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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⣿⠞⠉⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠶⠶⠚⠁⠈⠁⠀⠀⠀⠀⠉⠙⠓⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣖⣋⣧⡤⠤⠤⠶⠶⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⢤⡙⢶⣄⠀⠀⠀⠀⣠⣴⡾⠟⣻⡷⠞⠉⠀⢰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢉⡳⢤⡀⠀⠀⠠⠑⠀⠙⠒⠍⡳⣤⣴⣾⣿⡥⠶⠛⠉⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠒⠉⠳⣄⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⠃⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⠾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠀⣀⣀⣤⠤⠴⠒⠙⢮⡉⠉⠁⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡾⠋⠀⠀⠀⠐⠒⠤⣤⣀⡐⠉⠡⠔⠒⠒⠊⠉⠉⠀⢠⣀⠀⠀⠀⠀⠛⢦⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⣱⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⢠⡟⠁⠀⠀⠀⠀⣀⠀⢰⡿⠀⠉⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡀⠀⠀⠈⠻⣦⣀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⢀⡿⠀⠀⠀⢀⡴⢚⡅⢀⣿⠃⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠀⠹⣿⠷⣄⡀⠀⠙⢿⢶⣄⠀⠈⢧⣀⣠⣤⠴⠞⠋⠁⠀⠀⠀⣰⡟⠁⠀⢀⣀⣠⣤⡴⠖ ⠀⣾⠃⠀⣠⠞⢩⡴⠋⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠙⢲⣤⡀⠀⠀⠈⢳⣄⠝⢦⡀⠈⢳⡙⢦⡀⠈⢷⠀⠀⠀⠀⠀⠀⢀⣲⠾⠛⠛⠛⠋⠉⠉⠁⠀⠀⢀ ⢠⣿⠀⠈⢀⡔⠋⡇⠀⠀⡏⡻⠀⠀⠀⠀⠀⠀⠀⡞⠀⢀⣠⣿⣿⣿⣦⣄⠀⠀⠙⣷⣆⡙⠦⡀⢳⡄⠙⠄⠈⣧⠀⠀⣠⠤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾ ⢸⡇⠀⡀⡏⠀⠀⡇⠀⢠⡇⡇⠀⠀⠀⠀⠀⠀⠀⠹⣤⠾⡟⣿⣿⣿⣿⣿⠛⢦⡀⠈⢯⠻⣦⡈⠀⠻⣄⠈⠀⠸⡆⠀⠐⠒⠒⠒⠲⠒⠒⠀⠀⠀⠀⠀⢀⣴⡟⠀ ⢸⡇⢸⢠⡇⠀⢀⡇⠀⢸⡧⠗⠒⣦⠀⠀⠀⠀⠀⠀⠈⠃⣧⠻⣿⣿⣿⠟⠀⠀⠙⢶⣄⢳⡈⠻⣆⠈⢻⣷⣄⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠁⠀ ⢸⣧⠸⠀⣿⠀⠐⣷⠀⢸⡀⣀⣠⣨⣷⡄⠀⠀⠀⠀⠀⠀⠘⠤⡀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣿⡄⠈⢳⣌⣧⠙⢦⡸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠁⠀⠀⠀ ⠘⣿⠀⠀⢹⡀⠀⢹⡄⢸⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⢸⠙⣾⣆⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠻⢯⣄⠀⠀⠀⠀⠀⠀ ⠀⢻⡇⠀⠀⡇⠀⠈⣇⢸⣿⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢿⡴⠏⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀ ⠀⠀⢿⡀⠀⢹⡀⠀⢿⡸⡟⣆⠙⠛⠛⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢰⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀ ⠀⠀⠘⣧⠀⠀⢷⠀⠘⣷⣧⡈⠓⠂⠀⠀⢼⣥⣀⠀⠀⠀⠀⠀⢀⣠⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣖⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀ ⡴⠶⢶⡼⢧⠀⢸⣧⡀⢿⣿⣷⡀⠀⠀⠀⠀⠈⠙⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⢿⡉⠀⠈⢧⡀⢿⣷⡘⣞⢿⣷⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢃⡀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠦⣀⠀⢳⡜⣇⠳⣽⡆⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⠟⠀⠀⠀⠀⠹⣆⠀⠀⠘⣿⡛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠒⣻⣿⣦⣽⣿⡄⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠀⠀⣹⣶⣿⣷⣾⢿⣶⣶⠶⠦⣤⢤⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠟⣻⣿⡟⠉⠻⠀⠀⠀⣙⠳⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣯⣄⣈⠀⠉⠳⣦⡙⢦⡈⠻⣷⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⡋⠁⠀⠀⠀⠀⠀⣀⡾⠃⠀⢀⡀⠈⠉⠙⠒⠦⣤⣀⣀⡴⠛⠙⣇⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⡿⠋⠉⠙⣦⡀⠈⢷⡄⠻⡄⠘⢿⣷⡄⠀ ⠀⠀⠀⠚⠛⠉⠈⠙⠓⠶⢤⣤⣤⣾⣯⣤⠴⠶⣿⠃⠀⠀⠀⠀⢀⣄⠉⠁⠀⠀⣀⠘⣇⠀⢀⣴⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠈⢳⡄⠀⢳⡄⠹⣄⠈⢷⡹⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡴⠟⢷⠀⠀⢀⡾⠋⠳⣿⣶⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢻⡄⠸⣆⠈⢷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣴⠿⠀⠀⢸⡆⣠⡟⠀⣠⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⢻⡀⠹⣆⠈⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣾⠃⠀⠀⠀⠀⠻⠏⠀⢰⣿⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⢷⡀⠹⡆⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⣽⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠈⢷⡀⢹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⢷⡀⠱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠈⢷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⢀⣠⣤⣤⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⢧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⣴⣾⣿⠉⠸⡿⣷⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠈⠳⡄⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢀⡾⣿⠏⠾⡶⠀⡿⢻⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠻⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣾⢻⣿⣶⣶⠃⢰⠇⣼⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠏⡏⠀⠀⡟⠀⡞⢠⡿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠸⣷⠙⣄⠀⣡⠜⢁⣾⠃⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⣷⡘⠉⣁⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡴⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠳⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡗⠚⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠃⠀⠀
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