⠀⠀⠀⠀⠀⠀⣖⢤⡀⠀⠀⠀⠀⠀⠀⠀
⡐⠣⡄⠀⠀⠀⠑⡄⠙⠆⠀⠀⠀⠀⠀⠀
⡇⠘⢄⡄⠂⠉⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀
⢃⡐⠁⠀⠀⠀⠀⠀⠀⡼⠆⠀⠀⢀⣴⠂
⠀⢁⠀⠀⣠⡀⠀⠀⠀⠀⢸⢀⣴⣿⠏⠀
⠀⠈⣿⡄⢹⣿⡄⠀⢀⡀⢠⣿⣿⠏⠀⠀
⠀⠀⠈⢇⠀⢉⣥⣾⣿⣷⣿⣿⠏⠀⠀⠀
⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣯⠱⡀⠀⠀
⠀⠀⠀⠀⠙⠋⢻⣿⣿⣿⣿⣿⡄⡇⠀⠀
⠀⠀⠀⠀⠀⠘⣼⣿⣿⣿⣿⣿⣷⡇⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡿⠛⡿⣿⡇⡇⠀⠀
⠀⠀⠀⠀⠠⠟⠋⠀⠈⠂⠌⠺⠇⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⡆⠀⠀⠀⠀
⠀⠀⢀⡴⠋⠙⠿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⢀⡞⠁⠀⠀⠀⠀⠉⠉⠉⠉⠀⠙⢿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀
⠀⢸⠃⠀⠀⠀⠀⣠⢄⡀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⢧⠀⠀⠀
⠀⣸⠀⠐⠳⣤⠀⠿⠾⠃⠀⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀⠸⡇⠀⠀
⠸⣟⣇⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠻⠿⠃⠀⠀⠀⠀⠀⢠⡇⠀⠀
⠀⠈⢻⠀⠀⠀⠀⠀⠀⢘⡟⠁⠀⠀⠀⠁⠓⠷⠀⠀⢀⡾⠀⠀⠀
⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⡅⠀⠀⠀
⠀⠀⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠓⠚⠁⠀⠀⠀
⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠶⠶⠶⠖⠾⠽⠋⠉⠛⠉⠁

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⢻⣶⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⢻⡀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⣿⡟
⠀⠀⠣⡀⠀⠀⠀⠑⢄⢀⣀⣀⣀⣀⣀⣀⠤⠒⠉⠀⠀⠀⢠⠟⠀
⠀⠀⠀⠑⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢤⠊⠀⠀⠀⠀
⠀⠀⠀⠀⡘⠀⠀⢮⣽⠀⠀⠀⠀⠀⠰⣭⡇⠀⠀⠈⢆⠀⠀⠀⠀
⠀⠀⠀⠀⢃⠠⢄⠈⠁⠀⠰⠶⠀⠀⠀⠈⠀⡀⣀⠀⠸⡀⠀⠀⠀
⠀⠀⠀⢸⠠⣀⣠⠇⠀⠀⡠⠐⠒⡄⠀⠀⠨⡀⢀⠅⠀⡇⠀⠀⠀
⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠘⠤⠠⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀
⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠰⠀⠀⠀

⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⢦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣨⡷⠖⠛⠋⠛⠛⠛⠛⠷⣼⡃⠀⠀⠀⠀⠀
⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀
⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀
⠀⠀⣿⠀⠀⠀⠀⠀⠘⠃⠀⠈⠃⠀⠀⠀⠀⠀⢻⠀⠀⠀
⠀⠀⢻⠀⠀⠀⠀⠀⠀⢀⣺⣂⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀
⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⡉⢻⡄⠀
⠀⠀⢰⡋⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠾⠁⠀
⠀⠀⠈⠙⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡇⣰⠦⢤⣤⣤⣤⣤⣤⣼⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠻⠛⠀

⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⣿⣶⣄⡀⣀⣀⣀⣀⣠⣴⣾⣿⢿⠇⠀⠀⠀⠀⠀⢀⣠⣤⣶⡖
⠀⠀⢙⣯⣿⣿⣿⣿⣿⣟⣿⡾⣿⡽⠁⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⠁
⠀⢠⡚⣿⣻⡿⣿⣻⣋⠻⣯⣿⣟⣷⣄⠀⢴⣾⣿⡯⠿⠛⠉⠁⠀⠀
⠀⣧⢴⣿⡿⣿⣿⣷⣄⣤⣿⢿⣽⣿⣿⣆⠀⠘⠻⣦⣄⠀⠀⠀⠀⠀
⠸⣾⣿⣿⣟⣿⣟⣿⣿⣿⣜⣵⣿⣿⣿⣿⣂⠀⠀⣹⣿⠷⠀⠀⠀⠀
⠀⢨⣟⣯⣿⣷⢿⣻⣟⣿⣿⣿⣿⢿⣿⢣⣾⢠⣾⣟⠁⠀⠀⠀⠀⠀
⠀⣸⣿⣻⣽⣾⣿⢿⡿⣟⣽⣿⢟⣿⣻⣿⢫⡃⢈⢜⢕⢆⠀⠀⠀⠀
⠀⠘⢹⣿⣿⣽⣟⣿⢿⣳⣻⣽⣿⣟⣿⣵⢿⡇⡇⠁⠁⠀⠀⠀⠀⠀
⠀⠀⠀⢻⣿⣯⣿⣻⣿⢿⣯⣿⣾⣿⣽⣾⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⣮⣿⢿⢽⣟⣿⡺⣿⣾⣷⣿⡻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠰⠿⠿⠓⠁⠀⠀⠀

⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⢦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣨⡷⠖⠛⠋⠛⠛⠛⠛⠷⣼⡃⠀⠀⠀⠀⠀
⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀
⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀
⠀⠀⣿⠀⠀⠀⠀⠀⠘⠃⠀⠈⠃⠀⠀⠀⠀⠀⢻⠀⠀⠀
⠀⠀⢻⠀⠀⠀⠀⠀⠀⢀⣺⣂⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀
⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⡉⢻⡄⠀
⠀⠀⢰⡋⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠾⠁⠀
⠀⠀⠈⠙⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡇⣰⠦⢤⣤⣤⣤⣤⣤⣼⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠻⠛⠀

⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⢦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣨⡷⠖⠛⠋⠛⠛⠛⠛⠷⣼⡃⠀⠀⠀⠀⠀
⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀
⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀
⠀⠀⣿⠀⠀⠀⠀⠀⠘⠃⠀⠈⠃⠀⠀⠀⠀⠀⢻⠀⠀⠀
⠀⠀⢻⠀⠀⠀⠀⠀⠀⢀⣺⣂⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀
⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⡉⢻⡄⠀
⠀⠀⢰⡋⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠾⠁⠀
⠀⠀⠈⠙⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡇⣰⠦⢤⣤⣤⣤⣤⣤⣼⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠻⠛⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⢦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣨⡷⠖⠛⠋⠛⠛⠛⠛⠷⣼⡃⠀⠀⠀⠀⠀
⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀
⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀
⠀⠀⣿⠀⠀⠀⠀⠀⠘⠃⠀⠈⠃⠀⠀⠀⠀⠀⢻⠀⠀⠀
⠀⠀⢻⠀⠀⠀⠀⠀⠀⢀⣺⣂⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀
⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⡉⢻⡄⠀
⠀⠀⢰⡋⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠾⠁⠀
⠀⠀⠈⠙⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡇⣰⠦⢤⣤⣤⣤⣤⣤⣼⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠻⠛⠀⠀⠀⠀