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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢟⡾⣾⠿⢿⣼⠅⠀⠀⠀⠀⡼⡘⣶⠏⣤⠀⠀⠘⢷⡈⢖⣩⠾⣙⣳⣬⣽⠲⡷⢽⡛⣷⡚⢶⠲⠶⠾⣭⣭⣛⡳⠮⣴⠱⣨⠟⠀⠀⢠⡥⢹⣧⠚⣆⠀⠀⠀⠀⠰⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⣷⣰⡆⣿⡾⠀⠀⠀⠀⣸⢱⢱⣿⡸⠸⣆⡀⠀⢸⠱⣎⣶⠿⢏⡉⢶⡈⢇⠹⣆⠱⣿⢸⢁⠏⡉⠷⠶⣆⣉⠹⣷⣆⡇⣹⠀⢀⣰⠏⣰⣹⠹⣇⠾⡆⠀⠀⠀⠀⣰⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣘⡆⢀⡾⣿⣡⢸⠏⠀⠀⠀⢰⡇⣎⠏⠀⠙⢧⡢⢕⠣⡜⣻⢹⡐⣋⠦⡙⢦⡙⡬⢓⡬⢓⡼⡑⢎⡹⢜⡱⢣⡒⣌⠳⡰⣊⢽⡟⡑⢎⡡⣺⠴⣇⣤⡹⣦⢹⡀⠀⠀⠀⠩⡜⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠻⢿⣿⣟⠋⠀⠀⠀⠀⣼⢇⡿⡀⣰⡆⣂⣉⠛⠒⡁⢻⢦⡙⢤⠓⣭⠲⢥⡛⢦⡱⢣⡜⡩⢎⡱⢎⡱⢣⢹⡰⢍⡱⡌⢶⠃⣽⣶⣿⣿⣿⣻⣟⣧⢱⡻⣤⠀⠀⠀⠀⠙⣚⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣻⠂⠀⠀⠀⡠⢞⠣⢎⠇⠁⠛⠃⠈⠛⠛⠟⠋⢸⢦⡹⢌⠓⠠⠁⢂⠐⠠⠠⢁⢚⠁⢂⠐⡀⠂⠉⠄⠓⠪⢵⣪⡹⡄⠛⠟⠈⠛⠟⠻⣿⣿⡟⡕⢪⠳⢄⠀⠀⠀⠘⠬⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣴⢻⠃⠀⠀⠀⠀⠀⢮⣑⡿⠤⠔⡒⢉⠩⢉⠉⡉⢉⠉⡉⡑⠳⠼⣠⣁⠂⠌⠠⢁⠂⢼⠈⡀⠂⠄⡁⢌⣤⠲⠥⠒⠋⡉⢉⠉⡉⢉⠉⡉⠒⠒⠥⢏⣯⡑⢦⠀⠀⠀⠀⠀⠘⡍⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⢧⠇⠀⠀⠀⢀⣠⠖⠋⡁⠐⡈⠐⡀⢂⠐⡀⢂⠐⡀⢂⠐⠠⢁⠐⡀⢉⠺⣤⣁⠂⠌⢸⠀⠄⣁⡶⠜⢋⠀⢂⠡⢈⠐⡀⠂⠡⠐⢂⠐⠠⠁⠌⡐⠠⢀⠉⠳⢆⣀⠀⠀⠀⠀⠸⡸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣠⣾⠀⠀⢀⡴⠋⠄⡈⠐⠠⠁⠄⠡⠐⡀⢂⠐⡀⠂⠐⠠⢈⠐⡀⢂⠐⡀⠂⠄⠛⣟⠰⠶⠞⠘⡿⠁⠌⠠⠈⠄⠂⠄⢂⠠⠁⢂⠁⠂⠌⠡⠘⠠⡐⢁⠂⠌⠐⡀⠉⠶⣄⠀⠀⢀⣷⣜⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢻⢿⣿⡖⠋⠠⠐⠠⢀⠡⢂⠉⠄⡑⢂⠰⢀⠂⠄⢡⠈⠄⠂⠠⠐⠀⠌⠠⠡⢈⢂⠘⣆⠀⠀⡞⡁⠌⠠⠁⠌⠠⠁⠂⠄⢂⠁⠂⠌⠄⠃⡄⢃⠰⠀⡌⢐⠈⡐⠠⢁⠂⢈⠓⣶⣿⡿⡟⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⣧⣠⠋⡀⠌⡀⢁⠂⠄⠂⡔⠈⡔⠠⠊⠐⠠⠊⠌⡀⠂⠄⡁⠂⠌⠐⢈⠠⢁⠢⠐⡈⠜⣆⣸⠡⠐⡈⠄⡁⠂⠁⠄⡁⠂⠄⠊⠄⠃⡌⠡⠐⠀⢂⠥⠐⡈⡐⠠⠁⠂⠌⡀⠐⡈⠻⣀⣵⣦⣑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⡀⠀⠀⠀⠀⠀⠀⠀⢸⢼⠂⡄⠂⠄⡐⠈⠠⢁⠐⠀⡁⠠⠁⢂⠈⠠⢀⠂⠄⡈⠐⡈⠄⠬⣄⣂⡌⠐⡐⣆⡛⢬⡓⡬⣙⢧⢺⡜⣣⢍⡚⢬⢗⡈⢐⣀⢂⡌⠴⢈⠠⠁⠄⡈⠐⠀⠄⡁⠠⠐⠠⢀⠂⠠⠐⠀⠄⢂⠐⠠⢁⢺⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⣏⠐⠠⠈⠄⠐⢈⠠⠀⠌⠐⢀⠁⡐⠠⠈⠄⠂⡀⠂⠄⠡⠐⠈⠠⠑⢎⡜⡣⢜⡴⡙⢦⡱⡱⣟⢢⡙⣧⢇⠮⡙⢆⠮⣐⠣⡜⡌⠐⠡⢀⠐⠈⡀⠄⠁⠌⡀⠄⠁⠄⡁⠠⢀⠁⠂⡁⠈⠄⡈⠔⡀⠢⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⢰⣉⠇⡈⢀⠁⠈⠰⢀⠰⠈⢀⠈⢀⠰⠀⡀⢁⠰⢀⠀⢁⠀⢁⠈⡀⠁⡈⠀⣎⢱⡎⣰⠹⣆⢱⣹⠇⣾⡈⣹⡎⢷⣉⡎⢶⠉⣶⠁⣀⠁⠆⡀⠈⠰⠀⡈⠰⢀⠀⠆⢁⠰⠀⠁⡀⠈⠰⠀⠁⠆⡈⠰⢀⠁⢱⢱⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⢼⡃⡐⠠⠈⠄⠡⠀⠄⠂⠄⡈⠠⢀⠂⠐⡀⠄⠂⢈⠠⠐⠀⠂⠄⠡⢀⠂⠌⣆⢳⣡⢓⡻⣦⡿⡑⢼⢢⠹⣏⣶⢿⡘⢎⡱⢂⠡⢀⠂⡐⠀⡁⠂⡐⢀⠐⡀⠈⠄⠠⠐⡀⠡⠐⠈⡀⠂⡁⠂⠄⡁⠂⠌⣽⢺⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠸⢸⠡⡀⠡⢈⠀⠂⢁⠐⠈⠠⢀⠁⠄⠠⠁⠠⠐⢈⠀⠄⠂⡁⠌⠠⢁⠂⠌⡐⢬⠲⢥⢎⡱⢻⣧⣍⢮⣇⣧⣿⢏⡖⣩⠎⡼⢀⠂⠄⢂⠀⡁⠄⢂⠀⠂⠄⠠⢁⠈⡐⠠⠐⢀⠂⢁⠠⠁⡐⢀⠂⠡⢈⡐⢼⣺⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡧⡗⢠⠁⠂⠄⠁⢂⠈⠄⡁⠄⢈⠀⢂⠁⠂⡁⠄⢈⠀⠂⠄⡐⢀⠂⡈⢐⠠⢊⠽⣘⠦⣙⠣⣿⠀⠀⠉⢉⣿⠸⡜⡤⢋⡴⠁⠌⡐⠀⠂⠄⡐⠀⠌⠐⢈⠠⠀⠂⠄⡐⢀⠂⢈⠠⠀⢂⠐⠠⢈⠁⢂⠰⡇⡍⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠘⡹⡂⠌⡐⠈⡐⠀⢂⠐⢀⠐⠠⠈⡀⠄⢁⠀⠂⠄⡈⠐⠠⠐⢀⠐⡀⠂⢄⠫⣜⡱⢎⡱⢣⢟⡄⠀⠀⠀⣾⠹⡜⢲⡉⠶⣉⠐⠠⢁⠈⠄⠠⢈⠠⢈⠀⡐⠈⠄⠂⠠⢀⠂⠄⠠⠁⠄⡈⢐⠠⠈⠄⡺⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠹⡔⠠⢁⠠⢈⠠⠐⠀⠌⢀⠂⠄⡈⠠⠈⠐⠠⢀⠁⠂⠌⢀⠂⠄⡉⢄⡳⢌⠶⣩⠞⣽⡺⠀⠀⠀⠀⡷⣏⠽⣡⠞⡱⢣⡌⠐⠠⠈⠄⠂⠄⡐⠀⠂⠄⡈⠄⢈⠐⡀⠄⡈⠐⡈⠐⡀⠂⠄⠡⡸⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢹⣦⠀⡐⠀⠄⡈⠐⢈⠀⠄⠂⡀⠡⢀⠁⠂⠄⡈⠐⡀⠂⠌⡐⠠⡞⣰⢋⡞⡱⣾⢣⠃⠀⠀⠀⠀⠘⡼⣏⠶⣉⠶⣙⡦⢁⠂⡁⠐⢈⠀⠄⠡⢈⠀⠄⠂⠄⠂⠠⠐⡀⠡⢀⠡⢀⠡⢈⣾⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣷⣤⡁⠠⢀⠁⠂⡈⠄⢂⠠⠁⠠⢈⠐⠠⢀⠡⢀⠁⠆⠄⡿⢱⡡⢞⣼⡽⣣⠃⠀⠀⠀⠀⠀⠀⠈⠝⣮⣱⠎⢦⠹⣆⠐⠠⠁⢂⠈⡀⠂⠄⡈⠠⢈⠠⢈⠐⠠⢀⠡⠀⠂⢄⣶⣿⡿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⣿⣿⣿⣿⣦⣄⣈⠐⠠⠐⡀⠄⢈⠐⡀⠌⠐⠠⢀⠂⠌⣐⣮⣱⣧⣾⣿⣿⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣮⣷⣘⣎⠠⢁⠂⡐⠀⠡⠐⢀⠡⠀⠂⠄⡈⠐⠠⣀⣬⣾⣿⣿⣿⢇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣶⣴⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠫⢻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣬⣤⣥⣦⣤⣥⣬⣴⣤⣷⣿⣿⣿⣿⣿⣿⡟⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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