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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⣼⣸⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠛⣿⣿⣿⣿⣽⣿⣿⣷⠀⠀⠙⠇⠀⠀⠀⠀⠈⠳⣦⡇⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣶⣽⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⣰⢟⣿⡟⣧⡀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠙⢻⣿⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⢀⣴⣏⣼⣿⡇⠘⣷⡄⠀⠀⠀⠀⢸⣧⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣸⣿⡄⠀⠀⠀⠀⠀⣰⡏⣷⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⣰⠿⢿⣿⢿⣯⡉⠙⢻⡝⢷⣄⠀⠀⠀⢿⡀⠀⠀⠀⢈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠋⠀⠀⠀⠀⠀⣿⡗⠃⠀⠀⠀⠀⣴⢿⣿⣿⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡾⠁⢀⣿⠇⠀⠀⠙⡇⠈⣷⠀⠈⣧⠀⠈⠛⢦⣄⣈⣷⡂⢸⠃⣸⠀⠐⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⡆⢠⠀⠀⠀⠀⠀⢸⣿⠛⠀⠀⠀⣠⡾⠥⠤⠿⢿⣇⠀⠀⠀⢀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⣿⡀⠀⠀⢀⡇⠀⢸⠀⠀⠸⣆⠀⠀⠀⠈⢻⡟⠓⠈⠀⠋⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣼⠀⠈⠁⠘⠃⠀⠀⣾⡟⠀⢀⣤⡾⠋⠀⢀⣠⠶⣟⣹⣇⡀⠀⠸⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡾⠁⠀⠀⢀⣾⣇⠀⠀⠘⣿⢤⡼⠿⣟⣦⢹⡄⠀⠀⠀⠘⣿⡔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⡀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠷⠚⠉⣼⠃⣠⠞⢋⣤⠶⠛⣿⣿⣷⡀⠀⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⣼⡟⠁⠀⠀⣸⠇⠀⠀⠀⠙⣾⡇⢻⡄⠀⠀⠀⢹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⡶⢤⣤⣤⡤⠤⠤⠖⠋⠉⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⣴⠃⠀⢿⣴⢿⡁⠀⢰⠏⣼⣻⣧⠀⢹⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⣼⠿⣏⠀⠀⢐⡟⠁⠀⠀⠀⠀⢹⡇⠀⢻⡄⠀⣧⠀⢻⡝⢧⣄⠀⠀⠀⠀⠀⠀⢿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⢀⣠⠞⣿⠃⠀⠀⣴⠋⠀⠀⣸⢿⡈⢿⡀⠻⠾⢳⠟⣿⠀⠸⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠀⠀⠀⣼⡟⠀⠙⣆⠀⢸⠧⣤⡀⠀⠀⠀⢸⡁⠀⠀⢻⡄⠈⢷⣄⠻⣴⣬⠳⢦⣄⡀⠀⠀⠀⠙⠻⠦⠤⠤⠤⠤⠤⠴⠒⠚⠛⠉⠁⠀⠀⠀⢀⣠⠴⠛⠁⣼⠃⢀⡀⣼⣧⡤⠤⣴⠏⢸⡗⠚⣇⠀⠀⠀⢠⣿⠆⠀⣿⡳⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⣼⣿⠁⠀⢰⡟⠀⣼⠀⠈⣷⣀⣀⣀⣬⠿⠦⣤⣀⣹⣆⠀⠙⣷⣽⣯⡳⢦⡈⠙⠲⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠛⠉⠀⢀⣠⡼⠃⢠⣾⣿⠏⣠⣤⣤⣀⣴⠏⠀⠀⣿⠀⠀⣀⡾⢻⡀⠀⢸⡇⠀⠀⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⣰⢏⡏⠀⠀⠀⣷⠀⣿⣤⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⢧⡀⠸⡇⠈⠉⠀⠙⠶⣄⡀⠀⠈⠉⠙⢳⡶⠶⠶⠤⣶⠶⠚⠋⠉⠀⠀⠀⠀⢀⣠⣾⡿⢁⡴⠋⡼⣡⡾⠏⣀⣠⠼⠃⠀⠀⠀⡟⠀⢰⣏⠀⠈⢷⠀⠀⢷⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢰⠏⣸⠃⠀⠀⠀⣸⠟⠁⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠸⡄⠀⠀⠹⣆⢻⡀⠀⠀⠀⠀⠀⠉⠳⢤⠀⠀⠈⠙⠓⠒⠚⣿⠀⠀⠀⠀⠀⠀⠠⠞⣫⣼⣫⡶⣻⠁⣸⡿⠋⣴⠟⠉⠀⠀⠀⠀⠀⠀⡇⠀⣨⡟⠀⠀⠸⡇⠀⠘⣇⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢀⣟⠀⡿⠀⠀⠀⣾⣁⠀⠀⠀⠀⢷⡀⠀⠀⠀⠡⠀⠀⠀⠙⠀⠀⠀⠘⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⣀⢻⡏⢰⣿⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣇⣷⠟⠀⠀⠀⠀⣿⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣼⠃⠀⡇⠀⠀⢸⠇⠘⣧⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⡇⣼⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⢸⡆⠀⠀⣻⡄⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡇⡀⠀⣠⡏⠀⠀⡇⠀⠀⡿⠀⠀⠈⢷⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣧⣇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠀⠀⠀⠀⣼⡇⠀⠀⢻⢷⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⣿⠀⢺⠁⠀⠀⡇⠀⢰⡇⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣉⣉⣓⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣼⠛⣧⠀⠀⣸⠘⣇⠀⠀⠀⠀⠀⠀⠙⠦⣄ ⠀⠀⠀⠀⠀⣿⢠⣿⡄⢼⣆⠀⠀⣿⠀⢸⡇⠀⠀⠀⠈⠻⢦⣀⣠⣄⡀⣀⣀⣀⣠⡞⠉⠀⠀⠀⣽⣎⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⡇⠀⠀⠀⠀⣠⣤⠤⠤⠴⠶⢦⣄⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡄⠀⠀⢠⡾⢣⡤⡏⠀⠀⣿⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀ 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