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⠀⠀⠀⠀⢦⡀⠀⠀⠀⢿⡀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠘⣇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⠀⠀⠈⢿⣿⣿⣼⠃⢸⡇⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠘⠀⠀⠀⢿⡀⢈⣿⣿⣿⡟⠁⣴⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀ ⠀⠀⠀⠀⠈⢷⡄⠀⠀⠘⣧⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⢿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣀⠀⠈⢿⣿⣿⣶⣾⡇⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⣿⣷⣿⣿⣿⡿⢀⣼⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠈⢿⣿⣿⣿⣷⣤⣤⣾⡇⠀⠀⢸⡇⠀⠀⢸⣷⣄⣴⣿⣿⣿⣿⡿⣡⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡝⢷⣿⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠈⢿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣼⣿⣤⣀⣼⣿⣿⣿⣿⣿⣿⡿⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⢿⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣾⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠛⠛⠉⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⣹⣿⡿⣿⣷⡀⣶⡀⠀⠸⡝⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠋⣀⣠⣤⣤⣶⣶⡿⣿⢿⣟⡿⣿⢿⣿⣿⢿⣹⣏⡷⣿⣿⡤⣷⠀⠀⢻⠀⠉⠙⠲⣄⠀⠀⠀⠀⢀⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⣿⣻⢯⣿⣽⣳⣯⠿⠽⠿⠾⠟⣿⣿⡻⣮⢯⣗⡾⣝⡾⣽⣷⡸⡆⠀⠈⠳⣄⣀⠀⠈⠳⣄⠀⠀⡼⠁⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠷⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⢀⣾⣟⡾⣝⣳⢯⣾⡵⣿⣻⠾⣿⡇⠙⠾⢦⡀⠈⣉⠳⡄⠀⠈⠳⣄⣇⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣟⣾⣹⡽⣞⣳⡿⣿⣳⡻⣿⢿⡷⣄⠀⠀⠙⢷⣦⣼⡇⠀⠀⠀⠈⠻⣦⠀⠹⡤⣄⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣹⢾⣿⣟⡛⠻⢧⣸⣷⠿⠷⣿⡃⠘⢢⣄⠀⠀⠉⠻⡝⢳⣄⠀⠀⠀⠙⣆⠀⢧⡽⢧⠀⢀⣴⡿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠹⣿⡽⣞⢿⡾⣯⣷⢦⣄⠉⠛⠛⠛⠳⢤⡀⠈⠻⣦⡀⠀⠘⣦⠙⠳⣤⡀⠀⠘⣧⠀⠀⠸⣇⣯⠀⢰⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠃⠀⣀⡤⠤⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣽⣞⣳⣯⢟⣷⣿⡿⣶⣤⣀⠀⠀⠉⢢⡀⠈⠱⡄⠀⠘⣧⠀⠀⠻⡄⠀⢻⡆⠀⠀⠹⣿⡆⢸⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⠉⠕⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣭⣙⣿⠺⢿⡟⠻⣯⣻⣶⣄⠀⠀⠙⢆⠀⠹⡄⠀⠸⡷⣄⠀⠙⣄⠈⣿⡄⠀⠀⢻⣿⡀⠳⣄⠈⢷⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠁⢠⣶⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣽⣿⢱⡄⠹⣧⠀⠙⣏⢿⣿⣷⡀⠀⠈⢧⡸⡇⠀⢠⣿⠘⣷⡀⠸⡆⠘⣿⡄⠀⠈⣿⡇⠀⢻⠀⣸⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠳⠿⠂⠙⢶⡝⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣾⣿⠈⣿⣆⡻⣧⣦⡈⢳⣿⡿⠁⠀⣾⡟⠀⣧⠀⠈⣿⡀⠘⢷⠀⢹⠀⢸⡇⠀⠀⣿⣧⢀⡏⠰⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢀⠈⠻⢄⣻⣿⢧⠘⣿⣷⡄⠀⠈⠻⣦⣸⣧⠀⣸⡷⠖⠚⠉⢹⡆⠀⣇⠀⢀⣿⣿⣼⣧⣾⣿⣿⡜⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠿⢺⠀⠉⠙⠻⢧⣿⡿⠿⠷⠤⢤⣉⣻⣿⠏⠁⠀⠀⠀⠀⣼⣇⠀⢻⠀⢸⣿⣿⣯⠉⢿⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⢰⣧⣀⡀⣉⣷⣾⠇⠀⣀⣀⣤⣤⣈⣹⠁⠀⠀⠀⠀⢰⣿⢻⠀⢼⠀⣼⢣⣾⠙⣧⠈⢿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⣉⣩⣤⣤⡄⠀⣈⣭⣽⣿⣭⡏⠀⠀⠀⠀⠀⢸⣿⣸⠀⣼⣰⣯⣾⠿⣧⠘⣆⠘⢷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⡇⣰⣿⣿⣿⣿⣿⡿⣿⣟⣯⣿⣟⠳⣤⠀⠀⠀⢠⣿⣿⣿⣦⣿⣿⣿⣿⣶⣿⣷⣹⠀⢘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠐⢿⣆⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣟⠃⠉⠀⠀⢠⡟⠀⠀⠀⠸⣿⠉⠛⠻⠿⢻⡿⣿⣿⣿⡿⣿⠀⣿⣑⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠐⠀⠻⢷⡀⠀⣠⣾⣿⡿⠛⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⣾⣁⣤⡀⠀⠀⣸⠀⠀⠀⠀⠘⣷⡿⠙⣇⣀⣧⠀⢻⢻⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣰⠇⠀⠀⠀⠰⡀⢨⠙⢶⣿⣻⠃⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡷⠀⣀⣄⣀⢰⣿⠛⣿⠀⠀⡞⠁⠀⠀⠀⠀⢀⣿⣃⡀⠀⠈⣿⢀⡟⢠⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⣴⠃⠀⠀⠀⠀⠀⢹⡀⠱⣎⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⡿⣿⣿⣿⣧⠀⢿⣿⣿⣿⣿⣧⣽⡄⠀⠁⠀⠀⠀⠀⣀⣴⠟⠁⠉⠀⠀⣾⡾⠁⠈⠀ ⠀⠀⠀⠀⠀⠀⣤⣄⣤⣤⠀⠀⠈⣿⡄⠩⠁⠀⠀⠀⠀⡀⠁⠈⠹⡀⠀⣿⣿⡷⡀⠀⠀⠀⠀⠀⢠⣿⣴⣸⢩⡿⣿⣿⣧⡘⢿⣷⣽⣿⠿⣿⣿⣆⡀⠀⠀⣀⣴⠏⠁⠀⠀⣷⠂⠼⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠏⠸⣿⣧⡀⣀⣼⣿⡇⠀⠀⠀⠀⠀⠹⣧⡀⢆⠀⠱⣴⣿⣿⠃⠙⣦⠀⠀⠀⠀⣸⣿⢿⣾⣰⢀⠋⡿⣿⣿⣾⣻⠻⢶⣶⡾⠟⠋⠁⢀⣼⣿⠋⠀⠀⡰⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣇⣀⡀⢿⣇⣹⡷⠻⣿⣿⠀⠀⠀⠀⠀⠀⠉⣳⡀⠡⣠⣿⣿⠋⠀⢦⡀⠳⡄⠀⠀⣼⣿⢏⠼⣿⣼⢀⠀⡞⢻⣿⣿⣷⣶⣦⣤⡀⣠⠶⢾⣽⡇⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡟⠋⣹⣿⠉⢀⡼⠛⣿⣷⠀⠀⠀⠀⠀⠀⢀⣹⣄⢸⣿⣿⢤⡀⠀⠑⣄⠘⢦⠀⢿⣇⠀⠜⠙⢻⣼⣰⡇⡄⠘⠛⣿⣿⣯⣽⣿⣷⣄⡀⣿⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠀⠀⠈⢿⣧⡟⠁⣰⣿⠋⠀⠀⠀⠀⠀⢠⠎⠉⠉⢻⣿⣿⣄⡙⢄⠀⠈⢳⣄⠀⢸⣯⡶⡀⢠⠎⡜⢻⣧⡇⡏⢠⠇⣹⠻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⢿⣧⠀⠀⠉⢿⣷⣤⣿⠃⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⣻⣿⡇⠀⠙⠲⣕⢀⠀⠹⡔⠨⣿⣿⣷⢃⡜⢠⠃⡐⢋⣧⣼⢠⠇⠠⠋⢹⠿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⠈⢻⣧⡀⠀⠀⠉⣿⡏⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⣿⣿⡇⠓⠀⠀⠈⠳⣄⠀⠈⢆⢻⣿⣿⣿⣶⡁⠀⠠⠂⣠⠋⡿⢤⡀⢠⠃⠠⠋⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠶⣜⠻⣷⣄⠀⠀⣿⠃⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⢠⣿⣿⠃⢀⠀⠀⠀⠀⠈⠳⣄⠈⢿⡻⢿⣿⣿⣿⣤⡀⠘⠁⡴⠁⡜⢙⠷⣤⣤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⠀⠈⡻⣷⣾⣿⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠳⡄⠀⠀⢰⡆⠈⠳⡌⢻⣽⣹⢿⣿⣿⣿⣦⡞⢀⡞⢀⡞⣰⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡇⠀⠉⠙⣻⡟⠀⢠⢦⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠉⢦⡀⢸⠃⠀⠀⠙⢦⠙⣷⣎⡝⢿⣿⣿⣿⣿⣄⡈⠀⠇⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⡄⠀⢀⣿⡇⠀⣼⡞⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠈⠳⣬⣿⣷⣌⡙⣿⣿⣿⣿⣿⣾⣀⣩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠋⢿⣿⣆⣸⣿⠀⠀⣷⠇⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⢿⣿⣇⢶⣿⣏⠻⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠀⠢⠽⣿⣿⡿⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠢⠀⠀⠀⠀⠀⠈⣿⣿⠛⣾⣿⣡⣿⡏⠛⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡇⠀⠀⠀⠉⣿⡇⠀⢼⡇⠀⠀⠀⣀⣠⠤⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⡅⠀⠀⠀⢠⣿⠇⠀⣼⠀⢀⡖⠋⠁⠀⠀⣿⣿⠋⠳⣄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⣿⣿⣧⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⡄⠀⠀⢸⣿⠀⠀⣿⢀⡏⠀⠀⠀⠀⢰⣿⣿⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⣴⣿⣿⢿⣽⣧⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⣿⢿⣄⠀⣽⡏⠀⠐⣿⡞⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠘⢦⠀⠀⠀⡀⠀⡇⠀⠀⣠⣾⣿⡟⠁⠸⣿⣿⡆⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⢩⡏⠸⢿⣷⣿⡇⠀⠀⣿⣷⣄⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠘⣇⠀⠀⡇⠀⡇⠀⠀⢿⣿⣿⠀⡈⠀⠙⣿⣷⠀⠹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⢧⡟⠀⣶⠀⢈⣿⠀⠀⢸⣿⣯⢻⣆⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⡄⠀⡇⠀⣇⠀⠀⠈⢻⣿⣷⡀⠀⠀⠹⣿⡇⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣗⡾⢿⣾⠟⠀⣸⡏⠀⠀⣼⣿⡿⣶⢻⣆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⣠⣤⣷⢀⡇⠀⢻⠀⠀⠀⠀⢻⣿⣿⣶⠀⠀⠻⣿⡄⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡿⢻⣇⠀⠛⠀⢠⣿⠁⡀⠀⣿⣹⣿⣿⣶⢿⣦⣤⣽⣛⡀⠀⠀⠀⣠⣾⡋⢸⡏⢿⡇⠀⢸⡆⠀⠀⠀⠀⡙⠻⣿⣧⠀⠀⣻⣿⡀⠺⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⠁⠀⢻⣦⠀⢀⣾⠏⠀⢣⠀⣿⡟⡇⠀⠀⠀⠙⠻⠿⠿⣿⣷⣦⡾⣡⠞⢻⢸⡇⢸⡇⠀⠀⢷⠀⠀⠀⢠⠇⢰⢻⣿⡄⠀⠀⢿⣧⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡆⠀⠀⠹⢿⣾⠃⠀⠀⢸⣴⣏⠀⢹⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠿⢺⡇⠀⡷⢤⣀⢸⠀⠀⠀⡞⢀⣾⢺⣿⣷⠀⠀⠈⢻⡆⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣷⠀⠀⠀⠈⠀⠀⠀⠀⠈⣿⣿⣶⣛⣝⣿⡳⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⢸⡇⠈⣷⠀⠈⢳⡀⠀⢠⠇⣸⡏⠀⣿⣿⡄⠀⠀⠘⣿⣄⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣶⠀⠈⠀⠀⠀⠁⠂⠀⣿⡏⣿⡿⣿⡟⡷⠀⠀⠀⣴⡟⣿⠻⡗⠀⠀⠀⠀⣧⠀⣿⠀⠀⠀⢻⠀⡾⢠⡏⠀⠀⠸⣿⣷⠀⠀⣤⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣆⠀⠀⠐⠀⠀⠘⢒⣿⡇⢿⣷⠤⡿⠃⣴⠆⠀⣿⢿⣿⣷⠸⣆⠀⠀⢀⡿⠀⣻⠀⠀⠀⢸⣦⡇⡾⠀⠀⠀⠀⢻⣿⣶⣿⣿⠟⠇⢿⡿⣿⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣽⡯⢹⡏⣿⣆⠈⠙⠛⠷⠤⠟⠶⠭⣭⣤⡼⠆⢀⣼⠇⠀⣻⠀⠀⢐⠁⣿⣼⠃⠀⠀⣶⣶⣿⡿⠟⠋⠀⠀⢀⣸⣷⣿⡿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢧⠊⠈⠁⣈⣿⢡⢃⢣⢹⣿⣶⣄⣀⠀⠀⠀⢿⣭⣶⣶⣤⣴⠟⠋⠀⠀⢸⡀⠀⠁⣸⣿⠃⠀⠀⠀⢸⣿⡇⠀⠀⠀⣠⣴⣿⡟⣻⡛⣿⣻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣆⠈⡁⣹⢇⠢⣍⠆⢾⠋⣷⡈⠙⠛⠛⠛⠛⢟⠋⠉⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⣿⠃⠀⠀⠀⠀⠀⢿⣿⣤⣴⣿⠟⣿⡉⣧⣿⣷⣿⣧⣿⣿⡿⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣆⢠⠏⡆⡓⢬⡘⣿⠀⠘⣧⣴⣶⡆⠀⡀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣾⡗⠀⠀⠀⠀⠀⠀⠘⠟⠛⢹⣇⠀⢹⣇⠻⢻⡿⠁⢿⣿⣸⡧⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⡎⡜⢲⡍⢢⢼⡏⣠⠀⠘⣿⣿⡇⠀⠈⢄⠀⢣⡀⠀⠀⠀⠀⠀⠀⣿⣾⣿⠁⠀⠙⢦⡀⠀⠀⠀⠀⠀⠸⣿⠀⠈⣿⠀⠘⣷⢀⣾⣿⣿⡇⠸⣆⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⢤⢩⢆⣼⡧⠇⠀⠀⠹⣿⣷⠀⠀⠀⠠⠀⠱⢄⠀⠀⠀⠀⠀⢸⣏⡟⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⢿⡇⠀⢸⡇⠀⣿⣿⠋⠸⣿⣿⣆⠘⢦⠀⠀⠀⠹⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⡍⢆⣿⠁⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠠⠀⠈⠳⣄⠀⠀⠀⠈⣿⣇⡀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠸⣷⡀⣀⣷⣾⡿⠁⠀⠀⠿⢿⣟⣇⠘⠀⠀⠀⠀⢹⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡜⢢⣿⡄⡀⠀⠀⢰⣿⣿⣿⣷⣄⠀⠀⠉⢆⠀⠈⢧⡀⠀⠀⠸⡇⠈⠙⠒⠦⣄⣀⠀⠀⠀⠙⠢⡀⠿⠛⠛⠉⠀⠀⡀⠀⠀⠀⠀⠈⢻⠆⠀⠀⠀⢠⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣖⠬⢷⣝⠆⠀⣼⣿⡿⠀⠙⠻⢿⣦⡀⠀⠑⣆⠀⠙⠳⣀⠀⣿⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⣀⡑⠆⡀⠀⠀⠀⠀⠙⠂⠀⣀⣠⡴⠟⠀⠀⠀⢀⣯⣿⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣽⣿⣶⣿⣿⡇⠀⠀⠀⠀⠈⠛⢦⣀⠈⠳⣄⠀⢀⣿⡇⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⣸⣿⠏⢹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢠⠀⠻⢿⣯⡒⢤⣄⡀⠀⠀⠀⠉⠓⢦⣈⣴⡟⣡⣧⠀⠀⠈⠉⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠀⢰⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣇⠨⡄⢸⣿⡿⣟⣣⣈⠉⠛⠶⣄⡀⠀⠀⠈⠉⢻⡦⢿⡀⠀⠀⠀⠀⠀⠉⠳⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡼⠋⠀⣐⣾⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⡻⢷⣝⣿⣿⡇⠀⠉⠉⠙⠲⠤⠈⠙⡛⠖⠛⣱⣾⣿⣽⣧⣀⣀⣀⣀⡀⠀⠀⠀⠈⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⢰⡾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠘⢦⡈⠛⢿⣿⣄⠀⠠⠀⢠⢶⣞⡭⠷⠂⢈⣽⣧⢌⣹⡟⠉⠉⠛⠛⠛⠛⠛⠛⠿⠿⠶⠒⠶⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢬⣾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⠈⠷⢄⣾⣿⡟⠛⠲⠒⠛⠛⠓⠚⠛⠛⠋⢩⣟⠖⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠙⢦⣐⢸⣿⣿⠇⠠⠄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣍⣚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣦⣶⣶⣿⡷⠾⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠳⢶⣄⡉⢸⣿⣿⡀⠀⠀⠀⠀⣠⠔⣁⣠⠶⢈⣯⣻⣝⢻⡛⡶⢶⣳⠷⡷⠿⠿⠿⠞⠛⠛⠛⠛⠋⠉⠉⢉⣁⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠠⠈⠙⠛⣿⣿⡿⠶⠶⠶⠿⠓⠛⠛⠀⠀⣸⠁⣿⣿⣿⣿⣷⣷⣶⣦⣤⣤⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ 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