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