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⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠙⢷⣌⠐⢌⠠⡘⢷⣄⠀⠀⠀⢻⡇⠰⢈⡘⣿⠀⠀⠀⠀⢿⡌⠒⡠⠙⣻⣄⠀⠈⠻⣤⣿⠛⠁⠀⠈⢷⡄⠀⠉⠻⣦⣵⣄⣧⣴⡾⠟⠋⠀⢀⣴⠿⢷⣄⣠⣀⣤⣤⣴⠶⠛⠉⠀⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣾⣿⣿⡀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠈⠻⣮⠀⢆⠡⢂⢻⣆⠀⠀⠈⣿⡀⢃⠄⣹⣇⠀⠀⠀⠈⢿⣆⢁⠒⡠⣿⠂⠀⣼⠟⠁⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠉⠁⠀⠀⣀⣤⡶⠛⠁⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⡟⡭⣻⣿⣧⠀⠀⠀⠀⢻⣄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠋⠀⢀⣿⠁⠆⡱⠈⢤⣿⠀⠀⠀⢹⣧⢈⠰⢀⣿⡀⠀⢧⡀⠀⠙⠷⣶⣵⠟⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣯⣿⣾⡿⠿⠛⠉⠀⠹⣶⣍⣿⣿⡆⠀⠀⠀⠉⠉⠹⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣴⠟⠡⠘⡐⠤⣩⡾⠋⠀⣀⠀⠀⣿⣄⣮⣶⠿⠇⠀⢸⡿⢦⣤⣀⣀⠀⢀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣍⡋⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⡾⣿⣷⠀⠀⠀⠀⣴⣦⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠘⣿⡠⢁⣣⣴⡿⠋⠀⢀⣴⣿⣦⡀⠈⠉⠁⠀⢀⣀⡴⠟⠁⠀⠈⠉⠙⣻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠘⠛⠛⠉⠁⠀⣠⡴⠟⠁⠀⣿⡿⠶⠶⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠐⣀⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⣿⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⡀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⢈⠀⠀⠀⢤⡀⠀⠀⠐⣿⣿⣿⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣿⣿⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⢥⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡄⠂⠀⠀⠘⣷⠀⠀⢈⣿⣿⣿⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⠀⠀⣼⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⡈⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣳⡄⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⢀⠀⠀⠹⣧⠀⠰⣯⣿⣿⡇⠀⠀⠀⠀⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⣿⣿⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⠿⣿⡆⠀⠀⢀⣿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⢻⣧⡐⣳⢽⣿⣧⠀⠀⠀⠀⠛⢷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡗⠀⠀⠀⠀⣿⣿⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⢘⣿⣧⠀⠀⢸⣿⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠈⠻⣿⣷⣀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠈⠀⠀⠀⠈⢻⣷⡹⡞⣿⣿⣆⠀⠀⠀⠀⠀⠘⢷⡀ ⠀⠀⠀⠀⣀⣤⡴⠶⠾⠛⠁⠀⠀⠀⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⠋⠀⠀⠘⣿⣇⠀⢸⣿⠀⠸⣿⣆⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⢀⣀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠰⠍⠻⣿⣷⣄⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⡀⠀⠀⠀⠻⣷⣽⡹⣿⣿⣷⣤⡀⠀⠀⠀⢸⡇ ⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠇⢀⡼⠁⠀⠸⣿⣆⣸⣿⠀⢀⣽⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠉⠛⠓⠶⣴⣿⣤⣤⡄⠀⠀⠀⠀⠀⠙⠻⣿⣦⣄⡀⠈⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⢀⠀⠀⠀⠈⠻⣷⣯⣽⡿⣿⣗⠀⠀⠀⢸⡇ ⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⡿⠃⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡏⢠⡾⠀⠀⠀⠀⠘⢿⣾⣿⡖⠋⠉⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⡟⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣶⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠿⠀⠀⠀⢸⡇ ⢰⣿⠀⠀⠀⢠⣶⣶⣶⣾⣿⡿⠟⣻⡿⠃⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⡼⠃⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠙⠿⣦⣄⡀⠀⠀⠀⠘⣿⣿⡅⠀⠀⠀⢀⢸⡇ ⢸⣿⢀⠀⠀⠈⠻⣿⣿⣍⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠀⠀⠀⠀⠈⠹⢿⣦⡀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⣴⡿⠋⢀⡤⠖⣀⣤⣶⣿⣿⣿⣿⣿⣷⡶⢤⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⠟⠂⠀⠀⢸⣿⣷⠀⠀⠀⠰⣿⡁ ⠀⢻⣎⠀⠀⠀⠀⠙⠻⣿⣿⣿⣧⣤⣤⣤⣤⣴⣶⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⣀⠀⠀⠀⣰⣿⠋⠀⠀⢀⣠⣾⠟⠁⠀⢁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣠⣼⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣀⣄⣤⣴⣶⠿⠛⣁⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⢸⡇ ⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⠻⣝⠯⠶⢹⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣰⡿⠃⠀⣠⣶⡿⠛⠁⠀⠀⢀⣾⡿⠋⣵⠿⠛⠿⣿⣯⣿⣻⣿⣿⣿⣿⣿⡍⠁⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣿⣿⠿⣟⣻⢛⡯⣻⡇⠀⢹⣿⠀⠀⠀⠀⠀⣻⣿⡇⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠙⢦⣤⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠰⣯⣿⣧⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⣡⣴⡾⠟⠁⠀⠀⠀⠀⢀⣼⠋⠀⢸⠏⠀⠀⢀⣿⣿⣳⣯⠿⣿⣿⡻⣿⣿⣦⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣯⡟⣼⢲⢏⡶⣽⡇⠀⢸⣿⣇⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⢸⣿⡏⠀⠀⠐⠀⣤⡜⣳⠼⣿⡄⠀⠀⠀⠀⠀⠀⠸⣿⣧⡀⠀⠀⠀⣦⡀⣀⣀⣀⣀⣀⡀⠀⠲⢦⡀⠀⠀⠀⠀⠀⠀⣾⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⣿⣷⣶⣶⣿⣿⣿⣿⣽⡷⣴⣿⡇⢹⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢿⣿⡽⢼⣹⣚⣼⣿⠀⠀⣿⣿⣿⡀⠀⠀⢠⣿⣿⠁⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⣻⡆⠀⠀⠀⢹⣿⡇⠀⠀⠀⢰⣿⡆⢹⢎⣿⣿⡀⠀⠀⠀⠀⠀⠀⡹⣿⣝⣳⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢯⣟⣷⠿⠟⠻⣿⣽⢯⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⢱⣿⣿⢞⡱⢧⢞⣼⡏⠀⣰⣿⣿⣿⡇⠀⠀⣼⣿⡏⠀⠀⠀⢘⣼⡇ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣿⣷⠀⠀⠀⣼⣿⣧⠈⢞⡱⢿⣷⡀⠀⠀⠀⠀⠀⠈⢿⣿⡻⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⢡⠚⣌⠣⠔⣻⣿⣿⠁⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⢹⣿⣿⢿⣿⡫⣝⣎⢯⡿⠀⢠⣿⣿⢿⣿⡇⠀⣰⣿⡿⠁⠀⠀⠀⣼⡟⠀ ⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢻⣿⣧⡀⠀⣿⣿⣿⣧⠈⢳⣭⢛⣿⣤⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣷⣈⡁⠆⣉⣆⣽⡿⠁⠀⢾⣿⠇⠀⠀⠀⢀⣀⣤⡾⠟⠋⠀⠀⣾⣿⠟⣼⣿⠵⣣⢞⣿⣃⣠⣿⣿⠋⣿⣿⢇⣼⣿⡟⠁⠀⠀⠀⢰⣟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠹⣿⣷⣄⣿⣿⠿⣿⣷⣄⠊⠿⣌⡻⣿⣦⣄⡀⠀⠀⠈⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠉⠀⠀⣠⣾⣁⣤⣴⣶⠿⠟⠋⠁⠀⠀⠀⢀⣼⡿⣣⢛⣼⣿⡹⢎⣿⡗⣳⣿⡿⠃⢀⣿⣿⣿⡿⠋⠀⠀⠀⠀⢀⡿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠈⠻⢿⣿⣿⣇⠈⠻⣿⣷⣎⡑⢣⢽⣿⣿⣿⣷⣶⣤⣤⣽⣿⣦⡀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣏⠳⡵⣋⣾⣿⢩⡿⣡⣿⣿⣿⠁⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⣴⠟⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠈⠛⢿⣿⣿⣾⣿⣿⣿⣿⣧⠹⣿⡏⠛⠛⠛⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣤⣤⣴⣶⣾⢿⣋⠷⣸⢏⣳⢥⣿⣯⣼⣶⣿⣿⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠋⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⢿⡿⣭⣙⢶⣩⠶⣭⢏⡳⡝⣎⣿⣿⣿⣛⣧⡿⠃⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢻⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠉⠁⣿⣿⠂⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢿⣿⠿⠿⡛⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⣓⢻⣿⣲⢹⣎⢧⣛⡖⣫⢳⠽⣼⣿⣹⣶⠿⠋⠀⠀⠀⠀⠉⠻⣿⣷⣦⣤⣄⣀⣀⣠⣄⠀⠀⠀⢸⢿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠲⣶⣦⠀⠀⠀⢀⣿⣿⠀⠀⠀⠉⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣴⡿⠉⢰⣿⠃⢀⡄⠻⣆⠙⢿⣷⡶⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⣫⡜⣧⠻⡜⣿⣧⢳⢎⡗⣮⢵⢫⣳⢋⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⠟⠀⠀⠀⢸⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠈⠙⠻⣶⣤⣀⠀⠀⢠⣿⠀⠀⣼⡇⢠⠈⠷⠀⠉⠀⠀⠘⢷⣄⠀⠈⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⡟⣏⢧⣛⣥⢻⡜⣏⡳⣍⣿⣧⢏⠾⣜⢮⢳⣱⢫⠿⣧⡀⠀⠀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠋⠀⠀⠀⠀⣸⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠞⠉⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠟⣿⢷⣾⡟⠀⠀⢻⣇⠈⠃⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣿⣿⣏⡳⣍⡳⣝⢮⢳⡎⣧⢛⡼⣱⠞⡜⣿⣯⡳⢮⡹⢎⡷⡭⢞⡽⣷⡄⠀⠈⠙⠻⠷⢶⣶⣶⣶⣿⣿⣿⠟⠋⠀⠀⠀⠀⢀⣼⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⣠⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢯⡹⢎⡮⣽⣧⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⡾⠿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠛⣿⣷⣷⣷⣮⢏⡳⣞⢥⡻⡜⣧⣫⢝⢦⠻⣿⣧⡯⣝⡲⣝⡏⡶⢭⢿⣦⡀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣦⡀⠀⠀⠀⠀⢴⡏⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠃⠀⠀⠀⠀⣠⣴⠄⠀⠀⣠⣿⢏⡶⡹⣭⣶⣿⣿⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠷⣶⣿⣿⣻⢻⣿⣿⣗⠀⠀⣠⡿⢄⣤⣿⣿⣯⢳⡭⣞⡵⣹⡹⣷⣮⣏⣳⣥⣛⣿⣷⣝⣦⢛⡼⡭⢮⡝⣿⣦⡀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡄⠀⠀⠀⠀⠻⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠷⠀⠀⠀⢠⣶⣶⣾⣿⡿⠛⠁⠀⠀⣀⣤⣶⣿⡿⠃⠀⠀⣴⣿⡹⢎⣶⣽⣿⣟⠉⢹⣇⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠉⢹⡟⣿⡿⢿⣿⣶⣾⣋⢰⡿⠉⣰⣿⣏⣳⡓⣞⡖⣣⠗⡭⣿⣟⣛⡛⣟⢻⣙⡏⣟⠮⣕⣫⣓⢮⣕⣫⢿⣦⡀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⢻⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡤⠀⠀⠀⠹⠿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⠟⠁⠀⢠⣾⣟⠲⣽⣾⠟⢿⣿⢿⠀⠈⢿⣄⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⣼⡇⣿⠇⠀⠀⠀⠈⠙⠻⢿⣾⣿⢏⡶⣣⡝⡶⣩⢗⣫⠵⣎⢿⣧⣛⡼⣣⢏⠾⣜⡽⢪⡵⢎⡷⣺⢴⣣⢏⡿⣷⣄⡀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠈⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣡⣿⣿⡿⠋⠁⠀⢀⣴⣿⠳⣬⢻⡿⠁⠀⠸⣿⡟⣧⡀⠀⠙⠻⠶⣦⣤⣴⣿⣷⣤⣤⣴⠾⠛⠁⠀⠀⠀⠀⢰⡿⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣏⢶⢣⡟⣼⣱⣎⢧⣛⡬⢏⣿⣷⠼⣱⢫⣛⡼⣜⢧⣛⠮⡵⣣⢻⢼⣿⡲⣍⢟⣷⣆⠀⠀⠀⠘⣿⣿⡀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠄⠀⠀⠀⠀⢀⣴⣿⡿⠟⠁⠀⠀⢀⣶⣿⠿⡸⣝⢲⣿⠃⠀⠀⠀⠹⣿⣜⡻⢦⣤⣀⡀⠀⢀⣾⠿⢿⣯⣿⣷⣄⠀⠀⠀⠀⠀⢠⣿⣱⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢎⣗⣫⡜⡶⣩⢿⣮⢳⡜⢯⠼⣿⣏⢞⡵⣋⠶⣭⢞⡼⢭⡳⢵⣋⢮⠽⣿⣜⡞⣲⢻⣷⡄⠀⠀⢻⣿⣧⠀⠀⠀⠘⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⢀⣼⣿⣿⢣⡏⡷⡭⢞⣿⣇⠀⠀⠀⠀⠈⠛⢿⣶⣬⣝⣿⣿⡿⠁⠀⠀⠉⢿⣿⣿⣿⣦⡀⢀⣰⡿⣵⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣩⢖⢧⡝⣞⡥⢏⣿⣷⡺⢭⢞⣻⣿⢎⢾⣩⣛⡴⣫⡜⣧⡝⡮⣝⢮⡹⣽⣿⣜⢧⣳⢚⣿⡄⠀⠈⣿⣿⡀⠀⠀⠀⢻⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⣠⣿⣿⠏⠀⠀⠀⢀⡴⣿⣿⡿⢥⣳⡹⡵⣛⢮⡜⢿⣦⣄⡀⠀⠀⣀⣀⣤⣿⣿⡿⠋⠐⠀⠀⠀⢀⣠⣾⣿⣿⣟⣿⣿⣿⣿⢿⣿⡿⠶⣶⣤⣤⣤⣤⣤⣶⣿⣿⢳⡹⣎⢧⣛⡼⣜⡣⢿⡿⣿⣓⠮⣽⣿⢎⣧⠳⣼⢱⣣⡝⣦⠽⣱⢎⣗⡳⡜⣿⣿⣷⣎⠽⣸⣿⠀⠀⣿⣿⡇⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⢰⣿⡿⠁⠀⠀⠀⢠⣾⢳⣿⡿⡱⣏⢶⡳⣍⡳⢮⣜⣧⣿⡿⢿⢿⣿⣟⣟⢫⣽⣿⠁⣀⣀⣤⣴⣾⣿⠿⠛⣿⣿⣿⣼⣫⢟⡼⣳⢾⡇⠀⠀⠀⢉⣩⣿⣿⣿⡟⣣⢻⡜⣮⢳⠮⡵⢎⡵⣻⣿⢹⣿⡝⣼⣿⣋⢶⡛⢶⣋⢶⡹⣲⢏⢧⣏⢮⡵⣙⣿⣿⢿⣿⣯⣓⠾⡇⠀⣿⣿⡇⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⢠⣿⢭⣿⣿⠳⣝⡬⢧⣝⡲⢭⢻⠿⠿⠿⠿⠿⡟⢿⢻⣿⣦⣿⣿⣿⢿⡿⠟⠛⢿⣄⠀⠀⠙⠻⠿⣿⣿⣿⣿⣷⣮⣷⣀⣤⣶⣿⣿⣿⣿⣿⣎⡵⣣⣛⢖⣫⢳⢭⡛⣴⣿⡏⣖⢻⣿⣼⡿⢬⣇⡻⣥⢛⡶⣍⡳⣎⠷⣬⠳⣎⣵⣿⣿⠀⠹⣿⣿⣯⣳⢀⣿⣿⠁⠀⠀⠠⣿⡁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢠⣿⣿⣤⣤⣄⣤⣿⣧⣿⣿⣿⣿⣼⣾⣷⣮⣽⣧⣿⣾⣽⣯⣿⣽⣞⣧⣿⣿⣿⡁⠈⢻⣾⣅⣀⣀⣀⣼⣷⣤⣤⣤⣤⣤⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣿⣮⣷⣯⣶⣽⣾⣿⣼⣽⣞⣿⣿⣷⣷⣮⣷⣮⣿⣶⣭⣷⣮⣿⣶⣿⣶⣿⣿⡟⠀⠀⠘⣿⣿⣿⣼⣿⡏⠀⠀⠀⢰⡾⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀