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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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