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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠐⠂⢀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣴⣤⣁⣼⣸⡼⠋⡠⠋⠀⣺⠁⠀⠀⠀⢸⡟⠀⠀⠀⢸⡗⠊⠙⠓⣶⢲⣿⠟⠀⣿⣇⠤⠊⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣤⠶⠚⠛⠁⠀⠀⠠⠄⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣰⣴⣾⣉⡠⠚⡠⠀⠄⡇⠀⠀⠀⠀⢤⠀⠀⠀⠀⢸⠁⠀⠨⢐⣿⣼⠃⠠⢸⣿⠘⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣐⠢⢤⡀⠀⠀⣀⣠⡴⠿⠟⠛⣫⡟⠀⢀⡇⠊⠀⣯⠀⠀⠀⣰⠃⠀⠀⠀⣰⣯⠀⠀⣀⠘⣿⣧⡐⢠⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡿⢃⠐⡼⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡹⣍⠁⠀⠀⢁⣀⣲⣿⠀⢠⠞⡀⢀⣿⣿⡄⠀⣰⡇⠀⣠⣶⣿⣿⣗⢀⣾⣿⠀⢸⣧⠹⣯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⢋⠐⡄⣺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠦⡄⢀⡤⠟⠺⣿⣠⠏⢠⢃⣾⣿⣿⣧⢰⣿⣇⡼⠿⣿⣿⣿⣿⣼⢿⣿⡀⠀⢻⣷⡾⠿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⡀⠂⢅⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⠋⠀⠀⠀⢻⣏⣤⣾⣿⣿⣿⡿⢿⣿⠁⠉⠀⠀⠛⣿⣿⣿⣿⣿⠸⣷⢀⣦⣿⣉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠠⢁⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣊⡡⡙⠲⣄⡀⣼⣿⣿⣿⣿⣿⠋⠀⢸⡏⠀⠀⠀⠀⠀⣸⠛⠉⠁⢿⣯⣿⡾⢻⣍⡿⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠥⠴⠶⠛⠚⢓⡛⠻⣿⣿⣽⣓⡶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡛⣲⠟⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⠰⠒⠒⠒⠦⠴⡁⠀⠀⠀⢸⣿⣿⡇⡿⠬⣭⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠐⠒⠒⠋⠉⠠⠴⢀⢺⣿⣿⣿⣿⣿⣾⣿⣦⣀⠀⠀⣖⡀⠂⡐⠠⠤⠤⣼⣗⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠛⠷⠖⣶⣇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⣸⣿⢻⣳⣁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⠈⠑⢾⡉⠁⠀⠈⠉⠁⠒⠺⠂⠳⢌⡐⢄⣀⠀⠀⠀⠀⠀⠀⣞⣁⣈⣄⣀⣬⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⠏⣼⢃⡽⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⢩⡱⡄⠀⠀⠀⠀⢉⠉⠻⢧⣼⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠯⡔⠻⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠂⣉⠥⠉⠉⠒⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠘⠆⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⣶⣾⣿⣿⡯⠭⠭⠭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣠⣤⣶⣿⣿⣶⢼⡀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣑⣸⡿⣟⣭⣦⣧⣦⣍⠻⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠉⠉⢓⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠿⠒⠼⠆⠀⠀⠀⠀⠀⢀⡠⢴⠖⠀⠀⣀⢀⠀⡀⠀⠀⠀⠀⣀⠔⠡⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠟⠀⣴⣾⠛⠿⣿⡟⠉⠀⠀⠉⠉⠉⠛⠛⢿⡿⢿⠟⢡⣾⣿⣿⣿⣿⣿⣿⣿⣷⣢⣤⣀⣀⠀⢀⣀⠤⠒⠡⠠⠙⠋⠤⠄⠀⠠⠾⠥⢀⣠⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢏⠛⠲⢤⣀ ⠀⠀⠀⠀⠀⠀⠀⠰⢯⣌⡙⠛⠿⣿⠠⣿⣿⡟⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣿⣿⡿⠋⠀⠀⠈⠺⠷⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠯⣁⠀⠈⠉⠉⠉⠛⠻⢿⣻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⡆⣾⣿⣿⣿⣶⣽⣼⡙⠻⢿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣴⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠄⠛⠀⠀⠀⠀⠀⠀⠀⠉⠛⣷⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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