊⣁⣀⡀⠄⠀⠀⡌⠉⠁⠄⠀⢳⠀⠀ ⠀⣰⠟⣢⣤⣐⠘⠛⣻⠻⠭⠇⠀⢤⡶⠟⠛⠂⠀⢌⢷⡀ ⢸⢈⢸⠠⡶⠬⣉⡉⠁⠀⣠⢄⡀⠀⠳⣄⠑⠚⣏⠁⣪⠇ ⠀⢯⡊⠀⠹⡦⣼⣍⠛⢲⠯⢭⣁⣲⣚⣁⣬⢾⢿⠈⡜⠀ ⠀⠀⠙⡄⠀⠘⢾⡉⠙⡟⠶⢶⣿⣶⣿⣶⣿⣾⣿⠀⡇⠀ ⠀⠀⠀⠙⢦⣤⡠⡙⠲⠧⠀⣠⣇⣨⣏⣽⡹⠽⠏⠀⡇⠀ ⠀⠀⠀⠀⠀⠈⠙⠦⢕⡋⠶⠄⣤⠤⠤⠤⠤⠂⡠⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠦⠤⣄⣀⣀⣀⣠⠔⠁⠀

⠀⠀⠀⠀⠀⣀⡴⠖⠒⠒⢒⣒⡖⠒⠒⠒⠒⠒⠒⠶⠶⠤⣤⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠋⠀⠀⠤⣪⣝⡲⠯⠭⠥⠀⠀⠀⠀⠀⣀⣐⣒⡒⠉⠙⢦⡀⠀⠀ ⠀⠀⠀⣼⠃⠀⠈⠰⠫⠋⣀⣀⣀⣀⠀⠃⠀⠀⠀⠸⠀⠀⠀⠈⠆⠀⠀⢧⠀⠀ ⠀⣠⡾⠁⠀⡀⠠⠄⢰⣿⠿⠿⢯⣍⣙⣶⠀⠀⢀⣠⣶⣾⣿⠶⠆⠤⠤⢜⢷⡄ ⡾⢻⢡⡞⠋⣽⠛⠲⠤⡤⠴⠋⠀⠀⠉⠁⠀⠀⠈⣿⠁⠀⢀⣀⣠⠶⠶⣽⣵⣿ ⣇⢠⢸⡥⠶⣟⠛⠶⣤⣀⠀⠀⠀⢲⡖⣂⣀⠀⠀⠈⢳⣦⡀⠉⠉⣽⡄⠰⣻⣿ ⠙⣮⡪⠁⠀⠻⣶⣄⣸⣍⠙⠓⠶⣤⣥⣉⣉⠀⠠⠴⠋⠁⣈⣥⣴⣿⡇⠈⣽⠃ ⠀⠈⢻⡄⠀⠀⠙⣆⢹⡟⠷⣶⣤⣇⣀⠉⠙⡏⠉⢻⡟⢉⣹⣅⣼⣿⡇⠀⡏⠀ ⠀⠀⠀⠻⣄⠀⠀⠈⠻⢦⡀⠀⣽⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠙⢦⣀⠄⡀⢄⡙⠻⠧⣤⣀⣀⣿⠀⠀⣿⢀⣼⣃⣾⣼⠟⠁⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠉⠓⢮⣅⡚⠵⣒⡤⢄⣉⠉⠉⠉⠉⠉⠉⠉⢀⡠⠀⠀⠀⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢦⣄⡉⠙⠛⠃⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⢤⣤⣀⣀⣀⣀⣀⣀⡤⠞⠁⠀

…ᘛ⁐̤ᕐᐷ

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

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠶⠶⠶⢶⣾⡿⠿⠿⠿⢿⣿⡶⠶⠶⠶⠶⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⣿⠇⠀⠀⠀⠈⣿⠁⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⠳⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⣿⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢸⣿⡇⠀⠀⢰⣿⣛⡛⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⡞⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⡇⠀⠀⠈⠉⠙⣿⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣆⠀⠀⠀⡇⠀⠀⢸⣿⡇⠀⠀⢠⣤⣤⡿⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⢸⣿⡇⠀⠀⠸⣿⣬⣤⡀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀ ⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡄⠀⢠⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀ ⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠶⠶⠿⠷⠶⠾⠷⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣿⠓⠈⠉⠋⠀⠀⠀⠀⠀⠀⢷⡀⠀ ⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣐⣾⣿⣿⠉⠉⠀⠈⢹⣷⣿⣤⣤⣤⣄⣤⣀⣀⠀⠀⠀⠀⠈⣷⠀ ⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣻⣿⡿⠿⠿⠛⠿⠿⣿⣿⡟⠋⠀⠀⢠⠀⠘⠛⣿⣿⣿⠿⠟⠻⠿⣿⠗⠒⠀⠀⠀⢹⡄ ⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣿⣿⣶⣦⠀⠀⠀⢀⣺⣿⠃⠀⠀⢠⣿⠀⠀⠀⣿⣷⠀⠀⠀⢀⣤⣌⡇⠀⠀⠀⠀⢸⠁ ⢸⡟⠀⠀⠀⠀⠀⠀⠀⠤⢤⣴⣿⣿⣷⣾⣿⡶⠶⢶⣿⣿⣯⡤⠀⠀⢸⣿⡄⠀⠀⢿⣿⣶⣶⡿⠾⠿⣾⣧⠀⠀⠀⠀⣸⠀ ⣿⡇⠀⠀⠀⣰⠟⣿⠓⢦⠀⠀⠀⠙⢿⣿⣿⡀⠀⠀⠀⡀⠈⠛⠁⠀⢸⣿⣧⡀⠀⠈⢻⣿⣿⣶⣦⠴⠖⢛⡿⠋⢣⠀⡏⠀ ⢹⠀⠀⠀⠀⣿⠀⠈⠳⣤⡁⠀⠀⠀⠈⠉⠉⠉⠉⠛⠁⠀⣴⡾⢧⣤⣾⣿⣿⣷⣤⣤⣺⡇⠈⠀⠀⠀⣴⠟⠀⠀⠀⢸⡇⠀ ⢸⣇⠀⠀⠀⠙⠀⠀⠀⠈⠻⣶⣤⡀⠀⠀⠀⠀⠀⠀⡀⣀⣻⣿⣿⣿⣿⣿⡛⣿⣿⣿⣛⣁⣠⣤⣶⣿⠋⠀⠀⠀⠀⢸⠃⠀ ⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⣉⣉⣭⣿⣓⣛⡯⣽⣿⣿⢿⢻⡿⠁⠀⠀⠀⠀⠀⣾⠀⠀ ⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣽⣿⣙⣿⣿⣧⣼⡟⠧⣤⡼⣷⣶⣿⣿⣿⣾⠟⠁⠀⠀⠀⠀⠀⢸⡟⠀⠀ ⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢭⣿⣉⣛⣿⣶⣿⣿⠭⠷⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀ ⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⣠⠤⠦⠤⣄⡤⠤⢤⠤⠤⣤⡤⡾⠿⣿⡿⠿⠦⠽⢦⡤⠤⠤⣄⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠋⠳⣄⠀⢰⠇⠀⣶⠀⢸⡧⠀⢸⠀⠀⡏⠀⢳⣄⣈⡷⡄⠀⢠⢾⠇⠀⠀⢹⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢾⠆⠀⣟⠛⢻⡇⠀⢸⠀⠀⣿⣤⡀⠉⠻⡄⡇⠀⢸⣾⠀⢸⠀⢸⡇⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠿⠀⢸⣇⠀⢸⠀⠀⣯⠀⠸⠆⠀⡇⡇⠀⢸⡏⠀⢠⡀⠀⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠦⠼⠛⠷⠤⠤⠾⣽⣶⣤⣤⣾⣁⣷⣤⠼⠧⠤⠼⠧⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠒⠒⠶⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢠⣶⣿⣿⣿⣷⡄⠀⠀⢠⣾⣿⣿⣿⣶⡄⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢸⣿⣿⣿⣿⣿⠇⠀⠀⠸⣿⣿⣿⣿⣿⡇⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠻⣿⣿⡿⠏⠀⣠⣄⠀⠹⢿⣿⣿⠟⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⣰⣿⣿⣆⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢿⡿⢿⡿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀ ⠀⠀⣰⠏⣛⡀⠹⣧⠀⠀⠀⠛⢦⡄⠀⣀⠀⢀⠀⠀⠀⠀⣀⠀⢠⡴⠛⠁⠀⠀⣼⠛⣁⠉⠻⣆⠀⠀ ⠀⢀⣽⠲⠟⠓⠀⠹⣇⡀⠀⠀⠀⢿⡀⠸⠀⢸⠃⠸⡇⠐⠏⢀⡿⠀⠀⠀⠀⣸⠇⠀⠘⠳⠶⣿⡀⠀ ⢀⡟⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⣄⣈⠉⠓⠒⠒⠒⠒⠒⠒⠚⠋⣁⣠⠴⠖⠋⠁⠀⠀⠀⠀⠀⠈⢻⡀ ⠀⢧⡀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠉⠛⠶⢤⣀⠀⠀⣀⡤⠶⠛⠉⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⢀⡼⠁ ⠀⠈⠙⠓⠛⠉⠀⠀⠉⠛⠶⢤⣀⡀⠀⠀⠀⠈⠙⠛⠧⣄⣀⠀⢀⣀⡤⠶⠛⠉⠀⠀⠉⠛⠒⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠟⠓⠶⣤⣀⠀⠀⠀⠀⠈⠙⠻⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠞⠛⠓⠦⣄⣤⠴⠛⠉⠁⠀⠀⠀⢀⣠⡽⠟⠲⢤⣄⡀⠀⠀⠀⠀⠉⠛⠶⢤⣠⡴⠚⠛⠲⣆⠀ ⢠⡇⢀⣼⠆⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠉⠁⠀⠀⠀⠀⠈⠉⠓⠶⢤⣀⠀⠀⠀⠀⠀⠀⠐⣦⡀⣸⡆ ⠀⠻⣿⠁⠀⠀⠀⢀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⡀⠀⠀⠀⠘⣽⠟⠀ ⠀⠀⢿⡀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⢀⡿⠀⠀ ⠀⠀⠈⠛⠶⠤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠤⠴⠛⠁⠀⠀

⠀⠀⠀⢀⣴⠾⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠿⢷⣦⡀⠀⠀⠀ ⠀⠀⢠⡟⠁⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠈⢿⣄⠀⠀ ⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀ ⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠚⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠒⠒⠛⠉⠉⠉⠉⠉⠉⠙⠛⠒⠒⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⢸⣧ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢸⣿ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢸⣿ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣤⣀⣀⣤⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⢸⣿ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⢸⣿ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⢸⣿ ⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⣄⣀⣀⣀⣀⣀⡤⠤⠤⠖⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⠾⠋ ⢿⣷⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣴⡶⠶⠿⠛⠛⠉⠁⠀⠀⠀ ⠀⠀⠈⠉⠉⠛⠛⠛⠛⠿⠶⠶⠶⠶⠶⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⠶⠶⠶⠶⠶⠶⠿⠿⠟⠛⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠃⠳⣄⠸⢰⣤⣖⡊⣝⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⣹⠀⠑⠀⢠⡟⣙⣶⢞⡛⠀⣈⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠙⢷⣄⢀⡼⡟⣿⡝⣮⣝⢿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⣤⠀⠀⠀⠀⠙⣿⣤⣇⡿⢷⣝⣛⣣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣦⠀⢀⣀⣀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡋⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿⣿⣦⣿⣿⣴⣿⣟⣿⣷⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣿⣿⣿⣿⣷⣿⣿⣿⠿⠋⠀⠀⢠⣿⠀⠀⢀⣤⡄⠀⠀⠀⠀⢠⣦⣀⡸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢻⣿⣿⣿⣿⣿⢿⡟⢿⣿⡆⠀⠀⣸⡏⠀⠈⠿⠋⠁⠀⠀⠀⠀⠀⢉⣋⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣁⣼⣿⠙⠿⣿⣿⡿⠃⠀⠀⣿⠃⠀⠀⣠⠞⠉⠉⠓⣦⣠⡞⠉⠉⠳⡄⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣻⣿⣿⣋⣀⣀⣀⣀⣀⣀⣀⣸⣿⠀⠀⢰⡇⠀⠀⣤⣄⢸⣿⠀⣷⡄⠀⢻⠀⣿⣀⠀⠀⠀⠀⠀⠄⠐⠈⠉⠉⠉⠓⠂⠖⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⡇⠀⠀⠘⣧⠀⠀⠙⠁⢸⠿⡆⠉⠀⠀⣸⠀⢻⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠈⠳⢤⣀⡴⠏⠀⠙⠦⣤⣴⡋⠀⠈⣿⡖⠂⠀⠀⠀⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠈⠒⠒⠒⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠐⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣴⠦⢤⣄⣀⣀⡤⠴⣻⠇⠀⠀⠹⡟⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠆⠒⠒⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⠿⣶⣶⣶⣴⣶⡿⠋⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠗⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⣿⣻⣿⣿⣷⣦⣄⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡿⢿⣿⡷⢾⣿⣿⣿⡞⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡾⠋⠀⠀⠈⠛⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠏⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣟⣿⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠃⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠿⠿⠿⠷⠶⢾⡿⢿⣦⡼⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡟⠀⠀⠀⠀⠀⠀⣼⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⣼⣧⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢷⣄⠀⢰⣄⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣷⣼⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣾⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡿⠟⠋⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠻⠿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢿⣿⣿⣿⣿⣿⣿⠀⠀⠈⢻⣿⣿⣿⡿⠅⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⡿⠿⠟⢿⣿⣿⣿⡟⠛⠛⠛⠛⠿⠿⠟⠛⠛⠛⠉⠉⠀⠙⢿⣿⣿⣿⣿⣄⠀⠀⠀⠙⢿⣿⣿⣿⣿⣧⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠈⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡄⠀⠀⠀⠀ ⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀ ⠀⠸⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⣀⠀⠀⠀⠀⢸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣾⠝⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⠙⠢⣀⠀⠀⠀⠀⠀⢸⣿⡟⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡈⠳⣄⠀⠀⠀⢺⠁⢙⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠴⢚⣿⣿⠞⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡒⣿⣗⠢⢄⣸⡀⣼⠤⠤⣄⡀⠀ ⠀⠀⠀⠀⠀⠐⡶⢁⣴⣿⣿⡏⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣿⣧⡀⠈⢿⠁⠲⠄⠀⠙⠢ ⠀⠀⠀⠀⣠⣾⣵⣿⣿⣿⣿⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⠈⣆⠀⠀⠀⠒⠀ ⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⡘⣧⠀⠀⠀⠀ ⢀⣴⡿⡿⣹⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢿⣿⣿⣷⣽⣷⡤⠋⠁ ⣾⠏⡜⢰⢳⡟⣙⡟⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡟⠇⢻⠈⣏⡆⠹⡍⠻⣿⣄⠀ ⣣⣞⣰⠃⡜⢀⢻⠁⡎⡇⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡎⡆⢸⠸⠘⡜⡄⠹⣿⣆ ⠻⢿⣿⣴⠁⡌⡐⢠⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⡇⠀⠀⠀⣇⣮⡁⢸⢸⡄⣇⣽⣼⣼⣽⣿ ⠀⢸⣿⣿⣾⣧⣇⣾⣀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⣇⠀⠀⢸⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⡿⠿ ⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⠧⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡄⢠⠤⠾⢃⠀⠀⣸⡀⠀⠘⠿⠿⣿⣿⣿⣿⣿⣿⠃⠘⠆⠀ ⠀⠀⠀⠀⠀⣽⣿⣿⢻⠋⠀⠀⢀⡶⠿⣷⣶⣿⣶⣴⡖⠲⢄⠀⠀⠀⠉⠉⠁⣠⣴⣾⣶⣼⣿⢷⠀⠀⠀⠀⢻⠻⣟⠛⠉⢳⡀⠀⠀⠀ ⠀⠀⠀⠀⡜⢹⢋⣿⠈⡄⠀⠀⠈⣧⠀⣿⣽⡿⠿⡏⠑⠂⠀⠀⠀⠀⠀⠀⠘⠋⣿⡿⠯⢿⣏⢰⠀⠀⠀⠀⢸⠀⣿⣆⠀⠀⠱⡀⠀⡆ ⠀⠀⠀⡸⠁⣾⡞⠸⡀⡇⠀⠀⠀⠆⠣⣜⣳⣴⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠬⠽⣃⣜⠁⠀⠀⠀⠸⠀⢸⠈⠣⡀⠀⠹⡄⠃ ⠀⠀⠰⠁⢰⡟⠀⢠⠇⢃⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢻⣦⣀⠘⢦ ⠀⠀⠀⢀⡞⠀⢠⣾⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣷⣄ ⠀⠀⢠⠎⠀⣰⣿⠏⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠈⠻ ⢀⡴⠃⢀⡞⣽⠁⢀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣔⣦⡄⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⢠⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀ ⠎⠀⢠⣾⠁⡇⠀⣼⠀⠀⢠⠀⠀⠀⢻⣿⣦⣀⠀⠀⠀⠀⠀⣾⠛⠟⢿⠀⠀⠀⠀⠀⣠⣾⣿⠁⠀⠀⢰⠇⠀⠰⠀⠀⣾⣿⡿⠀⠀⠀ ⠀⣰⣿⡟⠀⢧⠀⢿⠀⠀⠘⡄⠀⠀⠘⣿⣿⣿⣷⠦⣀⠀⠀⠈⠉⠀⠉⠀⠀⣠⣴⣿⣿⣿⣿⠀⠀⢀⡇⠀⠀⠀⠀⢰⣿⣿⠇⠀⠀⠀ ⢼⣿⣿⡇⠀⢹⠀⠘⡀⠀⠀⣇⠀⠀⡄⢹⣿⣿⣿⠀⠈⠑⠢⠄⣀⣀⡠⠔⠋⢸⣿⡇⣿⣿⡇⠀⠀⣸⠀⠀⠀⣿⠀⢸⣿⡟⠀⠀⠀⠀ ⣾⣿⣿⠁⠀⢸⠀⠀⡇⠀⠀⠹⡀⠀⢻⠈⢿⠃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠉⠻⣿⠀⠀⢀⡿⢀⠀⢸⣰⠀⣼⡿⠁⢀⠀⠀⠀ ⣿⣿⣿⠀⠀⠀⣇⠀⢱⠀⠀⠀⢱⠀⢨⡸⢸⡈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⢀⣼⡇⢀⣾⡇⢸⠀⣿⣿⡀⣿⠃⠲⠥⠀⠄⠀ ⣿⣿⣿⡇⠉⠉⢻⠀⠉⢇⢃⣀⣈⡇⢸⡁⠀⠙⢿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢀⠞⢩⠁⠼⣿⡇⠃⠐⠀⠀⣽⠗⠊⢢⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠈⠁⠢⢀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀ ⠀⢀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀ ⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣄⠀⠀⠀⠀⠀⠀⠈⡄ ⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⢠⠃⠈⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⡇ ⠘⠿⠿⠷⣶⣤⣤⣤⣀⣀⡄⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⡰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣽⡿⠋⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⣻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣻⣿⡏⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣯⣿⣽⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣤⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣯⣿⠏⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⡏⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠣⢄⣀⡀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠶⠶⠿⣿⣫⣭⣟⣥⣒⢟⣹⡸⣻⡾⢶⣸⣃⠠⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⡿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⡇⠀⠈⠉⠛⠛⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣟⣉⣁⣀⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⠋⠉⠉⢉⣍⠙⣦⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⢻⡟⢀⡾⠟⠀⠈⠛⠷⠌⢷⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣸⠷⠶⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠇⡟⠀⡏⣀⣀⠀⢰⣿⣿⣦⠈⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡟⠀⠀⠀⠀⠈⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⣿⡏⠀⣇⠀⢸⣿⣿⡇⠸⣿⣿⡿⠀⣿⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⠀⠀⠀⠈⢻⡄⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠻⣆⠘⢿⣿⣃⡔⠯⠭⠀⣴⠃⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠈⣿⡀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⡏⠀⢀⣤⣼⣳⣏⡉⣿⡧⠀⠀⢙⣓⣤⣄⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠘⡇⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦⡀⠀⠀⢀⣿⠁⠀⠀⡏⠉⠁⢀⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⢿⡀⠀ ⠀⠀⠀⠀⠹⢿⣷⣌⠙⠿⣿⣦⡀⣾⢹⡄⠀⠀⣷⣴⣾⢿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠻⣿⡏⢘⣷⣠⡀⢀⢙⡷⠚⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠘⠈⢹⠓⠚⠏⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡟⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⣴⣏⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⠟⠁⠾⠤⠤⢤⣤⣤⣤⣤⣤⠤⢤⣤⣿⣿⣿⣿⣿⣿⣿⠗⢶⡄⣾⡃⣙⠛⡷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠀⣾⢸⠋⡹⠛⣻⠧⢬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡀⡿⢸⡀⣧⣠⠿⣄⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠟⠛⣻⣿⠿⣿⣄⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠇⠀⣿⠉⣷⣄⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣶⠋⢛⢟⣶⣰⡋⢙⢦⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠀⠀⡿⢸⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⠟⣡⣼⠟⢲⡤⣿⠁⠙⢯⢘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⠃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣧⡾⣻⠋⣰⢿⡇⣿⠀⠀⠈⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡏⢀⡇⢸⡅⢹⡄⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢧⣼⡅⠘⠷⠶⠛⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⠀⢸⣿⣿⣿⣿⣿⠀⠀⣤⣦⣄⠀⢀⣀⠀⠀⠀⠀⣼⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡄⢀⣤⣤⣄⢸⣿⣿⠿⣿⢃⣿⣿⣿⣿⣿⣿⣇⠰⢛⣿⣿⣧⣿⣿⣷⣄⠀⠀⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣷⣻⣿⣿⣙⣋⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣴⣾⣿⣯⣿⡇⣸⢱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠃⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⣤⢤⣤⣤⣠⢤⣤⢤⠀⡀⡀⢀⡀ ⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⣿⠿⠝⠛⠼⠻⡜⠤⠸⠀⠦⠃⠚⠃

⣿⣿⣷⣬⣿⣓⠰⢽⣎⣿⣿⣟⠛⠿⢤⣶⡥⣴⣶⣦⡖⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠛⠋⣡⣴⣟⣛⣿⣭⢗ ⡿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣦⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⢿⣥⣿ ⣿⠹⣿⣿⣿⡌⢿⣿⣷⣌⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣄⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⠿⣫⠶⢿⣿⣿ ⣿⡧⠘⣿⡻⣿⠺⣿⢿⣿⣿⣦⠄⠀⠀⠀⠀⠀⠀⢀⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⡿ ⣿⣿⣆⠘⢷⠹⣇⢯⣿⠿⠋⠀⠀⠀⠀⠀⠀⢀⡴⠁⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠘⢦⠀⠀⠠⣤⣤⣤⣶⣿⣿⣿⠿⣟⣦⣶ ⢻⣷⡽⣧⠈⠷⠉⠉⠁⠀⠀⠀⠀⡀⢀⡀⢀⡟⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠈⠣⣄⠀⠰⣌⢽⣯⠉⠻⢶⣿⣿⣿⣿ ⡀⠙⣷⡙⣧⠀⢯⢩⢱⠶⢤⠶⢋⡡⠏⢠⡟⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢸⡈⠳⣄⣈⣑⣲⡤⠄⠀⠉⢿⣿⣿ ⠛⢦⡈⠳⡌⣦⠈⢧⢸⡴⢋⡴⠋⠀⠀⢹⢷⣀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⢠⡷⠋⠘⡇⠀⠀⠀⠀⠀⠀⠀⠙⣿ ⢧⡀⠑⠀⠙⢮⠃⣠⢏⣠⡟⠀⠀⡀⠀⣿⠀⠻⣿⣶⣦⣤⣤⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣠⣤⣤⣴⡾⠋⡇⠀⠀⢳⡀⠀⢀⠀⣼⣶⣖⣂⣺ ⠀⠈⠂⠀⠀⠀⠚⢛⡝⢹⠇⠀⠀⠁⢀⣿⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠟⠋⠀⢠⡇⠀⠀⠈⢣⡀⢸⣶⣅⣛⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣠⠞⣠⣼⠀⠀⠀⠀⠉⣿⣄⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⣸⠿⣄⠀⠀⠀⠉⠒⢛⡉⠛⠛⢻⣿ ⠀⠀⠀⠀⠀⠴⠗⠋⢸⡿⠀⠀⠀⢠⠇⢿⡟⢿⣶⣤⣤⣤⣀⡀⠀⠉⠙⠿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠋⠁⣀⣠⣤⣤⣶⣶⠋⣽⠀⡟⢳⣶⡦⣤⠤⠴⣦⣽⣶⣾⣿ ⠀⠀⠀⠀⠀⠀⣠⣞⣫⣴⠂⢀⡴⡿⡆⠀⣧⠈⢻⡄⠀⠀⢸⠛⠻⢶⣦⣄⡈⠛⢿⣷⡀⠀⠀⠀⠀⣰⡿⠛⢁⣤⡾⠟⠉⠁⠀⠀⣸⠇⠀⣧⠀⢹⣸⠀⠉⠘⢷⣄⣹⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠉⠁⠀⣼⣁⢴⡏⠀⠑⣇⠀⢹⠀⠱⣿⣄⠀⢸⡀⡀⠴⠈⠙⣿⣦⡀⠉⠧⠀⠀⠀⣰⣛⠂⣾⢿⠋⠀⠀⠀⠀⠀⢠⣿⠞⠀⡟⡄⠈⢿⠀⠀⠀⠈⢿⣷⣦⣼⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢾⡟⠁⠀⢷⠀⠀⣿⠀⡀⡇⠀⠙⠚⢦⣀⠳⣤⠒⡀⡤⠃⠘⢻⠃⠀⠀⠀⠀⠀⠁⡴⠃⠈⠷⣤⣀⢠⣲⡴⠋⠁⠀⢀⡇⢷⠀⠘⣆⠀⢀⣀⠀⠉⠻⣿⣿⣿ ⠀⠀⠀⠀⠀⠈⠉⠛⠦⣄⠀⠈⣧⢠⠏⠀⠀⢣⠀⠀⠀⠀⠘⠉⠑⠒⠒⠒⠈⠉⠉⠁⠀⠀⠀⠀⠀⠸⠉⠉⠉⠉⠒⠚⠛⠊⠁⠀⠀⠀⣼⠁⠸⠀⠀⠘⢆⠀⠙⠻⣤⣤⣤⣭⣭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡘⡞⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢠⡀⠀⢨⣖⢦⣦⣀⣉⣭⣽⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠈⣧⡀⠀⠙⠯⠛⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢧⠀⢀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⢹⠀⠀⢸⣿⣾⡲⠤⠀⠙⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠸⣆⢸⡼⣇⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠤⣤⣀⢀⣀⣤⠤⠖⢦⡀⠀⠀⠀⠀⠀⠀⢀⣾⠃⣷⡼⣷⡀⢸⣸⣿⣿⣦⡀⢤⣈⠻⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⣿⣆⣧⢹⣦⠀⠀⠀⠀⠀⢰⣿⢶⣤⣤⣀⣀⣀⣀⣠⣤⢴⡿⣷⡀⠀⠀⠀⠀⢀⣾⣧⡀⠣⠁⣿⣿⣶⣿⣿⣿⣿⣿⣦⡙⢾⣷⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣸⣿⣿⣿⡈⠳⣄⠀⠀⠀⠸⣇⠈⠓⢤⣀⠀⠀⠀⠀⠠⠊⢀⡼⠁⠀⠀⠀⢠⡾⢻⡀⠈⠓⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠙⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣟⣧⠀⠘⢷⣄⠀⠀⠈⠓⠦⢄⣀⣀⣀⣀⡠⠤⠖⠋⠀⠀⠀⢀⡴⢿⡇⡆⣷⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣽⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⠈⠳⢄⡈⢻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⣸⠞⠠⡿⠀⠀⠀⣼⠉⣿⣿⡏⢻⣿⣿⡇⢿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣷⣄⡀⠙⠲⣝⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⢁⡠⠞⠁⢀⣼⠁⠀⠀⠘⠁⠀⡏⢿⡏⠀⢧⣿⡟⣼⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⠏⢸⣿⣿⣿⣿⣦⣄⡀⠉⠛⠿⢿⣿⣶⣦⣤⣤⣴⣾⣿⡿⠅⠀⠁⣀⣠⣶⣿⣿⠀⠀⠀⠀⠀⣸⣿⢸⠇⠀⠈⣿⢁⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠂⢸⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠈⠉⠻⡟⠉⠉⠀⣀⣤⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣴⡿⠋⠀⠀⠜⢀⠋⠉⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠁⡀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠃⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⢀⣠⣾⠋⢀⡖⠀⠀⣠⡾⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠈⡷⡜⡎⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇⠈⠉⠁⡇⠀⣾⠁⠀⢠⣿⠇⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢸⣇⠙⠲⣄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠀⠀⠀⡇⣸⢸⠀⢀⡎⡇⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣀⠀⠀⢸⠈⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣇⠀⠀⠹⡟⠸⡄⣸⠁⠃⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢄⠘⠦⣄⡀⢀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠑⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠹⣿⣷⣯⣿⣟⣻⣄⣀⣀⣤⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠟⠛⠛⠿⣿⣿⣷⣄⣀⣤⣤⣤⣶⣶⣶⣦⣤⣤⣀⣠⣾⣿⣿⠿⠛⠛⠿⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⠏⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠘⣿⣿⡿⠀⠀⠀⠀⠘⣿⣿⡿⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⣀⣀⣀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠿⠿⠿⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⣼⣿⠏⠁⣀⣀⣀⣀⡀⠈⠻⣿⣆⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡀⠀⠀⠀⠀⣿⣿⠀⠀⠻⢿⣿⡿⠟⠀⠀⣿⣿⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣄⠀⠀⠀⠻⣿⣦⣀⠀⢸⣿⠀⠀⣀⣼⣿⠏⠀⠀⠀⣠⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣤⣀⠀⠈⠻⢿⣿⣾⣿⣿⣿⠿⠛⠁⠀⣀⣴⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣥⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⣾⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠉⠛⠛⠿⠿⢿⣿⣿⣿⡿⠿⠿⠛⠋⠉⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣷⣦⣄⠀⠀ ⢠⣾⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣷⡀ ⢸⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡇ ⠈⢿⣿⣷⣦⣤⣶⣶⣶⣿⣿⡆⠀⠀⠀⣴⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣄⠀⠀⠀⣶⣿⣿⣶⣶⣶⣦⣴⣿⣿⡿⠁ ⠀⠈⠙⠻⠿⠿⠿⠛⢻⣿⣿⡇⠀⠀⣼⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⠀⠀⢹⣿⣿⠛⠛⠿⠿⠿⠟⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣶⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣶⣶⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⠿⠛⠉⠛⠻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠟⠛⠙⠛⢿⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⣀⠀⠀⢀⣠⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣷⣄⠀⠀⢀⣀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⣴⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣾⣿⡿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⣿⣿⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⠏⠀⠀⠾⠿⠿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣷⡀⠀ ⠀⣾⣿⣿⣿⣿⡏⠀⠀⣤⣤⠀⠀⢸⣿⡿⠀⠀⢠⣤⡄⠀⠀⣿⣷⠀ ⢠⣿⣿⣿⣿⡿⠁⠀⢰⣿⠏⠀⢀⣾⣿⠃⠀⢀⣿⡿⠁⠀⣰⣿⣿⡄ ⢸⣿⣿⣿⣿⠃⠀⢀⣿⡿⠀⠀⣸⣿⠇⠀⠀⣾⣿⠃⠀⢰⣿⣿⣿⡇ ⠘⣿⣿⣿⠇⠀⠀⣾⣿⠁⠀⢰⣿⡟⠀⠀⣰⣿⠇⠀⢀⣾⣿⣿⣿⠃ ⠀⢿⣿⡟⠀⠀⣸⣿⠃⠀⢠⣿⡿⠁⠀⠀⠛⠛⠀⠀⣼⣿⣿⣿⡿⠀ ⠀⠈⢿⣶⣶⣶⣿⣿⣶⣶⣾⣿⠇⠀⢠⣶⣶⣶⣶⣾⣿⣿⣿⡿⠁⠀ ⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⡿⠀⠀⣸⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠰⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠩⣿⣿⠀⠀⠀⠀⠀⠸⣿⡞⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⣾⣿⠀⠀⠀⠀⠀⠀⣿⣧⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡟⠀⣿⣿⣯⣿⢯⡿⣩⠝⢿⣿⣧⣬⣿⣆⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣊⡭⣽⣿⣿⡿⣿⢿⣤⣬⣍⣛⠓⠁⣽⣿⣿⣿⣛⣛⡻⢗⣦⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠀⢠⠀⠀⠀⠀⡠⠚⠁⠀⠈⠁⣠⠝⠉⠔⣭⡮⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠪⡇⠀⠀⠀⢀⠀⡀⡀⢀⣀⣀⣀⠀⠀⠀ ⠀⠇⢸⠡⠀⢠⠞⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡾⣿⣧⣧⣿⣿⣏⣹⠶⠖⠀ ⣣⣧⣮⣴⡰⡇⠀⠀⢠⠃⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⢣⠀⠀⠀⡥⣤⡤⣅⣤⢨⢬⣥⡤⡄⠀ ⣿⣿⢿⣝⠏⠀⠀⢠⠃⠀⠀⡸⠀⠀⠀⠇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⢸⠀⠀⠀⠾⠥⠇⠏⠻⠸⠻⠿⠤⠇⠀ ⣼⣾⣞⡏⠀⠀⠀⡾⠀⠀⢠⠃⠀⠀⢸⠠⢠⠟⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢦⠀⠀⢿⡃⢰⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡝⠀⡄⢠⣼⠃⠀⢀⡏⠀⠀⠀⠇⠆⡾⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⢧⠀⠘⣧⠈⡄⢳⠀⠀⠀⠀⠀⠐⠲⠲⠂⠀⠀⠀⠀ ⣿⢿⠁⢰⠁⣌⡟⠀⠀⣼⠀⠀⠀⡼⠐⣼⠃⠀⡇⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡈⡧⠀⢹⣦⡇⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⢸⢸⠀⢻⠃⠀⣰⠇⠀⠀⣰⢁⢳⠇⠀⠀⢱⠀⠀⠀⠀⠀⢸⢹⠀⠀⠀⠀⣞⣵⠀⠄⢟⡇⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⡈⢸⢠⡏⠀⢠⡟⠀⠀⢰⠃⢪⠏⠶⠦⠴⢾⠀⠀⠀⠀⠀⡇⡎⠀⠀⢆⢰⠉⠹⣧⠘⡜⣽⠀⠀⡸⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⢧⠀⢸⠁⢀⣿⡹⠀⢠⠃⢠⠋⠀⠀⠀⠀⢸⠀⡇⠀⠀⡼⢸⠃⠀⢸⡜⡎⠀⠀⠙⣧⡸⢿⡆⡰⣡⠎⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⡄⣿⠀⠸⠀⡼⣳⠁⢠⠋⢰⣃⠤⠤⣀⡀⠀⠀⡆⡇⠀⢰⠃⡎⠀⠀⣷⢱⣗⣮⣥⣴⣿⢧⢹⠳⠟⠁⠀⠀⢈⠢⣄⠀⠀⠀⠀⠀⠀ ⡇⠁⡟⣴⡆⣼⢕⠏⣰⡷⣵⣯⣤⣷⣿⣷⣾⣿⣦⡇⡇⢀⠇⣸⠁⠀⣸⠇⣾⡿⢻⣟⣷⠿⣿⡞⡀⠀⠀⠀⠀⣾⠀⣆⣟⢲⢤⣀⡀⠀ ⡇⡀⣿⣿⡞⠛⢁⣴⠛⣡⠷⠾⠋⣿⣿⣿⡿⡌⠙⢣⢀⠎⢰⠃⠀⢀⡟⡸⠋⠀⠘⣿⣿⣷⠟⣿⡃⠀⠀⠀⠀⣿⢸⢹⢺⣾⣷⣮⣹⣿ ⣻⣧⢇⡿⣇⣰⡿⢁⡴⠁⢀⣀⡀⠻⣿⣿⠟⠁⢸⣸⠂⣠⠇⠀⢀⣾⢡⠃⠀⠀⠤⠬⠅⠐⠶⢻⡇⠀⠀⠀⢠⠀⣸⢸⣿⣿⣿⣿⣿⣯ ⣿⣯⠞⣠⠞⡷⠒⣏⠀⠀⠀⠈⠛⠛⠒⠀⠀⠀⣸⣣⣶⠃⠀⠀⣸⣏⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣆⠀⠀⢸⡇⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠀⢇⣸⢇⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣿⡇⠀⡀⡤⣟⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣘⠀⠀⡘⣿⣸⢿⣿⣿⣿⣿⣿⣿ ⡇⠸⣇⠂⠋⢻⠀⢹⡇⠀⠀⠀⠀⠀⣀⣴⢟⡽⣿⡟⠇⡸⡸⡰⡟⠀⠀⣀⠀⠀⠀⠀⠀⠢⠀⠀⡇⣇⠀⠀⣷⠉⣿⣾⣿⣿⣽⣿⣿⣿ ⣧⣼⠹⡎⠑⣄⢣⠈⢯⢀⣀⡤⣴⠾⣫⠷⠛⠁⣼⣷⠀⠇⣇⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⢿⡇⣿⡟⠚⢻⣿⣿⣿⣿ ⣿⣿⣠⣟⣆⠈⠚⠣⠸⠞⠒⠿⠓⠉⠀⠀⠀⠀⣇⡏⣾⣾⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⢸⣰⣇⢿⣳⣰⣾⣿⣿⣿⣿ ⣿⣿⣽⡿⡾⠓⡦⠬⣟⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡸⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⡏⢠⢸⢸⣿⢧⡈⠙⢿⣿⣿⣿⣿ ⡿⣧⣕⡽⣿⠀⢇⡟⠈⢯⣦⠀⠀⠀⠀⠀⠀⠀⢸⢿⡇⡇⠀⢀⣤⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⡇⡇⠸⡀⠻⣿⠘⡷⡀⠀⠈⠻⣿⣿ ⡟⣿⣟⣱⣿⢰⢸⡇⠀⣀⣹⢷⣄⠀⠀⠀⠀⠀⠈⣼⢣⡇⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠘⣧⡇⣿⠀⢳⢱⡤⢄⢸⣿⣿ ⣿⣇⡟⡇⣿⢸⡌⡇⠀⣏⢼⠀⣿⠳⣄⡀⠀⠀⠀⠙⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⡇⡇⡇⢹⣧⢸⠀⢸⡀⢣⠈⣹⣿⣿ ⣿⣿⢹⠀⣿⢸⣷⠀⢰⠁⠘⠀⡿⠀⡈⢫⡳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⢸⡇⡇⢰⣸⢸⢸⠀⢐⡇⠘⣿⣿⣿⣿ ⣿⣿⡇⢠⡟⣺⣿⣀⢎⠀⡇⠀⡇⠀⠹⡄⡱⡀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⢸⠁⠀⢸⣿⢸⠸⠀⠀⢸⠀⠝⣿⣿⣿ ⣿⣿⠁⠸⡇⣿⢿⠈⠁⠀⡇⠀⣷⠀⠀⠙⣜⢿⣄⠀⠀⠀⠈⠙⠒⠒⠒⠚⠋⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠸⡀⠀⠀⠸⠀⢰⣿⣿⣿ ⣿⣿⠀⢀⡇⣿⢸⠀⠀⢰⠁⠀⢹⡀⠀⠀⠈⢆⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠈⣄⣆⡆⡄⡇⠀⠀⡇⠀⢸⣿⣿⣿ ⣿⡇⠀⢸⡇⣿⡇⠀⢠⠇⠀⠨⡷⡝⣄⠀⠀⠀⠳⡘⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⣻⢰⡿⣿⣇⡇⠁⠀⢸⠃⢀⣿⣿⣿⣿ ⣿⡇⠀⠈⡇⣿⠃⠳⣵⡇⠀⠀⢹⣧⠘⢦⡀⠀⠀⠘⣾⣄⣡⣄⠀⠀⠀⠀⠀⠀⠀⣀⡠⡋⠀⡇⠀⠄⣿⡟⣇⣰⠀⡾⢀⣼⣿⣿⣿⣿

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⠀⠈⠉⠉⠀⠀⠀⠉⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⣤⣤⣤⣴⣶⣶⣶⣶⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⠀⠈⠻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠈⠑⢤⡀⠹⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠟⢋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠙⢦⢹⣿⡟⠛⠛ ⣿⡛⠛⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢏⠉⠉⠐⠒⠀⠀⠙⣿⣧⡀⠀ ⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢂⡟⢰⠀⠀⠀⠀⢠⡀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⢻⣿⠙⠀ ⣿⡟⠀⢀⡄⠀⠀⠀⠀⠀⡤⠀⢀⠇⢸⡇⢸⡄⠀⠀⠀⠘⣷⡀⠀⢹⣷⣄⠀⢆⠀⠀⠘⡄⡇⠀⠀⠀⠀⠇⠀⢀⣤⠖⠁⠀⢸⣿⠀⠀ ⣿⡇⢀⠏⠀⠀⡆⠀⠀⣸⠃⢀⣾⠀⣞⡇⠈⣧⠀⣀⠀⠀⢹⣷⡖⠚⢿⣟⠳⡼⣦⠤⢀⣧⢰⠀⠀⠀⠀⢸⡿⠛⠁⠀⠀⠀⣼⠛⠀⠀ ⣿⡇⡼⠀⠀⣼⣿⠀⢀⣿⠰⣾⡟⢸⠏⢹⢠⢿⣆⢸⣧⡀⠈⣟⣿⡄⢸⠘⢧⠁⣿⡀⠀⣿⠸⠀⠀⠀⠰⡟⠀⠀⠀⠀⢀⣾⠏⡇⠀⠀ ⣿⢃⣿⠀⢠⡟⡇⢇⢸⣿⠀⣿⣣⣼⠖⢾⣼⢈⣿⡄⠻⣷⠀⢹⠻⣿⣼⣷⣼⣷⣿⣇⢠⣿⡆⠀⠀⠀⢸⠃⠀⠀⢀⡴⠋⡼⠀⡧⠀⠀ ⠃⣸⠋⣇⢸⠁⣧⠘⣾⣿⣴⡿⢿⣿⣷⣦⣿⡀⠙⣧⠀⣿⡆⢸⣴⡿⠿⣿⣿⣿⣿⣿⣿⣧⣀⡤⠀⢠⣟⣠⢞⣵⣿⠃⢰⠃⠀⡇⠀⠀ ⣿⣿⡀⠙⣿⠀⠘⣆⠙⣿⣿⠇⣴⣿⣿⣿⣿⡁⠀⠘⣶⢻⣧⡜⠋⢰⡞⢿⣿⣟⣿⠋⣽⣿⠉⠀⢀⣾⠟⠀⣠⠞⠁⣰⡏⠀⢰⠀⠀⠀ ⣿⣿⣧⠀⢸⡄⠀⠘⣦⣹⠙⠃⢿⡙⠉⣽⡇⠀⠀⠀⠟⠀⠟⠀⠀⠘⣦⡈⢉⣭⡿⠀⠉⡇⠀⢠⣿⣿⣴⠾⠧⢤⡚⢹⠃⠀⡆⠀⠀⠀ ⣿⣿⣿⣷⡀⢷⡄⠀⠘⣿⡇⠀⠀⠻⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠻⠉⠀⠀⢸⠇⣰⣿⡿⠋⣡⠖⠲⣾⣷⡼⠀⢠⠇⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣦⣤⣹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣾⣿⣿⠁⢰⠋⡇⠀⢀⣿⡇⠀⢸⡆⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣫⢿⠇⢀⣼⡴⠁⢀⡾⢹⠃⠀⣾⡇⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⣬⠔⠛⢉⣤⢶⡿⠀⢸⡀⠀⡿⡇⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣰⢿⣶⣶⣏⣱⣿⠃⠀⣼⡇⢰⠀⠹⣄⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠸⣈⡷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⡿⠀⢀⡏⣿⠋⣨⡿⢡⣿⠀⠀⣿⣷⠸⠀⠘⢟⣦⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢿⣀⡾⠛⠦⣀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠟⠋⠀⡇⠀⡸⠀⣿⣴⢿⡇⢼⣿⠀⠀⢸⡎⢳⡄⠀⠈⢿⡳ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢀⣿⡿⠀⠀⠀⢈⣷⡦⢤⣶⡖⠋⠁⠀⠀⠀⠀⢀⡇⠀⡇⠀⢹⢿⣤⣧⢸⠙⡇⠀⠀⢷⡀⠙⣆⠀⠀⠹ ⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⡾⠋⠀⠀⠀⣠⢾⡟⢰⠋⢈⣿⡀⠀⠀⠀⣀⠔⠋⢱⢸⣿⠀⢸⣄⠼⠛⢶⣄⢹⠀⠀⠈⠳⣄⠈⢳⡄⠀ ⣿⣿⣿⣿⣿⣿⣿⡏⠀⢠⣾⠁⠀⠀⣀⣰⣇⣸⡧⠴⠞⠉⣠⡗⠤⠴⠊⠁⠀⠀⠈⢿⣀⡦⠚⠁⠀⠀⠀⠈⠛⠳⣦⣄⣀⣙⣧⣀⠹⣄ ⣿⣿⣿⣿⣿⣿⡟⢀⡴⢻⣾⠟⠋⠉⠁⠀⠀⠀⡄⢀⣾⠞⢉⠇⠀⠀⠀⠀⠀⠀⢀⣼⣿⡅⠀⠀⠀⠀⣠⣤⠶⢛⣉⣥⣤⣤⡬⠽⣿⣿ ⣿⣿⣿⣿⣿⣿⣾⣿⡇⢸⣿⡀⠀⠀⠀⠀⠀⠰⢁⣾⣅⣀⡈⠀⢀⡤⠤⠤⣤⠖⠉⠀⣿⠁⠀⣠⡴⠟⢉⣤⣾⡿⠟⠋⠉⠀⠀⠀⠀⠈ ⣿⣿⣿⣿⠋⢀⡟⠸⡇⠘⣿⡇⠀⠀⠀⠀⢀⠇⡞⠉⠀⠀⠈⠳⣄⠀⡠⠞⠁⠀⠀⢸⢋⣤⠾⠋⣠⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣧⡀⢸⡇⢸⣷⠀⢿⣿⠀⠀⠀⠀⢸⡾⠀⠀⠀⠀⠀⢀⡸⠊⠀⠀⠀⠀⣠⠏⡼⢁⣴⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠟⠻⣤⣷⣼⠀⢇⠘⣿⣇⠀⠀⠀⢸⠇⠀⠀⠀⢀⡴⠋⠀⠀⠀⣀⣴⢾⡏⣰⣿⠋⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡏⠀⠀⣿⠙⣿⠀⠘⣆⠹⣿⡄⠀⠀⡸⠀⠀⢀⠔⠋⢱⣄⣤⡶⠟⣋⣡⣞⡾⡿⠃⣸⡟⠁⠀⠀⠀⢀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⢦⣿⠶⡿⠀⠀⠸⣆⠹⣿⣆⣀⡇⣀⢔⣡⣤⣶⠿⣿⣛⣲⣯⠾⠛⢁⣾⠁⣤⡟⠀⠀⢀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⣀⡤⠴⢲⡖⠲⠶⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣾⠁⠁⣄⠀⠐⠃⠀⠒⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡰⡋⠈⡁⠀⠀⠁⠀⠀⠘⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠻⡃⠀⠀⢀⣠⣴⡆⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡌⠃⢰⣾⡿⢻⡟⠻⣄⠀⠀⠀⠀⢀⣏⣠⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠉⠉⢉⣲ ⠀⠹⣄⠈⠨⣏⡙⢇⢷⡈⣧⠴⠒⠉⢉⣤⡴⣾⣿⠿⠃⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⣤⣖⣻⠽⠋ ⠀⠀⠈⠑⠦⣿⣷⣬⠟⠋⠀⠀⣀⡠⠿⠿⢯⠁⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⣀⠤⠚⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠋⠀⢀⣠⠶⣏⡡⢴⣚⣡⣼⣀⡀⠤⠤⠒⠊⢻⠁⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⢀⣴⣿⠀⠀⠘⢿⡉⠁⡸⠀⢀⠀⠀⠀⠀⠀⣼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢯⠀⠰⣯⢸⣿⠀⠀⠀⠀⠹⡶⠃⠀⢸⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣆⣀⠇⢸⠙⣆⠀⠀⠀⠀⢱⠀⠀⠘⡷⠲⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣧⠝⠀⣸⠀⠈⠷⣀⣀⡴⠋⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣜⣀⣀⡠⠤⠤⠄⠒⠒⠒⠛⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠿⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠙⠻⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⣀⣤⣶⠿⠟⠛⠋⠉⠉⠉⠉⠛⠻⢿⣷⣦⣄⠀⠀⠈⢻⣷⡀⠀⠀⠀ ⠀⠀⢀⣾⠟⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄⠀⠀⢿⣧⠀⠀⠀ ⠀⢀⣿⠏⢀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠈⣿⡄⠀⠀ ⠀⣼⡏⢠⡘⣷⡿⠁⠀⠠⣴⠶⠶⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⢦⣤⣈⢿⣷⡀⢹⣇⠀⠀ ⠀⣿⠀⠈⢻⣿⠃⠀⠀⣠⡴⠖⠒⠛⠒⠶⣤⠀⠀⠀⠀⢀⣴⠖⠛⠓⠶⣤⡀⠀⢿⣷⠸⣿⠀⠀ ⠀⢻⡆⢀⣿⡇⠀⢀⡾⠁⠀⠀⢀⡀⠀⠀⠸⣧⠀⠀⢰⡟⠀⠀⢀⣀⠀⠈⢷⡀⠘⣿⣧⣿⠀⠀ ⠀⢸⣧⢸⣿⠀⠀⢸⡇⠀⠀⠰⣿⣿⠀⠀⠀⣿⠀⠀⢿⡀⠀⠀⣿⣿⠇⠀⢸⡇⠀⢹⣿⣿⡇⠀ ⠀⢈⣿⣿⣿⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠙⢷⣄⠀⠀⠀⠀⢀⣾⠁⠀⢸⣿⣿⠁⠀ ⢰⣿⡿⢿⣿⠀⠀⠀⠀⠙⠳⠦⠤⠤⠖⠛⠁⠀⠀⠀⢠⣀⠙⠓⠶⠶⠞⠋⠁⠀⠀⢸⣿⢿⣶⡄ ⢸⣿⡇⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢶⣤⣀⣹⡆⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⣹⡇ ⠀⠻⣿⣶⣼⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⢀⣼⣿⣥⡶⠟⠁ ⠀⠀⠀⠉⠙⠛⣿⣧⡀⠀⠀⠀⠐⠿⣦⣄⣀⣀⣀⣀⣀⣠⣤⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⢀⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⠿⣷⣶⣤⣀⣀⣀⡀⠀⠀⣀⣀⣠⣴⣾⠿⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠈⠙⠛⠛⠿⠿⠿⠛⠛⠛⠉⠉⠀⠀⠀⣌⠛⢷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢾⣄⠹⣧⡀⠹⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠿⠿⠶⢶⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⢿⣄⠹⣧⣘⣷⣄⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠶⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀

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⠀⣤⣴⡶⣶⣦⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣭⣷⣬⣝⠳⢤⣑⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢋⡥⠞⣛⣯⡀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⢿⣉⢻⣿⣿⣿⣷⡞⠻⠓⣦⠙⣿⣦⣀⣠⡤⠤⡤⠤⠤⠤⣤⣤⣀⣀⣤⣾⡿⣫⠖⠁⣠⣾⣿⣿⡗⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⡿⣿⣿⣿⣿⣿⣗⠀⠉⢻⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⡞⠁⣀⣴⣿⣿⣿⣿⠃⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⡧⠘⢿⣿⣿⣿⣿⡷⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣿⣿⣿⣿⣿⠉⠰⡻⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⡄⠘⢻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠏⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣆⠀⠈⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠠⡀⠀⠀⠀⣄⠤⠠⣄⡀⠀⠀⠀⠀⠉⠁⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⣠⠚⠁⢀⣀⣀⠀⠀⢹⡇⠀⢰⠃⠀⣀⣀⠉⠓⢦⡀⠀⠀⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠇⠀⠀⣠⠞⠁⢀⣴⣿⣽⣿⣿⣦⣀⡏⠐⢸⣠⣿⣻⣿⣿⣆⠀⠙⣄⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⠀⠀⢰⠃⢀⣴⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠈⢿⣿⣿⣿⣿⣿⣷⣄⠈⡆⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠸⡀⣾⣿⣿⣿⣿⣿⣿⠟⠉⠉⢣⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠂⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⡠⣷⠤⠶⢶⣓⣿⣿⣿⣿⣿⣟⣧⡀⠀⣠⣾⣷⣾⣤⡀⣸⣿⣿⣿⣿⣃⡞⠒⢲⠷⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⣀⡼⢶⣶⡖⣛⣻⣿⣿⣿⣿⡿⣟⠀⠘⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣏⣙⡛⢲⠞⠦⠤⣀⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠊⠉⢀⣀⠤⠘⠋⠉⣹⠿⢛⣿⡿⠛⠷⢤⣀⣰⣽⣿⠿⣆⣠⠴⡿⠿⠿⡟⠿⡋⠙⠒⠤⣄⡀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢀⡀⠔⠊⢁⠔⠊⠁⣼⠁⣰⡇⠀⠉⣽⠿⠿⠏⠉⠀⠀⣹⣦⡀⠈⠑⠦⡉⠒⠤⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠋⠀⠠⠞⠁⠀⠀⢀⣿⠀⣽⠀⠀⢀⡇⠀⡄⠀⠀⠀⠀⢸⠈⠛⠲⣤⠀⠘⠦⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⣴⣿⠀⢀⣾⠁⡾⠀⢸⡄⠀⠀⢸⠀⠈⠃⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢰⣿⠀⢸⡟⣴⠃⠀⠀⣹⠂⢀⣾⠸⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠀⠸⢿⡆⢸⡇⠀⠀⠀⠀⠈⢣⣿⡇⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢃⡀⣘⣻⣾⡇⠀⠀⠀⠀⠀⢀⡿⠀⠀⢀⠠⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢿⣷⣿⣿⣇⣀⠀⢀⣠⣴⣿⣿⡀⠀⠘⠋⢻⣦⣾⣦⣶⡤⠴⣶⣶⣶⡶⠢⣤⣄⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣴⡿⣿⣿⠟⠛⣿⣿⣿⣿⣿⣿⣷⣀⣤⣤⣤⣿⣿⣿⡿⠀⢰⣿⣿⡏⠀⣾⣿⣿⣿⣿⣧⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⢹⣷⣾⡟⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣘⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢿⣿⣿⣿⣾⡏⠉⠉⠉⠀⠀⠀⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⠓⢄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⡀⠈⢧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠱⡀⠈⢇⠸⣿⣿⡿⠟⠛⠋⠉⠉⠉⠉⠙⠻⡟⠁⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠑⣄⠈⣆⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣈⠳⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢀⡴⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠏⣿⣿⣿⣿⣿⠇⠀⢀⣀⣠⣤⣤⣤⣄⣀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⡠⠖⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣤⡀⣨⣿⣿⣿⣿⡀⠈⣿⣡⣾⣿⣿⣿⣿⣿⣿⠒⣾⣏⣉⣿⣿⣿⣿⣿⡅⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⠿⠟⠛⠛⠋⢹⠃⠀⢸⣿⠿⠟⠛⠛⠛⡿⢈⠷⠒⠒⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠻⢤⣀⣀⣠⠴⠃⢠⣀⡀⠙⠦⣄⣠⡤⠞⣿⠃⠀⡠⠒⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⡀⠀⠀⠀⠀⠀⢄⣀⠭⠤⠤⠇⠀⠀⠀⠀⡏⠳⢾⠀⠀⣠⠤⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠁⠀⡴⠃⠀⠉⠲⠤⣦⣠⣤⠀⣠⢀⣤⢠⣀⣴⣶⡶⠛⠛⠢⣜⢟⣛⣿⡆⠀⠀⣟⠉⠛⠛⠿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⢹⡙⠛⠓⠛⠛⠛⢛⣿⠋⠀⠀⠀⠀⠈⢲⢌⣀⠀⠀⠀⠈⠳⡀⠀⠀⠈⠹⣿⣿⣿ ⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⣀⣀⠀⠑⢄⡀⠀⠀⢠⠎⠀⠀⠀⠀⠀⢀⣀⠼⡆⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠘⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠢⡄⣈⠉⠲⡀⠀⣀⠴⠛⠒⠒⠉⠉⠉⠉⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢻⣿ ⣿⣿⡇⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡅⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⣼⣿ ⣿⣿⣧⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠂⢀⣿⣿ ⣿⣿⡿⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⣠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿ ⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⠉⠒⠢⠤⠤⠤⠤⠤⠤⠴⠋⠙⢦⣀⣀⠀⠀⠀⠚⠁⣀⣀⣠⠞⠁⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿ ⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠄⠀⠀⠀⠀⢰⠀⠀⠀⠉⠉⠉⠭⣉⡉⠁⠀⠀⠀⣀⠤⠚⢻⣶⣤⣀⠀⠀⠀⢰⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⣦⣤⣀⣀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠀⠀⠀⠀⣸⣿⣿⣿⣷⣤⣤⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⢛⡝⢻⢯⠻⣟⣿⢻⣿⢯⡋⢣⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠗⣶⣿⣆⢈⣻⣿⣿⣶⣿⣿⠇⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠤⠽⣿⠈⠉⠁⠹⡄⣻⡋⢹⣿⣿⡃⠀⠀⠀ ⠀⠀⠀⠀⣷⢉⠒⢎⠍⠐⣀⣴⣿⡷⣄⠰⠤⠈⣂⣴⡿⠿⣿⠿⠗⠂⠑ ⡠⠐⠉⠀⠂⠠⠕⢄⣡⡋⣴⡨⠐⢉⡭⣳⡶⢿⣿⠋⠀⠔⠊⠆⠀⠀⠀ ⠓⢄⠀⠀⣀⣀⢀⣀⣀⢀⡀⢀⡠⣞⣒⣺⣿⣷⣇⡰⠀⠂⠉⠰⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣤⡟⠵⠤⡑⠀⠥⣶⢺⣿⣏⣋⡄⠠⠂⣁⡚⡅⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⢻⣾⡇⠘⡐⠠⢍⠆⠋⠁⠸⣥⠔⡁⠠⣈⢃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠧⣀⠘⠛⠥⠐⠄⠀⠴⠓⠆⡀⠀⡿⠗⠃⠀ ⠀⠀⠀⠀⠀⠀⢠⡤⣏⣀⣀⢠⢏⠃⠒⠠⠄⣀⠀⠀⠀⣈⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡿⢱⣿⣿⣿⣿⡎⠸⠣⠄⠰⡆⠈⠁⠒⠊⠐⠃⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⣾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠈⠾⡿⢉⣻⠙⣿⣿⣿⡻⣿⣛⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⠻⡟⡀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡆⡄⣠⣿⡏⠀⢹⣌⠹⣇⠈⠻⣿⣶⣿⣭⡁⠹⢿⢻⣿⠻⢷⡌⠀⠁⣿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣿⣿⣥⡤⣦⡹⣷⣿⡄⠀⠈⠹⢿⣿⣿⣷⣾⣯⣿⣄⣸⣿⣶⣾⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡟⢇⠹⣿⣿⣿⣿⣷⣀⠀⣀⣤⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠃⠘⠦⣟⣿⠛⠙⢿⣯⠉⠙⢯⣼⣿⡿⢻⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⡒⠦⢼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠙⠛⠋⠐⠋⢰⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡒⢦⣄⡀⠀⣀⣰⣿⣶⣞⠉⡀⠀⠘⠀⠀⣿⣿⣧⠀⠀⠀⠀⢠⡀⠀⠀⠙⢧⡈⠙⠿⠈⢠⣿⣿⣿⣿⣿⣿⣿⣶⣤⣒⢂⣀⣤⡤⠖ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠉⠛⢮⣐⠤⣀⠀⠉⠺⠀⣀⣤⣾⣿⣿⣿⡟⢦⡀⠀⢀⣉⣀⣀⣀⠀⠳⡄⣀⣴⣿⣿⣿⠿⣿⣿⠿⢿⣿⠿⠿⠛⠉⠉⠙⠂ ⠀⠀⠀⠀⢀⣀⡤⢤⡒⠛⠋⠉⠳⢄⡀⠀⠈⠳⡄⠙⣀⣴⠿⠟⢛⣻⠝⠋⣹⢃⣠⣻⡳⣄⠉⠉⢉⣠⣤⣶⣿⣿⣿⡿⠋⠀⠀⠈⠻⣝⠲⠤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⠞⠋⠁⠀⠀⠙⠲⠤⣄⣀⡀⠙⢦⡀⠀⢹⢴⢫⠀⣄⡿⠋⣤⣠⠜⠛⠉⢠⡀⡹⢮⡿⢿⣟⣿⣷⢟⣱⡿⠋⠁⠀⠀⣠⠔⠊⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠚⠓⠢⠼⠼⣮⣼⣽⡷⠞⠋⠀⠀⠀⣨⢿⣏⣠⠼⢷⣯⣉⠀⣱⡿⣿⠛⠀⠀⠀⠈⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀ ⠸⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣉⣤⠤⠶⣮⣿⣿⣿⣦⣜⠁⠀⢀⡆⠀⢀⡤⠒⠉⠉⠉⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⠠⠤⠤⠤⠤⠤⠤⣶⢦⣀⠠⠤⠴⠋⠻⣥⡤⢤⡤⢤⣿⣿⣿⣿⣿⣿⣶⣄⡾⠀⠀⢀⡠⠈⠀⠀⣀⡘⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢐⣞⡗⠶⣇⡀⠈⠳⣄⡀⠠⠛⡝⢀⣾⡤⣾⣿⣿⣿⣿⠿⣟⡋⠁⠃⠀⠀⠉⣠⠤⠚⠉⣀⣸⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣺⣯⢫⡏⢸⢳⠚⠛⠲⣄⠈⠉⠙⠒⠒⣿⣿⡁⠻⣿⣿⣿⣿⣦⡀⢙⣦⡇⣠⠖⠋⠁⢀⣀⣀⣀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣳⡵⣿⠸⣷⡞⠁⠘⣦⣤⣄⠀⠀⠈⢝⠧⡄⠹⣿⣿⠟⠛⠉⣿⡾⠁⠁⠀⣤⠔⠋⠁⠀⠉⠑⢾⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢯⣹⣿⣷⣿⡇⠀⠀⠸⡄⠀⠙⠲⣾⢂⡴⢷⠀⠀⠀⠀⠀⠀⠸⣟⣦⣴⠞⠁⣀⣀⠤⢤⣀⠀⠀⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠙⣦⣴⣄⡿⡞⠀⢸⡀⠀⠀⠀⠀⠀⢀⣾⣿⠀⡠⠎⠁⠀⠀⠀⢿⣿⣦⣈⣳⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⢧⣀⠀⠀⠀⠘⠛⠿⠧⣇⣀⣀⠹⣄⣀⡀⠀⠴⣣⡿⠉⢻⣅⠀⠀⠀⠀⠀⢸⣿⡿⠟⠋⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠉⠒⠒⣦⣤⣄⣀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠑⠢⣄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡼⡵⠁⠀⠀⠀⠀⠀⢰⣿⠁⣸⠉⠉⡒⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⣸⣧⣶⣶⣿⣶⣶⣄⣮⡇⢠⠏⣆⢀⠇⠀⠀⠀⠉⠙⡖⠶⢤⣀⠀⠀⠀⠈⠳⢶⣆⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡞⠀⢫⢿⡳⠀⠀⠀⠀⢸⣧⠀⠀⠀⠉⠛⠲⠤⠤⠤⠉⣀⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠏⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠘⡆⠝⠛⠓⠂⠀⠸⢈⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠈⠳⠠⣌⣵⠴⠶⠢⣤⣄⣉⠉⠛⠛⠿⢷⣶⣦⣤⣤⣀⣙⡇⠀⠀ ⠀⠀⠀⠈⠊⠠⣰⣴⠿⡟⢿⣿⣷⣦⣴⣖⡠⢤⠄⢀⠙⠙⠗⠠⡀ ⠀⠀⠀⠀⠀⠀⠀⢿⣾⣇⠶⠿⡿⣿⣿⣍⣻⣿⣶⣾⣭⣭⣤⠭⣀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄⠙⠀⠀⢉⣿⣧⣥⣿⡿⣻⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠈⠉⠒⠠⣸⣿⣿⣿⣿⣾⣿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢖⠂⠀⢠⣿⣿⠇⢟⠿⣿⣿⣷⣤⣀

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣆⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣽⣥⣙⡟⠿⣌⡁⠺⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⠀⠉⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣤⣿⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⣀⣤⣒⣀⣀⣈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡟⠛⢏⡟⢻⣿⣿⣶⠞⡁⢻⣡⣴⣿⠿⠿⣿⠆⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣦⣾⣧⢤⣽⣿⣿⣦⡀⠘⢿⣿⣿⡆⠀⡾⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⣿⣿⣼⣶⣯⡝⠻⣿⣦⣀⢻⣿⠧⠚⠁⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⣿⣷⣿⡈⠀⠀⠉⠛⠿⣤⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣿⣿⣿⡏⠿⣷⠂⠀⠀⠀⠀⠀⠉⠙⠲⠤⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣿⣿⣷⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣧⡀⠈⠀⣠⠤⠤⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⣝⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣿⡿⠙⣿⣿⣿⣧⠀⠉⠛⠻⠿⠦⠄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⣿⣿⣿⣶⣄⡀⠀⣀⣤⣾⣿⣿⣿⠟⠀⠀⣿⠻⣿⣿⣷⣶⣿⠿⢛⣛⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⢋⣼⣿⣿⣿⣷⣦⣍⣻⣿⣿⣿⣻⡟⠁⠀⠀⠀⠹⡄⡿⣿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠴⠋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣯⣭⣿⣍⠲⢄⠀⠀⢹⡇⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢈⣙⣛⠿⣿⣬⣧⠀⣸⢰⣿⣿⣿⣿⣿⣿⣿⠟⢉⡥⠤⣌⡻⣿⣷⡀⠀⠀ ⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⡠⠊⠉⠉⠉⠓⠺⢿⣿⣵⠁⣼⣿⣿⣿⣿⣿⡟⢀⡔⠉⠀⠀⠀⠙⢮⡻⣿⡄⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣿⣿⣿⣿⣿⣿⠃⠊⠀⠀⠀⠀⠀⠀⠀⠱⡼⣿⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣄⣆⠀⣀⡀⠀⠀⠀⠀⠀⣿⣿⠁ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢏⠁⠀⠀⠀⠀⣠⡖⣿⡟⠀ ⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣇⠀⠹⣭⣲⠦⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣤⣴⠀⠀⠀⠀⠈⡄⠀⠀⠀⠘⣷⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡆⠀⠙⣿⣤⣯⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠸⡄⠀⠀⠀⢹⣿⣿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢸⣿⣿⡇⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⢇⠸⠋⢩⣿⣿⠋⣿⠃⠀⠀⠈⣟⠙⢷⠀⠀⠀⠈⠻⣮⣙⣿⣿⣿⣯⠉⢿⡿⠇⠑⠈⠛⢻⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡏⢀⠀⢨⡾⣀⣴⠃⢀⣤⣤⣐⣻⡄⢸⡄⡴⠖⠁⠀⠈⢿⣿⣀⡈⢹⣆⠀⠀⠀⢀⣰⡦⣿⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⡇⣷⣿⣿⠶⠛⠉⠉⢻⣿⢿⣿⣧⠀⠐⣻⡿⠿⠿⢿⣿⣷⣶⠉⣿⣿⢠⣾⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⣿⣿⣿⡟⣧⠀⠀⡞⣠⣶⢻⠈⢻⣿⡄⢀⠇⢠⣀⢰⠀⠘⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⠹⣄⠀⠯⣭⠏⠈⠀⠀⢻⣿⡀⠀⢸⣛⣸⠀⢀⡼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠉⠓⠢⠤⠒⠀⠀⠀⠀⠹⣷⡤⠤⢭⣥⠴⠊⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣄⠀⠀⠀⠀⠀⢀⣾⣟⣲⣄⠀⠀⠀⠀⠈⠀⠀⣠⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣦⡀⠀⠀⠀⢸⠟⠉⠁⠉⣷⠀⠀⠀⢀⣠⣾⣿⢿⣿⣿⣿⣯⣀⣀⣀⣠⠴⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣦⡄⠀⠘⣄⣀⣀⡴⠋⠀⣠⠴⠋⣵⡿⠉⣾⣿⢿⣿⣿⣿⣉⣩⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⣿⣽⣿⣷⡦⣄⠀⢀⣠⠔⠊⠁⢀⡾⠋⡰⢰⣿⣿⣿⣿⣭⣿⣷⣾⣿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠷⡈⠉⠉⠀⠀⣠⠴⠁⠀⣰⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣵⣾⣿⣿⣿⣿⡇⡇⢳⠀⠀⠀⠀⠀⠀⠀⣠⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⢾⡀⠀⠀⣀⣤⣴⠞⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡀⠀⠀⠈⠉⡰⠋⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣧⠀⠀⡰⠊⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢈⡴⠋⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢹⣿⣿⡿⠛⠻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⣾⣿⡟⢀⡤⠖⠃⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⣿⡏⠀⠉⡀⠀⠐⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠘⠳⠤⣈⠙⢿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠸⠿⠇⠀⠀⠀⠀⠀⠰⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⠖⠒⠀⠀⠀⠉⠑⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠿ ⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠒⠄⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡦⡲⣩⠫⠑⡉⢏⡩⢒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠔⡻⢰⠟⢁⣔⢁⡇⣸⠿⣆⣕⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⠀⠀⢀⣀⣤⣃⣴⡁⡏⣤⠞⠛⠙⠀⠃⠀⠈⢾⣮⣻⣶⠖⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠉⣿⠻⡇⣿⡎⠤⠄⠀⣀⠀⠀⡀⠤⠀⢱⢳⢃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠁⠀⡇⢻⡁⢹⣠⡴⠒⠚⠄⠀⠀⡝⠉⠉⢳⣧⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⢳⠈⣃⠈⡏⠀⠀⠀⢀⠀⡀⡇⠀⠂⠀⡏⢿⠀⠀⠀⠀⠠⠀⠀ ⠀⠀⢀⡴⠋⠀⠈⡟⠽⢂⢡⠠⠤⠐⠊⡬⠥⠌⠐⠒⣸⢳⣿⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠈⠳⣄⠀⢀⢇⡠⠀⢂⠆⠀⠀⠀⠀⠀⢀⠀⡔⣌⣼⠙⢂⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠈⡷⠁⣮⠃⢹⢻⠌⠶⣤⣄⣒⣒⣪⡞⣰⠞⠋⠐⢾⡀⠀⠀⠀⠀⠀ ⣀⡤⠄⡡⠾⠃⡸⢁⡴⠊⠉⠘⣧⠖⢻⡿⢋⣸⢡⠙⡄⠀⡤⠂⠉⠉⠁⡂⠄⣀ ⠛⢉⠮⣢⠻⠀⡡⠁⠀⠀⠀⠀⢺⠒⠊⠉⢠⢳⡺⡄⠳⣼⠀⠀⠀⠀⡌⢷⢆⠀ ⡸⣱⠋⢸⠀⠀⢱⣄⠀⡒⠀⠀⠘⠀⡠⠁⡆⡟⢇⠹⢦⣀⠀⠑⢴⢴⠸⠸⠘⡆ ⡜⠁⠇⢀⢠⠀⣦⡟⢻⠀⠀⠀⡄⠐⠀⢰⣷⡇⡀⠉⠛⠛⠀⠀⠈⠺⢆⡀⠀⠓ ⠘⠀⢸⢸⢸⡼⢻⠀⠀⣇⠀⠠⢸⠀⠀⣨⠋⠁⠀⠉⠢⡀⠀⠀⠀⠀⠀⠈⢶⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⣺⡿⡉⢻⡄⠀⣾⡉⢳⡆⠀⠀ ⢀⣀⠠⢄⣀⣀⣀⠄⠂⠉⢁⠊⠙⠀⠃⠈⢲⠣⣸⣧⠀⠈⠓⠛⣷⣤⣎ ⣎⢊⠒⠒⠤⢤⢞⡠⢄⢖⠁⠀⠀⠀⠀⢀⠜⠉⠒⢽⣄⠀⢀⢔⣷⢀⢩ ⠸⡌⢢⡀⢠⢪⠋⠀⠀⣧⠏⠒⠒⢒⠈⠁⡀⠀⠀⠠⠘⣦⠘⠬⠷⢺⠃ ⠀⠹⡀⢱⠇⠸⣄⠴⢊⡏⠀⠀⠀⢸⠆⠀⢰⠀⠀⢀⡃⡘⣇⠀⠀⡸⡀ ⠀⠀⡙⠋⠀⠈⠁⢀⡞⢰⠀⠀⠀⢸⠸⠤⠘⠒⠒⠁⢑⠁⣸⡆⢌⣠⠁ ⠀⠀⡇⠀⠀⠀⠀⣼⠁⠀⡟⠒⠀⠁⠀⠀⠀⣰⣷⡖⢻⢀⢧⣻⢠⠹⡀ ⠀⠀⠇⠀⠀⠀⠀⡟⠀⠀⣀⣤⣿⣖⠀⠀⠀⠟⡩⠇⠈⢁⣼⠏⠈⣦⡑ ⠀⠀⠸⡀⠀⠀⢰⣿⡀⠠⣩⡷⣉⠝⠀⠀⠀⠀⣠⣴⡉⡟⠁⠀⢎⢸⠀ ⠀⠀⠀⠘⠤⡀⠘⠚⠿⠭⣅⣀⣤⡴⣠⣶⣶⣯⣿⣧⠃⠀⠀⠾⠆⠁⠀ ⠀⠀⡀⠀⠀⣨⠷⣶⣶⣶⣖⣿⡿⡳⡲⣿⡝⡜⣟⢠⡠⠾⣍⣲⡄⠀⠀ ⠀⠀⢠⠤⠰⡗⠋⠉⠿⡟⠀⠋⢛⠴⣥⡝⢋⡩⣾⡛⠒⠊⠉⠲⣿⠀⠀ ⠀⠀⠈⠓⠰⠧⣀⡀⣀⠏⠢⢔⢿⣞⠉⢉⣸⣉⣴⡁⠀⠀⢀⠰⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠛⠋⠙⠋⠀⠀⠉⠉⠀⠀⠀⠀⠀

⠀⠀⠠⠑⠄⠀⠀⠀⠀⠀⠀⠠⠄⠤⢄⡀⠀⠀⠀⠀⠀⠀⡔⡆⠀⠀ ⠀⠀⠀⠈⠀⢀⡠⠊⢁⠄⡢⢂⠁⠀⢠⠀⠈⠁⠢⠀⠀⠀⠋⠀⠀⠀ ⠀⠀⠀⠀⣠⠊⢀⠔⢡⢞⡕⠅⠀⢠⣿⣸⡀⢳⡀⠀⠐⡀⠀⠀⠀⠀ ⠀⠀⠀⠔⢇⣤⡿⡰⡏⠞⠔⠠⠂⠛⠁⠃⠙⠄⡏⣄⡀⠘⡄⠨⠂⠀ ⣀⣠⣼⣻⣯⢁⣧⠀⠠⣀⠀⠀⠀⠀⠀⠠⠄⠈⠀⡵⣌⣿⣷⣦⣀⠀ ⠈⠉⢹⠻⡗⡟⠁⢀⣀⣠⠀⠀⠀⠀⠀⠀⣄⣀⠀⢻⠘⡟⡻⠏⠉⠀ ⠠⣀⢐⠠⡇⡄⣴⠋⣴⡮⣳⠀⠀⠀⢰⡪⢭⣬⡳⡼⡆⣯⠚⡀⠀⠀ ⠰⢁⣾⡴⣳⣿⡇⡓⠢⠽⡙⠀⠀⠀⠀⡻⠣⠟⡱⣿⡃⡿⡀⣇⠠⡠ ⠁⡌⠘⡀⠈⡏⠁⠀⠒⠈⠀⠀⠀⠀⠀⠈⠀⠀⠁⢱⡰⠘⡅⢺⡀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⣿⣿⠿⢿⣿⣆⠀⠀⠀⠀⢀⣼⡿⣟⣿⣄⣀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣶⣿⣏⣱⠿⡫⣄⠀⠀⢿⣿⡀⠀⠀⢸⣿⣍⣀⠀⠋⠱⣹⡇⠀⠀⠘⣇⠑ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠚⠛⢛⡽⢻⡟⠋⠙⣿⠛⠻⢧⣞⣁⡼⠃⠀⢸⣟⣷⠀⠀⠀⠙⠻⣯⠁⢀⣼⣿⣁⠀⠀⠀⢈⠧ ⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠀⠀⠀⠀⡴⠋⠀⠘⠷⠤⠞⠃⠀⠀⠀⠙⣏⠓⠦⣄⢸⣿⣿⡄⠀⠀⠀⠀⠈⠓⠚⠛⠳⢭⣗⣦⣤⣞⠀ ⢠⡾⢻⣯⠉⠉⠉⠉⠉⠛⠛⠻⢶⣾⣇⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣀⡈⠛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠛⠙⠛⣛⢻ ⣿⠀⢿⠛⠛⠷⠶⢶⣦⣤⣀⣈⣠⣾⠋⠀⠀⠀⠀⣶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠈⠙⠷⣦⣽⣧⡀⠀⠀⠀⠀⠀⢀⣠⢾⣿⡷⠄⠀⠀⢨ ⣿⡀⠸⣧⠀⠀⠀⠀⠀⠀⠉⢉⡟⣡⡶⠟⠛⠛⢷⣜⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠙⠻⣿⣦⠀⠀⠀⣰⠟⢠⡞⣻⠄⢀⡞⢠⡟ ⠘⣿⡀⢹⣧⡀⠀⠀⠀⠀⣰⢏⣴⠏⠀⠀⠀⠀⠀⣻⡆⢨⡟⠲⠦⠤⠤⠤⠴⠖⠚⠋⠁⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⢿⡄⠈⢩⣥⣴⢿⣣⡿⠀ ⠀⢻⣷⠈⠈⢷⡄⠀⠀⣰⠃⣼⠇⠀⠀⠀⠀⠀⢀⣽⣿⡟⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢿⣷⡀⠀⠙⠛⠛⠉⠁⠈⣿⠃⠀ ⠀⠈⢿⣿⠀⠀⠻⣦⢰⠇⠀⣿⣆⠀⠀⠀⣠⡴⠟⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⣧⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀ ⠀⠀⠈⢿⡄⠀⢀⣽⡟⠀⠀⠘⣿⣀⣴⠿⠋⠀⣰⡟⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⢹⡄⠀⠀⠀⢸⡄⠀⠀⠀⠀⢸⡆⢸⠀⢠⠃⢻⣧⡀⠀⠀⠀⠀⣰⠇⢠⠀ ⠀⠀⠀⠈⢻⣿⣿⡿⠁⠀⠀⠠⠟⠋⠁⠀⠀⣰⣿⠁⢠⠃⠀⠀⠀⠀⠀⠀⠀⢸⠈⢧⠀⠀⠀⡼⣷⠀⢀⣀⡤⠞⠛⣿⣠⠟⢀⠈⣿⣇⠀⣤⠤⠾⠋⢠⡏⠀ ⠀⠀⠀⠀⢸⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣸⠤⠖⠚⠉⠉⠉⠉⠁⠀⠀⠀⠘⡇⠀⠘⣧⢹⣿⡄⠳⣄⡀⢀⣼⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠇⣠⣾⠀⠀⠀⢀⣠⡼⠋⠉⠀⠀⠀⠀⠀⠀⠀⣠⠤⢀⣀⣀⣠⣇⠀⠀⢸⡜⢹⣿⡄⠀⢉⡿⡇⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⡽⠈⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣷⣿⣿⡛⠛⠛⣿⠀⠀⣸⢧⠀⣿⡇⠀⡎⠀⢷⡀⠀ ⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⡇⠀⠀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⣾⠛⣿⣿⣿⣷⠀⢠⣇⣠⠴⠋⢸⣧⣿⡇⠀⡇⠀⢸⣇⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⡇⠀⢀⣠⣿⣶⣶⣶⠶⡄⠀⠀⠀⠀⠀⢿⡟⠛⠉⣠⡿⠀⠈⠁⠀⠀⠀⣼⣿⡟⠀⠀⠹⣦⢸⠘⢆ ⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣧⣴⣿⡟⢿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠈⠛⠓⠛⠋⠀⠀⣀⣀⣠⡴⣾⡿⠋⠀⠀⠀⣠⠿⣿⢧⡈ ⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠸⣏⢹⣷⠟⠋⠉⢩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠙⠙⠳⡾⠋⠀⠀⠀⢀⡾⠁⠀⣾⠀⠈ ⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⣼⣿⢿⣾⣆⠀⠀⠘⢦⣌⣶⡝⠶⠶⠾⠛⠁⠀⠀⠀⠀⠀⠈⠁⠀⣠⣴⣿⢿⣷⣄⣠⡾⠁⠀⠀⠀⠀⠘⢷⣄⢀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠠⣄⢄⠹⣿⣄⣹⣿⣟⠲⠖⠚⠉⣀⣀⡀⠀⠀⠀⣀⡀⢀⣀⣀⣤⣤⣾⠟⢿⣻⣿⣧⢹⡍⠁⠀⠀⠀⠀⢠⣶⢦⠀⠈⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠉⠙⠛⠛⠿⢶⣶⣾⣭⣭⣽⣿⣿⣽⠏⢙⡛⣻⣿⣿⣿⣿⣿⣻⡇⢿⣿⡾⠁⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⡀⠀⠀⠀⣀⣄⣀⣭⣽⣿⣿⣿⣿⣯⣄⣛⣋⣿⣟⠻⣟⠋⢿⣿⣷⠞⠉⠀⠀⠀⢀⣴⠶⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡶⠾⣿⣿⣿⣿⣿⣿⣿⣏⣺⣿⣿⡿⠟⢩⡿⢹⡟⣿⡽⣦⠈⣿⠉⢻⣝⠒⢒⡆⣠⡾⠻⠻⣧⣀⡀⢙⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠞⠃⠀⠀⠀⠀⠀⣼⣏⣀⣀⣤⣿⣿⣿⣿⣿⣿⠿⠟⢛⣿⣿⣷⡴⠋⣰⠟⠀⢸⣷⣹⣷⣿⠴⠞⢛⣷⣾⡿⠋⠀⣀⣘⣬⣿⣏⠉⠹⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⡤⠤⠴⠶⣿⡟⠛⠋⠀⠀⠈⢿⣿⣿⡇⠀⠰⠛⠁⠈⠟⢷⣾⣇⣀⣤⡴⠟⠋⠁⠀⣠⣴⣿⣿⠛⠛⠛⠛⠉⠁⠀⠀⠙⠻⣶⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⣽⡇⠀⠀⠀⠀⠀⠀⠈⣻⣇⠀⠀⠀⠀⠀⣠⣟⠁⣸⢛⣿⣷⣤⡤⢶⢺⣿⣭⠿⢼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⠷⣤⣴⣯⣥⣄⠄⠀⠠⠀⠀⢀⣾⠛⠳⣤⣀⣠⢞⣿⣿⡟⠛⠉⠉⠀⠀⠀⣸⠉⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣤⣤⣴⡾⠇⠀⠀⠀⠉⠠⣏⣿⠉⠷⣦⣄⣀⣠⣤⣴⣿⣿⣿⣿⠛⠦⣤⣀⣀⣀⣀⣀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡷⠶⠾⣿⡿⠟⠋⠙⠿⠴⠟⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣄⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀⠀⠀⣀⣴⡷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢛⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠉⠑⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣥⣶⣞⣿⣯⠛⠙⣿⣿⠟⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠻⣯⡳⣄⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⠋⣁⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠻⣿⣿⣿⣿⣿⣿⡽⣷⣮⣿⣌⢳⡄⠀⠀⠀⠀⠉⠲⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢋⣠⣶⠟⠛⣋⣩⣴⣿⣿⣿⣿⣿⣛⣩⣽⠿⣟⣷⣦⣀⡀⠙⢿⣿⣿⣿⣿⣾⡻⣿⣿⣷⣝⡳⢤⣀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣩⡿⣡⡾⢋⣠⡄⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠷⣦⣌⠙⢿⣿⣿⣿⣮⡻⢿⣿⣿⣷⣌⣉⡉⢂⣀⡀⠈⢢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣫⣶⡏⣰⣿⣿⣿⣣⣤⣭⣽⣿⣿⣿⣿⣿⣟⡻⢿⣿⣿⣿⣿⣿⣷⣦⣈⠙⢳⣮⣿⣿⣿⣿⣿⣷⣭⣟⣛⣛⣛⠛⠛⠉⠀⠀⠀⠹⣄⠀⠀⠀ ⠀⠀⠀⣠⣴⡿⢫⣿⣿⣿⣿⠟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣍⠻⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀ ⠀⠀⠛⡿⠿⠶⣿⣿⣽⠟⢁⣴⢏⣵⢿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⡻⣿⣷⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣆⠀⢦⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀ ⠀⢀⡾⠀⠀⠀⢸⡿⢋⣴⡟⢁⣾⣿⢼⣿⠛⢉⣛⣿⣿⣡⣄⠀⠙⣷⣿⣯⠙⣦⢻⣷⡹⢿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠘⠿⣿⣿⣷⡀⠱⣄⡐⠒⣻⡇⠀⠀⠘⡆ ⠀⣾⠁⢀⣀⠞⢉⣴⣿⣿⣧⣿⣿⣿⢸⡏⠀⠁⠈⠁⠀⠀⠀⠀⠀⢻⣿⡿⠀⠙⢇⠻⣿⣯⣿⣿⡟⠋⢤⠀⠀⠀⠀⠀⠐⢮⡙⢿⣿⣶⣤⣹⠟⠋⠀⠀⠀⠀⠙ ⠀⡿⣤⣌⣁⣴⡟⣹⣿⠟⠉⣿⣿⣿⠸⣧⠀⠀⠀⠀⠀⣆⠀⠀⠀⢸⣿⠃⠀⢀⣠⣶⣿⣿⣿⣿⣧⡀⠀⠀⠲⢀⣀⠀⠀⠀⠙⢷⣌⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠁⠈⢙⣿⣿⣿⣿⣿⠀⠁⣿⣿⣿⡄⢿⣤⣀⠀⠀⠀⠉⠀⠀⠀⢸⣯⣴⠞⣫⣥⣴⣶⣿⣿⣿⣿⣿⣶⠟⠛⢿⣙⣷⡶⣦⣤⣄⣙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡌⢀⣴⣿⣿⣿⣿⣿⣿⣄⠀⣿⣿⣿⣷⣈⣷⣍⡙⠳⠀⠀⠀⠀⠀⠞⠉⢀⣨⣿⣿⣿⡟⢣⠛⣿⣟⢿⣿⣦⣀⣸⣧⣳⡅⢦⣀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠈⠛⠛⠛⠛⠁⢈⣿⣿⣄⠻⣿⣿⣿⡛⣿⢻⣿⣷⣦⠀⠀⠈⠁⠂⠀⠞⠣⢿⣿⠿⠻⣋⣾⠙⣿⣦⡙⢿⣟⠙⠻⢿⣿⠦⢬⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠐⠛⠋⣿⢹⡄⠛⢿⡜⢻⣌⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠨⡿⣿⣆⠉⠳⠤⠤⡤⢿⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⠘⡇⠀⢸⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⡌⠻⢷⣄⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⣧⣤⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣿⣿⡆⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⢃⣼⣿⣿⡿⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣿⠀⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠘⣿⣿⠀⠘⣿⣷⣤⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⣤⠞⢻⠘⣿⠈⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⢸⡿⣿⣝⠲⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⢟⣡⣴⣿⢠⣿⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⢱⡉⠻⣷⡀⠉⠓⠲⣤⣤⠖⠋⢁⣴⣿⡿⠿⠿⠋⡿⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀ ⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⢳⡀⠀⠉⣳⠴⢱⣿⣿⣿⣾⣿⡿⠋⠠⠆⢀⣴⠃⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀ ⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡁⢀⡼⠉⠱⣾⠈⢿⣿⣿⠟⠀⣴⣾⣿⣿⣏⣼⡅⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⢄⣨⣾⣿⣧⠈⢻⠋⣐⣶⣿⠿⣿⣿⣿⣿⡏⢈⣿⣷⣤⣤⣀⣀⠀⠀⠀⠀⠀⠤⠀⠀⡠⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⣀⣀⣤⣤⣤⣲⡟⠠⠬⢯⣽⠟⠋⠇⢸⣠⡿⠿⡿⠀⢯⣙⠿⠟⠀⣨⣟⡿⢿⣿⣿⣿⣿⣶⣶⠖⠤⡄⠐⠦⢤⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣳⡾⠟⠋⠉⢁⣼⣿⣿⢷⠂⠐⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠉⠀⢠⢾⣿⣿⡿⣶⣦⣀⣉⡉⠙⢻⡄⠀⢿⡖⠒⠒⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣰⠾⢏⣧⠀⠀⢀⣾⣿⣿⡇⠀⠀⠊⣠⠄⣀⡀⠁⢸⠷⣄⠀⢠⡀⠀⠈⠂⣸⠀⣿⣇⠀⠘⢿⡿⢋⡉⢻⡌⣯⠀⠈⢿⣦⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠎⠙⡆⢄⡽⠀⠀⣾⣿⣿⣿⠟⠞⠀⠀⣻⣶⡋⠀⣿⣾⣟⡊⣷⣾⠃⠀⠀⠀⠙⢧⣙⢿⣆⠀⢸⣿⣿⣿⠈⣧⠸⣆⠀⠘⠹⢿⠓⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⢯⠽⠿⡗⣺⠁⠀⣰⣿⣿⡟⠁⠀⠀⠀⠘⢷⣿⠇⠀⢘⣿⣋⣿⣳⣿⠃⠀⠀⠀⠀⠀⠙⢧⡙⢷⣼⣿⠿⣿⠀⠻⣧⢹⣦⣤⡄⢘⣦⣤⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣀⠀⠀⠀⢀⣠⣤⣿⢒⣒⡒⠒⠒⠦⣄⠀⠀⢀⠀⠀⢀⡠⠀⠂⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣶⡖⠋⣵⠏⢻⡿⠿⣿⣿⣷⣶⡌⠳⣄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⣠⢾⣇⠜⠁⠀⠈⠉⢉⣩⣽⡇⠀⣿⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣈⣙⣳⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⠟⢋⠝⢡⡏⢻⡮⢅⠁⢾⣿⣿⣿⠃⢀⣼⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠛⠋⠁⠀⠹⢦⣄⡀⠀⠀⠀⠀⠀⣀⣴⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡏⠀⠠⠯⣤⡜⡇⠀⠈⣦⣥⣼⣿⣿⣧⡴⣻⠋⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠚⠋⣁⣠⣤⡔⠚⠉⠁⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⢿⣿⡇⠀⠀ ⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠸⣷⣷⠀⣼⣿⡿⠟⠉⢡⣾⡾⠁⠀⠀⠀⢀⣠⠴⠚⠉⢁⣤⣤⣶⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡒⠑⠦⣀⣈⡻⣷⣏⣁⠀⣀⡴⠞⠁⠀⢀⣠⠴⠊⠉⣀⠴⠖⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⢿⣿⣷⢶ ⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣶⣤⠴⠖⠋⠁⠀⣀⡴⠞⠉⣀⡤⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣦⣤⣀⡈⠻⣦ ⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⣠⠴⠚⢁⣠⠔⠛⠁⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣾⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠐⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣠⠴⠋⢁⡤⠖⠉⠀⠀⠀⠀⠀⢀⣠⡴⠚⠉⢹⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⣀⣤⠖⢋⣡⠴⠊⠁⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⠃⠀⠀⠀⢻⣿⣿⣿⡟⢻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⢋⣉⡠⠖⠉⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⡿⣿⠀⠀⣄⠀⠈⢿⡏⠉⠉⠀⠳⢻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢀⠠⠴ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⢋⠡⠶⠚⠉⢁⣀⣠⢤⣶⡿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡿⠇⡟⠀⠀⠈⠛⠷⠮⢿⣦⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⠤⠖⠚⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢊⣁⣤⡶⠾⠧⢶⣶⣾⣿⣿⣿⡿⣿⣿⣷⢿⠿⠛⠛⢻⠉⠉⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⢦⠀⢦⡹⣿⣿⣿⣿⣿⣿⠿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⢙⣿⣿⣧⡏⠁⠈⢻⡂⠤⠀⠘⢧⣄⣰⣜⣷⣦⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⢻⣷⣌⢻⣽⣿⣿⣿⣿⣿⣧⡈⢻⡿⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠉⠁⢀⣾⣿⣿⢹⡇⠀⠀⢸⠛⠿⣶⣦⣀⠀⠁⠉⠙⣿⣿⠀⠀⠀⠀⢀⣠⣴⡾⠛⠁⢸⡿⣿⣿⣿⢽⣓⢿⣿⣿⣿⣷⣄⠹⣝⢿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⢀⣾⣿⣿⣿⢸⣿⡄⠀⠸⡄⠀⠈⠙⠻⢷⣶⡄⠀⠈⠻⠆⠀⢀⣶⡿⠛⠉⠀⠀⠀⢸⠃⢸⠏⢻⣼⠀⠀⠙⢿⣿⣿⣿⣦⡘⣆⠙⢷⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢀⣾⣿⣿⣿⢻⠀⢹⣿⡄⠀⢷⢠⣤⠴⠶⠛⠛⠁⠀⠀⠀⠀⠀⠀⠙⠻⢿⣦⣤⣀⠀⡞⠀⡞⢀⣼⠃⠀⠀⠀⠀⠈⠻⣿⣿⣷⣌⢇⠀⠈⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢀⣾⣿⣿⣿⣏⡇⠀⢸⣿⣿⢷⢬⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣳⢃⣼⠁⢸⡿⣤⠤⠤⢤⣀⡀⠀⠈⠻⣿⣿⣮⢧⡀⠀⣠ ⠀⠀⠀⡤⠊⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⠁⡇⠀⠈⢻⣿⠸⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⢠⣿⠀⢉⣶⠂⠀⠀⠉⠲⢤⡀⠈⠻⣿⣿⣇⠀⠉ ⢀⡴⣪⢠⠂⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠀⠀⡇⢀⠀⠘⣿⠀⣿⣦⣀⠀⠀⠀⠀⠀⣶⠖⠲⠖⠂⠀⠈⠁⠀⠀⣠⣾⣟⡿⣱⣼⡏⣛⢦⡏⠀⠀⠀⠀⠀⠀⠉⠲⣄⡈⠻⣿⡄⠀ ⣨⡾⢡⠏⠀⠀⠀⢀⣾⣿⣿⣿⣿⠏⠀⠀⠀⢹⢸⡄⠀⣿⠚⣿⣿⣿⣷⣦⣄⣠⣾⠃⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣽⢣⣿⣿⠀⠈⠛⢿⡀⠀⠆⠀⠀⠀⠀⠀⠀⠹⡆⠘⢿⠀ ⡞⢡⡞⠀⠀⠀⢠⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢸⡿⣿⣦⣿⠀⠹⣿⣿⡿⠿⢋⣹⠟⡻⣷⡒⣶⠿⠟⣹⣿⣿⣿⣿⠇⢫⣿⣿⣿⠀⠀⠀⠀⢳⠀⠸⡄⠀⠀⠀⠀⠀⠀⡇⠀⠈⡇ ⠀⡞⢠⠀⠀⠀⣾⣿⣿⣿⣿⠅⠀⢤⣤⣤⣤⣾⠻⣿⣿⣿⣧⠀⠸⣿⢇⣴⣿⣧⠀⣧⣀⣙⣁⣀⣴⣿⣿⣿⣿⣿⣵⢏⣽⣿⠏⠀⠀⠀⠀⢸⠀⠀⠅⠶⢶⡶⠀⠀⢰⠇⠀⠀⢹ ⣸⢱⠏⣠⣶⣴⣿⣿⣿⠏⢸⠀⠀⢸⣿⠀⠀⢾⡄⠙⠪⠻⢿⣷⣴⢡⣾⣿⣿⣿⡇⣿⣯⣉⣿⣿⣿⣿⡿⠟⠩⣚⣵⣿⡟⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀ ⠏⣿⣾⣿⣿⣿⣿⡿⠃⠀⢸⠀⠀⢸⡇⠀⠀⣾⡶⠶⠶⠶⣚⣫⠅⣿⣿⣿⣿⣿⣷⡌⠋⢱⡉⢻⡿⠿⠿⠿⠛⠋⠁⠀⠊⠝⣒⣶⠶⠶⣖⣻⠂⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⡟⠁⠀⠀⣸⠀⠀⢸⡇⠀⠀⣾⠈⠉⠀⠀⠀⠀⡤⠿⣿⣿⣿⣿⣿⣿⡀⠈⠿⣄⡙⢦⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀ ⣾⣿⣿⡏⣿⡏⠀⠀⠀⠀⡀⠀⠀⢸⡇⠀⣸⢼⠀⠀⠀⣀⠴⣻⢷⠲⢤⣙⠻⣿⣿⣿⣧⢀⡤⠴⠛⠃⠈⠙⠓⠶⢾⣙⠦⣄⠀⠀⠀⠀⢰⢳⡀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀ ⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⣰⡿⢾⣄⡴⢚⣥⣶⣷⡘⣧⣤⡌⠳⣌⢻⣿⠉⢻⠀⠀⠀⣰⣾⣿⣶⣤⣾⣿⡶⢮⣓⠦⣤⣤⣿⠽⢑⡆⠀⠀⠀⡿⠀⠀⢸⠀⠀⠀⠀ ⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⡇⠀⠀⢀⡿⢵⣶⣯⣽⣾⣿⣿⣿⣿⣷⣸⡇⠙⢦⠘⣆⢹⡗⡿⣤⣤⣴⡿⣟⣯⠭⠁⢽⣿⠀⠀⢈⣩⣶⣶⣶⣾⡁⠀⠀⠀⠀⣇⠀⠀⢸⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⣼⣿⣯⡻⣿⣿⠀⠈⠙⣿⠟⠶⠟⠁⣿⢘⠞⣹⣿⣿⠷⠋⠁⠀⠀⠀⢀⣷⣶⣾⣿⣿⣿⢟⣿⣿⣷⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀ ⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⡇⠀⠀⢸⠇⢰⣿⣿⣿⡄⠓⠿⣄⣀⡞⠁⠀⠀⠀⢸⣏⣜⠀⣿⠟⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⣿⡿⢹⣿⣿⣿⣿⣧⠀⠀⠀⢸⡆⠀⢸⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⡄⠀⠀⠀⠀⡇⠀⠀⢸⣤⣿⣿⣿⣿⣇⠀⣀⡽⠋⠀⠀⠀⠀⠀⣞⣧⣊⣠⠛⣦⣄⠀⠀⠀⠀⠀⣠⣿⣯⠞⠉⠀⢀⣾⣿⣿⣿⣿⣿⣧⡀⠀⢸⡇⠀⢸⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⢠⣯⠖⠉⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡆⢸⣇⠀⠻⡄⠈⠳⣄⠀⢰⣿⠎⠁⠀⠀⠀ ⠂⠀⠀⠀⠀⠠⠋⠀⠀⢀⡴⠁⠀⠀⠀⢀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡻⡄⢟⢦⡀⠘⢷⣂⢬⣳⣾⠋⠀⠀⠀⠀⠀ ⡠⠗⠄⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢠⢦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣝⣿⣶⣤⡈⠑⠿⣍⠀⠀⠀⠀⠀⢰ ⠐⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⣮⢯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠢⣭⣉⠉⠁⠐⠛⣳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⣼⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⡰⢀⡜⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⢯⠙⣟⡏⠉⠄⢸⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⣯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⣸⢇⠞⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⡅⢹⣧⠀⠠⠈⢧⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⣰⣷⠏⠀⠀⠀⠀⡿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻⠀⠀⠀⢿⠀⢻⡆⠀⡄⠘⣆⠀⠀ ⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⢸⠁⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⣾⡀⠀⠀⠘⡇⠸⡿⡀⠸⡄⠘⣆⠀ ⠀⠀⠀⡼⠁⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢠⡿⡇⠀⠀⠀⢧⠀⢻⣷⡀⠘⡄⠈⢧ ⢀⠀⢰⠇⠀⠀⠀⠀⣠⠋⠀⠀⡰⠃⠀⠀⠀⠀⠀⢀⣼⣿⠋⠀⠀⠀⠀⠀⢀⡤⠋⠀⠀⡀⠀⠀⠀⢀⣼⠁⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⢸⠃⡇⢳⡄⠀⠘⠀⢸⠎⣿⢦⣻⣄⠀ ⡆⢀⣿⠀⠀⠀⢀⡜⠁⠀⣠⠎⠁⠀⠀⠀⠀⠀⣠⡾⣵⠉⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡼⠁⠀⠀⠀⣾⡇⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⢀⣿⠀⡇⢌⢏⠲⢤⣀⣈⣧⠿⠀⠘⣿⣻ ⠀⢼⡇⠀⠀⣴⠯⠄⠒⠚⠛⢲⣶⠦⢤⣤⣠⡼⠯⡼⠁⠀⠀⠀⣤⣾⡉⠀⠀⢀⣴⠟⠀⠀⠀⠀⡼⡝⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⣸⣹⣧⣇⠘⢿⣧⡀⠈⠉⠀⠀⠀⠀⣿⡏ ⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⡧⠀⠀⠀⠀⠸⠥⠤⠤⣀⣀⣼⠀⠈⣹⡿⠻⠥⣄⣀⣀⣀⣼⡟⠀⠀⢀⡴⣣⣁⠀⠀⠀⠀⠀⢰⢿⢿⣿⣿⠀⠈⠻⣟⣃⣀⡀⠀⣀⣴⣻⣇ ⢸⣼⠀⠀⠀⠀⠀⢀⣀⠴⠖⠋⠁⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠓⠺⠛⠀⠀⠀⠀⠀⠉⠉⠉⠉⢉⡽⣿⣫⣿⣿⡿⠶⠶⠦⣄⣿⠏⣼⠃⣿⠀⠀⠀⣸⡏⠻⢷⡞⢋⡉⢻⡇ ⡏⣿⠀⠀⢀⣤⣾⠋⠀⠀⠀⠠⠤⠒⠋⠉⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣞⣽⣾⣿⠟⣿⠉⡷⠀⠀⢀⣀⣩⣽⠟⠀⡏⠀⠀⠀⡟⠀⠀⢈⣿⡟⢿⡄⠀ ⣡⣿⢀⣴⣿⠁⡿⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣋⣁⣨⣷⣾⠶⠿⠛⠛⠋⠉⠉⠁⠀⠀⡇⠀⠀⡼⠀⢠⠀⢸⣿⡇⠈⢷⢳ ⣻⢸⡿⢹⠏⡀⣷⠀⣐⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣬⣍⡙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠍⠁⠀⠠⠀⠀⠒⠂⠀⠀⠀⠀⢸⠁⠀⡼⠁⠀⡼⠀⢸⡇⠀⠀⠈⢸ ⡇⣸⠃⡏⢀⠃⡿⣿⠛⢿⡏⠉⠉⠀⠀⠀⠀⠀⢸⡏⢹⣏⢹⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⡼⠁⠀⢠⡇⠀⣿⣧⠀⠀⠀⣼ ⢡⣿⢸⠁⢹⢠⣷⣾⡄⠈⣿⣆⠀⠀⢀⣀⣠⣤⣶⡿⠶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⡞⠁⠀⠀⡼⠀⢰⢿⡿⠀⠀⠠⠃ ⡿⡟⡾⠀⡞⣸⣯⠉⢧⠀⠈⢙⣷⣾⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⣠⠃⢰⣿⠘⠷⠂⣠⠤⠀ ⢿⠃⠇⢠⡇⡟⡾⣷⡜⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⢠⠃⢰⣳⠃⠀⣰⠞⠋⠀⠀ ⡿⠀⠀⢸⢣⣷⢧⠛⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣰⠏⢀⢷⣇⣠⠞⠁⠀⠀⠀⠀ ⠳⠀⠀⡏⢸⠁⠸⡆⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠃⠀⢠⡼⠁⠀⠀⠀⢀⣴⠃⣠⣾⣿⣿⣃⡀⠀⠀⠀⠀⠀ ⡀⠀⢠⢃⡇⠀⠀⢱⡀⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⣀⠖⠋⠀⠀⠀⢀⣤⣾⣿⢿⡿⣻⣫⣯⡅⠙⣧⠀⠀⠀⠀ ⠃⠀⠀⢸⠃⠀⠀⠀⠱⣄⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢋⣠⣤⢤⡶⠞⠉⠀⠀⠀⣠⣴⣿⡿⠛⣱⣶⣷⣿⠈⣿⡇⣷⣸⠆⠀⠀⠀ ⠀⠀⢀⡇⠀⠀⠀⠀⠀⠈⢷⡜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠦⠤⠤⠤⣄⣀⣀⣶⣿⣗⣿⣽⡾⠟⠋⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣶⣛⣵⣿⣿⣤⡀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢳⡜⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢶⣾⣿⣿⣛⣙⣛⡫⣁⠄⠀⣀⣴⣾⣿⣿⡿⠋⠻⡻⣿⣿⣿⣿⣷⠈⣿⣿⣿⣆⠈⠻⣿⣿⣷⣦ ⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣌⣧⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣭⣶⣿⣿⣿⣿⢃⣤⣾⣿⣿⣿⣿⡿⠁⠀⠀⢳⠈⠛⣿⣿⣿⡇⠈⡿⣿⡏⠙⢦⣀⠙⢿⣿ ⢠⠋⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣤⡀⠀⣀⡤⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⢷⠀⠈⢻⣿⣇⠀⠸⡜⣇⠀⠈⠳⢭⣙⣉ ⠎⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠹⣿⠀⠀⢳⡸⣄⠀⠀⠀⠀⠈ ⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢸⠀⠀⠘⡇⠹⡄⠀⠀⠀⠐ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣋⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠘⡆⠀⠀⢸⠀⢱⡠⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣠⡾⠉⠉⠛⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⣷⠀⠀⠈⣆⡼⡃⠀⠀⠀ ⣿⣿⡿⢟⣻⣿⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⢀⣿⣵⣇⠀⠀⠀ ⣽⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢹⠀⢰⢿⣶⡄⠙⡇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠓⠫⠿⣟⡿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⢷⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⢸⡄⠿⣇⣤⣦⣀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠈⠁⠈⠙⠻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢷⡄⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⠀⠀⠙⠶⡾⢿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⠊⠀⠀⠀⠀⠂⠨⠉⠓⡶⡂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠲⢏⠂⠀⠀⠀⠀⠀⢸⡄⣀⡔⠚⣷⠀⠀⠀ ⠀⠀⠀⠀⠤⠀⠲⡀⠀⠀⠀⠀⢀⠋⢘⠀⠀⠀⠀⠀⠀⡄⠌⠢⣄⡵⣿⣇⠀⠀ ⠰⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣸⠀⠸⠀⠀⡄⣄⠘⢸⠹⣷⡶⣼⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠇⣇⢾⠷⠛⠘⠛⠀⠙⠃⠿⣇⣹⡎⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠛⢾⣾⣼⣂⠀⠀⣠⣤⣤⡀⠀⣰⣿⠿⠛⡀⠀ ⠀⠀⠀⠻⡾⠿⠃⠀⠁⠄⠀⠀⠐⠈⠟⡻⡿⣷⣤⣈⢀⠀⢰⣾⠟⠉⠀⠠⠡⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠸⠁⣾⠚⠇⠙⠏⠁⠇⠰⡆⠛⠁⢀⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠸⡆⠈⡆⢥⣀⠤⣴⣖⠠⡄⣰⠇⠰⠳⡇⠀ ⠀⠀⠀⢀⣀⠀⢀⡠⠀⠀⠀⠀⢠⣆⡈⢄⡟⠢⠙⢛⠷⠞⡞⠛⡁⢴⣥⠁⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡁⡟⠤⢄⠀⠙⠉⠈⠋⠁⡀⡠⢧⡁⢩⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀⠀⠀⠀⠉⢐⡂⠈⠉⠀⠀⢸⣿⣿⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠉⠛⠦⢤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠤⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠖⠒⠛⠋⠉⠉⠉⠉⠛⠒⠲⠦⠬⣍⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠉⠳⢤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠦⢤⣄⣀⣀⣈⣷⠀⠀⠀⠀⢻⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀ ⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠤⠤⠤⠤⠤⣤⣀⣀⠀⠀⠀⠀⢠⡾⠁⠀⠀ ⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣤⠤⠴⢖⣲⡶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢴⣋⠀⠀⠀⠀ ⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣀⡴⠟⠉⠀⣀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀ ⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡼⠋⠀⢀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢧⠤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠈⢙⡦⠀⠀⠀⠀⠀⢹⡆ ⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃ ⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀ ⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⢀⣠⡴⠖⢛⣭⠟⠋⠉⠉⠉⠙⠻⣦⣤⣤⠤⠖⠋⠁⠀⠀ ⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠃⠀⠀⠀⠀⠀⣴⠟⠁⣠⡾⠋⠀⠀⠀⠀⠀⡀⠀⠀⠈⠛⠲⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠒⠒⠶⠶⠒⠚⠛⠛⠉⠀⣿⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⣠⣤⡏⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠘⣧⡀⠸⣿⣷⡀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⣤⣀⣀⣠⡤⠶⠚⠉⠀⠀⠀⠀⠈⠙⠷⣿⣏⡀⠀⠀⠀⠸⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡻⠶⠀⠀⠀⣸⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠖⠚⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡟⠳⡻⠝⡋⠏⠟⠟⠛⠟⠓⠚⢻⡻⡛⠂⠀⢙⡻⠺⠘⠛⠟⠟⠾⠾⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠉⡉⡐⠤⠾⢟⣉⠪⠤⡱⠍⣉⡒⣳⣦⡤⠖⠒⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡌⠚⠒⠀⠀⠀⠈⠓⢎⢁⡴⠊⠉⠀⠀⠲⠇⢰⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣴⢒⠒⢄⠀⠈⠋⢀⣔⣂⠐⢀⠀⠰⡋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠁⠀⠘⣿⡟⠀⢸⠀⠀⠀⢸⣿⡟⠀⢠⠀⠀⢱⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠀⠀⢀⣨⣴⣂⠁⢲⡈⢁⠖⠉⣀⣬⣄⠀⠀⢸⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⠀⠀⠈⠙⠛⠉⠀⠀⠱⠋⠀⠀⠉⠉⠉⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⢀⣀⠤⠤⠤⣀⡀⠀⠀⠀⣠⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠖⠁⡸⠃⠒⠒⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⢏⠢⡀⠀⠀⠀ ⠀⠀⠀⠀⡴⠁⠀⢰⠁⢠⠀⠀⢀⡄⠀⠀⠀⣠⡀⠀⣠⢀⡀⠘⡆⠈⢆⠀⠀ ⠀⠀⢀⡜⠀⠀⠀⡏⠀⠀⠈⠉⠁⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⢳⣀⣈⣆⠀ ⠀⠀⣾⢀⠴⣄⣼⠁⠀⠘⣀⠀⢀⠄⡀⢀⡀⠦⢀⠠⠒⠒⠊⠀⢸⢣⢁⢸⡆ ⠀⣼⢆⢆⢃⠱⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠈⡘⡈⣷ ⢠⠿⡈⡸⡌⡆⣄⣇⠀⠀⠱⢄⣀⠴⢄⣀⡀⠦⠤⠤⠊⠀⠀⢠⠧⣇⡧⠟⠋ ⠸⣇⡷⣇⡠⠿⠟⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⡆⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⣧⣤⣤⣖⠚⠁⡵⣲⢦⣾⢻⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣑⣾⣳⣦⣽⠀⢸⡿⠻⣿⠟⠿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⣿⠋⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⢻⡾⠛⣶⠠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢻⠀⠈⠁⣶⠿⣿⠛⠉⠙⠳⣦⣄⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣜⣻⠾⣿⣷⣿⣽⣦⡟⠀⠀⠀⠀⠀⠙⠻⣦⣾⠋⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠉⠙⢷⣿⣮⣿⡿⣿⡇⠀⠀⠀⠀⠀⢰⡾⣋⣿⢿⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠨⣿⠙⠇⠉⠁⠀⢰⣧⡄⠀⠀⠛⠋⠁⠁⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⠀⢀⣄⡀⠀⠀⢻⣦⣄⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠿⢿⡇⠀⠀⠀⢿⡿⠂⠀⠛⠉⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣋⣴⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢿⣏⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢺⡋⣻⡋⣹⣏⢹⣏⣹⣏⣙⣏⣹⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⡟⢁⣴⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⢀⣤⣦⣄ ⠀⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣇⠀⠀⠀⠀⠀⡇⠀⠀⠀⢴⠾⠿⣶⠏⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⣰⣿⣿⣿⣿ ⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣻⠶⢟⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⣰⡏⠁⠉⣿⠿ ⢸⡟⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿⣤⣤⣤⣶⣶⣿⣶⣦⣤⡾⠋⣰⣿⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣾⣿⣿⣷⣼⠋⠀ ⢸⡇⠀⠀⠀⣤⠶⠛⠛⠋⢉⣉⣈⣀⣀⢀⣠⣴⠿⠿⠿⢶⣶⠋⣠⣾⣃⣀⣀⣉⡉⠛⠛⠷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠈⣿⡿⠁⠀⠀ ⢸⡇⠀⠀⠀⣿⢦⣤⣀⣴⣛⠉⠀⠈⠉⠋⠁⠀⠀⠰⠶⠿⠛⠛⠿⣦⠉⢉⣉⣉⣻⣧⣤⠴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⡾⠋⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⣻⣄⣀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⢀⣀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⠀⠀⠀⠀⠀⠀ ⣸⠃⠀⠀⠀⠸⡟⠻⠿⢿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⡿⠿⠿⠟⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣴⣴⡿⠷⣦⡈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⢁⣀⢰⣌⣿⡟⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⣴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠛⣿⡁⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⡟⠿⠋⢹⣧⣤⣙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⡿⠎⠙⣷⡈⠛⠳⠶⣤⣤⣀⣀⣀⣀⣀⣠⣤⡤⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣟⣀⣴⠟⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⠛⠛⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣄⠀⠙⠿⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠈⠉⠉⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠛⠛⠿⣿⣿⣿⣿⣿⠿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠀⠀⠀

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⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠻⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣰⣶⣶⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⠀⠀⠀⣀⣀⣀⣸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠉⠉⠀⠀⠀⠀⠀⠈⠁⠒⠠⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠈⢀⣀⣀⣀⣀⡀⡀⠄⠒⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠀⢀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀ ⠀⠀⢀⣾⠿⠮⢉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀ ⠀⢀⣾⠇⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠰⡀ ⢀⣾⡋⡜⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠸⡀⠀⠀⠀⠀⠀⠀⢣ ⠈⣿⠆⣧⣄⠀⢀⡀⠁⠀⠀⠀⣀⣀⣀⣀⣤⡤⠞⠃⠀⠈⠀⠀⠀⠀⠀⠀⢸ ⠀⣿⣦⠜⣿⢄⣀⣾⢯⠉⣹⣿⣿⡟⠉⣭⠑⡇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⢹⢻⣄⠉⠛⢿⣿⠈⡐⢻⣋⠻⢿⡄⣉⣼⡥⠊⠁⢰⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠘⢿⣿⡷⢤⡼⢯⡇⢀⡖⡸⠛⠲⢌⣉⣁⠤⡒⠆⠸⠀⠀⠀⠀⠀⠀⢠⠁ ⠀⠀⠘⣿⢳⡱⣄⠀⣇⡜⢁⠀⠀⠀⠀⢈⡥⠊⠀⣰⡤⠀⠀⠀⠀⠀⢠⠎⠀ ⠀⠀⠀⠈⢿⣿⣌⢙⡛⠒⠺⠶⣀⠒⠛⠋⠀⠀⣼⠟⠃⠀⠀⠀⠀⣠⠃⠀⠀ ⠀⠀⠀⠀⠀⠙⣾⣦⡈⡂⠀⠫⡁⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠷⢄⣀⠃⠀⠀⠀⠀⠀⠀⢀⡠⠄⠊⠀⢱⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⡖⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⣀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠖⠋⣉⡠⠤⠬⠿⠶⣄⡀⣀⠴⠋⢀⣤⠖⠒⠢⣍⠳⢏⣅⠀⠈⠑⢦⡀⠀⣀⣠⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⢁⠔⠋⠀⠀⣀⣠⣶⣶⣶⣿⠯⢄⣴⠟⠁⠀⠀⠀⣀⠙⠪⣻⡀⠀⣀⠤⠿⠯⣕⠒⠒⠲⢌⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣮⠖⠁⠀⢀⠴⢊⠕⣹⠛⢡⠞⠉⣷⡿⠃⠀⠀⢀⡴⠋⠉⠒⠢⢌⡷⢊⣀⠤⢤⣀⡈⢷⢄⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡿⠃⠀⠀⡰⠋⣰⠋⣰⠁⣰⠋⢀⡞⡹⠁⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠻⣧⠘⡌⢧⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡼⠁⠀⠀⡴⠁⣰⠃⢀⡇⢰⠇⠀⡜⢠⠇⠀⠀⡼⢹⠄⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢡⠘⡄⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀ ⣼⠁⠀⠀⣸⠁⢠⡏⠀⢸⠁⢸⠀⢰⠁⢸⠀⠀⢰⣧⣀⣴⣦⣬⣳⡀⠀⠀⠀⠀⠀⢀⣠⣖⣻⣷⢸⠀⡇⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⢠⡇⠀⣾⠀⠀⢿⡆⠈⢆⣾⡄⠘⡄⠀⢸⠈⢻⡀⠠⠤⡙⢿⠒⠀⠀⢀⣴⢛⡉⠛⣿⠉⢸⠀⡇⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⢸⠀⠀⣿⠀⣠⣼⣷⠀⠸⠀⢷⠀⢣⠀⠘⡄⢈⠉⠓⠒⠓⠋⠁⠀⠀⠘⠧⠤⠤⠼⡇⠀⢸⣿⠁⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀ ⣿⡀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣧⠀⢧⠀⢧⠘⡆⠀⡇⡎⠀⠀⠀⠀⠀⠀⣠⡀⠳⡄⠀⠀⠀⣧⢀⣿⠏⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀ ⣿⣧⠀⢸⠀⠀⢸⣿⣿⣿⣿⣿⣷⣄⡙⠺⡆⢱⠀⡇⣇⠀⠀⠀⠀⠀⠀⠙⠛⠚⠁⠀⠀⢰⠏⣼⠏⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠙⠳⣼⣇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣓⣧⢸⠀⡇⢸⠀⠀⠘⠻⣶⣶⣶⣶⣶⡶⠃⣠⡏⣼⠏⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⢬⡦⣸⣿⣿⣿⣿⣿⣿⣷⣈⣿⠀⢠⣷⣬⣧⠀⠀⠀⠀⠉⠙⠛⠉⢀⡜⡁⣼⡏⠀⣠⠏⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⠀⠙⠣⢄⡀⠀⠀⠀⢀⡴⠛⡀⣼⢻⠀⢠⡇⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⡏⠈⠹⡼⠿⣷⣄⠀⠀⠤⣈⡙⢲⣶⣯⣄⡀⢳⠛⣼⡄⠀⢧⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠃⣰⣿⣿⣿⣶⣤⣤⡤⢾⣿⣝⣿⣿⣷⣦⣬⣧⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣷⣶⣶⣯⠙⠿⣿⣿⣿⣿⣿⡄⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠖⠋⣩⠟⠛⠿⣿⣿⣿⠉⢉⡇⠀⠀⠉⠙⠛⠻⠷⠔⠋⠀⠹⣿⠿⢿⡿⢿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⢊⡤⠒⠉⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣄⣽⡀⠈⠉⢻⡿⢿⣿⣿⣿⣿⣶⣤⡀⠀⠰⠠ ⠀⢀⠴⠋⠔⠋⠀⠀⠀⠀⠀⠀⠀⢠⡿⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⠀⠀⠀⢷⡀⢈⣙⣻⣟⠉⣉⠁⠀⠀⠀ ⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣸⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⢸⡟⣿⠉⠉⣿⣿⣿⣶⣦⣀⡴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢇⠀⠀⣹⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⡄⢸⡇⡟⠀⠀⠙⣮⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⡎⠁⠀⠀⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡇⠀⠀⠀⠙⣧⣿⣿⣿⣿ ⠀⠀⠀⠀⣀⡤⠞⠛⠀⢹⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢇⣤⣀⣀⣠⠃⠙⠻⠿⡏ ⣀⣠⡔⡋⠁⠀⢀⡀⠐⠃⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⡇⠹⠁⠀⢨⠏⠀⠀⠀⠀⠁

⠀⠀⢐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠈⢑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢦⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⣿⣾⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠸⣦⠀⠀⠀⠀⠁⢀⢰⡄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢻⣿⠀⠀⣀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠻⣟⠦⣤⣿⡍⠓⢼⡻⣦⣄⠀⢀⢷⣄⠀⠈⠙⠢⣄⠀⠀⣄⣿⡇⠰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿ ⡀⢳⠹⣄⠀⠀⢙⠂⠀⠉⠈⠛⠓⢌⡛⠏⠓⢄⠀⠀⠈⠳⣤⣿⣻⣿⡀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣿⣿⡿⠋⠿⠋⠉⠀⠾⢫⡿⠟⣿ ⣷⠈⢷⣺⣷⡀⢨⡳⢤⣠⣀⠀⠀⠀⠉⠀⠀⠀⠑⣄⣀⣄⣿⣿⣿⣿⣷⡄⣹⣿⣿⡆⠀⠀⠀⠀⠀⢀⡼⠟⢫⣿⣿⣿⣿⣿⣿⡿⢋⣿⠀⡘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⣿ ⣿⣄⠀⠉⠙⣿⣦⡁⠀⠀⠈⠙⠦⡄⠀⠳⣵⣄⡀⠀⠙⠛⠻⠿⣷⣿⣿⣿⣌⢻⣿⣷⠀⠐⠒⢈⡉⠀⡀⣴⣿⣿⣿⣿⡿⠻⢏⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿ ⠘⣿⣆⠀⠀⣿⣉⡉⠳⢶⣤⣀⣀⠘⣶⢄⠙⠀⠙⠈⠳⣄⠀⠀⠘⠯⢿⣿⣿⣆⢻⣿⠀⢀⡇⢸⡇⠀⣰⣿⣿⡿⠟⠉⠀⣠⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⣶⣿⣿⣿⣿ ⠀⢸⣧⠀⠀⣿⠀⡽⢦⣌⢻⣞⠛⠿⠿⣾⣿⣄⣀⠀⠀⠈⢣⡀⠰⢤⡀⠻⣿⣿⣶⣿⠀⢸⣇⢸⠀⣸⣿⡿⢁⣤⠀⣠⡼⠟⠁⠀⢀⣀⣠⣤⣤⠶⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢦⠈⣿⣄⠀⡟⠀⠀⠀⠉⢉⣻⣷⡀⠀⠀⠈⢦⡉⠻⠶⠦⣤⣁⠀⠀⠙⠂⠻⢿⣿⣿⡀⣼⣿⣸⠀⣿⣇⣠⡟⠷⠚⣉⣤⡤⠶⠶⣋⡽⠿⠤⠤⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡀⠳⡜⢿⣧⡇⠀⠀⠀⣴⡯⠵⠯⠛⠶⣤⣀⠀⠉⠓⠒⣚⡍⠉⣛⣶⣄⣀⣤⣼⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣤⣶⣿⣋⡟⠓⠒⠚⠉⠀⣀⣤⣶⢿⣿⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿ ⣷⡀⠈⠀⢿⣿⡄⠀⠾⣁⠀⠠⣤⡄⣤⣞⣉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡨⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⠏⢹⣆⠀⠀⠀⠻⣄⠈⠙⠚⠛⣂⣉⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠻⢿⡏⠙⠛⠋⢿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣿⣶⣿⢿⣾⠿⢿⣿⣿⡋⡵⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣸⠻⣷⣤⣀⡀⢸⣿⣦⣀⠀⠉⠛⠛⠿⠿⠿⠿⠛⠛⠋⠁⡴⠋⣽⡏⠀⠀⠀⠀⠇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⢿⣿⣿⣻⣿⣿⣿⣿⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⣿⠂⠈⠙⣮⣍⣙⣿⣝⢯⡳⣤⡀⠀⠀⢀⣠⡴⠂⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⡆⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣤⣭⣿⣯⠉⠉⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⠁⠀⠀⡞⣹⡿⠋⡇⠸⣆⠙⡆⠉⠛⢋⡽⠋⠁⠀⠀⠀⠀⢀⣼⣿⣿⣄⠀⠀⠀⢣⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠛⠛⠹⠿⣻⢿⣧⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡿⡇⠀⢹⠀⠹⡆⠉⣰⠞⠉⠀⠀⠀⠀⠀⣠⠾⠟⣛⣿⣿⣿⠷⣄⡀⠸⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⣶⣾⣥⣿⣷⣿⣽⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⡇⠀⢸⡆⠀⢹⡀⢸⠀⠀⠀⠀⠀⡰⠋⢁⣠⣾⣿⣿⣿⡇⠀⠀⠀⠀⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⡇⠀⢸⣷⠀⠀⣷⠈⣇⣀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⢸⠁⠀⠀⣿⣿⣿⣿⣿⣿⣯⣿⣟⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠣⣄⢸⣿⡌⢧⠉⠓⠿⣽⣍⠒⠒⠚⠿⠿⠉⠉⠉⠉⠉⠈⠻⣷⣄⣻⠀⠀⠀⣿⣿⣿⠿⣟⣋⠉⠉⠙⠛⠛⠉⠉⢉⣩⣽⡿⠟⢋⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣧⣈⣻⡉⠓⠺⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⢿⣤⣤⣶⣿⣟⣷⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠚⠛⣉⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⡟⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠍⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⣻⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢹⣼⣿⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠈⣿⠛⣲⠂⠀⢀⣠⡴⢂⣀⣤⠤⢂⣀⠀⢀⣠⣴⣾⠗⠋⣽⢋⣠⣴⣶⣿⣶⣆⣄⠀⢠⡀⠈⠻⣗⡶⠦⠿⠷⣤⣴⣲⣤⣤⣤⣤⣬⣽⡿⠿⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢹⡾⠷⢶⡾⠉⠉⠛⠋⠁⠀⠘⢉⣵⣞⣿⣿⣞⣡⣶⡿⠓⠛⠛⠛⠿⠛⠛⠛⠻⣷⣦⣻⣷⣄⡙⢷⣦⣀⠀⢠⣬⣉⠉⢁⣤⣄⡀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠈⣧⣰⣫⣶⣯⠴⢶⣾⣯⣵⠶⠻⠟⢹⡇⠾⠋⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣽⣿⣶⣽⣿⣿⣶⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠉⠁⠀⠀⢸⠱⣄⢿⡆⠀⠀⠘⡇⠀⠀⠙⢷⣶⣦⣤⣤⣤⣤⣤⣶⣶⣿⡏⣵⠴⠌⠁⣦⣤⣿⣿⣿⣿⣿⣿⣿⢟⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⢸⡄⢿⣿⣇⠀⠀⢸⡟⠀⠀⠀⠀⠉⠛⠷⠧⣴⣿⣿⣿⣿⣿⡇⣀⠀⠀⠈⣴⣛⣿⣿⣿⣿⣿⣿⢿⣯⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠙⢦⡀⢈⡇⠈⣇⠹⣧⡀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠇⠿⠀⠀⢠⣯⣿⣿⣿⣿⣿⣿⣿⢻⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢹⠣⣄⠀⠀⠀⠀⢻⣾⠀⠀⢹⣇⠘⢿⣶⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⣿⢠⡄⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠈⠀⠈⠣⡀⠀⠀⠈⣦⠙⠦⡀⢻⣀⠈⢷⡙⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡇⣹⠘⠃⣸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⢆⠀⠈⠛⢷⣄⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠟⠱⠶⠉⠀⠰⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⣧⡄⠀⠀⠙⠳⣦⣿⣄⠀⢀⣀⣀⣀⣠⣶⣿⡟⠁⠀⣀⠀⢠⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡾⠟⠛⠛⠻⠷⣶⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⣀⣀⣀⣀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⢟⣥⡾⠟⠛⠛⠙⠛⠻⢷⣦⡀⠀⠙⣷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⠋⠁⠀⣴⡿⠋⠀⠀⠀⠀⠀⢀⡀⠀⠙⢿⣆⠀⢹⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⠀⠀⣰⡟⠀⠀⣠⣶⡄⠀⠰⣿⣿⠄⠀⠀⢻⣆⠈⣿⡆⠀⠀ ⢀⢠⣤⢠⡄⠘⣿⣆⠀⣿⠃⠀⠀⠹⠿⠇⠀⠀⠈⠁⠀⠀⠀⠸⣿⠀⠹⣿⣄⣀ ⠻⣿⣿⡿⠃⠀⠈⢻⣇⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢸⣿⡀⠀⠈⣻⣿ ⠀⠀⢹⣷⠀⠀⣤⣼⡿⠘⣿⡄⠀⠀⠀⠀⠀⣀⣀⣼⠏⠀⢠⣿⠛⠻⠿⠟⠛⠁ ⠀⠀⠀⣿⡆⠀⢿⣯⣄⣤⣼⠿⣦⣀⠀⠀⠈⠛⠛⠁⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣷⠀⠀⠉⠉⠉⠁⠀⠈⠛⠻⠷⢶⣶⠾⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⢰⣶⣄⡀⢸⡟⠀⣠⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣷⣤⣀⠀⠀⠀⢸⡇⠙⠿⣾⣷⡾⠟⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⣿⢷⣦�