Squidward Dot Art

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠟⠛⠛⠛⠛⠛⠛⠻⠷⣶⣤⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡾⠟⠋⠁⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠈⠙⠻⢷⣄⠀⠀⠀ ⠀⢀⣾⠋⠀⠀⠀⠀⠶⠶⠿⠛⠛⠛⠛⠛⠛⠿⠶⠶⠀⠀⠀⠀⠙⣷⡀⠀ ⠀⣿⠃⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠘⣿⠀ ⠘⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿⠃ ⠀⠻⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⠟⠀ ⠀⠀⠙⢷⣄⡀⠘⣿⠛⠛⣿⡟⠛⢻⡟⠛⢻⣿⠛⠛⣿⠁⢀⣠⡾⠋⠀⠀ ⠀⠀⠀⠀⠉⠻⢷⣿⣧⠀⠉⠁⣠⡿⢿⣄⠈⠉⠀⣼⣿⡾⠟⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣶⣾⡟⠀⠀⢻⣷⣶⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⢀⣿⠁⠀⠀⠈⣿⡀⣿⣇⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⡟⠋⢉⣉⣀⣸⡏⠀⠀⠀⠀⢹⣇⣀⣉⡉⠙⢻⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡀⠘⠛⠛⠉⣹⣷⠀⠀⠀⠀⣾⣏⠉⠛⠛⠃⢀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠻⠷⠾⠛⠛⠛⠛⢷⣤⣤⡾⠛⠛⠛⠛⠷⠾⠟⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⠖⠛⠉⠉⠛⠀⠀⠀⠸⠉⠛⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠔⠋⡀⠀⠀⠐⠟⠂⠀⠀⠚⠃⠀⠀⢦⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠞⠃⠀⠚⠃⢀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⠏⢀⡄⠀⡠⠊⠁⣀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠉⠀⠈⢁⠔⠋⠁⢀⣀⣤⠤⠴⠶⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⣠⡀⠀⠰⠃⢀⣴⣚⣉⡴⠋⠙⠓⢦⡀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⡤⠤⢦ ⣇⠉⠀⠀⠀⡴⡿⠋⠉⠹⡇⠀⠀⠀⠀⣿⣤⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⡼ ⠹⡄⠀⠀⠘⢱⡇⠀⠀⣀⣿⡷⢺⣯⠉⠉⢹⡀⠐⣾⣅⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⢀⣀⡀⣠⠞⠁ ⠀⠙⢦⣀⠀⠀⣷⠿⣾⡅⠀⢧⠈⢿⣧⡀⠈⡇⠐⠊⣉⣁⣈⣙⣦⠀⠀⠀⠀⠀⢀⣀⡠⠴⠚⢩⠀⠀⠀⠀⠀⢀⣤⣤⣿⠿⠛⠁⠀⠀ ⠀⠀⠀⠈⠉⠙⠻⡄⠹⣿⣄⡼⠱⢄⣙⣁⣜⣡⠔⠋⠉⠀⠀⠈⠉⠙⠓⠲⢶⠚⠉⠁⠀⢀⣀⡬⠴⠒⠋⠙⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠛⣦⣌⣻⡇⠀⠀⣹⠾⠻⣀⣤⣀⡀⠀⣤⣄⡀⢀⣀⣠⡾⠶⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⣸⣀⡤⠊⠁⠀⡴⣟⢿⡟⠛⠶⠿⠿⠖⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠔⣩⠜⠁⠀⠀⡠⠊⠀⠘⣎⣧⠀⣀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢲⠞⠁⠀⠀⡠⠊⠀⠀⠀⠀⡿⠉⠈⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⢃⠀⠀⢀⠜⠓⠤⣄⣀⣤⠞⠁⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠷⣶⣾⣥⠤⠶⠚⠉⠀⢿⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⣀⣠⣤⣤⣀⣀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠁⠀⠀⠀⠀⠉⠙⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠐⠒⠒⠲⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠴⠛⠁⠀⢈⠀⢒⣀⡤⠤⠄⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠑⠚⠀⠀⠁⠀⠒⢉⣤⠤⠒⠒⠒⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡞⢡⢦⠀⠀⠀⠀⠀⠀⠚⠁⣀⡤⠔⠒⠒⠒⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡏⣠⠾⠈⠀⠀⠀⠀⠀⠀⠀⠀⢁⣠⠤⢖⠒⠒⠛⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠈⢧⣀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡤⣶⣮⣿⡽⣶⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡤⠖⠊⠹⣿⣽⡗⠚⠻⠷⣒⢶⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⠳⠤⢤⣤⡤⠤⠴⣦⠀⠀⠳⣄⣀⠀⣙⡿⢣⠀⠀⠀⠈⠻⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⢻⠛⠒⠀⠀⠉⠉⠁⢀⣸⡇⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠚⠃⠒⠒⠒⠒⠉⠉⣁⣀⣷⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠒⠚⢻⡉⠉⢹⡄⠘⢷⡀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⢧⠀⠈⠛⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠘⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠻⣄⢳⡙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠣⡀⠘⣿⣿⠛⡟⠲⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⠋⠀⠀⠀⡈⠛⠃⠙⠀⢳⡀⠀⠙⣶⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠟⠉⣷⣄⣠⣾⠁⠀⠀⠀⠀⠸⡗⠦⢴⣁⠉⠳⢤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣠⠎⠛⠛⠁⡇⠀⠀⠀⠀⠀⠀⢻⠀⠀⠈⠳⣄⠀⠈⣷ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠐⢦⣞⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡜⠁⠀⢰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠈⠙⠲⠤⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⢹⣠⠞⠀⠀⢠⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⢠⣷⣒⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣓⣦⡀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⢳⠀⠀⣯⣭⢁⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠹⣷⣾⣿⡄⠀⠀⢀⣿⣤⣤⣤⣤⠴⠚⣏⠀⠀⠸⣠⠎⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣈⠉⠁⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠹⢦⡀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⢰⠖⢻⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡞⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢸⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠙⡆⠀⠀⠀⣸⠀⠀⡇⢸⡀⠀⠀⠀⡶⠏⠉⢦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⡺⢦⣸⣀⣠⢴⠇⠀⠀⡇⠘⣧⠤⠤⢼⡣⢦⣤⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢹⣏⡇⠀⠻⡗⠶⠋⠀⠀⢰⡇⠀⢻⣀⣠⠏⠀⣞⣮⢻⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠊⠁⡼⠀⠀⠓⣃⣸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⠺⢭⣽⣦⠤⠤⠤⠒⠒⠉⠉⠉⠒⠤⠤⣄⣠⣯⣷⣿⣟⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠶⠶⠶⠚⠛⠛⠶⠶⠶⢶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠈⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠘⣦⣀⠀⠀⣀⣤⠎⣰⡟⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠦⢤⣀⣀⣠⣤⣤⠾⠛⢢⡀⠀⠀⠀⣞⡴⢋⣁⣭⣛⣛⣿⣤⡾⠋⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⠛⠀⠀⠀⠀⠀⣴⠁⠈⣁⠤⣶⣶⣶⡖⢿⠀⠀⢸⣿⠋⠉⠸⣿⣿⠏⣿⠃⠙⢷⣄⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠉⢑⣲⠆⢻⣴⠊⠀⠀⠙⠛⠋⣠⡟⠀⠀⠀⠙⠛⠶⣦⣀⣤⡾⠋⠀⠀⠀⠙⢷⡀ ⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠐⠋⠀⠀⠀⠙⠳⠦⣤⣤⠴⠞⠋⣠⠇⠀⠀⠀⠀⠀⠘⣿⣅⣀⡀⠀⠀⠀⠀⠈⣷ ⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣄⡀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⢀⣼⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⠉⠑⠂⠙⠿⣶⣤⣤⣴⠶⢶⣤⡀⠀⠀⠀⠀⣴⠚⠛⠒⡆⠀⠀⠀⢀⡿⡄⠀⠀⠀⢀⣠⣴⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠘⣷⠀⠀⣠⠊⣇⠀⢀⣄⠀⠀⠀⠀⢸⡇⢹⠀⠒⣾⡟⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⢸⠀⡼⠁⠀⠈⠃⠈⠘⣷⡀⠀⠀⠀⣷⠘⡆⢠⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣤⠿⠀⠁⣾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⢶⣴⠖⠲⣄⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠈⠁⠀⣠⢸⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⠒⠚⠹⠤⠤⠞⢁⡟⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⣠⠞⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀ ⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠒⠋⢁⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀ ⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡴⠋⠀⠀⢄⠀⠀⠀⠙⠿⣦⡀⠀⠀ ⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠘⢿⡀⠀ ⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⣸⠇⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⢠⠴⠒⠄⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢀⣠⣴⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣼⡘⠋⣹⢀⠰⠒⢿⠀⠀⣗⠆⠀⣠⢤⣄⠀⠀⢈⡙⠿⢶⣦⣤⣄⣀⣀⣀⣀⣤⣤⡾⠟⠙⠋⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡁⡇⢠⠚⢢⣵⠋⠙⢷⣀⣧⣿⣼⣀⡞⠉⠙⡆⢀⣴⡿⠋⠉⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤⣡⠞⠹⡞⠱⢸⠇⢰⠲⠆⢸⠃⢊⣨⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣛⠷⣿⣶⣥⣤⣤⣭⣿⠷⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡴⠞⡟⢉⠉⠁⠙⠉⠽⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⡟⠁⠉⠀⠠⠤⠄⣂⠔⠁⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡾⠁⠀⠀⠀⠉⢒⣒⣉⣵⠴⠳⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⢻⠀⠉⠙⣆⠀⠱⣄⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣄⠀⠀⠀⠀⢘⣦⠤⠒⣾⣍⣩⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠒⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⠒⠦⠤⢾⠹⢄⣠⠿⡆⠀⠉⢳⣄⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢫⣥⡀⠀⠈⠛⠲⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣨⣷⣖⣻⣿⣿⡀⠀⠀⣧⡇⠀⠀⠀⠀⣠⠖⢋⣠⠖⠋⠈⠛⠦⠤⠴⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡻⣿⣟⣻⣿⣿⢿⠦⠖⠁⢀⣀⣀⡴⢛⣡⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⠽⠟⠋⠀⣿⡌⣷⣴⠊⢹⣯⣥⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠿⣿⢿⠻⡤⠴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⣇⣠⢾⠉⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⢩⠖⠛⠚⠃⠀⣧⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠳⣜⡓⠦⠤⢄⣀⢸⠀⠀⠀⣀⣘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⠈⠙⢷⡖⠉⠁⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⡷⠀⠀⡧⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠦⠴⢾⢧⠀⡴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠼⣤⢡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢿⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣤⣸⢻⠀⡇⢿⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠹⢾⣥⠏⡜⠀⢱⣾⣶⡴⠟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣈⣀⣀⣇⠀⢹⣋⣏⣳⣼⠿⠃⠀⠀⠀⠀⣠⣤⣤⣤⡄⣤⣴⣶⠀⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢿⡛⠋⠀⠀⠀⠀⠀⠀⠀⠈⣉⠉⠉⠉⠉⣛⡛⡉⠉⢉⠉

⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠤⠤⠤⢀⣀⠀⠀⠀⠀⠀ ⠀⠀⢀⡤⡪⠕⠀⡀⠔⢈⠄⠑⠌⠁⠢⢌⠑⠢⡀⠀ ⠀⢠⢋⠊⠀⢠⠊⠀⠠⠃⠀⠀⠘⡄⠀⠀⠉⢢⠘⡄ ⢀⢃⠃⠀⠰⠁⠀⢠⠃⠀⠀⠀⠀⠇⠀⠀⠀⠀⢱⢸ ⢸⢸⠀⠀⡃⠀⠀⠘⠀⣤⣤⣤⣤⣴⣤⣤⣤⡄⡺⠚ ⠸⠬⠤⠤⢤⠤⠤⠤⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠐⠈⠁⣲⠘⠿⠿⠿⠿⡛⢿⡿⠿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠭⠂⠀⠀⠀⠀⡇⠀⠑⣄⠀⠀⠀ ⠀⠀⠀⠀⢠⡎⡤⠄⠒⢈⣉⣉⣸⠀⠀⠀⠉⣣⠀⠀ ⠀⠀⠀⠀⠀⠣⠔⠒⢹⠀⡜⠀⢸⠀⠀⠀⡜⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢧⠀⠚⠤⠠⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⢺⣾⡮⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠃⢨⠉⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡜⠀⡄⠀⢸⢰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠈⡈⡆⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠶⠶⠦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠞⢋⣉⠠⠀⠀⠀⠉⣉⡴⠖⢢⠈⠳⣄⠙⠲⠦⣀⡀⠈⠉⠛⠶⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⠛⢁⡤⠞⠉⠀⠀⠀⣠⠴⠛⠀⢀⡴⠃⠀⠀⠘⢆⠀⠀⠀⠉⠳⢤⣀⠀⠀⠉⠳⣦⡀⠀⠀⠀ ⠀⠀⠀⢠⡾⠋⢠⡜⠋⠀⠀⠀⠀⡠⠞⠁⠀⠀⢀⡞⠁⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠈⠓⢦⣄⠀⠈⠻⣆⠀⠀ ⠀⠀⣰⡏⠀⡴⠋⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠹⣧⠀ ⠀⣰⠏⢀⡼⠁⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⢹⡆ ⠀⡟⠀⡾⠁⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣿ ⣼⠇⢰⠇⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿ ⣿⠀⣿⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣄⣀⣀⣀⣀⣀⣀⣄⣤⣤⣾⣤⡿ ⣿⠀⣿⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⣼⠋⠈⠀ ⣿⠀⢿⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀ ⠛⠓⠚⠛⠒⠒⠒⠶⢶⣖⠲⠶⠶⠶⠶⠶⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⢤⡈⠛⠶⠤⣤⣀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⣄⠉⢹⡀⠀⢿⣿⣿⣿⣿⣿⣿⡿⣿⡏⠙⠻⣿⡿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠋⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⠤⣤⡟⠀⠀⠀⠀⠀⠸⡿⢦⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⣀⢀⣠⡤⠶⠚⠛⠉⠁⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⣷⠈⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠋⠁⠀⠀⢀⣠⣤⠴⢶⡶⠒⠒⠒⡿⠀⠀⠀⠀⠀⠀⠀⢻⡀⣾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⣈⣤⣧⠶⠟⢻⠁⠀⠀⣼⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠁⠀⠀⠀⣸⡇⠀⢀⡏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡿⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⡇⠀⢸⠃⡄⠀⠀⡈⢿⡀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇⠀⣿⢰⡇⠀⠀⠀⠈⠛⠲⠤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⣀⣿⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢹⡿⣿⣟⡟⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢿⠟⣾⠟⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢰⠀⠁⠀⢸⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⣼⠀⠀⠀⢸⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⢰⡇⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢸⡇⠀⠀⠀⠘⡇⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣸⠀⠀⠀⠀⠀⣿⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡿⠀⠀⠀⠀⠀⣿⡄⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠛⠉⠉⠉⣉⡉⠩⡉⠩⣉⡙⠒⠲⠤⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡴⠛⣡⠔⠊⠁⠀⣠⠔⠋⢁⠔⠁⠈⢢⠀⠈⠑⠢⣄⡀⠉⠓⢦⡀⠀⠀⠀ ⠀⠀⢀⡾⠋⡴⠋⠀⠀⢀⡴⠊⠀⠀⣠⠋⠀⠀⠀⠀⢣⠀⠀⠀⠀⠉⠲⣄⠀⠙⢦⠀⠀ ⠀⢠⠟⢀⠎⠀⠀⠀⣠⠊⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠈⠳⣄⠈⢧⠀ ⠀⡟⢠⠏⠀⠀⠀⡼⠁⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠆⠸⡇ ⢸⠃⡞⠀⠀⠀⣸⠁⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇ ⣾⢠⡇⠀⠀⢠⡇⠀⠀⠀⠀⠀⠃⠀⢠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠲⡾⠿⠃ ⣿⠸⠇⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⠁⠀⠀ ⠙⠓⠒⠒⠒⠒⠶⣖⡒⠒⠒⠒⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠤⠉⠛⠲⠦⡄⠘⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⣷⠀⠉⠉⠛⠛⠉⠉⠙⡇⠀⠙⢯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠉⠁⢀⣀⣠⠤⠤⠄⠒⠒⢲⠇⠀⠀⠀⠀⢻⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⠁⢰⠖⠚⠉⠀⢀⣀⣠⣤⠤⠤⣼⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡸⣧⣈⣠⠤⠖⢺⡋⠀⢠⠇⠀⠀⡏⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡞⠀⠀⠀⣧⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡇⡄⠀⠐⠘⠦⣀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣇⣸⣃⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢹⣿⣿⡟⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢘⠉⠋⠠⡼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢸⠀⠀⠈⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡟⠀⠀⠀⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⡇⠀⠀⠀⢧⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠇⠀⠀⠀⢸⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⡀⠔⠂⠀⠀⠒⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡴⠚⠀⠀⠀⡂⠭⠐⠒⠀⣣⠀⠀⠀⠀⠀⠀⠀ ⢠⢊⠌⠀⠀⠀⠀⠀⢂⠩⡤⠴⢇⠀⠀⠀⠀⠀⠀⠀ ⣎⠀⠀⠀⠀⠀⠀⡎⠀⢀⡰⣤⣀⣦⠀⠀⠀⠀⠀⠀ ⠙⣄⡀⠀⠀⠀⠀⠱⡄⠊⢻⣿⠛⠛⢖⡄⠀⠀⠀⠀ ⠀⠀⠉⠉⠉⡩⢕⠀⠈⠒⠒⢉⡆⠀⠀⢡⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠃⠬⠈⠩⢭⠤⠔⠲⡀⠀⢈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠘⡀⠙⠒⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢆⣱⣢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠢⠟⠏⡏⠒⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠚⣹⣦⢾⠁⠀⠀⢸⠒⠮⡑⠢⣀ ⠀⠀⠀⠀⢠⠊⠤⡊⠀⠀⠈⠀⠀⠀⠀⡇⠀⠜⠀⡜ ⠀⠀⠀⠀⠈⠢⡀⠈⠁⠒⢦⡀⠀⠀⠀⢸⠊⠀⣼⢄ ⠀⠀⠀⠀⠀⠀⡀⣱⣦⠀⠀⢱⠀⠀⠀⣀⠆⠰⠏⠜ ⠀⠀⠀⠀⠀⠀⠐⠍⣙⣃⣠⠎⠉⠉⠁⢨⠓⠒⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⢀⠤⡎⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⢰⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣉⢃⠀⣠⠁⠀⢠⠀⢀⣞⡉⡆ ⠀⠀⠀⠀⠀⠀⡰⠿⠀⠹⠛⠃⠀⡄⠘⡅⡜⢩⡿⡏ ⠀⠀⠀⠀⠀⠀⣿⢦⣦⣀⡀⠤⠔⠃⠄⢀⣀⣦⣶⠇

⣿⣿⣿⣿⣿⣿⣿⣧⣿⣴⣷⣟⠱⠟⡒⠿⠿⠦⢤⣤⡬⠍⠁⠠⠟⣿⣧⣤⣀⣸⣇⡀⠀⢠⣀⠟⠉⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿ ⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⢿⣧⣴⡆⣠⠀⠈⠙⣦⡴⠖⠋⠉⠁⠀⠀⠀⠈⠉⠳⢦⣄⠈⠀⠀⠀⠀⠀⣸⠴⠾⠛⠿⣿⣿⣿⣿ ⡣⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⢠⣅⣰⣶⠿⣿⣶⡄⢁⣈⢻⣿⣿⣿ ⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢫⡍⠙⣿⣷⣾⣿⣾⣿⣦⣽⣿⣿ ⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⢹⠀⠘⣿⣿⣿⣿⣙⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠿⣿⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⣬⣛⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣞⡁⠀⠀⠀⠀⣠⣴⠾⠿⣿⣶⣄⠀⠀⠀⠙⢦⡀⠀⠀⠀⢀⣴⡟⠉⠉⠁⣸⣿⠋⠉⠛⠿⠏⢻⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⢆⠀⠀⢀⡟⠁⠀⠀⠀⠉⠉⠳⠤⠀⠀⠈⣿⡆⠀⠀⠸⠉⠃⠀⠀⠀⣤⠀⠀⠀⢀⣀⡀⢸⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣿⣿⡀⠀⠈⣧⠀⠀⣇⠀⢤⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⢡⣾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡤⢬⣧⠀⠻⢄⣼⣶⡖⠒⣲⣶⢾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣷⣿⣿⣿ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣀⣦⡿⠀⠀⠀⠙⠿⠥⠴⢛⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿ ⣷⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⡄⠀⠀⠀⢀⣴⣶⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣷⣸⢿⣄⠀⠙⠧⣬⣿⠿⠟⠁⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⡇⣸⣿⣎⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢸⣏⣿⡹⣿⢸⣿⣆⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣻⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠻⠿⣿⣿⡆⠑⠂⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢀⣽⣿⢻ ⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⡃⠐⣿⣟⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢫⣴⣾⣿⣻⣿ ⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠘⣿⢿⣿⡧⢰⣿⣿⣯⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⢣⣾⣿⣿⣿⡟⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢹⡟⢶⣿⠿⣿⣿⣿⣾⣿⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠃⠀⠀⢀⣴⡾⠯⢞⣵⣿⣿⣿⣿⣿⠠⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢷⣴⣿⣿⣿⣿⡿⣷⡟⢷⡀⠑⢶⣤⣤⣤⣤⣴⣾⣿⡀⣀⣀⣴⣶⡿⠟⢉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣽⣿⣿⣦⡙⢦⡀⠀⠳⠬⠽⢯⣝⣿⣫⣹⠯⠄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠛⠛⠋⠹⢿⣿⡿⢿⣿⣇⠀⠀⢸⣿⣿⣿⣟⣿⣟⣿⣿⣏⣿⣾⣟⢦⣀⠀⠀⠀⠈⠁⠈⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢀⣀⣠⣤⣭⣽⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣤⣴⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠲⠦⠉⠉⠉⠏⠉⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠲⠃⢀⣤⠀⠀⠀⠲⠂⠀⠠⠆⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⢁⡴⠚⠉⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠔⠒⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡆⢰⠆⠀⠋⣠⠔⠉⠁⣀⡠⠄⠒⠂⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠁⠀⠀⠀⠀⠀⣠⡴⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⡜⠁⣠⠔⠋⢁⡔⠒⠒⠤⡀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢀⣀⣤⣶⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡆⡶⠀⠀⢀⡜⠁⢀⣀⢸⠀⠀⠀⠀⠈⢆⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⢀⡀⣴⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠘⠀⡞⠁⠀⠉⢇⠀⣿⣄⠀⠈⡆⠀⠕⠒⠉⣉⡒⡄⠀⠀⠀⠀⢀⠤⠊⠁⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⢇⠀⣤⡄⠈⢢⡈⠻⡖⢀⡞⣀⠔⠊⠁⠀⠀⠉⠐⠒⠠⢎⢁⡠⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢂⠘⢿⣦⡇⠉⠓⢶⡫⠞⠁⣀⣤⣤⣤⣤⣤⣤⣤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠦⠭⡇⠀⡠⠊⠀⣠⣮⣬⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⠔⡧⠊⠀⢀⡜⠁⠙⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣡⠎⠀⠀⢠⠊⠀⠀⠀⣸⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⣰⣧⣀⣀⡠⣴⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣤⣤⣾⡿⠿⠋⠁⠀⢹⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠛⠛⠛⠻⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡰⢤⣀⣀⡄⢠⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠃⠀⠀⠈⢻⡆⠀⠀⠀⣠⣾⡶⠿⠿⣶⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⢸⣇⠀⠀⣼⣿⠋⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⣼⠏⠀⢸⠏⡇⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⣠⣤⠶⠖⠶⠿⠛⠛⠒⠒⠒⠀⠈⠙⠲⠾⣯⣤⣤⣨⣸⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⡶⣿⡟⠉⠉⢥⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠛⠻⢶⡤⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⡽⠊⠁⠀⠀⠀⠈⣷⠀⠀⠀⢶⡾⢿⣿⣿⠛⠶⣦⡀⣀⣠⣤⣴⡶⣴⣤⣀⠀⠀⠀⠀⠀⠛⠉⠳⣦⡀⠀⠀⠀⠀⠀ ⠀⣰⣿⠏⠀⠀⠀⠀⣠⠄⠀⢸⡇⠀⠀⠈⠻⢿⣿⣇⣤⢶⠿⠁⢿⣅⣸⣿⣿⠀⠈⢻⡗⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀ ⢀⣿⡇⠀⣶⣿⡆⠸⣿⣿⠀⢸⣧⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠉⠻⠿⠷⠶⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⠀⠀ ⠀⣿⣛⠀⠈⠉⠁⠀⠈⢁⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡄⠀⠀⠀⠀⢹⡆⠀ ⠀⢹⣿⡄⠀⠀⠀⠀⠔⢃⣼⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⠙⢻⡧⠤⠤⢤⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠉⠻⢷⣤⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⣶⣤⠒⠿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢹⡄⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀ ⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣽⡀⠀ ⠀⣜⠁⠀⠀⠀⠀⠀⠈⠈⠙⣦⠀⠀⠀⠀⠀⢹⣟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⣡⣾⣿⣷⡄ ⠀⠉⠓⠦⠤⠤⠤⠤⠤⠴⠚⡁⠀⠀⠀⠀⣴⣾⣿⣷⣍⡓⠢⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠶⢾⣫⣴⣿⣿⡾⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣶⣤⣬⣉⣙⣋⣓⣒⣚⣉⣉⣥⣤⣶⣿⣿⡛⣿⡇⠨⠇⠘⢻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⡄⠀⠐⣿⠿⠿⠿⠛⠛⠛⣿⣿⣩⢹⠩⣿⡏⠉⠉⠉⢉⡉⣹⣿⠛⠉⠛⠀⣷⣶⣤⣦⠀⢸⣿ ⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⢀⣀⣀⣠⣤⣤⣶⠶⣟⣿⣶⣿⣾⣶⣿⣿⣄⢀⠰⣾⡿⡿⠿⠶⠶⣶⣶⣿⣿⣿⣿⠄⣾⣿ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢡⣿⣿⣿⣿⠁⣨⣷⣿⣭⣭⣿⣿⣿⣿⣿⣗⣝⣀⣀⣀⣠⣤⣀⣴⣿⣿⣿⣿⣿⣿⡇⢹⣿ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⣾⣿⣿⡟⠛⠛⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣦⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀ ⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣄⡀⠀⠀⠀⠀⢀⣴⣶⣿⣷⣶⣄⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣼⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣴⣾⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣠⣶⣿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢁⣴⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢿⣿⣿⣿⣿⠟⢁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠠⢄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠁⠐⠛⠫⡉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠁⢀⣠⣶⠯⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⢀⣠⣶⠟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠍⢑⡨⣴⣶⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⢀⠔⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢤⣼⠃⠀⠈⠈⣰⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⡄⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣘⣿⠇⠀⠀⠰⢚⣽⣿⡿⠿⣿⡆⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣀⠤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢽⡏⠀⢠⣴⣶⣿⣿⠙⡇⠐⣸⣁⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠊⠀⢀⣿⣿⠿⠉⠉⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠂⠀⠀⡼⢿⣍⠀⠀⠀⠀⠀⣠⠂⠀⢈⢿⣿⣿⣿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡔⠁⠀⠀⢰⣿⣿⣿⣷⣄⠀⢀⣼⣁⠀⠀⣼⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠎⠀⠀⠀⠠⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⡇⣮⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⣀⠀⠀⡠⠔⠺⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⢸⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠉⠉⠀⠙⠿⠿⠋⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠑⠁⠀ ⠀⢀⣠⣤⡀⠀⠀⣠⠞⠁⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⡆⠊⢡⠀⠀⠀⠀⠀⠀ ⠈⢿⠿⣯⢈⡟⠋⡆⣄⠀⠀⠀⠀⠀ ⠀⢀⠁⡱⠕⠐⠎⠪⣈⠆⠀⠀⠀⠀ ⠀⠈⠋⠀⠀⠀⣠⠴⣤⠺⣥⠀⠀⠀ ⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠱⣄⠀ ⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠘⡇ ⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢸⠁ ⠀⠀⠀⠀⢀⣜⣂⠀⠀⠀⠀⢀⣎⡀ ⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠉⠉⠉⠉⠉⠙⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⠬⣍⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢮⣙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠈⠳⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠈⢳⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⢠⠏⢀⡴⠒⡆⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⢿⣆⠀⠀⠐⣆⠀⠀⠀⠀⠙⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⠿⠿⠿⣿⡟⢠⡾⠋⢹⢷⡆⠀⣀⡄⠀⠈⠞⠀⠀⣻⠀⠘⠦⠾⠃⠀⣠⠞⠑⣿⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠸⣆⠀⠀⠘⢧⡀⠀⠀⠀⠘⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢠⡿⠁⡟⠀⠀⣼⠿⠁⠀⣼⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡴⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⣸⣿⡀⠀⠀⠈⢿⣄⠀⢠⠖⠻⣏⣿⡿⠿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⠃⠀⠻⠤⠞⠁⠀⠀⢠⡇⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢠⣞⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣧⠀⠀⠀⠀⢿⣧⣸⡀⠀⠘⠿⣧⠀⠁⠈⣿⣿⠘ ⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⣠⠏⠈⠓⢤⡀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠈⢿⣿⣧⠀⠀⢀⣿⡄⠀⠀⣿⣿⠀ ⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠉⠳⢤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠈⣿⡏⢧⣀⣸⡟⣷⠀⠀⢿⣿⠀ ⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⢿⡄⠀⢸⣿⠀ ⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⢸⣷⣶⣿⣿⣿⣿⣿⣶⣤⣀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢸⡾⣷⣾⣿⣿⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠀⠀⠀⢀⡽⠿⢽⣿⢿⣷⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠈⡇⡟⠛⢻⣿⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣰⠋⢠⡤⣄⠝⣆⠉⠉⢣⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣷⡇⠀⢸⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⣧⠀⢸⣄⡟⠀⣿⠀⠀⠈⢧⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠹⣄⠀⠘⣧⣀⣈⣀⡴⠋⠀⠀⠀⠘⣆⠀⡇⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⣿⡇⠀⢸⡧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣇⡠⠙⢦⡀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⢸⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠢⣄⠀⢸⠻⡄⠀⢷⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢚⠀⠝⢦⣻⣿⣶⡆⠀⠀⠀⠀⠸⡇⠀⢸⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣹⡇⠀⠀⠀⠀⢠⠁⠀⠘⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡞⣁⣴⡽⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿⡏⠁⠀⠀⠈⠙⠲⠤⢤⣀⣀⣀⣀⣤⣴⣶⠀⠀⠀⠀⠀⠀⠀⣸⣽⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠀⠀⠀⠀⠀⠀⢠⡿⡏⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣿⠻⣦⡀⠀⠀⠀⠀⠀⠈⠉⠓⠶⠤⣄⣀⣀⣀⣀⣠⠶⠋⠀⠀⠀⠀⠀⠀⣠⣿⠿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣷⠀⠀⠀⢠⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢻⣿⢿⠉⠳⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⣸⠃⠀⠀⠀⠀⣹⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠙⡇⠀⠀⠐⣷⡀⠀⠀⢺⣼⡄⠀⠀⠀⠀⠀⠘⣿⢻⠀⠀⠀⠀⠉⠓⠢⠤⣄⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⡤⠶⠛⠋⠀⠀⠀⢀⣿⠀⠀⠀⢸⠀⣻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠀⠀⠹⣆⠀⠘⡏⠻⣄⠀⠈⣿⣷⠀⢰⡀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣿⣿⣯⡉⠉⣉⠉⠁⢀⣶⠀⠀⢀⣶⠂⢸⡟⠀⠀⢠⡏⢀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣸⣦⡀⢳⠒⠛⠷⣄⢹⣿⣆⠘⣧⡀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⠋⠉⠻⣾⣿⠀⣠⡾⣻⠀⢀⣿⣧⣶⣿⠃⠀⠀⣾⡇⣸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⢞⣁⠀⠀⣈⣛⣠⠤⠤⠬⣉⣿⣿⣆⣿⣷⣄⠀⠀⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⠀⠀⣰⠟⣿⡴⠋⢙⣷⡶⠛⢻⡿⠯⡼⠀⢀⣼⣿⣇⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡴⠋⠀⠀⢈⡽⢿⣅⠀⠀⠀⠀⠀⠀⢻⡈⠛⢿⣧⣙⣷⣀⢸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠘⠀⢻⡀⣠⡿⠞⢛⣷⡟⠛⠉⣻⡿⠿⢦⣤⠇⢀⣞⠁⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠋⠀⠀⣀⡴⡋⠀⠀⠹⣆⠀⠀⠀⠀⠀⢀⣧⣤⠴⠟⠙⠳⡿⠷⣿⣿⢿⡓⠲⠤⣄⡀⠀⠀⣀⢈⣿⠏⢀⡼⠋⠉⢙⡷⢚⡿⠃⠀⠀⢻⡴⠻⡜⣧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

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▕╮╭┻┻╮╭┻┻╮╭▕╮╲ ▕╯┃╭╮┃┃╭╮┃╰▕╯╭▏ ▕╭┻┻┻┛┗┻┻┛ ╰▏ ▕╰━━━┓┈┈┈╭╮▕╭╮▏ ▕╭╮╰┳┳┳┳╯╰╯▕╰╯▏ ▕╰╯┈┗┛┗┛┈╭╮▕╮┈▏

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣩⣭⣉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢁⣀⠀⣀⡈⠙⢢⡀⠀⠒⠒⠂⣀⡤⠖⠒⠒⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢰⣿⣿⡿⠛⠃⠀⠀⣹⠀⠀⠀⠸⡇⠀⠀⢰⣶⣤⣀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⠏⠉⠁⠀⢀⡠⠞⠋⠀⠀⠀⠀⠻⣄⠀⠀⠨⢿⣿⡷⠄⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠿⡀⠈⠀⢀⣀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠹⣷⡆⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⢀⠝⠋⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⢠⢏⣴⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠙⠢⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⢀⡏⡞⢸⡄⠨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠸⡇⡇⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⢳⡄⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⡇⣷⠈⠉⢷⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡧⣾⠃⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⢸⡘⡆⠀⠙⣆⠀⠈⠑⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⢰⣿⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⣳⣳⠀⠀⠘⣆⠀⠀⠀⠀⠉⠙⠛⠿⠶⢤⣤⠤⠤⠤⠤⠶⠆⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⣼⢏⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⢀⣠⠴⠚⢉⣡⣡⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⠇⢀⡄⠀⠀⠀⠀⠀ ⣇⡤⠖⣉⣀⣠⣴⠞⠋⠁⣷⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢞⠗⠁⣠⠟⠀⠀⠀⠀⠀⠀ ⡧⣚⠿⠛⠉⠊⠁⠀⠀⠀⣿⡄⢈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠂⠁⠀⠈⠁⣀⠔⠁⠀⠀⠀⠀ ⡏⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠳⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⡀⢀⠀⠰⢾⣿⡀⠀⠙⣆⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⠇⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⡠⠊⠁⠀⠀⠘⠈⣿⣧⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢀⡇⠀⠀⠀⠸⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠘⡆⠀⠀⠀⠀⠘⠼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⢄⠀⣧⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⢀⣀⡤⠤⠴⢲⠃⠀⠀⠈⠳⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠈⢧⢹⡄⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠈⠉⠉⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠈⠀⠉⠙⠒⠒⠒⠀⠐⠒⠀⠀⠀⠀⠀⠀⠈⠀⢷⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⣠⠴⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⣿⣷⣤⡀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⣠⠞⠁⠀⡇⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⣾⡟⠛⠉⠙⠳⢦⣄⣧⠀⠀⠀⠀⠀⠈⠧⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⣼⠃⠀⠀⢀⡴⠊⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡟⠸⡇⠀⠀⢸⠛⣧⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⣸⠃⠀⢀⡴⠋⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣼⠁⢰⢿⠀⠀⡏⠀⠘⣷⡄⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠸⡏⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⣰⠃⡀⡀⢸⡇⠀⡇⠀⠀⣸⣷⡀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⠀⠀⢰⠃⠀⠀⠀⢸⡇⢸⢃⣤⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣰⠏⠀⠀⠀⠀⢹⡇⣼⣿⣿⡿⠉⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣰⠋⠀⠀⠀⠀⠀⠈⢡⣿⡿⠟⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢘⣿⠧⠀⠀⠀⠀⠀⠀⠒⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⢀⣸⣥⡤⠶⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣭⣥⣽⣶⣿⣿⣷⣦⣤⣤⣤⣤⣤⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢶⡲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠑⡌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⣆⠀⠘⣎⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⣇⢀⠈⢾⣧⡀⠀⠀⠀⣀⣀⠀⠀⠀⣀⣀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠞⣉⣲⣞⣿⡙⠋⠀⠀⣿⡏⠉⣉⣭⠁⠀⠉⠉⠁⠀⠄⠈⢁⣠⠞⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡴⠚⠉⠀⢉⣉⡛⠉⠉⢲⣶⣾⠟⣿⠀⢠⣒⠒⠒⢢⠄⠀⠀⠀⣀⡞⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⠾⢅⣀⣀⠤⠤⣄⣉⣀⡠⠔⠋⠀⢀⣴⠯⢤⣀⣈⡩⠥⠤⣀⡠⠤⣞⠁⠀⢀⠤⡀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣄⠀⠠⢴⡄⠀⠀⠀⠈⠷⣆⣐⣶⠟⠁⠀⠀⠀⣀⣤⠖⠒⡦⢄⡀⢘⡆⢀⠏⠀⡷⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀ ⠀⢨⣷⢁⣸⠄⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⡨⠧⠴⢇⡀⠉⠸⡀⠈⠣⠴⠃⠀⢷⡀⠀⠀⠀⠀⠀⡠⢚⡅⡇⠀⠀⠀ ⠀⣧⣞⣩⣤⡀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⢀⣀⡈⢆⠀⠱⡄⠀⠀⣤⡆⠀⢻⣿⠟⠉⠛⢿⣤⣿⠀⡇⣀⣀⠀ ⠀⢸⢾⣿⣿⡇⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠸⣿⣿⣿⡼⠀⠀⢸⠀⠀⠙⠃⠀⣸⠃⠀⠀⠀⢀⣿⡏⢀⣿⣿⠹⢳ ⠀⠈⠲⢍⡁⢀⣀⠴⠋⡠⢂⡄⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⣨⠽⢛⡁⠀⠀⠘⣆⠀⠀⢠⣾⡇⠀⠀⢀⣤⣾⣿⡇⢸⠛⡧⢆⡎ ⠀⠀⠀⠀⠹⣏⣁⠴⠊⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠊⠉⠀⠀⠈⠀⠈⢢⠀⣿⠘⡷⠒⠒⠻⢷⣾⣿⣇⠘⠋⣀⡎⠀ ⠀⠀⠀⠀⣴⠉⠀⠀⣀⠞⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⠛⠁⠀⣴⡀⠀⡇⠀⣿⣿⣟⠙⣿⠀ ⠀⠀⠀⠀⠈⠒⠚⡏⠁⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⠿⠿⠟⠀⠀⠀⢀⣀⡀⠀⠀⠈⠓⣄⠀⠀⠉⠀⠀⣣⠀⢸⣿⣿⣶⣿⠇ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⡾⣿⠿⠛⠋⣁⣀⠤⠤⠒⠃⠀⠀⠣⠄⠀⠀⠀⠀⠀⠸⣄⣀⡀⠀⠀⢧⠀⠀⣿⠿⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡰⠻⣉⠠⠔⠚⠯⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⠀⠀⠀⢱⣴⣴⡾⠖⠊⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⢰⠁⠀⠀⠀⠀⠀⢀⣤⣿⣶⣶⣦⣤⠖⠒⠒⠒⠒⠒⠒⠒⢲⣶⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠇⠀⠀⠀⠀⠀⠀⢈⡿⢋⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⢋⡿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢏⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣾⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠒⠲⣿⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠔⢂⡉⠁⠤⠉⢈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡠⠊⠄⢀⠨⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠰⢠⠀⢊⠠⠒⣈⠠⠄⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠉⠉⢁⡜ ⠀⡀⠀⢂⠔⠁⠰⠉⠁⠢⡀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠀⢀⣤⡴⠞⠋⠀ ⠘⡄⠀⠊⠘⠉⠙⡄⢷⡀⢱⠀⢒⠀⠐⣄⠀⢀⡠⠐⢁⠠⠐⠈⠈⠁⠀⠀⠀⠀ ⠀⠈⠐⠀⠒⡘⢧⡸⠂⢭⡮⠂⣁⡀⣀⡀⣀⠼⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠨⠊⣃⡠⠊⡠⢾⣾⣟⣻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⡢⠊⢀⠌⠀⠀⡟⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣁⣠⣊⠴⠒⢪⠔⠀⡁⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠄⠒⠒⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⡀⢀⢀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡣⠑⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣮⠙⠓⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⡵⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢴⡯⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⣶⣿⣿⣷⣦⡀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢀⠔⢔⠊⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⡟⠉⢙⢟⢵⢿⠗⢨⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣿⠛⠙⢏⣑⠖⡱⣮⠄⠁⢀⡾⢀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠓⠒⢉⡵⣊⡴⣃⣠⠄⠉⣠⠞⢡⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠖⢠⢔⣡⠞⠋⠀⠐⠶⡖⣀⡀⠘⠩⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠃⢺⡿⠋⠁⠀⠀⠀⠀⠀⠈⠁⠴⢄⠐⠧⣠⣞⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡾⠟⠈⣿⡿⠃⠺⠷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⢿⡋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣛⡃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣩⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⣤⢲⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⡶⣰⠤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠒⠁⠁⠀⠀⠀

⠀⠀⠈⢻⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⣿⡿⠟⠻⠟⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡟⣿⣿⠁⠀⠀⠀⠀⠺⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⡇⢸⡏⠀⠀⠀⠀⠀⠀⠘⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣷⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⣿⣿⣿⣂⣀⣀⣀⡀⠀⠀⠀⠀⠀⠹⣞⡇⠀⠀⠀⠀⠀ ⠀⠀⡿⠟⣛⡟⠉⠁⠀⠀⠀⠉⠓⣆⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀ ⠀⢀⡇⠐⢚⠶⠀⠀⠀⠶⠋⠁⠀⠹⣣⡀⠀⠘⣿⡄⠀⠀⠀⠀ ⠀⠈⣷⣶⣾⣶⣦⠀⢰⣿⣿⣿⣿⡿⠁⢣⠀⠀⢿⡇⠀⠀⠀⠀ ⠀⠀⢽⠾⣿⣧⣿⣦⡘⢧⡾⠿⠿⠂⠀⠘⡇⠀⢽⡇⠀⠀⠀⠀ ⠀⠀⠸⡇⠀⠈⡏⠀⠳⠀⠀⠀⠀⠀⡆⠀⡇⡆⢈⣇⠀⠀⠀⠀ ⠀⠀⠀⣿⡀⠀⢈⣷⣃⣀⠀⠀⠀⠠⠁⣸⠇⠀⠸⣿⠀⠀⠀⠀ ⠀⠀⠀⠹⣯⡀⠈⢩⣉⡍⠁⠀⠀⢀⠜⠛⠁⠀⢈⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣦⡀⠙⠁⢀⣠⠶⠋⠀⠀⢠⢠⣸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⡟⣷⠒⠋⠁⠀⠀⠀⣄⠀⢨⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⣿⠁⣿⠀⠀⠀⠀⠀⢰⡿⠃⣾⠛⠢⣄⠀⠀⠀ ⠀⢀⡔⢱⣿⡿⣿⣅⡅⠀⠀⠀⠀⣰⡿⠁⣰⣿⠈⠉⠀⠉⢦⡀ ⢀⣿⡧⠏⣼⣧⣽⣿⡇⠀⢀⣤⡾⠋⠀⣠⣿⣿⣴⢳⡄⠀⣤⡇ ⠈⠉⠀⠀⠻⣿⣿⣿⣷⣾⣯⣁⣀⣠⣾⣿⣿⠋⠀⠀⠙⠟⠛⠀ ⠀⠀⠀⠀⠀⡽⣿⣿⣿⣯⣡⣤⣶⠟⠋⢹⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠃⠈⠛⣿⢿⣿⡿⡇⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠀⠀⠀⣸⠄⠀⠀⢹⡀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡉⠉⠉⠁⠀⠀⠀⠛⠤⠤⠤⠐⠃⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠉⠉⠉⠐⠠⢀⣀⠤⠐⠂⠀⠒⠠⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢀⡠⠤⠤⠤⣀⠀⢣⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠁⠀⠀⠊⠁⠀⠀⠀⠀⠀⠉⠚⢆⠀⠀⠀⠀⠀⠐⠒⠠⢀⠀⠀ ⠀⠀⠀⣀⢴⠁⠀⠀⠀⠀⢀⡠⣂⠭⠓⠒⠒⠒⠠⠵⣤⠲⠬⠉⠛⠋⠉⠼⢷⡄ ⠀⠀⡜⠁⠈⠀⠀⠀⢰⣚⣒⣈⣀⠠⢤⡴⣶⣤⡈⠉⢱⠄⠒⢀⣽⣿⣿⣍⠉⠻ ⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠨⡑⠤⣀⣾⣿⣿⣽⠿⠤⡢⠤⠀⣸⡿⠿⠶⠿⣦⠎ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⢒⡲⠎⠉⠀⣀⠀⠀⠀⢀⡠⠔⠁⠀ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠉⠋⠉⠀⠑⢄⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⡰⠉⣀⣀⣉⠉⠐⠒⠂⠤⠤⠄⠀⠀⢀⣀⠠⠤⠐⠊⡽⠀ ⢃⠀⠀⠀⠀⠀⠀⡄⠣⠤⠤⠤⠄⣈⣉⠁⠐⠒⠒⠒⠀⠀⠀⠀⠒⠒⠒⡪⠀⠀ ⢈⣦⣀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠐⠒⢒⡲⠒⠈⠀⠀⠀ ⠀⠊⠑⠫⢕⡒⠠⠤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠄⠂⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠀⠀⠠⠤⠤⠤⠐⠒⠉⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⡖⠐⡆⠀⠀⠀⠘⣿⣿⣿⡇ ⢷⠀⢶⢶⣶⠖⣶⣦⡀⠀⠸⣇⠀⠀⠘⢯⣙⣛⡾⢁⡜⠀⠀⠀⠀⢸⢿⣿⣿⣿ ⠎⠣⣈⡓⠂⠐⣿⢻⡷⡄⠀⠈⠓⠤⣀⣀⠀⠠⠔⠉⡠⠀⠀⠀⠀⠀⠀⠙⠛⠁ ⠀⠀⠈⠉⠉⠀⢠⡎⠱⣳⡀⠀⠢⣀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠑⠢⠤⠖⢩⣷⢠⣇⢧⠀⠀⠀⠉⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣽⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⢙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣦⡄⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣔⢄⡀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣦⠹⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠕⢁⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣧⠹⣿⣦⡀⠀⠀⠀⢀⣠⣤⠶⠚⢉⣀⣴⣾⡿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣧⠻⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⢧⣙⠿⢿⣿⢿⡿⠿⣋⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣧⣴⣷⣞⠛⢷⡿⠓⠶⣿⣿⣦⣄⢀⣤⣤⣭⠉⠁⡀⣼⢿⣟⣓⢠⡀⠀⢸⣇⠀⠀⠀⢀⡀⢸⠞⠋⠀⠀⠀⠀⠀⠀⠁⠈⠀⣙⣻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣶⡟⠀⣠⡀⠀⠀⠋⠻⢷⣄⠁⣈⣠⣶⠶⠛⠛⠉⠉⠉⠉⠛⠳⢦⣄⡈⠙⠂⠲⠀⠀⠀⠀⠀⠀⢰⡖⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿ ⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣹⣿⣿⣿⣆⣼⣇⠀⠀⢀⣼⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⣄⠀⣀⢀⣠⣴⡟⠉⠉⢀⠈⢹⣿⣿⣿⣿⣿ ⣛⢢⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⢠⣤⣤⣽⣟⠛⠿⠿⢿⠆⠀⢤⡈⢻⣿⣿⣿⣿ ⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⠟⣍⠉⠻⣿⣿⣶⣾⣿⣷⣿⣿⣦⣽⣻⣿⣿ ⣿⣯⡀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢸⡟⣆⠀⠘⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿ ⣿⣿⣷⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢻⣿⣿⣿⠀⢙⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣇⣿⠀⠀⣹⣿⣿⣿⣿⣶⣶⣾⣿⣼⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠛⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠰⠟⠁⢶⣬⣍⣤⣶⠿⣿⣿⡿⣿⣿⣿⢿⣿⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡀⠀⣠⣞⡉⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠉⠈⠁⣀⣾⣿⡃⢉⡙⠻⡿⣿⠸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⠟⠻⣦⠀⠀⠀⠀⢰⡿⠟⠁⠀⠀⠈⠙⠛⠻⣦⡀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⣾⠛⠷⠀⠀⠀⠀⠉⠉⠉⠀⠈⠀⠀⢐⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣿⣿⠀⠀⠈⢷⡀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⣼⣿⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⢀⣤⡒⣴⡖⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣴⣿⣿⣿⡄⠀⠀⠀⣷⡀⠀⠸⣧⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣷⡿⢠⣿⣿⣿ ⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⣈⣳⠀⠀⢻⡄⣠⣷⣶⡟⢛⠛⢳⣶⣾⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣿⣿⣿⣿ ⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⣌⣿⠃⠀⠀⠀⠻⣿⣝⡃⠼⣾⠾⠃⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿ ⣇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠷⢼⣿⠏⠀⠀⠀⠀⠀⠀⠉⠉⠩⠥⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿ ⣿⣿⣿⣿⣿⡻⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡆⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣟⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⢠⣿⡄⠀⠀⢤⣠⠊⠿⣿⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⠷⢟⣾⡛⣿⣆⠀⠀⠙⠳⠶⠿⠛⠋⠁⠀⠀⠀⠀⠒⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣿⢀⣿⣿⣷⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⢿ ⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢠⣿⢸⣿⢹⣿⡇⢻⣟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢿⡿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⠟⣷⣿⣪⣻⣇⢺⣿⢻⣆⠠⢄⡀⠠⠤⠤⠶⠶⠛⠛⠛⠛⠛⠛⠂⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠣⢺⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣟⣿⠘⠻⠸⣿⣽⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⠀⢠⣾⣿⡇⣸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣧⣿⢿⣷⡉⠀⠸⣿⣿⡈⣷⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢋⣤⣶⣾⣿⠉⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣿⡿⣾⣿⣧⠀⢰⣿⣿⣿⢹⣿⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⢇⣴⣿⣿⣟⢿⣿⠿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠹⣇⣿⠙⣿⣥⣿⣹⣿⣿⣟⣙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⣀⣤⡶⢋⡵⣣⣾⣿⣿⢿⣿⣿⡏⠀⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⡎⠻⢿⣟⢹⣿⣷⣿⣿⠟⢿⣧⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠋⠀⠀⠀⠀⣠⡼⣿⣛⠒⢋⣴⣿⣿⣿⣿⣿⣿⣿⡄⣛⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠘⣷⣾⣿⣿⣿⣿⣿⣿⠻⣿⣏⠙⣧⠀⠈⠳⣖⣶⣤⣤⣤⣶⣶⣟⣫⣒⡈⢠⣤⣤⣾⣟⣻⠗⠋⣀⣶⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿⣝⣿⣿⣿⣿⣿⣋⣷⣿⣿⣧⡌⢷⣄⠀⠈⠙⢥⣤⣍⣻⡟⡛⢻⠛⢛⢻⣿⣑⠇⠉⣉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾ ⣿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣏⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣦⡨⣷⣆⡀⠀⠀⠂⠀⠈⠓⠾⠉⠟⠛⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿ ⣀⠀⠀⠀⠛⠛⠛⠛⠛⠛⣻⣟⣧⠀⠀⠀⢸⣟⣿⣾⢿⣧⣿⣿⣆⣿⡿⣿⣼⣿⣿⣿⣎⣻⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠤⡤⠤⠤⠤⣤⣼⠀⠀⠀⠈⣿⣟⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠶⠟⠛⠛⠛⠛⠛⠻⠶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⡿⠋⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⠅⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⠁⠄⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⡏⠀⠀⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⡇⠀⠀⣀⣿⣦⠴⠶⠛⠛⠛⠛⠛⢻⠶⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣠⡿⠋⠁⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⣠⠔⠉⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⠁⠀⠀⠀⠀⠀⣠⠔⠁⠀⢀⡠⠚⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠶⠶⠶⠶⢶⣤⣤⣀⠀⠀⠀⠀⠀ ⠀⢹⣯⠀⠐⠀⢀⡠⠊⠁⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣄⡀⠀ ⠀⣾⡿⣇⣀⠔⣉⣤⡴⠖⠛⠛⠉⠉⠙⠛⠳⢦⣤⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆ ⣸⣿⠀⣻⣷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻ ⣿⠿⣶⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾ ⣿⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣦⣤⣴⣶⡶⠶⠤⠤⣄⠀⢀⣠⣾⡟ ⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢿⣿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠿⠛⠁⠀ ⠀⠻⢷⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⢶⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⠛⢛⣫⣯⣭⣭⣭⡽⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⡇⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠉⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⠇⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⡟⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡇⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⢰⣿⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠿⣷⣄⣹⣆⠀⠀⣀⣀⣀⣼⠟⠁⠀⠀⢸⣿⣄⡙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠙⠻⠿⠿⢿⣷⣶⣶⣶⣶⣾⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠟⠛⠿⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠱⠀⠀⠀⠀⠈⠜⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠘⢺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠋⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣯⡀⠀⠀⣤⣀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣿⣿⣶⣶⣿⡿⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⢦⡄⠁⠈⢛⣧⣞⡀⠀⠀⠀⠀⠐⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⣾⠉⠁⠀⠀⠈⠙⠲⠶⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠻⣶⠖⠋⠀⠘⣧⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠳⠶⠶⢦⣄⣀⣿⠁⠀⣴⣾⠁⣤⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠃⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⣄⠉⢹⡆⠛⠁⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⢹⡄⠀⠀⠻⢾⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣍⠻⣿⠿⣤⣄⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠐⠈⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⢿⣦⣤⣼⠀⠀⠈⡿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠈⣵⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣄⠀⣼⠁⠀⠈⠛⠶⣄⠀⠀⠀⠀⠀⠀⠀⡠⣾⣿⡿⠀⠀⠀⢸⡇⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠘⠾⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⣼⣿⣿⠟⠁⠀⠀⠀⠈⣷⠀⠀⠀⠸⡇⠀⠀⣠⡶⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠻⣅⡤⠒⠂⠀⠀⠀⠀⠸⡇⠀⠀⠀⣇⢠⡾⠋⠀⠀⠀⠀⠀⠀⠂⢻⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⠳⣦⠀⠀⠀⠀⣠⠀⠀⠀⢠⢷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣰⠏⠀⠀⠀⠀⠈⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠷⣤⣄⡀⠀⠀⠀⣾⣩⡥⠀⠀⠀⠀⠀⠙⠳⠶⠶⠾⠋⠀⠀⠀⠀⠀⠀⢀⣠⢿⠹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠐⠤⣭⣛⠲⢦⣤⣌⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠛⣫⠥⠚⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⢠⡌⠉⢙⠛⠲⠦⠌⠉⠉⣉⣉⡛⠛⠛⠋⠉⠉⠉⢁⠤⠒⠀⠊⠉⠀⠀⠀⢈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⢰⣿⠟⠉⠉⠹⣿⣿⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⣤⣦⣤⣄⡠⠊⠀⠀⠀⠀⠀⠀⠿⣄⣀⣀⢠⣿⠏⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢼⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀ ⠘⢧⣀⠀⢉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⣿⠿⢦⡀ ⠀⠀⠈⡏⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣧ ⠀⠀⠀⡇⠀⠀⠀⢀⡀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⠀⠀⠀⢃⠀⠀⣼⣿⣿⣠⣤⣶⣿⣿⣉⡟⢻⣿⣿⠛⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠁⠀ ⠀⠀⠀⢘⣄⣠⣿⣿⣿⣿⣿⣿⠟⠛⠛⢿⡟⢻⡟⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣤⣿⡿⠋⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢁⣠⣴⡾⠿⣿⠟⠛⠛⠻⠿⢿⣿⡿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⡶⠒⠉⠁⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠟⠉⠻⢶⣄⡀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⢿⠏⠀⠀⠀⠀⠈⠙⣷⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠿⠿⠶⠶⠶⠶⠶⠾⠿⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣽⣿⣿⣾⠏⠀⠀⠀ ⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⣀⣀⣀⣠⠴⠛⠒⠤⠴⠚⠉⠀⠉⠉⠀⠀⠈⠛⠲⢄⠀⠀⠀⠀⠀ ⠀⢀⡤⣖⠒⠚⠋⠉⠉⠛⠛⠁⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⣀⣀⠀⣈⣓⣦⠀⠀⠀ ⠀⢸⠀⠈⠛⠉⠉⠑⠦⠤⠤⢤⣀⣀⠀⢀⣀⣀⡠⠴⠚⠢⠤⠤⠖⠋⠀⠉⠓⠚⠁⠀⠈⠉⠁⠀⣨⠇⠀⠀ ⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣾⠀⠀⡞⠁⠀⠀⠀ ⠀⣾⠁⠀⠀⠀⠀⠀⣠⣾⣿⠀⢨⠇⠈⢣⡀⢀⣳⣄⣀⣞⠀⠀⢀⣸⣄⣰⡀⢀⠀⠈⠁⠀⢰⠃⠀⠀⠀⠀ ⠀⢹⡄⠀⠀⠀⠀⠸⠿⠟⠁⢰⡋⠀⠀⢀⠟⠉⠀⠀⣀⣈⠓⣾⠋⠀⠀⠀⠉⢻⡀⠀⣠⠖⠁⠀⠀⠀⠀⠀ ⢀⡜⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⣷⠀⢠⡏⠀⠀⢠⣿⣿⣿⣇⠈⡇⢠⣾⣿⣷⡀⣧⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⢸⡁⠀⠾⠃⠀⠀⠀⠀⠀⠀⡴⠻⡷⠸⡇⠀⠀⢸⡘⡿⢯⡟⠀⡞⢸⣿⣿⣿⠃⡏⢀⡇⠀⠀⠀⠀⠀⠀⠀ ⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠁⠀⠹⣄⠀⠀⠙⠛⠉⢀⡼⢧⣄⣙⣫⡥⠚⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠇⠀⠀⠀⠀⠀⢀⣤⠀⢀⡼⠀⡄⠀⠀⠈⠛⠒⠤⠴⠚⠋⢦⡓⠦⣤⣤⣤⣤⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⢯⡀⠀⠀⠀⢀⣼⣿⡿⠀⣞⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⣀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⡇⠀⠀⠀⠸⠿⠋⠀⠀⢘⡆⠀⠀⠠⠖⠚⠉⡽⠉⠛⠒⡖⡖⠒⠚⣿⠉⠁⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡎⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⡀⠀⠀⠀⠸⠓⠒⠒⢴⡇⠛⠒⠒⣻⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡆⢀⣤⠀⠀⠀⠀⠀⠘⣆⠀⠉⠁⠀⠀⠀⠈⠒⠒⠒⠋⠁⠀⠈⠉⢽⡆⠸⡧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠃⠉⠁⢀⣤⠤⢤⣀⡀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠛⠓⣾⣧⡆⢙⡇⠀⠀⠀⠀⠀⠀⠀ ⠻⢤⣀⠀⢺⠀⠀⠀⠈⠙⠓⢦⣀⣠⢤⡄⠤⣤⣤⣴⣿⠋⢣⡞⢁⣀⣠⣤⡿⢿⡝⣯⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣏⡑⠺⣆⠀⠀⠀⢠⡶⠷⠿⠤⢤⣽⣎⣠⣿⣯⣽⣷⣾⣿⣿⣿⣿⣿⡟⠉⠙⣮⠷⢦⣀⠀⠀⠀⠀⠀ ⠀⠀⣟⠹⣟⣺⣦⣀⠀⡟⢛⣷⣲⣶⡶⢥⣴⣤⣤⣤⣤⣈⣉⣩⣿⣿⠛⠛⠓⠤⠴⠃⠀⣜⠻⣟⣻⣲⡄⠀ ⠀⠀⢿⣧⣿⡿⠿⣿⢿⣷⣿⠿⠿⠿⢧⣀⣙⣉⣭⣿⣿⡿⠟⣛⣿⠏⠛⠛⠓⠲⢶⡀⢠⣌⠳⣌⠻⢿⡁⠀ ⠀⠀⠀⠀⠉⠛⠿⣦⣸⣇⣀⣠⣴⢾⡟⠛⠉⠁⠀⠙⢻⠛⡟⠛⠁⠀⠀⠀⠀⠀⠀⠙⢦⣙⠳⣌⠳⢦⣹⡆ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣶⣾⠃⠀⠀⠀⠀⠀⠸⡧⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠿⠟⠿⠿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣹⡇⠀⠀⠀⠀⠀⠀⠀⢠⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢛⡇⠀⠀⠀⠀⠀⠀⣴⣿⣤⣷⣄⣠⣴⣾⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⠃⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣍⣽⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣾⣦⣀⣴⣾⣿⣷⣄⠙⠛⠿⠽⠻⠿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠯⠛⠻⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣶⡄ ⠀⣠⣶⣿⣿⣶⣄⣠⣾⣿⣷⡄⣶⣿⣿⣿⣿⣿⣿⠃ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢣⣿⣿⡿⠿⠛⠉⠀⠀ ⠀⢻⣿⣿⣿⣿⣿⣿⠿⣫⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⣿⡿⢟⣡⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⢿⠿⢋⣴⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⣿⣿⡿⠀⠀⢻⣿⣿⣿⣿⣆⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⡿⠁⠀⠀⠀⢻⣿⣿⣿⣿⣆⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣆⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠘⠻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠙⠻⠟⠋⠀

⠀⠀⠀⠀⣴⠶⠶⠶⠶⠶⠞⠛⠛⠛⠶⠶⠶⠒⠛⠛⠒⠶⠶⠶⠒⠒⠒⠒⠶⠶⠖⠚⠓⠶⢦⣤⣤⣴⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⡇⠀⠈⠋⠁⠀⠀⠀⠈⢙⠷⠦⣄⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡇⠀⠀⡀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠈⠙⠲⢤⣸⣄⣤⠴⠖⠛⠉⠉⠁⠉⢢⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣷⠀⠀⠃⠀⠀⠀⡎⠀⠀⠀⡴⠋⡉⠲⡀⠀⢻⡏⠀⠠⠒⠐⠲⡄⠀⠀⠀⢇⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⢀⣀⣤⠤⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠸⣿⠂⡇⠀⣸⣇⠀⡇⠸⣿⠇⢸⠀⠀⠀⡜⠀⠀⠀⠀⢸⡇⢀⣀⣀⡤⠞⢋⣡⡤⣄⠈⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠙⠲⠶⠊⠀⡔⠉⠉⢳⡘⠢⠤⠔⠁⠀⠀⣰⠃⠀⠀⠀⠀⢀⡟⠉⠉⢳⣤⠾⠋⠁⠀⠸⡆⠘⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠠⠀⠀⠀⢀⡈⠳⢤⣀⣀⣀⠤⠒⡇⠀⠀⢠⠧⣄⣀⣀⣀⡠⠞⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⠈⡿⠀⠀⠀⠀⣀⡇⠀⢧⣀⡀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠀⠀⠉⠓⢒⣂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣠⣴⠞⠃⠀⠀⠀⢸⠁⡀⠀⠀⠀⢹⡆ ⠀⠀⠀⠀⣠⡼⢧⠀⠀⠀⠀⢀⠄⠊⣹⣿⣿⣿⠋⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠉⠁⠀⠀⠀⠀⠀⠀⢸⡟⠑⠀⠄⢰⣸⠇ ⠀⢀⡴⠟⠁⠀⠈⡀⠀⠀⠀⠁⠀⠀⠉⠛⠿⠃⢰⣿⣿⣿⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠾⠶⠋⠀⠀ ⢠⡟⠀⠀⠀⠀⠰⡇⠀⣦⠀⠀⠀⠀⠀⠤⠤⢄⡀⠉⠉⠁⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢷⡼⠉⡦⠀⢠⣿⠀⢉⣤⣀⠄⣀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⠁⡼⠤⠤⠋⢸⣤⡜⠁⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⠁⣸⣀⡤⠔⠊⢉⣠⣄⣀⠀⢀⡸⡾⢏⡉⠉⠓⢒⢶⠶⠶⠶⣶⡒⠲⠶⠦⢤⠤⠒⠒⠶⢤⣤⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣀⣠⣤⠴⠖⠚⢹⣇⣙⣒⣒⡧⠔⠀⠀⠈⠁⠒⠁⠈⢢⠀⡔⠀⠑⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣤⣤⣤⣤⣤⠈⢩⣭⣭⣭⣭⠏⠀⠘⣭⣭⣭⣭⡉⢉⣭⣭⣭⣭⣭⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⢄⠀⢀⠊⠉⠉⠉⠀⢀⠽⢛⡙⠟⠛⢉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣤⡤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣧⣤⣤⣤⣀⠀⠁⠀⢸⣀⢴⣶⡿⠠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠲⣤⣀⣀⠀⣁⣼⣿⣃⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⢻⠟⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⡼⠃⣼⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⡖⢋⣽⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣾⣿⡿⠋⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⣹⠟⢋⣽⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⣿⡥⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⠭⠛⠩⢍⠉⠉⠉⠉⢉⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⣶⡶⠒⠀⣱⠀⠀⢞⠁⠠⣤⣈⠲⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡇⠘⠁⢀⠄⠊⠁⠀⠀⠈⠢⡀⠙⢿⡀⣁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢔⠈⢀⠜⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢈⣀⡋⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⡎⢾⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠀⠀ ⡇⠀⠀⠀⣿⡈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣰⠀⠀⠀⠀ ⡇⠀⠀⠀⢰⢃⠘⢇⠈⠒⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠋⡿⠀⠀⠀⠀ ⡇⠀⢀⡠⠐⣋⠀⠈⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀ ⣇⣪⡥⡴⠊⠁⡇⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠺⠋⠔⢁⠀⠀⠀ ⠇⠁⠀⠀⠀⠀⣿⠐⢕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠚⠀⢀⠠⠂⠁⠀⠀⠀ ⠀⠀⢀⠀⠀⠠⢿⡆⠈⢎⠀⠀⠀⠀⠀⠀⠀⠀⡠⢫⠃⠀⢰⡅⠀⠀⠀⠀⠀⠀ ⠀⠐⠀⠀⠀⠀⠈⢷⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⠁⢸⠀⠀⠀⠺⡀⠀⠀⠀⠀⠀ ⠁⠀⠀⣀⠠⢤⠀⠀⠣⢄⣀⠀⠀⠀⠀⠀⠸⠁⠀⠆⡇⠀⠀⠀⢁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠀⠀⠀⡠⢤⠀⠀⠀⢀⠀⠀⠀⣿⣦⣀⠀⢣⠀⠀⠀⢠⠀⠀⠀⠀ ⠀⠀⠀⡘⠀⠀⡠⠊⠀⢸⠀⠀⠀⡜⣇⠀⢰⢿⠁⠈⠉⠺⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠁⡠⠊⠀⠀⠀⢸⠀⠀⢠⠁⢺⠀⡆⠈⢧⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢩⠊⠀⠀⠀⠀⠀⢸⠀⢀⠃⠀⢸⡆⣇⣴⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠊⠀⠀⠘⢳⣿⠟⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡇⠀⠀⡀⠀⣲⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣠⣴⣶⣏⣉⣀⣀⣀⣀⣀⣀⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣖⣊⣉⣁⣀⡀⠀⠀⠀⠀⠉⠉⠒⠦⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠤⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⢄⡀⠀⠀⠀⠈⠳⡀⠀⠀ ⠀⠀⠀⡰⠁⠀⠀⠀⠀⢀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠹⡀⠀ ⠀⠀⠀⢱⡒⠂⠒⠒⠒⡾⠁⠀⠀⠀⠀⢀⣀⠤⠖⠒⢤⡀⠀⠀⠑⣄⠀⠀⢣⠀ ⠀⠀⢠⣾⣿⡏⠒⣄⠀⠧⠤⠤⠤⠒⠊⠉⠀⠀⠀⠀⠀⠉⢢⡀⠀⠘⡄⠀⠘⡆ ⡤⠤⢾⣙⠛⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⣤⣤⣀⠀⠙⡄⠀⣧⠀⠀⡇ ⠘⢦⡀⣹⠉⠉⠉⠀⢿⠳⡦⣤⣄⣀⡀⠀⠈⢇⠀⠿⣿⠏⢣⣠⠃⢀⣼⣀⣀⡀ ⠀⠀⢹⠃⠀⠀⠀⠀⠘⢦⣁⡏⢠⡏⣹⠄⠀⠈⠑⠒⠒⠒⢻⠏⠀⡸⠀⠀⡰⡇ ⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⡷⠒⠊⢀⠇ ⠀⠀⠀⠀⠀⠈⠑⠢⠤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣤⡤⢴⠏⠀⠀⡰⠹⣄⠀⡜⠀ ⠀⠀⠀⢠⠎⢩⠓⠢⣄⠀⠈⡟⢫⠉⣩⠋⠁⠀⢸⡀⢏⣀⣀⠜⠁⠀⠘⠶⠁⠀ ⠀⠀⠀⢸⠀⠘⠚⢠⠋⠉⠉⡇⠈⡿⠟⠉⢳⣀⣀⠑⡆⠀⠘⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠣⠤⠔⠳⠤⠄⢼⠁⠀⡇⠀⣠⠇⠀⠈⠙⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠈⠉⠉⠙⠦⣀⣀⣀⣀⣀⡼⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠁⢀⠔⠀⠒⢤⡔⠈⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠀⡇⠀⠀⠂⢀⠂⠀⠂⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠑⠤⠀⠠⠊⠐⠤⠤⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠀⠀⠀⣀⣴⣶⣿⣿⣷⣦⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡎⠀⠀⠛⠻⠿⠿⠿⠿⠿⣿⣿⠛⠛⠛⠉⠀⢰⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀ ⢠⠇⠀⠀⠀⣠⠆⠀⠀⠀⠀⢁⣀⡠⢤⣼⣛⣲⣯⣭⣭⣭⠿⣆⠀⠀⠀⠀⠀⠀ ⡎⠀⠀⠀⡰⠃⠀⣀⡤⣖⠪⢿⣶⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠘⡄⠀⠀⠀⠀⠀ ⣇⠀⠀⡼⣁⢴⡪⠗⠉⠀⠀⠀⠻⠟⢋⣿⣿⣿⣿⣿⡆⠀⠀⠀⢳⠀⠀⠀⠀⠀ ⠘⢤⣼⣋⠗⠁⠀⠀⠀⠀⠀⠀⠀⣤⣘⣿⣿⡿⣿⣟⣥⠖⠀⠀⢨⣿⣦⣀⠀⠀ ⠀⢸⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⡿⠟⠋⠁⠀⠀⠀⡼⠁⠀⠈⠑⢆ ⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⣠⣦⡀⢠⣄⣠⠤⠷⣀⡠⠶⢄⣀⣼⣀⠀⠀⣀⣀⠜ ⠀⠀⠀⠈⠉⠒⠤⠄⣀⣰⣿⣿⣷⣿⡟⠁⠀⠀⠈⠱⡄⠀⠀⠀⠉⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠤⢀⣀⣀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⣠⠔⠚⠉⠉⠲⢦⣤⡴⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢾⣯⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⢀⡞⠁⠀⠀⠀⠀⠀⠀⢹⣧⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⠤⣤⠆⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⢀⣤⣖⣿⠏⠉⠿⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢶⣶⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠟⠉⠀⠀⠀⢀⣘⠿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠈⠂⡄⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⢀⣠⡴⠞⠉⠉⠀⢻⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠢⠀⠁⠀⠀⠀⠀⣼⣿⡏⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣷⣄⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⠀⠀⢀⣠⢤⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠀⠀⣾⣭⣿⣿⣿⣿⣶⣦⣝⡓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⢟⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠀⠀⠀⠀⠀⢀⣤⠀⠀ ⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠑⠫⢝⡛⠿⡿⢿⣿⡡⠖⠁⠀⠀⣈⠛⠶⢤⣀⡀⠀⠀⠀⠀⣀⣤⣾⠿⠛⠁⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⢁⣿⡿⠀⠀⠀⣠⡾⠋⠀⠀⠀⠛⠹⠯⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⢀⣴⣿⡟⠅⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢈⡦⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⠁⠈⠳⣤⣄⡀⠀⠀⠀⣿⣟⠀⠀⣾⠃⠀⠀⠀⢀⡔⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡔⡼⠁⠀⠀⠀⠈⠒⠢⢤⣦⣴⣿⣿⣄⣸⣟⠀⠀⢀⣤⢾⡄⠀⠘⠛⢷⠀⠀⠀⣀⣠⡤⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠊⣼⠁⠀⠀⣀⣤⣤⣤⣴⣿⠋⠀⠀⠙⠿⢧⣉⣙⣛⣻⣄⠀⠉⠀⠀⢰⠟⠒⠛⠩⠰⠂⠀⢻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⣸⡃⠀⣰⡾⠋⠁⠀⢠⡟⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢦⡀⠈⣷⡀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠖⠒⠛⠟⠛⣿⢿⡄⠀⠀⠀⠘⠿⣤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠘⢧⡀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⠉⠉⠉⠉⠉⠒⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⠋⠀⢀⣠⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⢀⡞⠁⠰⣾⡟⠛⢻⣿⣿⣿⣽⣿⠛⠀⠀⠀⠀⠀⠀⠀⣴⣦⣤⡀⠀⠀⠀⢧⠀ ⠀⠀⢀⠞⠀⠀⠀⠀⠙⠓⠊⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣷⣦⠀⠸⡄ ⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣟⠻⣿⡷⠀⡏ ⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⣇ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠴⠃⠀⠀⠀⠀⠰⠂⠀⠀⢰⠇ ⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀ ⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣏⡹⠿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄ ⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡻⢶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽ ⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃ ⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤⠤⠤⢀⣀⣀⣀⡀⣿⣀⣀⣀⠤⠤⠴⠒⠚⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣷⣷⣿⣙⡅⣛⠒⠶⢞⢁⡺⠿⠔⠘⠦⣀⠢⠋⠀⠀⠀⢀⣼⣿⣿⣿ ⣣⣿⣿⣿⣿⣿⣿⣷⣿⣿⡋⡠⠊⠁⠀⠀⠀⠀⠀⠀⠙⢆⣤⣶⣺⢦⣀⡘⣿⣿ ⣿⣨⣿⣿⣿⣿⡿⣿⣿⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡄⢻⣿⣿⣻⡿⣿ ⣿⣿⣿⣿⣿⣿⡇⢉⠿⠊⠀⠀⣀⣤⣀⠀⠀⠠⡀⠀⠀⠊⡨⠥⠞⣿⠿⢿⡿⣿ ⣿⣿⣿⣿⣿⣿⢷⣾⠑⢄⠀⠼⠁⠀⠉⠓⠤⠀⢹⡆⠀⠚⠃⠀⠨⠉⢈⣀⡄⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣄⣘⡆⠸⣈⣤⠤⢤⣴⠎⠁⠀⠀⠀⠀⠀⠀⠀⠈⣻⣼⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡏⠴⠏⠀⠈⠛⠺⠍⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠ ⣿⣿⣿⣿⣿⣿⢿⣯⣷⡀⠠⢚⣿⠿⠛⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿ ⣿⣿⣿⣿⣿⠏⢸⣼⣷⢿⡀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿ ⣿⣿⣿⣿⡟⠀⣿⣿⡾⢼⣽⡐⠂⠀⠉⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⣠⠏⣽⣟ ⣿⣿⣿⣿⡇⠀⢸⣿⣧⢸⣷⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣱⣿⣷⢿ ⣿⣿⣿⣿⣿⠀⠈⣏⣺⣻⣿⣗⣧⠢⢀⡀⠀⣀⣠⠐⠈⣀⣠⡾⣱⣿⣿⣿⣯⣾ ⣿⣿⣿⣿⣿⡆⠀⢸⡿⣿⣿⣾⣷⡕⣄⠙⠽⠿⢻⢷⠟⢋⣥⣾⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⣉⣉⣻⠀⠸⣿⣿⣿⣾⣿⣿⣿⣷⣆⣀⣀⣠⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⡀⠀⡀⠀⢀⡴⠋⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠘⡄⡇⠀⠈⡇⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⢀⣼⠆⠀⠀⠀⢿⣦⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠉⠀⠀⠀⣐⣿⡿⠀⠀⠀⠀⠈⢿⡶⣄⠀⠀⠈⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠶⢶⣿⡽⠛⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡶⢶⣋⣥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⣀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡶⠛⠋⠉⠉⠙⠻⣦⡀⠀⠀⠀⠀⣠⣾⠟⠋⠉⠉⠙⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢸⣿⠇⢀⣏⣀⣀⣀⡀⢿⠀⢸⣿⠇⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣼⣳⣄⠀⠀⠀⠀⢀⣠⠞⠋⢀⣀⣀⠉⠛⢧⣀⠀⠀⠀⠀⠀⣠⣟⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⣻⠿⠋⠀⢠⡾⠉⠀⠀⣙⢦⡀⠈⠻⢗⡒⠚⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢿⣿⣿⡀⣼⣿⣿⡗⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠚⢻⡁⠀⠀⠀⠀⠀⠀⠈⠙⢻⠛⠉⠁⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⠶⠶⠿⠤⠼⢧⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⠴⠶⢴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠂⠀⠀⢀⣼⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣴⣾⣷⣿⣆⠀⠀⠀⠀⠀⠀⣠⣶ ⣦⣤⡼⣀⢹⣿⣿⣿⣿⠿⢿⣿⣿⣦⠄⠐⠿⣿⣶⣾⣷⣶⣴⣶⣷⣶⣤⣶⣾⣶⣶⠿⠷⠤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣼⣿⣿ ⣿⣿⡇⠠⢿⣿⡿⠋⠀⠀⠀⠀⠀⠃⠀⠀⣀⣁⣠⣤⢥⣤⣤⣼⣧⣤⣤⣭⣄⣀⣉⠀⠀⠀⠹⡄⠀⠀⡄⠈⢻⣿⣿⡥⠄⣠⣿⣿⣿⣿ ⣿⣿⣿⡀⠈⢿⣷⣤⣴⣄⣀⣤⡷⠶⠟⠛⠛⠛⠛⠃⠀⠀⠙⠉⠙⠛⠛⠉⠁⠋⠛⠛⠷⢶⣦⣧⣀⣀⣹⣄⣀⣿⣿⠁⢠⣿⣿⣿⣿⣿ ⣿⣿⣿⣷⡄⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⡿⠛⠋⠀⣰⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣤⣤⣄⣀⣄⣤⣀⣀⣄⣄⣀⢀⣀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣥⣶⣶⣾⣿⣿⣿⣿⣿⣿⠒⠀⠀⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡀ ⣤⣄⠀⠀⢀⣄⣀⣀⣀⣀⣀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣇⠀⠀⠀⠀⠀⠈⢹⣿⡉⢿⣿⣿⣿⣿⠏⣿⡿⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣿⣿⣿⣿⣿⣿⣿⡇ ⢻⣷⠀⠀⠘⣿⡝⣿⣿⣿⣿⣿⢩⣿⣿⣿⣿⡀⠀⠀⠀⠀⠘⢧⣿⡀⠀⠀⠀⠀⠀⠈⠻⣷⡃⢈⣉⢁⡀⣿⠟⠁⠀⣀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣸⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢻⣧⠀⠀⠹⣷⣌⣛⠟⠋⠀⢸⣿⣿⣿⣙⣿⣦⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠁⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠋⣿⣎⣿⣿⣿⡿⠏ ⣷⢀⠻⢷⣄⠀⠀⠙⠛⠓⠒⠒⣚⣳⣿⠸⣿⣹⣿⢰⠀⠀⠀⠀⠀⠀⠙⠻⣦⣤⣀⡀⠀⠀⣀⣀⣀⣠⣤⠴⠛⠁⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠙⠛⠉⠀⠀ ⠈⠈⠀⠈⠛⠿⣶⣦⣤⣤⡤⠤⠟⠉⠙⡃⢿⡟⣷⢸⣇⡀⠀⠀⠀⢂⠀⠀⠀⠉⠉⠉⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⣤⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⡇⠀⠻⣌⠗⡇⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⢿⠇⡄⠀⣿⣴⠻⣆⠀⠀⠀⠀⠀⠉⠲⣤⣀⠀⠀⠀⠀⣠⣤⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠷⠶⣤⣤⣤⣤⡶⠟⠋⢁⣟⣠⡇⠀⣿⣷⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠸⢿⣿⡇⠀⣿⢻⣌⣇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⣰⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⣅⢀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣵⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣎⠙⠦⣄⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠄⠀⠀⠀⠀⠀⠀⡀⢀⣼⣟⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠘⢿⣦⣄⡀⠀⠀⠠⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⣠⠟⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⢻⣿⣿⣧⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣋⣤⠾⠃⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣖⡭⠞⠋⠁⠀⢀⣰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢻⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⣒⡯⠟⠛⠉⠀⠀⢀⣠⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢻⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠚⠉⠛⣩⠕⠊⠁⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢻⣿⣷⠹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠻⣿⣧⡘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠙⢿⣿⣦⣌⡛⡛⠿⠿⠿⠿⠿⠻⢿⠿⠿⠋⠉⢁⣴⢿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠿⠛⠒⠒⠯⠽⣳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢳⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡙⢦⠀⠀⠀⠀⠀⠀⠀ ⠛⢿⡒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣷⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢦⣀⢉⣑⡒⠤⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⠁⠸⣿⣿⣷⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣄⣀⣀⣀⠀⠘⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠀⠈⠙⠒⠤⣄⡀⠉⠉⠛⠒⠒⠤⣤⡟⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⠟⠉⢻⣿⣿⣿⣿⣿⣿⣭⣿⣿⡿⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣄⣀⠀⠈⢹⡆⣀⠀⠀⠈⠉⠿⠟⠽⠅⠀⣀⡈⠻⣿⣿⣿⣿⣿⣿⣿⠏⠀⡾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢺⡁⠀⠁⠀⠈⠙⠒⠤⢄⣀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠁⠠⠰⣇⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⣀⣀⠀⠀⠀⠀⢀⣠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃⠀⠉⠉⠉⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⣀⠀⠀⠀⣀⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀ ⢨⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⢸⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀ ⢠⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀ ⢸⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀ ⠘⡇⢸⣿⣿⣿⣿⣿⣿⣿⡏⠙⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠋⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⢈⣿⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⢸⠉⠛⢿⣿⣿⡿⢛⣿⣿⠀⠀⠀⢸⡷⢦⣄⡀⠀⠀⠀⠀⠀⠘⠻⠶⣦⣀⣀⠈⠙⢳⣄⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⢸⡀⠀⠀⠙⢿⣿⣿⣿⡇⠀⠀⠀⠀⣷⠀⠀⠙⠓⠶⠶⠒⠲⠦⣤⣄⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠟⠿⣿⣿⣷⣄⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀ ⠘⡇⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⠀⢸⡄⢀⣠⣤⡀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣤⣤⣤⣀⡶⢶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⢤⣄⡀⠀⠀⠉⠛⠷⣄⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⡄⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠈⣧⠚⠁⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣬⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠃⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣄⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠶⠶⣤⣀⠀⠀⠀⠀⠸⣾⡛⠶⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠾⢿⣿⣦⠀⠀⢀⡴⠿⢦⡀⠀⠀⢰⡇⢀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⣀⣈⠙⠳⠦⣤⣌⣙⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠳⣞⠉⣾⠻⣾⠛⠛⠛⠛⠛⢒⢦⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⣧⣀⠀⠀⠀⠀⠙⢷⡟⠒⠋⠀⣀⣤⣀⣀⣹⣬⠇⠀⠉⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⠶⣤⣀⣀⣤⠖⠛ ⠀⠉⣻⣶⣦⣄⣀⣼⠀⠀⠀⣼⠋⠁⠀⠈⠉⠙⠲⣦⣀⠀⢂⣙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢀⣤⠞⠋⠁⠀⠀⠀ ⠛⠉⠉⠁⠀⠀⠈⣿⠀⣠⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣼⠾⠃⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣩⡾⠋⠁⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⡀⠀⠀⠀⣸⡆⠯⠿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡾⠋⠀⠀⠀⠀⠀⠀⠀⣠⡾ ⠀⠀⢩⣿⣿⠿⠛⠉⢻⡄⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣰⢾⡿⣆⠀⠀⠀⢀⣀⣠⣤⠴⠶⠚⠛⠛⢛⣻⣝⠛⠛⠛⠒⠲⢤⣤⣼⠋⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠾ ⠀⢀⡼⠋⠁⠀⠀⢀⣠⣽⣄⠀⢒⡙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⠉⠁⠈⠓⠒⠚⠋⠉⣴⣿⡿⣀⣠⣤⣤⣼⣷⣭⣀⣀⠀⠐⢶⣻⡗⠉⠙⢶⣄⣠⣤⢤⡶⠛⠉⠉⠀⠀ ⢰⠿⠥⢤⣶⠖⠛⠉⠁⠀⠈⠳⣭⡀⠀⠀⠉⠙⠲⠶⠶⠶⠶⠶⠶⠛⠁⠀⣴⣾⣷⠀⠀⢀⣠⡾⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢺⢧⣄⠀⠀⢠⡤⣤⡄⠈⢷⡀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⣹⠟⠋⠉⠓⠲⠦⣤⣯⣻⠀⢀⣀⣀⣀⣙⠛⠋⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⠀⠺⠶⠋⣀⣠⡼⠧⣤⣶⡶⠶ ⠀⠀⠀⠘⣿⡷⠶⣤⡀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠂⢀⣉⠳⣄⠀⠀⠻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠉⠛ ⠀⢀⣰⠟⠋⠉⠓⠀⢹⡄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠀⠀⠈⢷⣄⡴⢺⡷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⢠⡞⠳⣤⡤⣄⣀⡀⠀⠀⠀ ⠀⢸⡾⠲⢤⣤⣤⡴⠻⣆⠀⠀⠀⠀⠈⠛⠒⠲⠦⠤⠴⠶⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠉⠻⣭⡀⠀⠉⠓⠲⠦⠤⣤⡤⠤⠤⠶⠚⠋⠁⠀⡀⣠⡴⠋⠀⠀⠈⠛⢦⡉⣹⡷⠒⠒ ⠀⠘⢷⣄⡀⠀⠀⣀⣠⣟⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣀⠀⢾⣹⠗⠀⠀⠀⢀⣀⣤⠶⠛⠹⣿⠶⣄⡀⠀⠀⠀⠙⢿⡄⠀⠀ ⠀⠀⢸⡋⠉⠉⠉⠉⢀⡿⠀⠀⠀⠀⠀⠉⠉⠉⠀⡾⠉⠉⠉⠉⢻⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠋⠉⠉⠙⣇⠀⠀⠀⠸⣶⢿⣽⣷⢦⣀⡀⠀⠙⢦⡀ ⠀⠀⠀⠛⠶⢤⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⣄⣀⡀⢀⠏⠀⡼⠃⠉⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠸⣟⣷⠇⢀⣾⠟⠓⠦⢤⣷ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠈⠉⠛⠤⠸⣅⣀⠀⠀⢠⠏⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⢦⡀⠀⠀⠀⠀⣸⡟⢦⣀⠀⡿⠋⣠⡾⠋⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠤⣄⡀⠀⠀⠉⠙⠲⠟⠀⠀⠈⠓⠀⠀⠀⠀⢀⡾⠉⠀⠀⢈⡇⠀⠀⢀⣴⠟⠀⢀⣍⡛⠃⣰⢿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠦⣄⣀⡤⠴⠆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡾⠁⠀⢀⣾⠋⠀⢀⣿⣿⠇⢰⡿⢸⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡟⢶⠶⠶⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠖⠋⠀⠀⠀⣼⢃⡤⠞⠋⠙⢧⣀⡿⠁⠈⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⠈⠳⣄⠀⠀⠈⠙⠳⢦⣤⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡿⠋⠀⠀⠀⠀⠈⣿⠁⠀⠀⢻⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠉⠉⠉⠉⠙⠒⠦⣄⡀⠀⠀⠀⠀⣀⡤⠤⠖⠒⠲⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⣄⣀⡀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣸⣄⡀⠠⠤⠤⠄⠀⠀⠠⢤⣤⣀⣇⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣋⣭⠭⠭⠤⠤⠤⠤⣍⣉⠳⣄⣀⠤⠴⢒⣊⣉⡭⢭⣍⣁⣒⣒⡿⣦⡀⠀ ⠀⠀⠀⠀⢀⡴⠚⢹⠁⠀⠀⠀⠀⠀⠀⢀⣤⠴⠚⣩⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⣻⠖⠚⠉⠉⠀⠀⢀⣀⣀⣀⣀⣈⣉⣻⣿⣀ ⠀⠀⠀⢠⠏⠀⠀⣾⠀⠀⠀⠀⠀⠀⣶⡛⠓⠒⠉⠀⠀⣀⣀⡤⠴⣶⣶⣿⣯⣍⡉⠀⠀⠈⢳⠴⠒⠒⠉⠉⣽⡿⢿⣿⣿⣦⡀⠈⠉⢻ ⠀⠀⢰⠏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⣯⡉⠉⠁⠀⢠⣾⣿⣴⣿⠟⢿⣿⣆⠀⢠⠇⠀⠀⠀⠀⢸⣿⣿⣿⣟⢻⣿⣷⠀⢀⡼ ⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣈⠓⠦⢄⣸⣿⣿⣿⣿⣷⠾⠿⠟⠒⣩⠗⠒⠒⠤⠤⠿⠿⠷⠿⠿⠛⠛⠛⣿⠟⠁ ⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠶⠤⠤⠤⠤⠤⠤⣴⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠋⠁⠀⠀⠀⠀⠲⢤⣀⣀⣀⣀⣀⠤⢴⡊⠁⠀⠀⠀⠀ ⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀ ⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠉⠉⠛⠒⠒⠦⠤⠤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠖⠋⣻⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠐⠶⠶⠶⠶⠦⢤⣄⣀⣀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⢀⣰⠟⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠘⠦⠤⠤⠤⠤⢤⣀⣀⡀⠀⠀⠉⠉⠙⠛⠒⠒⠲⠶⠶⠶⠤⠤⠤⠴⠶⠶⠒⠒⠒⠛⢻⡄⠀⠀⠀ ⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒⠶⠤⠤⠤⠤⠤⠤⠤⣀⣀⣀⣀⣀⣀⣀⣀⣠⠼⠋⠀⠀⠀⠀ ⢠⣼⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠠⠈⠛⠶⣭⡙⠲⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠉⠛⠶⢤⣄⣈⡉⠙⠓⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⣶⠾⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠛⠋⠁⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠉⠉⠉⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠴⠒⠋⠁⣤⣴⣶⣶⣤⠀⠀⠀⠈⠙⠲⠤⠤⠤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢯⠀⠘⠻⣿⣿⣷⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠢⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣀⣤⡼⢿⣟⣿⡄⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⣀⠀⠀⢹⡘⣧⠀⠀⠀⣼⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠀⠀⠀⠀ ⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣍⠳⢤⣀⢿⣹⠂⠀⠀⠉⢿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀ ⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠽⡟⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀ ⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢻⣶⣖⠋⠛⠻⢿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀ ⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠻⢿⡙⠶⢤⣀⠈⢿⡻⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣾⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠉⠓⠲⢶⡭⣿⣿⣄⡈⠛⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀ ⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢹⠇⠀⠀⢀⣀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠉⠀⠽⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠸⣄⣀⠀⡼⠉⠳⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⣀⠀⠀⠀⠀⣯⡉⠓⠦⣄⣉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⠶⡶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠈⠳⣶⢤⣤⣼⣿⣶⣤⣀⠈⠉⠓⠲⠤⣤⣀⣀⠀⠀⠀⣀⣠⣤⡶⠛⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠹⣆⠈⠉⠛⠿⢯⣍⣉⡓⠲⠶⠤⣤⣤⣌⣩⣽⣿⡿⠛⠉⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠸⡆⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⠶⠶⠶⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡄⠀⣧⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠤⠤⠤⠤⠤⠴⠶⠶⠶⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠒⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠤⠖⠚⠳⢦⡀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠳⠤⣄⣀⣀⣀⣀⣀⡤⠤⠴⠖⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡐⠉⠉⠉⣑⠂⠒⠊⠉⠶⡄⠈⠉⠓⠉⠉⠁⠁⢠⠖⠦⡉⠐⠒⠒⠊⠒⠐⢒⠢ ⡄⢂⡁⠸⠱⠉⡀⣁⣰⣟⠁⠀⠐⡀⢈⠐⢈⠁⠈⠘⣆⠀⠐⠈⢀⠀⠻⠣⠀⢀ ⠐⡄⣁⣐⣤⣲⣴⣿⣭⣈⡙⠲⣄⠀⠂⢈⠀⣠⡶⢛⣙⣿⣦⣥⣂⣌⣐⣀⡌⡎ ⣾⠝⣩⣿⣿⣿⣿⣿⣿⣟⣿⣦⠈⢳⡀⢠⡾⣣⣶⣿⣿⣿⣿⣻⣿⣿⣍⠉⢦⡁ ⡟⢰⣿⣯⣿⣿⣿⣿⠀⢨⣿⣿⣷⠀⢿⣟⣰⣿⣿⣿⣿⣿⣟⠉⢹⣯⣿⣧⠀⢻ ⡇⢾⡿⣽⣿⣿⣿⣿⣿⣿⣿⣯⣿⡇⢸⡇⣿⡟⣾⣿⣿⣿⣿⣶⣿⣿⣞⣿⠀⢸ ⡇⢻⣷⡻⣿⣿⣿⣿⣿⣿⣿⣹⡿⢀⣿⡆⢿⣿⢽⣿⣿⣿⣿⣿⣿⡿⣻⡿⠀⣼ ⣿⣀⠻⣿⣍⣟⡿⢿⣟⣛⣾⠟⣡⣾⠏⣷⡘⠿⣷⣛⠿⡿⠿⢿⣻⣼⡿⠁⣴⠟ ⠈⢻⣦⣥⣋⡛⢟⠻⢛⣋⣥⡼⡟⣼⡃⡿⣹⢦⣍⡛⠿⠿⠿⠿⢛⣡⣤⠟⣿⠈ ⠀⢸⡯⣝⢻⢳⠾⠶⣾⢟⡏⢇⡱⣻⡇⣧⠉⠞⡻⠷⠶⣶⠶⢶⠞⡛⠩⣰⡟⠀ ⠀⢸⠇⠈⢃⠊⠁⠃⠂⢈⠐⠠⣜⣿⡀⢿⡀⠐⢀⠉⠑⣸⢿⡌⠐⠈⠀⢿⡁⠀ ⠀⢸⡇⠈⠈⠃⠐⠀⢂⠀⢤⡿⠽⣿⠀⡿⠹⣆⠀⠠⢱⠏⣞⢻⡄⣞⢀⠏⠀⠀ ⠀⢀⣿⡄⠰⡶⣬⡐⠀⣠⡟⡠⢙⣿⠀⡽⠀⡸⢦⠄⣿⠘⣾⣤⠇⠈⡞⡀⠀⠀ ⢀⡞⠈⢧⣤⣬⣥⣄⣀⣻⢾⣥⣎⣿⠀⢼⣀⣛⣏⣤⣭⣳⣞⣉⣀⣀⠇⢸⠀⠀ ⠀⠛⢾⢿⣄⣀⣤⣀⣉⣉⠳⢤⣞⡗⠀⢾⠙⣭⠖⠋⠀⠁⠉⠉⠉⣿⣶⠂⠁⠀ ⠀⢀⣾⢽⣿⣿⣿⣿⢿⣿⣿⣿⣿⡇⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⠀⠀⠀ ⠀⠀⣼⢫⣿⣞⣷⣯⣟⣾⣽⣾⣽⣿⣶⣿⣯⣟⣾⣳⣯⣿⣽⣳⣯⣟⣿⠀⠀⠀ ⠀⠀⡝⣠⢛⡟⠯⡿⣟⣯⣟⣷⠏⠉⠉⠉⠉⢻⡿⣟⣯⣟⢿⢏⡟⢤⣻⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⠤⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠰⡜⢠⠂⠀⠀⠀⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⡀⠀⡇⣎⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢠⡤⠴⠚⢧⡀⠁⣮⣴⣦⣀⡀⢠⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠈⠶⢸⡋⠹⠿⢋⡇⠀⢿⡛⢿⣿⣷⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⡞⠀⠀⠀⠀⠈⢉⠩⠟⠀⠀⠀⡿⠮⠉⠀⠙⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⢧⡀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⡇⠀⠀⢀⡼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⢹⠒⠢⢤⠀⢀⣾⢶⣆⠀⠀⣿⠀⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢸⠀⠀⢸⠀⡜⠀⠀⣠⣍⣭⡈⡆⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⢤⠏⠀⠀⣸⠀⠀⠀⠀⠃⠰⣯⠴⠧⢾⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⠴⠒⠋⠉⠁⢰⠋⠀⠋⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⢲⠒⠚⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡴⠟⠉⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠢⠤⡀⠀⠙⣆⠀⠀⠀⠀⠀⠀ ⣞⣁⣤⣄⣀⣀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣀⠀⠀⠀⠀⠀⠀⣁⢀⣀⡼⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠸⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⡶⠀⠐⠚⢹⠍⠀⠀⠈⠋⠳⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠄⠀⠙⢆⢓⡇⡠⡀⠀⠀⠀⠀⠀⠀⢚⡁⠀⠀⣠⣎⠀⠀⠀⠀⠀⠀⠹⢷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣶⣾⡯⠉⢙⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇ ⣤⡄⠀⢠⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣰⣶⠀⠀⠀⠀⠈⢿⣟⢿⣿⣿⣿⢿⣿⠃⠀⣸⠃⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣧ ⠻⣇⠀⠘⣿⠻⣿⣿⡿⢹⣿⣿⣿⣆⠀⠀⠀⠘⢾⣆⠀⠀⠀⠀⠈⠻⣧⣤⣤⣤⡿⠃⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⡿⣿⣿⣿⣿ ⡄⠻⣆⡀⠈⠻⢦⣅⣄⠸⣿⡿⣷⣿⣧⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠳⢿⡿⠋⠁ ⠉⠀⠈⠻⢦⣤⣤⣀⡠⠔⠛⠓⢹⣿⡏⣧⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠒⠂⠈⠉⠀⠀⣠⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡆⠀⢣⡙⣇⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣀⠀⠀⠀⢀⣠⡴⢿⠇⡄⢸⣿⠙⡆⠀⠀⠀⠀⠉⠒⢤⣀⣤⡤⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠛⠛⠛⠁⠀⣾⣾⡇⢸⣿⡼⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣼⠇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣷⡄⣄⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣵⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣆⠙⢶⣄⡀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣠⢾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣧⡀⢻⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣖⣡⠞⠁⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡾⠟⠋⠁⢀⣤⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⢀⠤⠴⢖⡮⠟⠋⠁⠀⣀⣤⣶⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣥⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢻⣿⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠙⢿⣦⣍⠛⠿⢿⠿⡿⠿⢿⡿⠟⠛⣉⣴⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀ ⠀⠀⠀⠀⢰⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡶⠿⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠈⣷⠀⠀ ⠀⠀⠀⣴⡾⠋⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠐⠒⠒⠛⠛⠛⠻⣿⣿⠏⠀⠀⣀⡀⢀⣠⣶⠿⣿⣿⣿⣿⣿⣏⣉⣻⣿⣶⣤⣀⠛⣧⠀ ⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⣶⠟⢡⣴⢟⣹⣿⠾⠟⠛⠉⠉⠉⠉⠉⠉⣉⣉⣉⠛⢿⣿⠀ ⠀⣼⡟⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣶⣶⡶⣦⣤⣤⣄⡈⠙⠶⣿⣅⣴⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⡿⠋⠀ ⢀⣿⠁⣠⡤⠀⣠⡴⠞⢋⣉⣠⣼⣷⠼⠿⠿⠿⠷⠿⠶⠤⠼⣿⣷⣦⣌⣿⣿⣤⣴⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀ ⠈⣿⡿⢋⣴⣿⣭⡶⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣍⣿⡏⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁⠀⠀⠀⠀ ⢰⡟⣠⡿⠟⠉⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡿⠛⣧⠀⠀⠀⠈⠻⣦⣀⣀⣀⣠⣤⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣯⣤⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⢹⣷⠀⠀⠀⠀⠉⢿⣟⠻⣯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠉⠻⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⠏⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⢻⣧⡀⠙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠶⠶⠶⠶⠶⠶⠶⠛⠛⢩⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠈⠙⠻⢶⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠄⠀⠀⠀⠀⡤⣠⡿⠃⠀⠀⢀⡠⠒⣠⣶⡾⣿⡄⠀⠀⠀⠀⠈⠆⠻⣿⠻⣶⣄⡀⠀⠉⠻⢷⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⣨⣴⠿⠋⠁⠀⢻⣷⡄⠀⠀⠀⠀⠀⠀⢿⡆⣿⣿⣿⣷⣤⣀⠀⠙⢿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⣀⣼⣿⣿⠀⠀⠀⠀⠘⣿⡇⠁⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⣠⣾⣿⡿⣿⣿⡀⠀⠀⠀⢀⣽⣇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⣠⣾⣿⠟⣽⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣽⣿⣽⣿⣿⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢀⣤⣾⣿⡋⣡⢶⣷⢸⣧⣿⣧⡿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠟⣿⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣶⣿⣿⠟⠋⠙⠛⠛⠛⢷⡟⠈⢀⣀⣀⣀⣬⣿⣿⠿⢷⣦⣀⣀⣀⣤⡿⠋⠀⢸⣿⣶⠟⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣤⣤⣴⣶⣶⡶⠶⣿⡟⠛⠛⠋⠙⣿⡇⠀⠀⠀⠀⠈⠛⣿⠛⠉⠀⣠⣴⡿⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠷⣶⣤⣤⣀⣹⣇⣀⣀⣀⣀⣀⣀⣿⣶⡾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⣴⡾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⡴⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠟⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠶⠶⠶⠞⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⠿⢿⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⢶⣶⠎⠀⠀⠀⠓⠂⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣠⣤⣶⣾⣿⣿⣦ ⠀⠰⠀⣠⣄⣨⣿⡻⢿⡷⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠿⠋ ⠀⣠⣶⣿⣿⣿⣍⣹⡽⠃⣀⣴⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀ ⠸⣿⣿⣿⣿⣟⡫⠅⠒⢛⠏⠉⠉⠛⢿⡀⠀⠀⠀⠀⠀⠀ ⠀⠙⠻⠿⡿⠉⠙⠢⣤⡊⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡇⠀⠀⠘⠿⠇⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⢀⣠⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⢿⣿⣿⣿⣿⠟⠉⠛⠒⠛⠋⠉⠻⣿⣿⣿⣧⠀⠀⠀ ⠀⢠⣾⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⠄⠀ ⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀⠀⠀⠀⠀⠀⢀⡀⢀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡝⣆⠀⠀⠀⠀⠈⣻⣿⣿⠟⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡙⣦⢀⣤⣶⣶⣿⣻⡟⠀⣀⣿⣿⠃⣀⡤⠖⠒⠛⠒⠲⢤⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣾⣿⣿⠿⠛⠛⠛⠛⠛⠿⣏⡽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠻⣞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡟⠛⠛⠛⠛⢉⡵⠋⠀⠀⠀⠀⠀⠀⣀⡀⠀⠙⢦⠀⣀⣠⠤⠖⠒⠚⠉⠉⣉⣉⣙⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⠀⣧⠀⠀⠒⢠⠏⠀⠀⠀⣀⡴⠚⠉⠉⠉⠉⠉⠙⠚⣿⣍⡀⠀⢀⣠⣴⣾⠿⠛⠓⢋⣉⣙⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠁⠀⣀⣀⠀⢸⡆⠀⢠⠏⠀⠀⢠⠞⠁⠀⠀⠀⢀⣠⣴⣾⡿⠭⠭⠥⢽⣷⡿⠛⢉⣠⠴⣶⣿⣿⣿⣦⡀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⢠⡞⠁⠈⣷⢸⡇⠀⡽⠀⠀⠀⠀⠀⠀⠀⣠⢞⡿⠚⠉⠀⢀⣠⣤⡖⠚⠋⢳⠖⠉⠁⢰⣿⣿⣿⣭⣿⠿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡄⠀⢠⡟⠀⢷⡀⡇⠀⠀⠀⠀⢀⣴⣺⠵⠋⢀⣠⠴⣺⣟⣿⡿⢿⣶⣤⣼⡤⠤⠤⠼⠛⠋⠉⠁⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠙⠒⠋⠀⠀⠈⣇⠀⠀⠀⠀⠀⠻⠿⠶⠶⣞⣉⡀⠀⣿⣿⡿⠿⢟⣏⡵⠟⠀⣀⠀⠀⢀⣀⣤⠴⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠛⠛⠓⠓⠂⢉⡭⠟⠀⠀⠀⠉⠉⠙⠋⠁⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣾⣿⡇⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣹⡽⠶⣄⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢋⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡾⠋⠀⠀⢹⡄⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⠴⠶⢚⣛⣭⣴⠶⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⢸⡟⣦⢿⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⢋⣉⣉⣉⣉⣉⣉⣥⣤⣤⡴⠶⠶⠞⠛⢋⣉⣡⣬⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⠤⣤⣀⠀⣾⠁⡿⠸⡇⠀⠀⠀⠀⠀⠀⣟⣀⠛⢋⣉⣩⣭⣥⣤⣵⣤⡴⠴⠾⠒⠒⠛⠋⠉⢉⡤⠚⣿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣶⣯⠬⠾⣷⠿⠃⢰⡇⠀⠀⠀⠀⠰⣄⠙⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠈⢷⡝⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣰⢿⡇⠀⠀⠀⠀⠀⢸⡆⠀⠀⣀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠙⢮⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⡽⠃⢸⡇⠀⢀⣤⣦⠀⠀⢷⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠇⠀⠀⠀⠀⠀⠈⢷⡝⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣱⠃⠀⢈⣧⠀⠸⠿⠋⠀⠀⢸⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⡤⠤⠤⣤⠶⠚⠋⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⣟⢳⣖⢺⠃ ⠀⠀⠀⠀⠀⢀⣾⢳⠏⠀⠀⠘⢿⣄⣤⣀⣀⣀⣀⣻⣀⣀⡤⠴⠶⠶⢴⣖⠛⠉⣩⠟⢻⣿⣿⠈⠓⣦⢞⣁⣀⣠⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⢢⣿⠉⠀ ⣾⡛⠶⡤⠴⢾⣣⡏⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠉⡏⠁⠀⠀⠀⠀⢀⣈⣹⣾⣥⣤⡾⠃⢹⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢀⢸⡼⣇⠀ ⠉⠛⢻⡆⢰⡏⠙⡇⠀⠀⠀⠀⢸⣿⣿⣶⣶⣶⣶⣶⡷⢶⣶⣾⣿⣿⣿⣿⠹⣿⣿⣿⣧⣀⣰⡿⠟⠋⠈⠉⠁⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⢈⣧⢸⠀ ⠀⠀⣾⣀⣌⣃⣸⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣛⣋⣉⣄⣙⣡⣠⣨⣽⣯⣀⣀⣀⣀⣀⣠⡤⠴⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠞⠉⠉⠀

⢠⣀⡀⢀⣴⡎⡍⠫⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⢿⣯⣿⡦⣣⠁⢁⡱⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣟⣁⣽⣧⢤⡜⣝⣎⡆⠀⠀⣀⠠⠤⣖⣤⠀ ⠀⠀⢹⠟⠋⠁⠘⢿⣿⢣⠀⠙⠈⠁⠀⠀⣀⠼⠋⠀ ⠀⠀⢇⠀⣠⠤⣆⠝⠁⠈⡿⡀⠀⡠⠒⠉⠀⠀⠀⠀ ⠀⠀⠀⠉⠐⠛⡂⠔⠀⠀⠀⠁⢱⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⣆⣀⠀ ⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣀⢿⠟⡦ ⠀⠀⠀⠀⠇⠀⣠⠔⠈⠉⠐⠂⢄⡀⠘⡚⠪⢷⠵⠄ ⠀⠀⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠡⡀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠷⠶⠯⠀⠀⠀⠀⠀⠀⠀⠋⠛⠛⠂⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠶⠒⠶⢶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠉⠈⠀⢀⣠⣤⣤⣤⣤⣴⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⣶⣴⣾⠛⢉⣀⣀⣠⣄⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⡞⢫⣿⣿⠖⠛⠉⠁⠀⠀⠀⠉⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⠟⢻⣷⠋⢰⠏⠀⡄⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣘⣁⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⣄⣠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⣄⠀⣤⠶⠒⠲⣤⡀⠀⢠⣿⡷⡀⠀⠙⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠐⢯⣿⠁⠀⢠⣿⣽⣿⣆⣼⣿⣿⣿⣤⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠉⢙⢹⠀⠀⢠⣬⣿⣿⣿⣾⣿⣿⣿⣿⡇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡀⠀⠸⣿⢿⣿⣿⣯⠛⣿⣿⡿⢃⡴⠚⠓⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⣧⣀⣀⣙⠮⠭⢿⡏⠀⠈⠻⠤⣞⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡞⠀⠀⠀⠀⠛⠁⠀⠀⠈⢹⣤⠞⠀⣀⣀⣤⠞⠛⠛⠛⠀⠈⠳⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣨⠃⠀⠀⠀⠀⠰⠶⠶⠶⠚⠉⠙⢿⡉⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠙⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠏⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⠀⠀ ⠀⠀⠀⢠⠏⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀ ⠀⠀⢠⡏⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢻⠀ ⠀⣠⣿⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⣠⡟⠀ ⠙⣇⠉⠲⣄⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠢⣤⠴⠒⠋⠁⣠⠔⠊⠁⡇⠀ ⠀⠹⡗⠤⠀⠉⠒⣧⠀⠄⠀⠀⠀⠀⢀⣾⣀⣀⠤⠤⠤⠤⠤⠤⠶⠒⠚⠉⢹⠃⢀⣀⣘⣦⣀⣈⠉⠀⠀⠀⣸⠃⠀ ⠀⠀⠹⡀⠀⠀⠀⠘⢆⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣯⣴⠿⡾⢛⣶⣶⣿⠀⠀⠀⣰⣇⠀⠀ ⠀⠀⠀⠻⡄⠀⠀⠀⠈⠳⢤⣀⡤⠞⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣿⣛⡿⣧⣴⡾⠟⠛⢹⠀⠀⢀⡴⠃⠈⠻⣅ ⠀⠀⠀⠀⠘⠢⡀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⣄⡀⢸⠛⠊⠉⠀⠀⠀⠀⣞⣀⡴⠋⠀⠀⠀⣀⡿ ⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⢧⡀⠀⠀⠀⠀⢀⡴⠛⠓⠒⠒⠒⠚⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⣷⠤⠖⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠒⠒⠒⠒⠒⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀ ⢀⢤⢄⡀⠀⠒⠀⠒⠂⠉⠉⢁⣀⢀⣀⣉⢢⡀⠀ ⢘⠀⠀⠈⢁⠑⠀⠀⠈⠀⠉⢁⠀⠀⢠⠄⡔⠁⠀ ⢸⠀⠀⠐⠛⢐⠀⠕⠈⣉⡲⡂⣉⡲⢀⠔⠀⠀⠀ ⠆⠘⠁⠀⠀⡞⠆⡀⠸⡿⠇⡇⢿⡧⡩⠀⠀⠀⠀ ⡄⠀⠀⣤⢀⠃⠀⠈⠒⠒⠘⢞⠉⢠⠆⠀⠀⠀⠀ ⡄⠀⠘⠉⢠⠂⠀⠈⠍⠉⡶⠬⡏⠰⠀⠀⠀⠀⠀ ⡅⠒⣀⢀⠰⠈⠀⠀⠉⠈⣀⡈⠧⣴⢢⠀⠀⠀⠀ ⠑⣆⢇⠀⢨⠵⢖⡕⢶⣿⣽⣶⣶⡟⠵⢄⡀⠀⠀ ⠀⢿⣿⡶⡷⠿⢯⣙⠻⣷⣶⡟⠂⠩⢅⢜⢕⢇⠀ ⠀⠀⠀⠹⢷⠯⠅⠀⠀⢸⡇⠀⠀⠀⠀⠑⠓⠛⠁ ⠀⠀⠀⠀⢀⠻⠀⠀⢠⣾⣧⡴⣶⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣶⣴⣶⣦⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠋⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢦ ⠀⠀⠀⠀⣀⠔⠉⠁⠀⠀⠀⠀⢀⣥⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⣸ ⠀⠀⢀⠌⠀⠀⢠⠖⠀⠀⠀⠴⢿⣞⡻⣿⡇⠀⠀⠀⠀⠀⢀⣠⣴⡶⠟⣿⣿⠟ ⠀⣠⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣇⣤⣴⠒⠚⡿⣧⣤⣬⣿⠿⠋⠁⠀ ⣼⣿⡟⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣿⣇⣹⣀⣶⣿⣿⡿⠋⠁⠀⠀⠀⠀ ⠙⠿⠷⡟⠀⠀⠀⠀⠀⠀⢠⣾⣷⣶⣀⣼⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢄⠀⣾⣿⡿⢀⣨⣽⠛⠉⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠿⠿⠾⠿⠌⠀⣀⣿⠟⠁⠀⠉⡋⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣀⣒⣀⣰⣴⡾⠟⠁⠀⠀⠀⠀⠘⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡙⠓⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⡋⠀⠙⢶⣤⣤⣄⠤⠤⠤⢶⣯⣥⢄⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠁⣀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠈⠙⢿⣷⣿⢿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣤⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣖⣶⣄⠀⠀⠀ ⠀⠀⠘⠿⠿⠷⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠿⠿⠿⠋⠀⠀⠀

⠀⠀⠀⠀⠀⡠⠒⣉⠤⠜⠓⠋⠛⠒⡆⠹⣄⠙⠻⢷⣄⣠⡀⠀⠀⠀ ⠀⠀⠀⢀⠞⣰⠉⠀⠀⠀⠀⠀⠀⠀⢹⡄⢹⣶⣤⣼⣿⡏⠾⣗⣄⠀ ⢀⣠⡴⠟⣣⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡸⣸⠰⠙⣿⣇⠃⣇⣿⣎⠆ ⡴⠣⢱⣼⡿⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠄⠁⠀⠆⢹⡿⢻⣿⠉⠸⠸ ⠳⢥⢾⡟⠃⣤⣤⣤⡀⠀⠘⠙⣿⣏⠀⠀⠀⠀⠀⠸⣿⣾⣿⠀⠀⠀ ⠀⠀⠈⢧⠀⠈⠛⠑⠇⠀⠀⠈⠁⠀⠀⠀⠀⠀⡀⠀⡿⢿⣿⠀⠀⠀ ⠀⢰⠂⢸⣇⠀⠀⠀⢕⢀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠐⡠⠊⣻⠀⠀⡄ ⠀⢸⠀⢸⣟⠀⠀⠀⠰⠷⠢⠄⠀⠀⠀⠀⠀⠎⠀⠀⢃⡰⣿⠀⣾⠁ ⠀⠸⡆⢿⣿⡀⠀⠀⠀⢁⠁⠀⠀⠀⠀⢀⠊⢀⡠⠺⠁⠀⣿⣤⡿⠀ ⠀⠀⢡⢸⣿⠘⠂⠄⣀⠀⠀⠀⠀⣀⠔⠁⠀⢸⠀⠀⠀⠀⣿⣿⡇⠀ ⠀⠀⠈⣼⢻⠀⠀⠀⠀⠈⠉⢹⡟⡇⠀⠀⠀⣀⠦⠄⡀⢀⡇⢸⠀⠀ ⠀⠀⠀⠸⠈⡄⠀⠀⠀⠀⢀⣨⠗⢀⡀⣀⡞⠁⠀⠀⠈⢾⠁⠘⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⡔⡱⠋⠀⠁⣀⡎⠀⠁⠀⠇⠀⠘⡀⠀⠀⠀ ⠀⠀⠀⣤⣤⣀⣠⣀⣰⣼⣀⣀⣀⣾⡿⣵⣀⣆⡀⢰⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠙⠛⠛⠓⢚⡻⠏⠾⠟⠛⠻⠽⡛⠛⠟⠛⠈⠀⠀⢠⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⢠⡀⠀⣸⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢸⣟⠀⢀⣀⣀⠐⣄⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⣿⠋⠙⠛⠿⠟⠛⠛⠳⢶⣤⠖⠛⠿⣷⣦⣠⣤⣴⣶⣦⣤⣤⣤⣄⡀⣄⣀⢀⣀⣠⣰⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠘⣿⡄⠀⠀⣠⣄⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠛⠻⠿⠟⠛⢿⣦⡀⢸⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠁⣿⡄⢠⣾⡇⠀⢰⡇⠈⡇⠀⠀⣰⠋⣀⠈⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⢸⠃⠉⠙⠻⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢻⠄⢸⣿⠁⠀⠀⠻⠞⠁⠀⠠⣄⡀⣸⣁⢀⣤⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠛⠁⠀⢠⡏⢴⣟⢦⡀⠀⠈⢙⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⡇⠀⠀⠀⣾⠀⢸⣿⠀⢀⣤⠀⠀⠀⠀⣠⣿⢿⠁⠈⠙⠣⣄⢻⣴⢶⡖⠛⠛⠻⣍⠁⠀⠀⠀⠀⠀⠈⣇⠘⢿⡀⣹⡄⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⡄⠀⢸⡆⢸⣿⠀⠘⠿⠀⠀⣄⣾⣿⡧⠮⣄⣀⡀⠀⣹⣿⡟⣠⠇⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⡾⠀⠀⠙⠋⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⡇⢠⣧⠀⣾⡷⢸⡿⠀⠀⠀⠀⢰⣯⡭⠀⠀⠀⠀⠸⢽⣷⣟⠛⠋⠉⠉⠙⠒⠲⢤⣘⡆⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣗⣼⠇⠀⠙⡀⣿⣷⢹⣿⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⢻⡋⠀⠀⠀⠀⠀⠀⠀⠰⢬⡷⠀⠀⠀⠀⣿⠀⠀⠀⣿⡆⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠈⣿⡏⠀⠀⠘⠷⣇⣿⣸⣿⡆⠀⠀⣤⠖⠒⠻⠤⣄⣀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢀⣼⢷⡀⠀⠀⠀⢸⢽⣿⣿⠀⠀⠀⢧⡀⠀⠀⠀⠀⠈⠉⠙⠒⣛⠈⠳⣄⣀⠀⣀⣠⠖⠉⠀⠀⠀⠀⠀⢰⠏⢰⡟⠳⣄⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠀⠀⠀⠀⠀⠀⢸⠘⣇⠀⠀⠀⠀⣿⢻⣿⠀⠀⠀⠀⠉⠓⠲⠶⠶⢶⡶⣺⡿⠛⠳⣤⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⣿⡀⣸⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⢿⠀⠀⠀⢸⣼⣯⣿⠀⠀⣿⡄⠀⠀⠀⣠⡴⢿⡾⠉⠀⡀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠙⠋⠀⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⢸⣀⣀⣀⣀⣤⣤⠾⠶⠿⣤⣴⣴⣿⣿⠿⣿⠀⠀⠘⡀⠀⠀⢸⢃⣾⡟⠀⣰⣟⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣀⡠⢴⠇⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⣿⠋⢭⣭⡥⠴⠾⣷⣿⣿⠟⠛⠛⠛⠻⣾⣿⠀⢀⡞⠻⡄⠀⢸⡘⢿⣷⡴⠛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⢋⣉⣡⠴⠾⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⢷⣮⡙⠳⣤⡞⢻⡙⢿⠙⢷⠀⠀⢰⣽⣿⠀⢸⡆⣠⠟⠀⠀⠛⠦⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢋⣠⠴⠚⢹⡇⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⡏⠀⢹⡟⣶⡾⠷⣤⣧⣼⣦⣼⣗⣂⣤⣿⡏⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢉⣠⠖⠋⠀⠀⠀⣼⠃⠀⢴⣶⠀⣰⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠇⠈⢳⡖⠒⠒⠛⠠⠤⠤⠴⠶⣤⣭⣍⣉⣩⢭⡟⠒⣶⣖⡒⠢⠤⣤⣤⣄⣀⡀⣠⠞⢁⡴⠛⠁⠀⠀⠀⠀⠀⣧⠀⠀⠈⠀⠀⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⢦⣐⣒⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣏⠹⡏⠛⠒⠲⠶⠭⠶⣟⣉⣉⣉⣑⡒⠲⠶⡦⠤⣀⣠⣿⠤⣄⡤⢤⡴⣿⡇⣿⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠙⠲⣌⡳⢦⣀⠀⠀⠀⠀⠀⠀⠹⡄⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠻⢿⡯⠼⠷⠿⠷⠿⢾⣿⠀⡉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠀⠈⣿⣷⠮⣗⣦⣀⠀⠀⠀⠀⢻⡄⣷⠦⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠾⠧⠤⠤⠤⠤⣀⣼⡟⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠀⠠⠀⠀⣷⣦⣤⣤⣔⡋⠿⣿⣄⣈⣙⢮⣓⢦⡀⠀⠀⢳⣸⡗⠦⠤⠤⣄⣉⣙⠛⠒⣦⠖⣛⡭⡶⠛⢻⡟⠛⠲⣶⠶⠓⣾⣇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠾⠷⠤⠤⠤⠤⠴⠿⠧⠿⠾⠷⠶⠾⠾⠿⠿⠴⠶⢿⣿⢟⣿⠿⠿⢿⣇⠀⢸⠀⠀⡨⠋⣩⣿⣥⣞⣉⣀⠀⠀⢸⡇⠀⢀⣀⣀⣀⣾⣿⣾⣧⣤⣀⣴⣤⣤⣤⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣡⠞⠁⠀⠀⠈⠙⣄⠘⠆⡼⢁⡴⢋⡾⠋⠀⠀⠉⠛⠒⠛⠋⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⡼⠋⠀⠀⠀⠀⠀⠀⠈⠓⢾⣷⢟⣱⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣌⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣝⢷⣄⠀⠀⠀⠀⠀⠀⠀⠹⢷⣌⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣶⠖⠛⠋⠉⠓⠟⢷⡀⠀⠀⠀⣀⠀⠀⢀⣩⣷⣌⡻⠦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣟⣳⣠⡴⠞⠛⠛⠁⠀⠀⣿⣻⣻⣿⣋⠁⠀⠈⣀⣤⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣧⣀⣀⣿⣧⣀⣼⡟⠀⠀⠀⠀⠹⣧⣀⣀⣿⣇⠀⣰⡷⠀⠀⠀ ⠀⠀⣰⠟⠉⠀⠀⠀⠀⠈⠙⢷⡄⢀⡴⠚⠉⠀⠀⠀⠀⠉⠻⣇⠀⠀⠀ ⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀ ⢸⠁⠀⠀⠀⠀⠀⡴⢋⣭⣽⣷⠀⢷⠀⣰⢚⣭⣽⢣⡀⠀⠀⠀⠘⡇⠀ ⢸⡀⠀⠀⠀⠀⠈⣇⢿⣿⣿⣿⠀⡾⠀⢧⢿⣿⣿⢇⡇⠀⠀⠀⢀⡇⠀ ⢸⣧⣤⣤⣤⣀⠀⠈⠓⠾⠒⠁⣰⣇⠀⠈⠓⠾⠶⠛⠀⠀⣀⡤⠼⢄⠀ ⢸⠁⠈⠠⠄⠛⠳⣄⠀⣀⡤⠞⠁⠈⠳⣄⡀⣀⣠⠴⠖⠋⠁⠀⠀⣰⡇ ⠀⠀⠐⢲⡶⠄⠠⠟⠉⠉⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢀⣀⣠⡴⠾⠋⠀ ⠀⠀⠀⢸⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣋⡉⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⡶⠶⠶⢶⣶⣶⠶⠒⠒⣶⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿⣿⣀⣀⣀⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢷⣄⣀⡀⠉⠀⠀⠉⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⣤⣈⣉⣙⡛⠛⠛⠛⠛⠉⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢘⣀⠟⠀⠀⠀⢀⡀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣾⡇ ⠀⠀⠀⡠⠂⠉⠀⠀⠉⠒⢄⠘⡄⠀⡠⠐⠉⠀⠀⠉⠐⢄⠀⠀⠀⠀ ⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀ ⠀⡬⠤⠀⠀⠠⠤⠤⠄⠀⠀⠄⣶⠤⠀⠀⠠⠤⠤⠄⠀⠠⠤⢇⠀⠀ ⠀⢢⠐⠒⠒⢲⠲⣶⡶⢒⠖⡎⠁⠈⡖⢖⢲⣶⡖⡲⠒⠒⠂⡔⠁⠀ ⠀⠈⢄⠀⠀⠀⠑⠈⠑⠊⠀⡄⠀⠀⡇⠈⠂⠭⠑⠁⠀⠀⡠⠀⠀⠀ ⠀⠀⠀⠢⢀⠀⠀⠀⢀⡠⠊⢃⠀⢠⠓⢄⡀⠀⠀⠀⡀⠔⠁⠀⠀⠀ ⠀⠀⠁⠀⠠⠄⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⣤⠀⠀⠃⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀ ⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⢀⡀⠀⡀⠀ ⠀⠀⠛⠃⡠⡀⠀⠀⠀⢴⠂⠉⢈⠁⠀⠀⡇⠀⠀⠀⣰⠃⠀⠀⣸⠀ ⠀⠀⠀⡜⠀⢸⠀⠀⠀⠈⠀⠀⠈⠈⠀⠀⠁⠀⠀⠀⠘⠄⠠⠔⠁⠀ ⠀⠀⠀⠳⠤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠆⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠖⣋⣁⣀⠀⠀⠙⠢⢄⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠀⠀⠀⠀⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠿⠀⠉⠻⣿⣷⡄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠲⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣍⠉⠉⢟⣧⠀⠀⢸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠀⠀ ⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⣕⣢⣼⣿⠃⠀⠈⢻⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀ ⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡏⠀⠀⠀⠀⣬⡽⠿⢿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀ ⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠘⢿⡖⠤⣈⡙⢿⡿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄ ⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⡇⠀⠀⠸⡄⠀⠀⠀⠈⠙⠒⢾⡿⠷⢄⡙⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠰ ⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠀⠀⢰⠦⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⢸⡓⠢⢬⣉⠒⠃⠀⠈⠀⠀⠀⠀⠐⠤⠤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠳⡀⠀⠀⠀⡸⠁⠀⠀⠉⢲⠢⢴⣿⣷⡦⣄⣉⠁⠒⠦⠤⠄⣀⣀⣤⣴⠶⠋⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢄⠀⠀⢳⠀⠀⠀⠀⠀⡷⠀⠀⠉⠓⠲⠬⢭⣍⣓⣒⣶⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠣⡀⢸⡇⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣀⣀⣀⠀⠤⠤⠤⠠⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠄⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⡀⠀⠀⣀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠑⠦⠄⠀⣜⡁⠀⠀⠀⠀⠀⣀⣀⡀⠤⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡴⡒⠒⠲⠶⠒⠒⠛⠓⠲⠶⠒⠒⠚⠓⠶⠶⠤⠤⠤⠶⠶⠦⠤⠤⠴⠶⠦⠤⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠟⠀⢱⠀⠀⠀⢀⠴⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠶⠋⣀⡀⠸⡆⠀⠀⢏⠀⠀⡠⠃⢰⣄⠀⣸⣇⣀⣴⠇⠀⠀⠀⣶⡀⢀⣿⠀⠀⣤⠀⠸⠤⠊⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠏⠀⡜⠁⢸⠀⠙⡄⠀⠀⢉⢉⠀⠀⡠⠛⠉⠉⠉⠉⠉⠳⣄⢀⠴⠊⠉⠉⠉⠉⠙⢧⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠁⠀⠀⢇⠀⡼⠀⠀⢱⠀⠀⠉⠁⠀⡞⠀⠀⠀⠀⠀⡠⠤⣀⠈⡏⠀⢀⣀⣀⡀⠀⠀⠀⢱⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢛⡗ ⣷⡀⠀⠀⠈⠙⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡎⣴⣿⡎⡆⠸⠀⡏⣶⣷⣽⡄⠀⠀⠀⡇⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡼⠋⠀ ⠈⢳⡄⠀⠀⠀⣀⡀⠀⠘⡆⠀⠀⠀⠀⣧⣀⣀⣀⠀⠘⠪⠭⠛⢠⡇⠀⠑⠭⠭⠞⠀⠀⣀⣸⣀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣴⠚⠺⣟⣩⠷⡄⠀ ⠀⠘⣧⠀⠀⡎⠀⡇⠀⠀⡇⠀⠀⠀⠀⡅⠈⠀⠘⠙⢦⣀⡠⠖⠁⠈⢢⣄⣠⠤⠔⠂⠉⠀⢀⡸⠀⠀⢸⡆⠀⠀⠀⠀⠐⡇⠑⡶⣏⣀⢆⡇⠀ ⠀⠀⠙⣦⠀⠧⠴⢁⣀⣀⢡⠀⠀⠀⠀⠀⠈⢻⡀⠀⠉⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⡤⠴⠖⠋⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠙⡆⢀⣈⣡⠟⠀⠀ ⠀⠀⠀⠈⡇⠀⠀⢸⠀⠈⡏⡄⠀⠀⠀⠀⠀⢸⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⡤⠤⣭⠶⠄⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⣰⠃⡞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢧⡀⠀⠸⡄⡰⠁⢱⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢸⣿⡇⠀⠀⡇⠀⠀⢠⠖⠓⢢⠀⢇⠀⠀⠀⠀⠀⣰⠃⡼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢱⡀⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠀⠀⠀⠸⣤⠤⠊⠀⣾⣀⣀⡀⠀⣰⠋⡼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣧⣄⡀⠎⡐⠈⡆⠀⣰⠆⠀⠘⢏⠉⠙⠛⠟⠛⠿⣿⣿⡇⠀⠀⠀⠀⠀⣀⠤⡄⠀⢸⠋⢠⡶⠗⢚⣡⠾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠃⠀⠹⡋⠀⠀⠃⠀⠠⠒⢢⠀⢄⠙⠒⠶⠶⠶⠶⠞⠛⠀⠀⠀⠀⠀⠀⠧⠴⠃⠀⢸⠀⢀⣻⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠀⠀⠀⣇⣀⠀⠀⠀⠣⠤⠊⠀⠀⠉⠛⠚⠛⠒⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⡟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢦⠤⡴⠋⠉⠉⠙⡟⠛⠉⠙⠛⠻⢟⡉⠉⢉⠟⢖⠒⡻⠻⣍⢉⡽⠛⠉⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡄⡟⣶⣶⣦⠴⡧⠤⠤⠤⠤⠤⠤⠬⠭⢥⣤⡼⠉⢷⣤⣤⣁⡀⣀⣀⣀⣠⡶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠉⠉⠀⡇⠀⠛⠛⠛⠛⠀⠘⠛⠛⠛⢧⠀⡸⠛⠛⠛⠁⠙⠛⠛⠛⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠇⠘⢶⣤⣄⣀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠸⣆⠸⣏⠉⠉⠉⠉⠉⣹⠏⠉⠉⠉⠉⠙⠯⣍⣉⣉⣀⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⣦⠸⡗⠋⠀⠈⠙⡗⣶⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⠶⠃⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣗⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣦⣄⣀⡀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣶⣾⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢴⣺⠿⢤⡬⠙⠲⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠧⠤⠼⠧⣄⣼⠁⠀⠀⠀⠀⠈⠉⠛⢻⠆⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡏⠀⣀⣀⣀⣀⣀⣈⠭⠶⣦⣤⡴⠶⠛⠙⠛⡒⠋⠉⠀⣸⢷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢼⠉⠙⠒⡋⠉⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠏⠀⠀⡞⠁⢸⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⣔⢉⡉⢳⡀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣶⣦⣤⣄⡇⠀⠈⠙⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣠⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⠉⢧⠘⣷⠀⠀ ⠀⠀⠀⠀⠠⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢦⡘⣄⠞⠀⠘⢧⡀ ⠀⠀⠀⠀⠀⢻⣿⣧⣿⣿⣇⠀⠉⠻⣿⣿⣿⣿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠙⢦⡀⠀⠀⠀⡧ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⣄⡀⠈⠻⢿⣋⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⠑⣄⢠⠞⠃ ⠀⠀⠀⠀⠀⠀⢸⠙⠻⢿⣿⣿⣿⣿⣷⢦⣤⡀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⠿⠟⠋⣽⠀⣀⣀⠀⠀⠫⠇⠘⣾⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢈⡅⣁⣴⣋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡏⠀⡇⠀⢣⠀⠀⢀⣴⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⡎⠀⠀⣀⠀⢿⣤⣶⠤⣄⣀⣠⠄⠀⠀⠀⠀⠀⠀⢰⠋⠈⡇⠀⣼⠁⠀⠙⠶⠛⠀⠀⢸⠇⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠺⠞⠀⠀⠀⠈⠳⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⠴⠃⠀⣷⠀⠀⠀⠀⡀⠀⢠⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⠀⣠⠞⢻⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡴⣶⠂⠀⠀⢰⠏⠀⠀⠀⠸⡷⣰⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣤⠴⡾⠀⢿⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⡟⠀⠀⡠⠖⠚⢉⣿⣄⣀⣀⡀⠀⠀ ⠀⢀⣴⡇⠀⢀⣧⡀⠀⢀⠀⢀⣠⣤⣤⣀⣠⡤⠶⢶⣤⡤⢴⣺⣿⣹⡓⠒⢶⠣⣄⠀⠣⣄⠀⢿⣠⡶⢦⡶⢋⣽⠀ ⣴⢿⣟⠛⠒⠉⣨⡏⠉⠉⠉⠉⠒⣤⣼⡿⠺⣲⣖⣉⣀⣐⡏⠁⠀⠀⣷⣦⡿⣄⠈⢳⡤⢬⣹⢖⡫⠖⣉⡶⠋⠁⠀ ⠙⠲⠬⣙⣓⠚⢹⣗⣒⣒⡒⠚⣿⣯⣿⣄⣠⣻⣶⣿⠀⢸⣷⣄⣀⣼⢿⣿⣿⣮⣕⢼⡳⠤⡌⠋⣤⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠇⣾⡿⠿⠿⠇⠀⢘⣋⣯⣿⣿⠭⠯⠶⠶⠾⠒⠒⠋⠉⠉⠉⠳⣝⡻⣿⣮⣲⠃⠀⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢦⣼⡿⣏⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢄⠀⠀⠀⠀⠉⢺⣟⣁⠜⡜⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠓⠦⣴⠀⢰⣄⣀⣀⣀⣀⣠⠤⠤⠼⣧⠈⢶⠒⠒⠒⠒⠒⠛⠓⠚⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢸⡏⠉⠁⠀⠀⠀⠀⠀⠀⠘⣆⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⢤⡶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣠⡴⡶⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣶⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣷⣿⣧⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠿⣿⣿⡗⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠯⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢬⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠙⢮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⣀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣈⣧⡀⠀⢀⠀⠀⠀⠑⣝⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⢿⣿⢃⡴⠒⡦⡄⠀⡀⠀⠸⠆⠀⡞⠀⠇⠼⠀⢀⡴⢹⠀⠀⠀⠀⠀⠀⢸⠁⠉⢣⠀⠀⠳⡄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣼⠃⡎⠀⣠⠟⠁⢸⠃⠀⠀⠀⢠⠇⠀⠀⠀⣠⠋⠀⠀⡄⠀⠀⠀⠀⠀⠈⠳⣄⣼⣇⠀⠀⠙⣦⠀⡔⠚⢿⣿⠿⠿⣿⣿⣿ ⠀⠀⠀⢠⡏⠀⠈⠈⠁⠀⠀⡎⠀⠀⠀⠀⢸⠀⠀⠀⡴⠧⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠸⣷⣧⠀⠈⢹⡆⠀⠘⣿⡇ ⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠈⠒⢄⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢹⣿⢦⡀⣸⣷⠀⠀⣿⠃ ⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⢀⠎⠀⣀⣀⡀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢿⠀⠉⠙⣿⡆⢀⣿⠀ ⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⠿⠛⠻⠿⣿⣿⣦⣄⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⠞⣉⡙⢯⠙⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢹⡇⠀⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⣇⠀⢧⡇⢨⠀⠀⠘⡄⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠱⠄⠘⠂⠠⠴⠊⠀⠀⠀⠹⣄⡇⠳⡀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠀⠀⠀⢸⡇⠀⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠢⣄⠀⢸⢆⠀⢤⠀⠀⠀⠀⠀⠘⡇⠀⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠈⠳⣼⣷⣤⠀⠀⠀⠀⡇⠀⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠸⡴⠚⠉⠓⠤⢄⣀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠈⠉⠉⠙⢿⡇⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⣿⣳⣄⡀⠀⠀⠀⠈⠉⠒⠒⠤⠤⠤⠤⠒⠉⠀⠀⠀⠀⣠⠾⢻⠀⠀⠀⢀⡿⠀⠀⠀⠀ ⠀⠀⠀⢰⢷⠀⠀⢰⡄⠀⠀⣼⡄⠀⠀⠀⠀⢸⣿⠀⠈⠑⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠁⠀⡾⠀⠀⢀⢠⡇⠀⠀⠀⠀ ⠀⠀⢠⠀⠈⢆⠀⠘⡟⣄⠀⢹⣷⠀⢄⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠈⠉⢱⣶⣖⡒⢛⠋⠉⢡⡄⠀⢠⡆⢸⡇⠀⠀⡎⢸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠬⠧⣄⡗⠚⠳⢬⣿⣇⢸⣆⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⣿⡋⠁⢹⣿⠀⣰⣿⡇⣠⣿⣷⣿⠁⠀⣼⡇⡎⠀⠀⠀⠀⠀ ⠀⢀⡴⠊⠓⢤⣤⠒⠓⠋⠉⠓⢻⠻⣿⣿⢧⡀⠸⣷⡄⠀⠀⠀⠀⠀⠸⠹⡇⠀⣾⡽⣿⡥⠼⢿⣥⣿⣋⡛⢀⡜⢿⡿⠁⠀⠀⠀⠀⠀ ⠀⠊⠀⢀⡴⠋⠈⢳⡀⠀⠀⠀⠈⣧⣠⠿⠛⠿⠶⣿⣿⣖⠢⢤⡀⠀⠀⡀⣻⠞⢁⠔⠛⢓⠦⣾⠋⠀⠙⣧⢾⢳⣾⡇⠀⠀⠀⠀⠀⠀

⢸⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀ ⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀ ⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⢸⣧⣿⣿⣿⣿⣿⣿⠁⢻⣿⣿⣿⡿⠛⠛⠛⠀⠀⠀⠀⠈⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⣸⠛⢿⣿⣿⠿⣿⡇⠀⠀⢻⣿⣁⡀⠀⠀⠀⠀⠻⢤⣄⣀⠙⠲⣤⠀⠀⠀⠙⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⢻⠀⠀⠙⢿⣿⣿⡇⠀⠀⠘⡆⠈⠙⠒⠒⠒⠒⠦⣄⡀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠿⠿⢧⣀⡀⠀⠋⠀⠀⠀⠀⠀ ⠘⡆⠀⠀⠀⠻⣿⡇⠀⠀⠀⢷⢠⠔⢲⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠾⣟⠻⠶⠀⠀⠀⠀⠀⠀⠸⠿⣶⡦⠀⠀⠈⠙⠲⠇⠀⠀⠀⠀⠀ ⠀⢻⡄⠀⠀⠀⠹⡇⠀⠀⠀⢸⠁⠀⢨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠤⣤⣀⡀⠀⠀⠀⢠⡤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠓⠺⢿⣦⡀⣀⣴⡳⣄⣀⣀⣾⠀⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⣙⡒⠦⠬⣽⣶⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠈⠹⣅⣿⣹⠏⠉⠉⠉⢩⣷⡒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⣀⣀⡀⠀⠀⢀⣠ ⠙⢲⣤⣀⡀⢸⠃⠀⢠⡖⠛⠒⠚⠻⢤⡀⠈⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⢉⡹⠗⠊⠉⠀ ⠒⠉⠉⠉⠉⢹⡀⣤⣾⠀⠀⠀⠀⠀⠀⠉⠳⣿⠛⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣫⠟⠋⠀⠀⠀⠀⢀ ⠠⠤⣤⣤⣤⡴⣟⠛⠛⣆⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⢀⣳⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⢄⣀⣀⣀⡀⠀⢠⠞⠁⠀⠀⠀⠀⢀⣠⣾ ⠀⢀⡿⠋⠁⠀⢘⣆⠀⠨⠷⣄⡀⠀⠀⠀⠀⠀⠀⢳⡛⠟⠙⠦⠤⠴⠒⣻⣯⠋⢀⣀⣰⣾⡇⠀⠀⢠⡽⡿⠻⢤⣀⢀⣀⣠⠴⠟⠛⠉ ⠰⠿⢤⣤⠒⠚⠉⠈⠓⢤⣀⠀⠉⠓⠲⠤⡤⡤⠶⠚⠁⢠⣶⣦⠀⠀⣠⠟⠛⠉⠉⠉⠁⠈⠉⠉⠛⠒⠿⣄⡀⠀⣬⣭⠀⢹⡀⠀⠀⠀ ⠀⠀⠸⣿⣀⠀⠀⠀⠀⢀⡞⠉⠉⠉⠑⠒⠷⠷⣠⣤⠤⠤⣍⠁⠀⢾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠘⠛⣡⠤⠖⠓⠶⠶⣛ ⠀⢀⡤⠿⠯⠛⢢⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠈⠳⣄⢀⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠀⣰⣇⣀⡀⠀⠀⠀⠀ ⠀⣾⠷⠤⠀⠤⠾⡄⠀⠀⠈⠑⠲⠤⠤⠤⠤⠐⠒⠉⠁⠀⠀⠀⠈⠻⢏⡀⠉⠓⠶⠤⢤⡤⠤⠤⠖⠋⠁⠀⣠⠞⠁⠀⠙⢯⣉⣳⠖⠢ ⠀⠙⣦⠄⢀⠠⠴⡇⠀⠀⠀⢀⡀⠠⢤⣤⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⣸⣿⣇⣀⣀⡠⣤⠖⠋⠙⣗⣦⣄⡀⠀⠈⠻⣄⠀ ⠀⠀⠧⣄⣀⣠⠴⠁⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⢠⠋⣹⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠘⣿⣿⡏⢳⡦⢄⣘⣦ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠈⠉⠒⠃⠰⣁⡀⠀⢨⠓⢄⠀⠀⠀⠀⠀⢀⡤⠤⢄⠀⠀⠀⢘⡷⢄⡀⢹⠏⣰⠟⠁⠀⠀⠉ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⢤⡀⠀⠈⠙⠃⠀⠀⠁⠀⠀⠀⢠⠏⠀⠀⣸⠀⠀⣠⡟⠁⣠⣭⠉⣼⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠉⠀⠀⠀⠀⠀⠀⠸⣄⣀⠴⠃⠀⣰⠏⣀⠴⢿⡏⢰⠇⢸⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡏⠣⡀⠈⠉⠓⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠊⠁⠀⠀⢹⠋⠀⠘⣇⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⣀⡵⠁ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⡴⠋⠀⠀⠀ ⠀⠀⡴⠁⢈⣼⣿⡆⠀⠀⠀⠀⣀⣠⣴⣮⠀⡠⠊⠀⠀⠀⠀⠀⠀ ⠀⠸⠃⣤⣶⠟⠇⢧⣤⣶⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⠁⠀⠠⠀⡹⣿⣟⣵⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣿⣶⣷⣦⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠠⠼⠿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣿⣟⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣿⡿⠿⠟⠋⠿⠟⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡞⢡⠀⠀⠀⠙⣿⣤⠀⠀⠀⠀⠀⣠⣿⣶⣿⢿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⡇⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⢰⡿⣿⠟⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀⠀⠀⠀⠀⡇⣿⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣄⠀⠀⠀⢠⡷⢣⠀⠀⣸⠇⡟⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⢀⣠⣤⣤⠴⠶⠾⠟⠟⠭⠭⠥⠭⠤⠤⠄⠙⠛⠷⠤⢾⣁⣀⣀⡀⣁⠸⠀⠀⠀⠀⠀⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣴⣶⠾⠛⡛⠛⠉⠉⠘⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠺⣟⣶⣶⣤⣄⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⢟⣵⠿⠒⠀⠀⠀⢻⣆⠀⠀⠀⠀⢀⡀⣠⣦⠴⠾⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠻⣯⣉⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⣴⠏⠁⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠸⣿⡟⢹⣿⣿⡆⠉⠻⢿⣦⡄⣀⣂⣶⣶⢿⣿⠷⢾⣶⣦⣀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠻⢷⣤⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⠏⠁⠀⠀⠀⠀⠀⡠⠀⠀⠘⣿⡄⠀⠀⠀⠙⢿⣿⣻⢟⣁⣤⡤⣾⡿⠀⣿⣧⡀⣰⣿⣿⣷⠀⠈⠛⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣆⡀⠀⠀⠀⠀ ⣿⣿⠃⠀⢠⣴⣦⠄⢀⣿⣿⣦⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠙⠋⠃⠚⠁⠁⠁⠀⠀⠙⢻⣾⣙⣿⣁⣤⣤⣾⠟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⣦⡀⠀⠀ ⣿⢻⡆⠀⢸⣿⣿⠆⠈⠻⠿⠟⡆⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡇⠀⠀ ⣿⣮⡇⡀⠀⠀⠀⠀⠀⠀⠀⣴⢀⣿⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠆⠀⠀⠀⠀⠀⠘⣿⡀⠀ ⠘⣾⣿⡄⠀⠀⠀⠀⠀⣠⠞⢁⣼⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀ ⠀⠹⠿⣷⣦⣀⣀⣀⣀⣤⣶⣯⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆ ⠀⠀⠀⠘⢿⣭⣭⣍⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇ ⠀⠀⠀⠀⠀⠈⠙⠻⢷⣍⠓⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠙⠛⠿⠿⣿⣭⡶⠺⢏⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣰⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢿⡀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⢷⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠴⢛⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⡇⠀⠀ ⠀⣀⣀⠀⠤⠴⠶⠦⠄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣞⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠇⣾⣧⠀⠀ ⣴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣳⡄⠀⠀⠀⠀⠀⠀⠙⣷⡹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⢉⣤⣾⣿⣿⣷⡀ ⡎⠳⠶⣤⣀⣀⣀⣀⣀⣀⣀⣠⡾⢋⠀⠀⠀⠀⠀⠀⣶⣼⣿⣿⣮⣉⠳⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠾⢋⣥⣾⣿⣿⣸⣮⣿⣿⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢼⠀⠀⠀⠀⠀⢖⣾⣿⣿⣿⣏⣿⣷⣦⣌⣛⠛⠒⠶⠶⢦⣤⢤⣄⣀⣠⣤⠴⠶⠞⠛⠛⣏⣥⣶⣾⣿⣉⣿⠋⠿⠇⠀⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⡄⣼⣿⣿⢿⣿⣿⣾⣟⣿⣿⣿⣿⣿⢶⣶⣤⣤⣤⣤⣤⣤⣴⣦⣶⣶⣿⣟⣿⣿⣿⡷⢨⠭⠯⠀⠘⠂⠀⠈⣸⡿ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡶⡾⣷⠀⠀⠘⢼⣿⠿⠿⠛⠛⠋⠉⠉⢙⣿⢿⠉⡄⣟⠤⢿⣯⠉⠉⠉⠉⠉⢡⣀⣸⣿⡷⠙⠈⠉⠋⢸⣶⣿⣷⣶⡧⠀⠀⣿⡇ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⢿⣯⣦⣿⣦⣶⣶⣾⣿⣦⠀⠀⢠⣶⣾⣿⣿⣿⣧⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⡀⢠⢻⡇ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠞⣿⣿⣿⣿⣿⡏⠝⠺⣄⣽⡿⠿⠛⣿⣿⣿⣿⣿⣿⣿⢎⢾⠀⠙⠃⠁⠉⠈⠈⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣇⠸⣸⡇ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⢠⣿⣿⣟⣿⣿⣇⣀⣿⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣕⣕⣦⣤⣤⣦⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⠿⡇ ⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢐⣿⣿⣿⢿⡏⠉⠉⠛⠛⠃⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢸⣾⡇

⠀⠀⠀⠀⠀⣠⡤⡶⠶⡖⠠⢄⡀⠀⠀⢀⠤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⣢⢋⡎⠀⠀⠙⡷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⢖⣒⣒⣒⣒⣂⡤⢀⣴⣿⣏⣼⣀⡀⠀⢰⣃⠀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠔⠒⠀⠠⠄⠀⠀⠵⡫⠐⣊⣃⣻⣞⣿⢗⣒⣲⣒⣿⣷⡦⠀⠠⡀ ⠀⡠⠊⣀⡈⠄⠀⠀⠐⡖⢂⠤⢋⣁⠀⠀⣀⡀⠬⠇⠤⠐⠊⢉⠝⡻⠁⡠⠃ ⢻⠀⢸⠁⡅⡆⠀⠀⠀⠈⠒⠤⢀⣀⠀⠀⠀⠀⠀⠒⠒⢒⡈⠕⠊⠀⠀⡇⠀ ⠀⡀⠈⠉⠀⠡⠀⠐⠜⠀⠀⠂⠈⠇⡤⠌⡏⠉⠭⠭⡡⠶⠀⠀⠀⠀⢸⠀⠀ ⠀⢃⢀⡄⠀⢀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠠⠔⠀⠠⢀⣀⠠⠊⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⠀⡠⢄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀ ⠀⠀⠇⠸⡠⠎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠎⢰⠀⠀ ⠀⠀⠸⠀⠀⠀⢡⠀⠀⡠⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀ ⠀⠀⠀⠠⢂⡀⢈⠀⢰⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡀⠀ ⠀⠀⠀⣷⠁⠘⡌⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⡇⢠⠀ ⠀⠀⠀⡧⣄⡀⠏⠖⠒⠀⠁⠐⠂⠘⠩⡉⡩⢯⣹⠫⣁⠔⠋⠁⠀⠉⢷⠁⠀ ⠀⠀⠀⣿⡇⣷⣦⠤⠤⣤⣤⣤⣤⠔⢲⣶⣶⡾⠳⣶⣶⠒⣲⣶⣶⣾⢺⠀⠀ ⠀⠀⠀⣿⡇⡟⢻⠀⠀⠙⠉⠉⠉⠀⠈⠉⠹⡁⢀⡿⠉⠀⠀⠀⠀⢸⢸⠀⠀ ⠀⠀⠀⢈⠇⢷⣼⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⠋⢀⣀⣀⠀⣀⢤⠼⠸⡄⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⠞⠻⠋⠙⠉⠉⠹⠃⠀⠈⠉⠒⠤⣀⠀⠀⠀⣠⠞⣩⡿⠛⠻⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⣴⠃⣼⡏⠀⠀⠀⠀⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠇⢰⡏⠀⠀⠀⠀⠀⢐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠲⠍⣉⣉⣉⣉⣉⡩⠭⣉⣑⠒⠤⣤⣾⣿⣿⣿⣤⣿⣤⣄⣀⡀⠀⢀⣼⣇⠤⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⣀⣀⣀⣀⣀⣀⣀⣉⣳⡼⠛⣉⡤⠴⠓⡶⠲⣿⣯⣿⣿⣿⣭⣤⠤⢤⡤⢤⣾⣿⣶⣦⣄⣀⣀⣀⠀⠀ ⠀⠀⠀⠀⣠⠔⠛⢇⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠉⢹⣏⣀⠤⠤⠤⠟⠒⠛⠿⠴⠿⣯⡤⠤⠒⠒⠓⢺⣿⣿⣾⣿⣯⣄⠀⠘⢱⡀ ⠀⠀⣰⠋⠁⠀⠀⠈⢦⠀⠀⠀⠀⠐⢻⠓⠒⢀⣠⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣀⡤⠤⠖⠊⠁⠀⢈⡟⠛⡿⠉⠀⢀⡼⠀ ⣴⠚⠁⠀⡴⠋⠙⡄⢸⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠈⠉⠉⠁⠒⠀⠈⠉⠉⠀⠀⣄⣀⣀⣀⣀⣠⠤⠖⢋⡤⠊⠀⠀⠘⡏⠀⠀ ⠻⡆⠀⢸⡇⠀⣸⠃⡎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠴⠚⠉⠀⠀⠀⠀⢸⠇⠀⠀ ⠀⡇⠀⠀⠛⠋⠁⠀⠸⡀⠀⠀⢀⣀⠇⠀⠀⠀⣄⠀⠀⢹⠃⢀⣉⡉⢹⠉⠉⢻⣉⣉⣉⣁⣹⣤⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⢷⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠉⠻⠀⠉⠛⠆⠀⠈⠁⠉⠙⠢⠈⠉⠀⢀⠄⠀⠀⠀⠀⠀⢿⠀⠀⠀ ⠀⠘⡆⠀⣠⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⣀⠤⠒⠃⠀⠀⣄⡀⠀⢀⣀⠔⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⡇⠀⠛⠁⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⢧⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀ ⠀⠀⠈⡇⠀⠀⠀⣀⣀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⡞⠁⢘⡇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠓⡄⠀⢸⠀⠀⠀ ⠀⠀⠀⢸⠀⠸⣄⣠⠞⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⡰⠃⠀⡟⠀⠀⠀ ⠀⠀⠀⠘⡆⠀⠉⠁⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠁⠀⠘⡇⠀⠀⠀ ⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡤⠚⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⣤⡄⠀⠀⠸⠀⠀⠀⡎⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⠀⠀ ⠀⠀⠀⠀⢸⡈⢡⠖⠲⡄⢸⡀⠀⠀⠳⣄⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⡆⠀⠀ ⠀⠀⠀⠀⠀⣷⠇⠀⠀⢱⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣷⣧⣀⣀⡠⠤⠤⠤⣄⣀⣀⡤⣤⡤⠤⠤⠤⢤⣤⡤⣤⣤⠤⠒⠒⠛⣲⠶⠒⠚⠙⠒⠺⣯⣠⠼⠀⠀ ⠀⠀⠀⠀⠀⡟⢶⡤⣤⠴⠃⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⣠⠞⠹⣦⣼⠏⠳⣄⡤⠊⠁⠀⠀⠀⠀⠀⢀⡟⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⠇⢹⣤⣄⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣥⣤⣤⡿⢿⣤⣤⣤⣤⠤⠤⣴⣶⣶⣶⣶⣾⠧⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⣿⡏⠀⠀⢻⣿⣷⣷⣷⣿⣿⡇⠀⠘⣿⣿⣿⣿⡿⠀⠈⣿⣿⣿⡿⠀⠰⠿⠿⠿⠿⠿⣿⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⠀⢸⠉⢻⡇⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠁⠀⢼⡁⠀⠀⢨⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⢿⠀⢸⡀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡼⠀⠘⢿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠥⠤⢤⡤⠤⠤⠤⠤⢤⡴⢶⡾⠃⠈⠓⣄⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠉⠉⠀⠈⠉⠁⠒⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⢁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡀⠀⠈⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⣀⠠⢆⠘⣂⣄⠀⡰⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⢀⠀⠐⠍⢛⡽⠈⢋⡻⠾⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⢠⠀⠀⠀⠈⡄⠀⢘⠁⢀⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠉⠐⠀⠜⠓⠤⠼⡄⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡀⢠⢤⠏⠀⡀⠀⠐⠠⡮⠯⠷⠀⠀⠀⠀⠀ ⠀⣀⠔⠊⠉⠀⢠⠁⠈⠀⠀⡁⠀⠀⠀⠈⣋⡀⠠⡄⠀⠀⠀ ⠮⠤⠤⢄⡀⠀⠸⠀⠀⠀⠀⠉⠂⠄⣀⠀⠀⣨⡠⠶⣄⡀⠀ ⠀⠀⠀⠀⠙⣄⠀⠣⡰⣂⠀⠀⠀⠀⠠⠋⠀⡠⠁⠀⠀⠈⢆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠁⠀⠋⢦⢀⠀⠀⠀⠀ ⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣁⣀⠀⠀⠀⠀⠀⠱⢂⠀⠀⠀ ⠈⠒⠘⠡⠒⠀⠤⠀⣀⠃⢻⣿⣿⣿⡷⣶⣶⣖⣦⣤⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠂⠤⡇⠀⠠⢍⡑⠀⠘⠻⠿⠟⢁⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠄⣀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⡀⠀⠀⣀⠄⠈⠈⠁⠈⠀

⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠴⠶⠶⠶⠦⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠉⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠠⠤⠭⠤⠭⠭⠭⠭⣀⣀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠠⠔⠒⠛⠒⢶⡒⠒⠤⣄⠈⠉⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⡠⢶⠶⠶⣵⡤⠤⣬⣧⣄⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⢀⡜⡵⠁⠀⠀⠈⢿⠉⠀⠈⠻⡇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢴⣿⣻⠗⠒⢤⣤⠤⢼⡧⣤⣀⡀⣇⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣦⣾⣿⣿⣷⡞⠑⣶⣷⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠾⠦⠼⠷⠿⣶⡟⠀⠀⠈⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⣄⣀⡤⠤⠤⠤⠤⢴⡇⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣷⣋⣉⣠⡤⢴⠶⢶⡶⢾⠀⠀⠀⠀⢠⡇⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡞⠀⢸⡀⠀⠀⣠⡞⠷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⣸⠁⠀⠀⠉⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⢦⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢫⣷⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠤⠼⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⣿⣿⡿⠿⣛⣩⣭⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣤⣶⣆⡀ ⠀⠀⠀⠀⠀⠀⠘⢛⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠹⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠛⠛⢻⣿⣿⣃ ⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣶⣾⣿⣿⣿⡟⠀⠀⠀⠀⢹⣿⣟ ⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠒⠚⠿⣿⢫⣥⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⣀⣾⡿⠋ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⣶⣶⣿⣿⣿⠟⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀ ⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⢸⣿⡿⢟⣩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⢴⣿⣿⣿⣿⠇⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⣡⣾⣿⣷⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣾⣌⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⣠⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠉⠛⠿⠿⠿⠟⠛⠉⠁⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢋⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣁⣨⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⣿⠿⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⡿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠴⠁⠊⠀⡎⠼⠯⠿⢋⠡⠊⠀⠔⠁⢄⣀⢨⡀⠀⢡⠑⠙⢭⣮⢓⣄⣽⣿⣿⠄ ⠀⠈⠀⠀⠉⠀⠀⠈⠁⠀⠀⣘⣠⣤⣴⠃⢸⠈⣇⣀⡆⠀⠐⠭⠤⠈⢿⣿⣿⠁ ⢤⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠋⠁⠀⢈⠀⠈⠀⡟⠻⢿⣦⡀⠀⠀⠀⠈⣿⣿⡤ ⠋⠀⠀⠀⠀⣠⡾⢛⠁⠀⠀⢸⡀⠀⠀⠑⣆⠚⠁⠀⠀⠙⢿⡄⠀⠀⢸⢻⣿⡏ ⡄⠀⠀⠀⢰⠋⡄⢸⣯⢧⡄⠈⡇⠀⠀⠀⠫⠀⢸⠀⠀⡇⢀⠙⡄⠀⢸⠾⣿⣦ ⠁⠀⠀⠀⢘⢀⣇⣼⠔⣾⠲⠇⢇⡆⣖⠀⠀⢨⣾⢦⣀⡃⢈⠀⣠⠀⠸⠂⣿⣿ ⠀⠀⠀⠀⢀⠀⣇⢻⢠⠃⡿⠀⢸⣇⣿⠀⠀⡜⣷⣾⡀⣷⢨⠀⠨⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⢸⠂⣿⠊⡎⢠⠃⠀⠀⠞⡟⡇⡰⠁⡟⡟⣷⢩⣸⢀⣀⡇⢸⡂⣿⣿ ⠀⠀⠀⠀⢸⠴⣯⣤⣶⣶⡆⣥⠀⠠⠁⡷⠁⡨⣤⣥⡧⡘⣯⠠⣇⡇⢸⠦⣿⣿ ⠀⠀⠀⠀⠈⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢠⡏⢐⣿⡇⢸⣀⣿⣿ ⠀⠀⠀⠀⠀⡆⢏⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢱⡇⣸⣿⡇⢸⢩⣿⣿ ⠀⠀⠀⠀⠀⢿⠸⡄⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⣿⣧⣿⣿⠀⣾⣉⣿⣿ ⢤⡤⢄⡀⠀⢸⣧⡵⡤⣀⠀⠀⠙⠒⠒⠋⠀⢀⣠⣾⣿⢿⣾⡿⠃⢠⣧⣽⣿⣿ ⣺⣿⡷⣯⠕⣢⠽⢿⡿⣄⠈⠁⠒⠀⠴⠒⡿⣿⡿⠿⠓⠋⠉⢀⣤⣾⣿⣿⣿⣿ ⠊⠁⠀⠈⠂⢄⡀⠀⠉⠐⠢⠄⣀⠀⡰⢒⣉⣧⠤⠤⡴⠲⢾⡁⢸⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠈⠉⢙⠗⠠⠬⡅⣛⣞⠙⢢⠤⠐⠉⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⡿⠻⣿⣿⠿⠿⠋⠉⠙⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⠀⠀⠀ ⡎⠻⣿⣿⡇⠀⢛⠣⢄⣀⣀⡓⠠⠭⠶⠀⠀⠉⠛⠛⠻⢿⣿⣿⡄⠀⠸⠀⠀⠀ ⢰⠀⠈⢻⡇⠀⠸⡠⠲⠀⠀⠈⠑⠒⠂⠶⣲⠄⠀⠀⠀⠲⠶⠄⠈⠑⠴⠀⠀⠀ ⠤⢧⡀⢀⠧⡀⢠⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠤⣀⣘⠯⢔⣢⡄⠀⠀⠀ ⢄⡀⠈⢾⠙⢀⠀⢹⡇⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠤⢤⡠⠔ ⠒⠉⠁⢃⣠⡇⠀⠀⠈⠑⢾⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠂⠁⠀⢀ ⠉⡵⠒⠈⣄⠑⢄⡀⠀⠀⠀⢡⠴⠢⠀⠠⢤⡒⠒⢠⡄⠐⢒⢦⠎⡀⢀⣀⠴⠟ ⠚⢲⡆⠉⠀⠑⡤⠬⠑⣲⡖⠊⠀⠾⠆⡠⠊⠉⠀⠀⠀⠈⠙⠳⡄⠴⠆⣡⣀⡀ ⠀⡬⠋⠒⡀⠘⢄⠀⠀⠀⠀⢉⡠⠛⢄⣸⡤⡀⠀⠀⠀⠀⢀⠤⠁⡰⢅⣀⡀⠈ ⠘⣍⣀⡈⡇⠀⠀⣈⣉⣉⣁⡀⠀⠀⠀⠈⠢⠄⣉⣽⣉⣉⣠⠔⢺⢄⡀⠑⢾⠉ ⠀⠑⢠⠐⠁⠀⠀⢀⠐⠤⢀⠊⠍⠒⣄⠀⠀⠀⠀⢀⡀⠀⠈⢆⠀⢻⠏⡵⠂⠵ ⠀⠀⢸⠀⠀⠀⠀⠀⠑⠀⠀⢄⡉⠒⡁⠑⠀⠀⡐⠁⠸⠀⡠⠃⣭⢂⢾⠀⠀⠀ ⠀⠀⢸⡲⡒⠂⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠁⣰⠕⠈⠙⡞⠈⡆⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⡶⠎⠉⠉⠹⠟⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠴⠟⠁⣠⡄⠀⠀⠰⠿⠀⠀⢠⠄⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠋⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠟⠁⠈⠉⣠⠔⠊⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠤⣄ ⢀⡏⢠⡄⠀⠞⢀⡠⠒⠈⠉⣁⣀⠤⠴⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⠉⠀⠀⠀⠀⣠⠟ ⢸⠀⠀⠀⠀⡰⠋⠀⣠⠔⠋⣁⠤⠤⢄⡀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⢀⣤⣶⡾⠋⠀ ⢸⡀⡄⠀⠀⠁⡠⠊⠀⠀⢰⠃⠀⠀⠀⠉⢢⡀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⣴⣾⣷⠿⠛⠁⠀⠀⠀ ⠀⢇⠀⠀⠀⢸⠁⡰⠋⠉⠚⢇⠀⢴⣆⠀⠀⢱⡀⢈⡧⠔⠒⠒⠦⡀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⢀⡤⠖⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢧⡀⠀⠀⠀⣇⠀⣤⡀⠈⢦⡈⢿⣧⣤⢀⡇⢀⡠⠔⠊⠉⠑⠛⠢⠤⠤⣤⠚⠁⣀⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠓⠂⠐⠚⢆⠘⣿⣄⣸⠙⠲⢬⡤⣾⠴⠋⠀⣀⣀⣀⣀⡀⢀⢀⣀⡼⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⣿⡟⠀⠀⣠⠟⠁⢀⣞⣻⣿⣷⣿⣿⣷⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⣵⣠⠞⠁⠀⡴⠛⢿⡿⣾⣿⣭⣽⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠔⣡⠞⠁⠀⣠⠊⠀⠀⠀⣿⡿⠛⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡞⠁⠀⠀⣰⡁⠀⠀⠀⣠⠟⠀⠀⢈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⣀⡔⢁⣩⠿⠒⠙⣧⣜⠊⠀⢀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠀⠀⠀⠀⢹⢸⠀⠀⠘⠀⠨⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢸⠀⠀⢤⣴⣆⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠡⣀⣠⠤⠤⢤⣐⡺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠋⠁⠀⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠴⠏⠗⠶⠚⠃⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⢶⣾⣿⣿⣿⣿⣿⣿⣏⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣟⣯⣿⣶⣿⣿⣿⣿⡿⠶⢶⣦⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢷⣶⠄ ⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡼⣏⣀⣀⣤⣤⣤⣶⣶⣿⣿⠀⠀⣿⠇ ⣠⣿⣿⣿⣿⣿⣿⠟⠋⠉⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀ ⣿⣿⣿⣿⡿⣫⣿⣿⣗⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀ ⢿⣿⣿⣿⣮⡙⠿⣿⣿⣿⠿⠛⢋⣽⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⣿⣿⣿⣿⣤⡀⠀⠀⣠⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣮⣻⣿⣿⣿⣿⣿⣟⣯⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣿⣿⣿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠋⠉⠉⠀⠀⠀⠀⠀⠉⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣤⣄⣠⢤⣄⣤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣼⣾⠛⠛⠲⣼⣷⡘⠿⢿⡏⣉⡓⠶⢤⣤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠾⠟⠁⣤⣄⣀⣀⡀⠙⠓⠚⠷⡽⢿⣷⢀⣰⢿⣫⠿⠭⠟⠳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠦⣀⠈⣿⣶⡦⢤⣬⣉⣁⣛⣋⣀⣀⡀⠀⣶⣶⣌⠉⡿⠉⣽⣤⡀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠻⣿⠛⠃⣸⢻⣿⡗⠀⢸⠀⠉⠁⠀⠈⠛⠋⠀⣧⢸⣿⣿⣿⡄⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡴⠛⠛⠛⠛⠿⠿⣦⣉⣀⣠⡾⠆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠻⣿⡿⠁⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠚⡹⠴⣶⠟⠛⠛⠛⢳⡶⠲⢤⣙⠣⣅⠓⢩⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⠀⠰⣶⣦⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⡈⠳⠤⠿⠤⠤⠤⠤⠚⠓⠒⠒⠚⠳⠬⠳⡀⢠⣤⣄⠀⠀⠀⠀⢠⠏⣏⠉⠙⠻⢿⣁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣙⣶⡖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠦⢤⠷⠈⠉⠁⠀⠀⠀⠀⠘⣦⠈⣧⡈⠙⠲⢌⡑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⡀⠀⣀⠤⠒⣋⡥⠔⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢿⣿⡆⠀⠀⡟⠒⢬⡓⢤⡀⠀⠀⠀⠀⠀ ⠀⣀⣈⠉⣤⡖⠋⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢀⣤⣤⡀⠀⢹⡄⠀⠈⢀⣀⠀⢷⠀⠀⠈⠳⢍⠲⣄⠀⠀⠀ ⠉⠀⠈⠙⡇⢹⠀⠀⠀⠀⠀⠀⠈⣹⣶⠤⠤⢤⣤⣶⣯⣤⣄⣀⣀⣀⣀⠈⠻⡿⠋⠀⢰⠇⠀⢀⣈⣿⡧⣼⠀⠀⠀⠀⡠⠽⡞⠓⠢⢤ ⠀⠀⠀⠀⠻⠾⠀⠀⠀⠀⠀⠀⠰⣏⣭⡀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠉⣩⣍⠉⢻⡏⢉⣅⡀⠀⠀⢸⡄⠀⠀⡞⣰⠊⠉⠳⡄⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣫⠵⠛⠙⠒⣾⣿⣿⣿⣿⣿⠦⢤⣀⣀⣀⣠⣿⡋⠀⣰⢃⣈⣛⣁⡤⠤⠼⠃⠀⠀⠉⠉⠀⠀⠀⠸⡌ ⠀⠀⠀⣠⣤⠤⠖⠒⠊⠁⡖⠉⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠀⠀⠉⠉⠉⠉⠙⢮⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧ ⠀⠀⠀⢿⡿⠦⠔⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⠈⠓⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⣄⣀⣨⣿⡷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠛⠛⠛⠛⠓⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢀⡴⠊⠁⠀⠀⠀⠈⠙⠢⣀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠉⠑⢤⡀⠀ ⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠋⠀⠀⠀⠀⠀⡠⠂⠁⠢⡈⢢⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠎⢁⡈⢢⠱⡄ ⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠈⠛⠻⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⡁⢰⣿⡆⢱⠀⡆⠀⠀⡇⠀⠀⠀⠀⠀⠘⡀⠸⠿⢠⠀⢳ ⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠣⣀⠉⣁⠏⠀⡇⠀⠘⡇⠀⠀⠀⠀⠀⠀⠑⠠⠄⠊⠀⣸ ⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣷⣦⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢰⠃⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃ ⠀⡞⠀⠀⢠⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣀⠴⠁⠀ ⢰⠃⠀⠀⢺⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣤⣤⣤⠤⠖⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠓⠒⢺⠏⠁⠀⠀⠀ ⣾⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢸⠀⠀⠀⠀⠀ ⡿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢳⡀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀ ⡇⠀⢰⣿⣿⡆⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢧⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀ ⣷⠀⠸⣿⣿⡇⠀⢠⣿⣿⡿⠋⠉⠙⠻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢸⠇⠘⡆⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀ ⢹⠀⠀⠈⠉⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢱⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀ ⠸⡆⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⡇⠀⣷⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⠀⠀⠀ ⠀⢷⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢿⠀⢸⡀⠀⠀⠀⠀⠀⠀⡏⠀⡿⠀⠀⠀⠀⠀⠀ ⠀⠘⣇⠀⠀⠀⠀⠀⢿⣿⣧⣀⣠⣧⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡄⠈⣇⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡆⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠘⡇⠀⢻⠀⠀⠀⠀⠀⠀⡇⢠⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠻⣿⣿⡿⠃⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠸⡇⠀⠀⠀⠀⢰⠁⢸⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢿⠀⠀⣷⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⠀⠀⠸⡄⠀⠀⠀⡾⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⣄⠀⠀⠀⠀⢸⠀⠀⠀⢱⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢸⠀⠀⠀⠀⢇⠀⢰⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠉⠙⠛⠛⠒⠊⠋⠀⠀⠀⠀⠈⠲⠾⠶⠦⢼⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢘⡶⠴⠶⠒⠒⠒⠒⠒⠺⠿⠿⣿⣿⣁⣀⣀⠀⠀⠀⣀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⣴⡋⠉⠉⠉⠙⠦⣤⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣠⠤⠔⠒⠚⠉⠉⠉⠉⠒⠒⠤⠤⠤⠤⠤⠄⠂⠁⠈⠛⠒⢶⠄ ⠀⠀⠀⠀⠉⠛⠒⠒⠺⣦⣀⡀⣀⣀⣀⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⣀⣀⣠⠖⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠻⠶⢤⣤⡤⠤⠶⠖⠛⠉⠛⠷⠶⠶⠖⠛⠋⠉⠛⠳⢦⣤⣤⡤⠤⠒⠒⠛⠛⠶⠶⠖⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⡏⢀⣼⣿⣖⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢣⣼⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⠈⠻⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⢸⡏⠁⠈⠳⡜⣧⡀⠀⠀⠀⠀⠀⠀⣴⠟⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠙⢦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⣽⠘⣧⠰⣆⠀⠹⡼⣧⡀⠀⠀⠀⢀⡾⢁⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠈⠧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣿⠀⢻⣧⡻⣏⢀⠹⣜⢿⣆⠀⣰⠟⣡⡞⠁⠀⢀⣀⣀⡀⢀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢀⡿⢛⣲⣛⣿⡛⠛⠀⠈⣿⡏⠛⣿⣛⠉⠉⠙⠛⣯⣥⡌⠙⢋⣩⠟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⠒⠋⠀⠙⣛⠛⠋⠙⢶⣶⣾⠿⣿⠀⣩⣴⠖⠲⣤⡀⠀⠀⠀⣰⠏⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⣋⣀⣀⣠⣤⣈⠉⢉⣠⡴⠛⠉⢀⣼⣯⣀⣈⣉⣩⠭⣅⣀⣠⢤⡞⠉⠀⣀⣤⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⢩⣥⠀⠀⠈⠉⠹⣧⣤⣤⣶⡿⠋⠀⠀⠈⣁⣠⡴⢦⣄⡀⠀⢹⠀⢰⠋⠈⡇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣶⢂⣿⣀⣶⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⣾⢁⣸⣦⣼⣆⠉⠀⢸⠀⠸⣧⡼⠃⠰⣇⠀⠀⠀⠀⠀⢀⣴⢞⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣼⣋⣁⡀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠉⠀⠀⣀⣈⠻⡄⠘⢧⡀⠀⠀⣤⡄⠙⣿⣶⠖⠒⠿⣟⣵⡟⢸⣿⣿⣿⡟⠛⠛⠋⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣿⣿⡇⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣧⡿⠀⠀⣷⠀⠀⠿⠃⠀⡿⠃⠀⠀⠀⢹⣿⡇⢸⣿⡟⡽⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⡛⠋⠁⢀⡴⠏⣠⢀⡄⠀⠀⠀⠀⠀⡜⢦⣀⣀⣈⣙⡿⠟⣁⠀⠀⢻⡀⠀⠀⣠⣾⠃⠀⠀⢀⣴⣿⣿⠀⡿⢿⣷⢃⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣋⡤⠞⠁⣼⠁⠀⠀⠀⠀⠀⠀⠀⠛⠪⠤⠴⠒⠋⠁⢀⠀⠈⠳⣄⢠⣟⢻⡦⠤⠞⢿⣿⣿⣿⡀⢷⠋⣠⣾⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠁⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠛⠛⠁⢀⣤⠀⢸⠋⢹⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣤⠖⠋⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⠖⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠘⠟⠀⠸⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠛⠉⢉⣀⣤⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠰⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣟⣛⠛⢻⡆⠀⠀⠀⣠⣿⠛⣉⣤⣖⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠦⠤⣤⣧⣴⣾⣛⣛⣻⣛⣛⣛⣛⣛⣿⣿ ⣀⠀⠀⠀⠀⠀⠀⠴⠒⠒⠒⠂⠀⠈⠉⠉⠁⠁⠀⠈⢻⡀⠀⢰⡏⠙⠋⠉⠉⠉⢻⣷⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⣿⣿⠿⠍⠁⠀⢀⠀⠀⢈⣉⣉⣀⣤⠀ ⠀⠄⠀⠠⠤⠤⠤⠤⠤⠶⠦⠤⠴⠶⠶⠲⠶⠆⠀⠀⠘⠻⣦⡿⠗⠀⠀⠀⠀⠀⢺⣿⢟⣿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠉⠹⢿⣿⢻⣿⣿⣿⣧⡤⠠⠤⠤⠤⠄⠀⠀⠀⠀⠀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣰⣋⣵⣏⣹⣿⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣾⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⡤⠖⠚⠛⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠒⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣤⠞⠋⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠏⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⡈⢰⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇⢿⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢀⣀⣠⠤⠒⢯⡀⠘⠀⡨⢀⡦⣀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⢤⢰⠥⠤⣤⢤⡤⢽⠀⠀⣟⡡⢤⣤⣬⣧⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠐⠁⠈⠦⢄⣈⣉⢥⡎⠀⠀⠉⢦⣈⣛⡡⠊⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠤⠖⠋⠀⠀⠀⠀⢸⠛⠓⠂⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣏⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡶⠎⢳⣤⣄⣀⡀⠀⠀⠀⣼⣁⣀⠀⠀⠀⢯⡇⠀⢠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢸⡇⠀⠀⢹⠀⠀⡼⠘⠈⠋⠳⣄⡤⠞⢣⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢸⠀⠀⠀⠸⠀⢠⠁⠀⢀⡤⠖⣤⠖⣄⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⢤⡞⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠀⠰⣯⠤⠾⠤⠾⣼⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠚⠉⠉⢉⠞⠁⢠⠏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠤⠤⠴⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡴⠖⠋⠉⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠁⠀⠀⠀⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢦⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣃⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣠⡼⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⢦⠤⠤⠤⠖⠛⡏⠉⠀⠀⠀⠙⠉⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠹⣄⢰⣟⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠋⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠈⣷⣤⠊⣶⢱⢀⡀⠀⢀⡀⠀⣀⣀⠀⠀⠀⠀⠀⣀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡴⠀⠀⠀⠀⠀⠀

⠀⠀⢰⠋⢓⠊⠉⠉⠂⠉⠉⠀⠈⠉⠁⠈⠉⠐⠒⠒⢲⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠂⠻⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⢀⣀⠀⠘⠀⠜⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⡆⠠⠀⢠⠁⢀⠄⠉⢲⡖⡨⠭⡀⠐⡀⠀⠀⡜⠀⠀⢀⡀⡀⠀⠀ ⠀⠀⠀⡇⠀⠀⠐⠀⠠⠙⠜⡸⠢⠆⠃⠃⢀⠃⠀⠀⡧⠲⡪⠕⠲⠸⠀⠀ ⠀⠀⠀⠘⠀⠀⠀⠌⠂⠀⠂⠃⡠⠑⠀⠐⠀⠀⠀⢸⢀⣠⠃⠀⡄⠃⠓⠄ ⠀⢀⠔⠚⠀⠀⠀⠹⠿⢏⣷⡄⠀⠀⠀⠀⠀⣀⡀⢸⠁⠀⠀⠀⠸⡡⠠⠂ ⠀⣇⢀⠀⡄⢆⣀⡀⠀⠂⠈⠁⠂⠀⠀⠀⠀⠛⠁⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⢃⣂⠨⢑⡀⠀⣤⡤⠠⢤⣀⢤⠤⠄⣀⠤⢌⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠐⠒⠈⢹⢉⣐⣀⢀⣀⣀⠆⢂⣁⡀⢀⣀⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣈⣢⣌⣉⡁⠘⣍⣩⡍⡅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢨⢤⢤⣣⡀⠀⠀⠀⠈⠑⠢⠤⡟⣹⣤⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣘⠬⡿⣇⠀⠀⠀⠀⠀⠀⢼⣿⣟⠡⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⣰⠂⠀⢀⣿⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣷⢫⠏⠳⢠⣿⠏⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣒⡶⢾⡇⠘⠿⠒⢀⣿⠏⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⡹⣿⠹⣎⢧⣀⡀⠀⢸⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣡⣄⣠⣿⡟⣿⣿⣷⣷⠇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠂⠀⠈⠀⠈⠀⠀⠀⠀⠀⠈⠙⢻⡟⠛⠓⠒⠦⣤⣄⣀⠀⠀⠀⢀⣠⡤⠔⠒⠚⠛⠛⠛⠛⠛⠛⠻⢿⣿⣿⣧⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⢻⡷⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠧⣭⠛⠛⠳⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣦⣤⣤⣀⠀⣰⡿⠋⠀⣀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠈⠛⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢻⣦⠤⠾⣧⣀⣤⠀⠀⠀⠀⠀⢀⡄⠀⢰⡄⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢠⠞⠁⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢀⣸⡷⠤⠾⢧⣄⣶⠂⠀⠀⠀⠘⣆⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⡏⠀⠀⠀⢀⣠⣤⡀⠀⢿⠀⠀⣴⠋⠁⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⡆⠀⠀⠀⣿⣿⣿⣷⠀⣼⠀⢰⠃⣴⣒⣲⣄⠀⠀⠀⠀⢻⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠋⢷⡀⠀⠀⠘⠛⠛⠁⣰⠋⠀⢸⡀⢿⣿⣿⡿⠀⠀⠀⠀⣸⣀⣀⠀⠀⢸⡇⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡆⠀⢹⢶⠞⠓⠦⣴⡚⠁⠀⠀⠀⢧⡀⠉⠉⠀⠀⢀⣴⠟⠉⢉⡿⠉⠀⢸⠆⠀⠀⠀⠀⢸⣿⠻⣦⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠙⠄⣸⠘⢦⣀⡀⠈⠉⠉⠀⠀⠀⠀⠙⠲⠦⠤⣴⣟⠃⢀⡴⠋⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⠀⣿⣧⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⠀⢀⣠⡼⢧⣀⡀⠉⠉⠓⠒⠒⠁⠀⠀⠀⠀⠀⠀⢀⣼⠈⠓⠋⠀⠀⠀⠀⠀⢸⠀⠀⣠⡀⠀⢸⣿⠀⠺⣿⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⠀⠀⠀⠙⣿⢇⣀⡏⠙⢲⠦⢤⣀⣀⣀⣀⣀⣀⣠⠴⡶⠋⣽⣆⠀⠀⠀⠀⠀⠀⠀⣾⢠⠎⠉⢱⡄⢸⡇⠀⠸⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⠀⠀⠀⠀⠉⢦⣹⠓⠦⣼⣀⡀⡿⠀⠀⣿⠁⠀⣇⣠⡷⠶⣯⠟⠇⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⢧⢸⡇⠀⢠⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠙⠦⣄⡇⠈⠉⡏⠙⠉⡟⠋⠉⣇⣠⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣾⡇⠀⢸⣿⠀ ⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠛⠒⠃⠤⠔⠓⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⢤⣤⣤⡤⣿⣿⠃⠀⣸⡿⠀ ⠀⠠⠀⠀⠠⠀⠠⠀⠤⣄⠭⣤⠨⢭⠽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⠤⢤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡇⢸⠃⣿⡟⠀⢀⣿⠃⠀ ⢀⠀⠀⠀⠀⠂⣄⠀⡀⠘⢧⡘⢣⡄⢹⣾⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢰⡇⢸⢸⣿⡇⠀⣴⡟⠀⠀ ⡀⢀⡀⠀⢀⣐⣚⣒⣒⣒⣒⣒⣒⣺⣶⠟⠨⡟⠲⠤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸⡇⣤⣿⡿⠀⢀⣿⠀⠀⠀ ⠀⠤⠀⠠⠦⠶⠶⠶⠴⠦⠤⠤⣤⡾⢋⡀⠀⢿⡀⠀⠀⠈⠙⢤⡉⠉⢛⡿⣷⠒⢲⡦⢤⠤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣴⣿⠤⢶⡿⠀⢿⣿⡇⠀⣾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣈⣿⣿⡁⠀⠯⣿⣿⡒⠤⠤⣤⣝⣚⣁⠀⣸⣿⣟⠀⠈⢷⡤⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⢰⢇⣠⠟⠀⠀⢸⣿⠄⢠⡿⠀⠀⠀⠀ ⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡿⠛⠛⠛⠻⣧⣤⣴⣿⡿⠿⠿⣿⣿⠛⣶⣿⣿⠏⠀⢿⣿⣖⣒⡶⠶⠶⠶⠤⣤⣤⡤⡤⠴⢶⣿⣿⣷⣾⠀⠀⣾⣿⣇⣾⠃⠀⠀⠀⠀ ⣶⣶⣶⣴⣶⣦⣶⣦⣤⣤⣶⣶⣶⣶⣶⣾⣿⣶⣿⣿⣄⠀⠀⠀⠀⠉⠙⢷⡄⢀⣴⠿⠿⠿⠿⠿⠀⢠⣿⣿⣿⣿⡿⠀⣼⣿⢿⣿⡇⠠⢠⣿⣿⣻⡏⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢭⣿⠏⣩⣿⣿⡟⠉⠙⠻⢶⣄⠈⠻⠟⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠈⠀⣴⣏⣠⣶⢿⣻⣿⡿⢫⣰⡟⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢨⣿⣴⣿⡿⠛⠛⣦⠀⢠⣾⣿⣷⣶⡶⠶⠴⢶⣶⣿⣽⣍⣉⣉⣽⣿⡶⠾⣿⣿⣭⣶⣾⡛⣉⡀⢸⡿⠃⠀⠀⠀⠀⠀⠀