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