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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀ ⠀⠀⢀⡠⠒⢆⠤⠤⢄⠤⢒⠩⠤⠀⠀⠀⠀⠀⠒⠂⠀⠁⡂⠸⣉⣹⢓⠄⡙⢭⡐⢄⠀ ⢀⢔⣕⢡⠊⠀⢀⢞⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠝⡿⣿⣿⣷⡿⡃⠀⠑ ⠀⠈⡿⠦⠀⣔⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣿⣧⠀⣱⠀⠀ ⠀⠸⢀⣀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠐⢄⠀⠀⠀⠀⠈⢍⠁⠀⡇⠀ ⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠣⠐⠑⢄ ⠐⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⢃⠀⠂ ⠈⢢⠇⠀⠀⠀⠀⠀⠀⡜⠀⠀⡴⡆⠀⠀⠀⠀⠀⠣⠀⠀⠠⠀⠀⠸⡀⠀⠀⠀⢈⡅⠀ ⠀⢰⡀⠀⠀⠀⠀⠀⡐⠀⠀⡰⢅⣡⠀⢠⠀⠀⣠⡤⠓⢄⠀⠱⡀⠀⢃⠀⠀⠀⢸⠇⠀ ⠀⠸⠆⠀⠀⠀⠀⡐⠀⣀⠜⠀⠀⠈⡅⠨⠀⠀⢉⠁⠀⣀⣑⣠⡈⣂⠸⠀⠀⠀⢸⡆⠀ ⠀⠀⡶⠀⠀⠀⢀⣳⣼⠞⣿⣷⠶⢄⠠⠇⠀⠀⡘⡰⣿⡿⣭⡏⢻⣷⠳⠀⠀⠀⣈⠁⠀ ⠀⠀⠳⣂⠀⠀⢰⠙⢯⠈⣿⠁⡹⡆⠁⠀⡆⡰⠁⠀⣿⠤⢚⢇⠘⠁⠸⠀⠀⠠⡍⠀⠀ ⠀⠀⠀⠘⢆⠀⠀⣄⠀⠱⠜⠂⠓⠀⠀⠀⠗⠀⠀⠀⠈⠉⠁⠉⠀⠠⠰⠀⡰⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠑⠄⣘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠓⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠤⠒⠹⢦⡄⢀⠀⠀⠈⠐⠂⠒⠚⠁⠀⢀⡤⠴⡋⠀⠑⢤⡀⠀⠀⠀⠀ ⠀⠀⡇⣔⠊⠀⠀⠀⡠⠃⠀⠺⣷⣶⡆⠀⠀⠀⠀⠀⡞⠹⣿⠦⠈⢢⠀⠀⠉⢢⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⢀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣿⣿⡟⠻⠿⢿⣿⣦⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣿⣏⣿⣿⣿⣿⣇⡄⠐⠈⣹⣿⣌⣻⣿⣷⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢿⣯⣿⣿⣿⣿⣿⣤⠂⠂⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣇⣠⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢉⡶⠛⠲⣽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⢿⣿⣟⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣧⠀⡌⠀⠀⠀⠀⠀⠀⣠⠞⠁⠄⣿⠀⠀⢀⡿⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡶⠁⠀⠀⠀⠀⢀⣼⡁⠄⣡⣆⡈⠓⠒⢋⢀⣴⠿⠶⣤⣀⣠⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠐⠒⠒⠒⢲⠏⠀⡿⠈⠷⠾⣀⠡⢁⣦⠟⠳⡶⠻⢍⣹⠁⠀⠀⠀⠉⠒⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠢⡀⠀⠀⠀⢀⣾⠷⢚⢁⠂⣰⠟⠉⢹⣾⣁⣢⣴⣷⣤⣤⣮⣤⣤⣤⣄⣀⠄⠂⠙⠌⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡈⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠑⣄⠀⠈⠃⠀⠀⡼⣻⠀⠩⠀⠥⠸⠦⣴⡟⢉⣯⠽⢾⡄⠠⢀⣴⠏⠁⠀⠀⠀⠀⢀⠖⠢⡀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⢿⠁⠟⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⣼⢀⡇⣼⠗⠛⣦⠁⣶⢏⡰⣸⣇⣠⠼⢡⠘⣄⣾⣄⠀⠀⢀⣀⠔⠁⠀⠀⠙⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⣧⠀⣇⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⡇⢸⡠⣇⠀⢀⡟⣸⡟⣄⡿⠟⡀⣄⣸⣼⠿⠟⠛⠛⢛⣿⠟⠃⠀⠀⡠⠤⠀⠄⡀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⢹⠿⠋⠈⢧⠀⠀⠃⣠⠷⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢸⡇⢸⡅⢙⠲⢫⣼⡟⣼⡞⣥⠶⣿⠟⠛⢦⡀⢂⡑⣈⣾⡇⠀⠀⢀⠜⠀⠀⠀⠀⠀⣀⣸⣶⣶⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢀⠤⠊⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠳⠶⠚⣁⠛⠡⠈⣄⡷⠞⠶⡄⠡⠂⠉⢤⣿⡡⣼⡏⢰⠂⡀⠂⢷⣤⣤⣀⣀⣀⣠⣤⡠⠤⣴⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⡿⠛⠋⠛⠛⠈⠙⠛⠿⠿⢿⣛⡇⠰⠠⠡⠄⠌⡀⠃⣼⠁⠀⢀⡿⠀⠁⣬⡟⠁⠉⢻⢇⠢⢁⡴⠛⢻⣇⣀⣀⣠⣤⣤⡤⠶⢛⣩⠴⢟⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠹⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡇⠡⠑⢠⡼⠶⢦⡁⡌⠳⠖⠋⡁⢈⢐⣾⣀⣀⣠⣾⠈⡔⣼⡁⠀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣏⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢠⣇⠀⢀⣀⣴⣾⣿⣿⡟⠁⠀⠒⠠⡀⠀⠀⠀⠀⠀⢰⠤⠤⢴⡞⢉⠉⣸⣇⠑⡈⠌⠻⠖⢋⠐⡐⢂⡘⠄⠠⢀⣾⢡⡉⣌⢹⡏⠐⣠⡟⠑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⡼⢠⠖⢹⣇⡀⠙⣿⡟⠀⠀⠀⠀⠀⠈⣦⡀⠀⠀⠀⢸⠀⠀⣰⠃⣄⣦⣼⡷⢀⠘⡠⢁⠌⢂⢂⠐⠤⣀⡴⠶⣿⢃⡆⢱⡈⢾⣿⣉⣹⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢿⡇⠘⣿⣿⣿⣦⠈⠀⠀⠀⠒⠒⢢⠄⠈⢻⣦⡀⠀⠈⡗⠚⣁⠰⢿⡤⠟⣿⠀⢂⠐⣠⣈⡄⠢⢁⢂⠸⠦⣴⠇⡌⣰⣁⠌⡛⢃⣹⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⣽⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠻⡀⠙⣿⣍⠀⠀⠀⠀⠀⠴⠻⢾⣷⣦⡐⢿⡻⢦⣀⣿⠐⡐⠢⣀⠂⡐⣿⡁⢂⡿⠉⠀⢙⡧⢀⠈⠀⢠⣏⣲⠛⠉⠉⢻⠇⡀⠒⠀⣼⠻⣇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣀⣽⠉⠙⢿⠢⡄⠀⠀⠰⣃⢀⠤⢈⠑⠛⠶⡝⠒⢀⣸⣇⠩⢐⡀⢂⠐⡸⣧⠀⠛⠦⠤⠞⣁⠂⠀⢀⣾⠄⡻⣤⣤⠴⠛⢠⣬⣁⢲⡇⠀⠙⣿⣷⣶⣶⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⢠⣾⣿⣿⢿⠿⠁⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣷⢠⡌⠘⠳⠤⠴⠋⡀⠆⢐⣠⣶⠋⠀⠀⠀⠀⠙⠿⣿⣧⣀⡨⣿⡿⣦⡠⢿⣿⡶⠋⢓⠚⢉⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠋⠁⠀⠈⢻⣧⡈⣄⣁⠢⠄⢡⣡⠖⢋⡽⠃⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡉⠉⣿⣿⢀⡼⢋⣄⣡⣶⡞⠋⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⡀⠤⠤⠔⠂⣤⠞⠁⠀⠀⠀⠀⠀⢠⡟⠉⠛⠛⠁⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠂⠉⠁⠀⠀⠀⣀⠤⠔⢚⡽⠛⠛⣏⠉⣹⠆⢌⢸⣁⡤⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢻⣿⣇⠀⢹⣿⠿⣛⣭⣍⡄⠨⠙⣶⠚⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠂⠈⠉⠁⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⣄⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠁⠀⠀⠀⠀⠀⠀⣀⠴⠂⠉⢀⡤⠚⠁⠀⠀⠀⢈⣿⣇⣘⣶⠟⠉⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠁⠀⠀⣿⣿⣠⠞⡡⣺⠋⠀⠈⡷⢈⠡⡿⢁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡎⠙⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⣼⡇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠚⠙⠋⠁⠀⠀⠀⠀⠀⢻⣟⢋⡶⢡⠹⢦⠴⡚⣡⡶⢼⡇⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⠁⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⢷⣎⣌⢣⠝⣢⠣⠔⣻⣀⣼⡇⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⡇⠀⠀⢻⡟⠛⣿⢳⣿⣾⣶⡆⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠉⠀⠀⢀⠜⢹⣿⡄⠀⠀⠹⡖⠶⣆⠠⢐⠨⠿⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢀⡠⠒⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⢀⡴⠃⠀⣿⢿⣿⡄⠀⠀⠑⣄⣸⠐⣶⠞⢳⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠑⠒⠦⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢀⡤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣀⣠⣴⣾⣷⣶⣦⣤⠤⠴⣲⠖⠉⠀⠀⣸⣿⠿⣿⣿⣦⠀⠀⠈⢯⡀⠻⠖⢋⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠒⠒⠐⠒⠒⢂⣀⡿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠿⠟⠛⠋⠉⠁⠀⠀⢀⠔⠁⠀⠀⠀⢰⠁⣧⣰⣶⣷⡿⢧⡀⠀⠀⠳⡅⠌⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣤⣶⣿⣯⣱⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⣀⣠⠤⠖⠚⠉⠉⠉⠀⠁⠉⠉⠁⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⢰⠃⢰⠉⢻⠉⣱⠶⣆⠳⡄⠀⠀⣻⢴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣁⣽⣿⡏⣸⠉⠛⠻⣿⠿⣿⣿⡷⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠁⠀⣸⣧⢸⡞⣁⠴⠻⣦⣽⣦⡞⣧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠋⣴⣿⠂⣰⣿⡟⠀⠘⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⣿⣿⣿⣛⠒⠲⡏⠛⣿⣷⡙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⢡⣾⣿⣿⣰⣿⣿⠃⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⠞⢩⢿⠙⣍⠉⠓⠃⣰⡞⠋⣤⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣿⣿⠟⠁⣼⣿⣿⣦⣄⡀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠛⠶⠋⠘⣆⣸⠆⣠⣾⣣⣌⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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