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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠓⠙⠉⠉⠈⠀⠒⠒⠙⠐⠀⠀⠐⠀⠒⠀⠷⡸⣀⢀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⢚⣤⣤⣤⢠⠀⠂⠐⠀⠉⠛⠛⠄⠲⠃⠛⠋⠛⠖⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠑⠈⡀⢀⠤⡓⢌⠓⠀⠀⠀⠀⠀⠀⣧⣈⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡏⣠⠀⠀⠀⠀⠀⠁⡐⠋⡠⠀⠀⡀⣀⣁⣏⣰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠣⠈⠀⣄⠸⢆⠀⠀⠀⠀⠀⠀⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢠⠀⠀⠀⠀⠀⠁⡰⠎⢀⠁⠊⠒⠖⠤⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠘⠀⡄⠸⢁⠀⠀⠀⠀⠀⠀⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠋⣠⠜⢀⠀⡼⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠀⣆⡌⠘⠀⠀⠀⠀⠀⠀⣄⠘⠀⠀⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀⠀⠀⠞⢁⡔⠀⠀⠇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡌⠙⠀⢡⡆⠈⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀⠀⠁⡴⠋⡷⠻⠙⠀⡼⠀⠀⢆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⡆⢻⠃⠹⢧⠈⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⡼⠀⠀⠀⠁⠞⣡⠞⢤⡑⣿⣿⣿⢻⠀⡯⠛⢹⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡼⠀⠀⣮⣿⣽⠹⢆⠈⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢹⠀⠉⠖⣡⠞⣠⠀⠀⠀⣇⣿⣿⣰⣀⢀⠀⠀⠀⠀⠀⠀⢁⣉⣒⣖⠖⠴⠲⠓⠋⡨⠀⠀⠀⠀⠀⣀⠄⣀⠁⣀⠀⠁⠉⠈⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⢔⣀⢹⡍⢲⢀⣏⣿⡞⠲⣗⠻⠛⠛⠙⠟⢠⠀⠐⠂⠀⠀⡉⣯⠟⡿⢛⠛⠛⠙⠈⠀⡀⣿⣼⠀⠀⠀⠀⠀⠀⠀⠆⡠⢀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠲⠙⠚⠖⠶⠤⣤⣄⣶⠲⠖⣠⢀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠋⡾⣤⢀⠀⠀⡅⠻⠶⣮⣔⠤⠤⠀⡀⢀⠀⠤⠤⣤⣶⢦⠻⠟⡿⣬⣒⢐⠤⠤⠤⠤⡤⣂⣶⣯⠷⣻⢌⠓⠈⠀⠀⠀⠀⠀⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠶⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⢀⡀⠤⠠⠤⡀⢀⠀⢀⡁⠟⣿⣺⠖⠸⠀⠁⠞⣡⢔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡾⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠷⣙⢤⠒⠉⠉⠈⠀⡉⠫⠉⠈⠒⠒⠤⣤⠤⠓⠈⠀⠀⠀⠀⡇⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡤⠤⡤⣤⠤⡤⣤⢄⣀⣀⣄⣏⣿⣶⣠⢀⠀⠎⠀⠏⣻⠴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢷⠚⠒⡒⣶⣒⢓⠙⡉⢄⠢⠑⠀⠀⠀⠀⣀⢦⠙⠀⠀⡇⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀ ⠐⠀⠀⠀⠀⠀⠀⠀⠁⠛⠿⣹⠀⠀⠀⠁⠝⢋⡿⢶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠁⠊⠒⠀⠀⠀⠀⠀⠀⠀⠒⠑⠉⠀⠀⠀⠀⡀⣷⠘⠀⠀⠀⠀⠀⡀⣀⢤⠲⣙⠫⠈⠀⠀⠀⡀⢤⠑⡉⣿⣿⣿⣿⠻⠘⠀⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠟⡿⣿⣿⣿⣿⠻⠉⠟⣾⣠⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠀⠉⠖⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠢⠈⠀⠀⡃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⢷⠙⠁⠉⠋⡟⣿⣿⣿⣿⣿⣿⢿⠙⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣴⣀⠀⠀⡇⠀⠀⠀⠀⠀⠋⠐⠀⠀⠤⠤⠢⠒⠉⠀⢸⠀⠋⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠡⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀ ⠀⠀⠀⠄⠳⠁⣿⣿⣿⣿⣿⣴⢢⠙⠀⠀⠀⣧⠀⠀⠁⠔⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢹⡔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⡿⠉⠒⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⡤⣦⣿⣿⣿⣿⣿⣿⣿⣿⢦⠀⠀⠀ ⠀⠀⠀⠀⡄⡤⠀⡀⣀⣦⢸⠀⠀⡀⢄⠤⠂⡟⠈⠎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣾⣶⣶⣿⣾⣤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠻⠈⠀⠀⠀⠀⡀⢿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣿⣿⣿⣿⣾⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣳⠮⠑⠈⠀⠀⣇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⠟⣿⣿⣴⢃⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⠿⡙⢌⠠⠐⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡳⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠅⣛⡿⣿⣿⣾⣠⠀⡏⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⡿⣿⣿⣿⣿⣿⢿⠿⠛⣟⡻⠪⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠕⡏⢿⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠐⠙⠖⢟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⡉⠛⡿⣿⣿⣿⣾⣠⠀⠀⠏⣿⣿⣿⠂⠂⠙⠀⠀⠀⠀⠀⠀ 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