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