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⠄⠄⠄⠄⠄⠄⠄⠄⣠⣴⠶⠿⠛⠛⠛⠛⠛⠛⠷⠶⢶⣤⣀⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⣤⣶⠟⠉⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠈⠛⢿⣶⣤⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⣠⣾⠟⠁⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠻⣿⣿⣦⡀⠄⠄⠄⠄⠄ ⠄⠄⣼⣿⠋⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠹⣿⣿⣿⣆⠄⠄⠄⠄ ⠄⣸⣿⡇⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢸⣿⣿⣿⣧⡀⠄⠄ ⢰⣿⣿⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢰⣿⣿⣿⣿⣇⠄⠄ ⢸⣿⣿⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣿⣿⣿⣿⣿⣿⡀⠄ ⢸⣿⣿⢠⣤⣤⣄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣀⣀⣠⣤⡀⠄⢸⣿⣿⡟⣿⣿⡇⠄ ⢸⣿⣿⣿⠏⠛⠛⠿⣷⣶⣄⠄⠄⠄⠄⣠⣴⣾⣿⡿⠟⠛⠛⠛⠛⢦⣼⣿⣿⡔⣾⣿⡇⠄ ⠄⢿⣿⡟⢀⣤⣶⣶⠾⢿⣿⣷⠄⠄⢠⣿⣿⢛⡿⢿⣷⡶⠦⣤⣄⡈⢿⣿⣿⣿⣾⣿⠃⠄ ⣶⢾⣿⠄⠉⠁⠉⠉⠄⠤⠞⣿⠄⠄⢸⣿⡿⠄⠈⠄⠄⠁⠉⣽⠟⠄⠈⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⠄⠄⠄⠄⠄⠄⠄⠄⠃⠄⠄⢸⣿⡇⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣿⣿⣿⣿⣇⡏⣧ ⣿⣿⣿⡇⠄⠄⠄⠄⠄⡴⠄⠣⡀⢀⣸⣿⠿⣷⠄⠄⠄⠄⠄⠄⠄⠄⣠⣿⣿⣿⣿⣿⣿⢸ ⢹⣿⣿⣧⠄⠄⠄⠄⠄⠙⠚⣛⡊⣻⣿⡛⠗⠋⠄⠄⠄⠄⠄⠄⠄⢰⣿⣿⣿⣿⣿⣿⠏⡜ ⠈⢻⣿⣿⡆⠄⠄⢀⣴⣴⣿⣿⠿⢾⡻⠿⢿⣶⣶⣦⡀⠄⠄⠄⠄⣿⣿⣿⣿⣿⣿⣿⡜⠁ ⠄⠄⣿⣿⣿⠄⠄⣾⣿⣿⠿⠛⠛⠛⠛⠿⠶⣿⣿⣿⣿⡆⠄⠄⢀⣿⣿⣿⣿⣿⡿⠟⠄⠄ ⠄⠄⠄⢹⣿⣄⠄⠉⠁⠄⠳⢶⣶⣶⣶⣶⣾⣿⡟⠃⠄⠁⠄⠄⣼⣿⣿⣿⣿⣏⠄⠄⠄⠄ ⠄⠄⠄⠘⣿⣿⣆⣀⣀⡀⡀⡖⣸⣶⣶⣿⣿⣿⣷⣦⡀⠄⢀⣾⣿⣿⣿⣿⣿⣿⠄⠄⠄⠄ ⠄⠄⠄⠄⣿⣿⣿⣿⣿⠟⠁⠁⢿⣿⡿⠍⠻⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠄⠄⠄⠄ ⠄⠄⠄⣼⣿⣿⡿⣿⣿⣴⠄⠰⣿⣿⣇⢀⠄⠸⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⡀⠄⠄⠄ ⠄⠄⠘⠿⣿⣿⣿⣀⠙⠿⣷⣤⣼⣿⣿⣾⣷⣾⣿⡿⠟⠋⠉⠄⠄⣿⣿⣿⣿⣿⠇⠄⠄⠄ ⠄⠄⠄⠄⠈⠛⠿⣿⣶⣤⡈⠛⢿⣿⣿⠿⠛⠉⠁⠄⠄⠄⠄⠄⠄⣿⣿⣿⣿⣿⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠈⠛⠿⣿⣿⣦⣤⣀⡀⠄⠄⠄⠄⠄⠄⠄⠄⢘⣿⣿⣿⣿⡿⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠉⠉⠛⠻⠿⠿⢶⣦⣄⣀⣀⣀⣀⣼⡿⠿⠿⠛⠁⠄⠄⠄⠄

⠄⠄⠄⠄⠄⠄⠄⠄⣸⣿⣿⠁⠄⠄⢀⡀⠄⠄⠈⣿⣿⣇⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⢻⣿⣷⢀⣠⣶⣿⣿⣶⣄⡀⣾⣿⡟⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⣀⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣀⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠐⠶⣿⣿⣿⣿⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣿⣿⣿⣿⠶⠂⠄⠄⠄ ⠄⠄⠄⠄⠄⣦⡬⢙⠛⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⠛⡋⢥⣴⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⢠⣿⣇⢸⣿⣷⣦⣍⠻⣿⣿⣿⣿⠟⣩⣴⢾⣿⡇⣸⣿⡄⠄⠄⠄⠄ ⠄⠄⠄⢀⣾⣿⣿⢸⣿⣟⠻⣿⣷⣦⡹⢏⣴⣾⣿⠏⢻⣿⡇⣿⣿⣷⡀⠄⠄⠄ ⠄⠄⣠⣾⣿⣿⣿⢸⣿⣿⢀⡀⠹⣿⣷⣿⣿⠏⠵⣚⣾⣿⡇⣿⣿⣿⣷⣄⠄⠄ ⢴⣾⣿⣿⣿⣿⣿⡈⣿⣿⡸⣿⣷⣶⣶⣶⣶⣖⣾⣿⣿⣿⢁⣿⣿⣿⣿⣿⣷⡦ ⠈⢻⣿⣿⣿⣿⣿⣧⠸⣿⣧⡉⢻⣿⣿⣿⣿⡟⠋⣩⣥⠆⣼⣿⣿⣿⣿⣿⡟⠁ ⠄⠄⠙⣿⣿⣿⣿⣿⣧⡙⣿⣷⣼⣿⣿⣿⣿⣧⣾⣿⢋⣼⣿⣿⣿⣿⣿⠋⠄⠄ ⠄⠄⠄⠈⠻⣿⣿⣿⣿⣷⣌⠻⣿⣿⡟⣿⣿⣿⡿⣡⣾⣿⣿⣿⣿⠟⠁⠄⠄⠄ ⠄⠄⠄⠄⠄⠈⠻⡿⠃⣿⣿⣷⣌⠻⡇⣿⠟⣩⣾⣿⣿⠘⢿⠟⠁⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠈⠻⣿⣿⣷⣦⣴⣾⣿⣿⠟⠁⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢈⣽⣿⣿⣿⣿⣯⡁⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄

⠀⢀⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⣀⣀⡤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀ ⠀⢸⠀⠀⢹⠀⠀⠀⠀⠀⠀⢸⠃⠈⢹⠀⠀⢸⡛⠏⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⡔⠋⡟⡧⠀⠀⡟⠁⠙⢛⣁⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⣰⠛⠋⠉⠁⠀⠀⠀⠀⠀⠈⣷⠀⠀ ⠀⠸⠀⠀⢸⠀⠀⠀⠀⠀⠀⡼⠀⠀⢸⠀⠀⠀⠳⡀⠀⠀⠙⢦⠀⠀⠀⢀⡴⠋⠀⢀⡞⠁⠀⠀⡇⠀⠀⢸⠉⠉⠓⢢⡀⠀⢳⠀⠀⠀⠀⢻⠀⠀⡖⠒⠒⠒⠒⠒⠒⠚⠁⠀⠀ ⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠙⢦⠀⠀⠀⠑⣤⠴⠋⠀⠀⣰⠋⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⡧⠀⠸⡆⠀⠀⠀⢸⠀⠀⠳⠤⠤⠤⠤⠤⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⢸⡄⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠁⠀⢀⡜⠁⠀⠀⠀⠀⠀⡇⠀⠀⣇⣀⣀⣠⠴⠃⠀⢰⠃⢀⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀ ⠀⠀⠀⠀⢠⡖⠢⠤⠤⠤⢤⡀⠀⠀⢸⠀⣤⣴⣶⣦⣄⠀⠘⡆⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣠⠴⢃⣾⣿⣿⣿⢸⠀⠀⣼⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⡇⠀⠀⢸⡄⣿⠟⠙⢿⣿⣧⠀⡇⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣴⠒⠚⠋⠉⢀⣴⣿⣿⠟⢁⡜⢸⠀⠀⠹⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀ ⠀⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⢸⠇⡏⠸⡆⠀⢻⣿⡇⣇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣸⠀⠀⠀⢠⣾⣿⡿⠁⠀⣾⠸⡸⡆⠀⠀⠀⠀⠉⠉⠁⠀⠉⡇⠀⠀ ⠀⢳⡀⠀⣼⠀⠀⠀⠀⠀⠀⠳⠤⠤⢞⡼⠁⠀⣷⠀⠀⢻⣧⢿⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢳⣐⣠⠎⠀⠀⣠⣿⣿⡟⠀⠀⢰⡇⠀⠳⣝⠦⠤⣀⣀⣀⣀⣀⣀⡴⠃⠀⠀ ⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣰⣿⣷⢞⠞⠀⠀⠀⢸⠀⠀⠀⢻⣮⣓⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⣾⠀⠀⠀⠈⠹⡰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢋⡞⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢣⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⡜⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⡎⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⡞⠀⠀⠠⣾⠛⠲⣤⣇⠀⠀⠀⠀⠀⠉⣹⠈⠉⠉⢻⠉⠉⠙⡿⠛⠛⠛⡟⠛⠋⠉⠀⠀⠀⠀⠀⣾⡴⠚⡇⠀⠀⠀⠀⢣⢸⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⢸⠀⠀⣠⡶⠚⠓⠀⠀⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡼⠀⠀⠀⡇⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠗⠒⠦⡀⠀⠸⡈⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⢈⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢠⠇⠀⠀⠀⢳⡀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⣠⠇⢹⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠴⠋⠀⠀⠀⠀⠀⠓⠦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣶⡄⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⣿⣿⣿⣿⣿⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣷⡄⠀⠀ ⠀⠀⣿⣿⡿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⡿⠏⠁⠀⣸⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⣦⠀⠙⢆⠈⠛⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀ ⠀⠀⣹⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⡿⠛⢉⠎⠀⠀⣴⠏⠻⢦⣤⡴⠞⠻⢶⣤⣤⣤⡿⢷⡄⠈⢧⠀⠀⠈⠻⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣷⣆⠀ ⢠⣴⣿⠟⠋⠉⠛⠷⣦⣀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⡜⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠉⠉⠉⢹⣿⡄ ⢸⣿⡏⠀⠀⣀⣀⡀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢁⡠⢤⣀⠀⠀⠀⣿⣧ ⢸⣿⠀⢰⠋⠀⠀⠈⢳⡀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⢧⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⡰⠋⠀⠀⠈⢣⠀⠀⣿⣿ ⢸⣿⠀⢸⠀⠀⠀⠀⢀⠇⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠸⡄⠀⠻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⡎⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⣇⠀⠀⠀⠀⢸⠀⠀⣿⣿ ⢸⣿⠀⠀⠑⢄⣀⡠⠊⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠱⣄⠀⠙⠳⢤⣀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠛⠁⢀⠜⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠈⠲⠤⠤⠤⠎⠀⢠⣿⣿ ⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢷⡄⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⡼⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⢤⣀⣀⣀⣀⣠⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⢀⠾⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇ ⠸⣿⣇⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠘⡞⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⢣⠀⠈⢆⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢫⣿⣿⠁ ⠀⣿⣿⡀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⡼⠁⠀⠙⠑⠒⠦⠤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠤⠔⠋⠀⠀⠀⠈⢧⠀⠀⠉⠂⠀⠀⠀⠀⠀⠒⠉⠀⣼⣿⠇⠀ ⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣈⠑⣄⠀⢀⡤⠔⠊⠁⠧⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀ ⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀ ⠀⠀⠸⣿⣿⣄⣀⣀⣀⡤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣀⣀⣰⣿⡏⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢛⠳⠶⣤⠶⠒⠛⠛⠛⠛⠦⠴⠖⠚⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠤⠄⠀⠛⠀⠀⠠⠀⠀⠉⠀⠤⠬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠈⠢⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡰⠀⠀⣸⠠⣄⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣄⠀⠀⠀⠑⡄⠀⠐⠂⠀⣇⠀⣠⠿⡄⠀⠉⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⢀⠴⠊⣡⠤⠀⠤⣕⠢⣤⠤⠃⠀⠀⠀⠀⠈⠉⠁⠀⢳⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡔⠁⡴⠋⠁⠀⠀⡀⠀⠑⣄⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡜⢠⠞⠀⠀⠀⠀⠀⡇⠀⠀⠈⡆⢣⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⢁⡏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡀⡇⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⡏⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⡇⢰⠀⠀⠀⠀⠀⠀⣸⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⡿⣇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⢀⣷⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠁⡇⢻⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣷⢸⠀⠀⠀⠀⠀⣼⢻⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⢠⠘⡆⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⢸⡈⡀⠀⠀⠀⡰⢻⠈⢇⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠆⠀⢻⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢧⡀⠀⢀⡴⠁⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠉⢉⠩⢍⡙⠛⠋⣉⠉⠍⢉⣉⣉⣉⠩⢉⠉⠛⠲⣄⠀⠀⠀⠀ ⠀⠀⠀⡴⠁⠀⠂⡠⠑⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠐⠁⢊⠀⠄⠈⢦⠀⠀⠀ ⠀⣠⡾⠁⠀⠀⠄⣴⡪⠽⣿⡓⢦⠀⠀⡀⠀⣠⢖⣻⣿⣒⣦⠀⡀⢀⣈⢦⡀⠀ ⣰⠑⢰⠋⢩⡙⠒⠦⠖⠋⠀⠈⠁⠀⠀⠀⠀⠈⠉⠀⠘⠦⠤⠴⠒⡟⠲⡌⠛⣆ ⢹⡰⡸⠈⢻⣈⠓⡦⢤⣀⡀⢾⠩⠤⠀⠀⠤⠌⡳⠐⣒⣠⣤⠖⢋⡟⠒⡏⡄⡟ ⠀⠙⢆⠀⠀⠻⡙⡿⢦⣄⣹⠙⠒⢲⠦⠴⡖⠒⠚⣏⣁⣤⣾⢚⡝⠁⠀⣨⠞⠀ ⠀⠀⠈⢧⠀⠀⠙⢧⡀⠈⡟⠛⠷⡾⣶⣾⣷⠾⠛⢻⠉⢀⡽⠋⠀⠀⣰⠃⠀⠀ ⠀⠀⠀⠀⠑⢤⡠⢂⠌⡛⠦⠤⣄⣇⣀⣀⣸⣀⡤⠼⠚⡉⢄⠠⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠓⠮⣔⡁⠦⠀⣤⠤⠤⣤⠄⠰⠌⣂⡬⠖⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢤⣀⣀⡤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢰⡟⠛⠂⢠⡾⠛⠻⣶⠀⠀⠀⣾⣿⡄⠀⣰⢿⡇⠀⢰⣿⣇⠀⢰⣿⠀⠀⢸⡟⠛⢶⡄ ⠘⠻⣶⡄⢸⡇⠀⠀⣿⡇⠀⠀⣿⡏⣷⢠⡟⢸⡇⠀⣾⣁⣿⡄⢸⣿⠀⠀⢸⡇⠀⢸⡇ ⢠⣤⣼⠏⠘⢷⣤⣴⠿⠀⠀⠀⢿⡇⢸⣿⠁⢸⡇⣸⠏⠉⠹⣷⠸⣿⣤ ⢸⣧⣤⡾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠙⠋⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠹⡿⠁⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⡶⠶⠶⠤⠤⠤⡀⠀⠀⠀⠘⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⣾⣿⡧⠈⢂⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠃⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣖⣒⡒⠒⠀⠀⠀⠀⠀⡀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠻⣿⡿⠿⠿⠿⠿⠿⠟⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠖⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⢾⣿⢺⣄⡀⠀⠀⠀⢀⡴⠃⠀⣠⡎⢀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠁⢸⣿⣾⣿⣇⣀⠀⠐⠁⠀⣠⣶⣿⡟⠃⠑⣄⣴⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠖⠀⢀⣠⠿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠻⢿⣿⣿⣶⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⢸⣿⠉⠉⠉⢣⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠚⠋⠀⠀⠀⠸⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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