Wedel Penis Emojis & Text

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⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡄⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣾⣷⣴⣾⣿⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢻⣿⣿⣿⡿⠿⢿⡟⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠺⡿⠻⠟⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⣀⣀⣀⣠⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀ ⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀ ⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀ ⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠛⣿⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⣠⣾⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⣦⣤⣄⣀⣀⣀⣀⣤⣤⡶⠾⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡀⢻⣿⡿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡏⠁⠈⠋⠁⠀⠋⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⡄⠀⠀⠀⢀⣀⡀⢠⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣅⢀⣄⣠⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⠻⠿⠿⠿⠟⠛⠛⠉⠙⠛⠻⢿⣿⣿⣿⣿ ⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿ ⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿ ⣿⣿⣿⣿⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿ ⣿⣿⣿⣿⣿⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿ ⣿⣿⣿⣿⣿⣿⣦⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⢀⣤⠀⣸⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⠟⠁⣴⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⣉⠙⠛⠻⠿⠿⠿⠿⠛⠛⢉⣁⣴⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠁⠀⠀⠀⠀⠀⠈⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⡥⠀⠀⠀⠀⣠⠴⢀⣠⠤⢦⡀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡞⢸⠁⠀⠀⣠⢚⡥⠚⠉⠀⠀⠘⣗⡄⠀⠀⢰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢾⠇⡎⠀⠀⣰⡳⠋⠀⠀⣠⣤⠶⠢⡿⣸⣆⠀⠈⣧⣄⢸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡄⢳⣠⣾⡟⠓⠆⠀⠘⠙⢀⣤⣶⢿⣤⣹⡅⠀⣿⠈⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠸⡇⣾⡛⣶⡦⠀⠀⠀⠛⢱⢼⣷⠸⠋⢣⠀⡇⣹⠛⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢱⠀⠹⣏⠉⢟⣻⣀⠀⠀⠀⠐⠛⠛⠐⠀⠘⣴⡽⣇⠀⢸⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢇⠀⠘⡄⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⢹⡀⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢦⠀⢻⢦⡀⠈⠰⠶⠒⠂⠀⠀⢀⡤⠀⡇⢘⡆⢇⠀⠸⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠳⡼⡀⣟⡶⢄⡀⠀⢀⡠⠖⠁⠀⢀⡇⢸⢻⠸⡀⠀⣿⢇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠏⢳⠟⢀⠷⠈⣹⡇⠀⠀⠀⠀⣼⢣⡞⢸⠀⡇⢰⣼⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠎⣠⠋⢀⡼⠟⠊⠟⠀⠀⠀⠀⠀⣿⠀⠑⢯⣀⣇⣎⢏⡞⠀⠀⠀ ⠀⠀⠀⢀⡠⠾⠔⠓⢞⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⣀⡈⠛⠿⠯⣀⠀⠀⠀ ⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠉⠉⠉⠉⠉⣧⡀⠀⠀⠀⠀⠀⠀⠑⡄⠀ ⠀⠀⢻⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠀⠀⠀⠀⠀⠀⢹⡆ ⠀⠀⢸⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⡼⠃ ⠀⠀⠘⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⢠⠇⠀ ⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡎⠀⠀ ⢠⠇⣠⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⡄⠀⠀⡸⠀⠀⠀ ⢸⡀⠛⠄⢀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⠵⠀⠀⡇⠀⢀⠇⠀⠀⠀ ⠀⢷⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣰⠁⠀⣾⠀⠀⠀⠀ ⠀⠀⠑⢤⣀⠀⠀⢀⣠⠴⠋⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣀⡴⠁⠀⢠⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⢻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠉⡽⠀⠀⠀⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣾⠀⠐⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡄⠀⠀⢠⡀⠀⠀⠀⠀⠙⣄⠀⠀⠀⢰⠁⠀⠀⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡜⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣻⠁⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⠀⠀⠸⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣤⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⢿⠀⠈⠉⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣾⣿⣶⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤ ⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠉⠉⠉ ⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠚⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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whoever makes these kinds of things, you need help and therapy, there are literal kids in these websites 😕.. (you should know better.)

8==✊🏻==D~ —> 👄

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⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡠⢺⢡⠃⡜⢀⠀⢀⢾⢠⡀⠀⢇⠀⠀⣶⡀⠱⡄⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡜⣱⡟⢡⢴⠃⡇⠀⣌⣀⣮⡧⠀⢸⠀⣄⣹⣃⠰⡰⣤⢀⠘⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡷⢹⢠⣧⣼⣸⡇⣸⣅⣀⡘⠛⠒⠚⠳⠖⣘⣩⠶⠧⠚⡿⠀⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠶⣇⢸⣸⠃⡜⢻⢿⣿⠁⠈⢹⡇⠀⠀⣴⠟⠉⢹⣷⣶⠆⣱⣲⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⠛⣏⣿⠛⣷⠘⡅⠘⠖⠐⠊⠀⠀⡄⠘⠂⠤⠾⠋⡀⢀⡿⡏⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣻⡏⣸⢏⢙⡄⠑⡄⢣⠀⠀⠀⠀⠁⠀⠀⠀⢀⡷⠁⣸⡇⠻⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢙⢈⡏⢰⠙⣵⡀⣈⠺⣧⡀⠀⠀⠀⠀⢀⣴⣾⠇⣰⣧⡿⠑⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣾⢣⠘⣷⢿⣳⡌⢦⣈⡿⠢⠤⠒⢺⠋⠏⣿⣔⡱⠯⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠁⠑⠧⠤⠷⠈⢻⣏⢁⠀⠀⠀⠊⠏⠛⠉⠁⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠔⠋⠈⠈⢦⠀⠀⢃⡠⠂⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠈⠉⠑⠣⣄⠏⠀⠀⠀⠀⠀⠑⠦⠄⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠠⢄⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠱⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠑⠤⢄⣀⣀⣀⠠⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣆⡀⠀⠀⣀⡀⠀⠀⠀⢀⡠⠊⣀⢤⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿

⠀⠀⣠⢸⣾⣿⣿⣿⠟⠋⢁⣼⡵⠃⠀⣠⣾⣿⣿⣿⣿⣯⣴⣾⡿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢹⠀⡆⣇⢠⠘⣦⣷⠀⢤⢆⠀⠀⠀ ⣴⣿⣿⣅⠙⢿⣻⡌⠦⣀⣽⡿⠓⢲⣾⣿⣿⠟⠛⠋⠉⠁⣰⠟⢠⣿⣿⢿⢏⣼⠋⣿⣿⠃⠀⢲⠸⡄⣆⢸⣼⠀⠸⣿⡀⠘⡎⠀⠀⠀ ⣿⣿⠏⠉⠙⣲⣬⡙⢦⠉⡿⢀⣴⠟⣹⣿⠋⠀⠀⢀⢀⣾⡏⢠⣿⡿⠃⣾⠟⠁⢰⠇⡏⠀⢸⡄⠀⡇⣿⡄⠁⢰⠀⣿⣧⠀⠹⣄⠀⡄ ⣿⡿⠀⣠⣾⡟⠳⣼⣿⣿⣿⣿⣷⣾⣿⠃⠀⢀⣴⣿⣿⡟⢠⣿⣯⣀⡐⠁⠀⠀⢸⢠⣧⠀⣀⢱⠘⠀⣿⢳⡀⢸⠀⣿⢸⣆⠀⠻⢆⠘ ⡟⣠⣾⣿⠏⢠⣾⣿⣷⣿⡿⠟⢛⡿⠃⠀⣴⣿⣿⣿⡿⣠⠃⠘⠻⣿⣿⣶⣄⠀⢸⠸⢹⠀⢸⠀⠀⠀⣿⡇⡇⠘⠀⡎⠀⢿⡆⠸⡈⢧ ⣾⣿⣿⢋⣴⣿⢿⣿⡿⠁⠀⠠⣼⠁⣠⣾⣿⣿⡿⣻⡿⠁⠀⠀⠀⠉⠉⠛⢿⣿⣾⣾⠈⡇⢸⡇⠀⠀⣿⣿⠀⠀⠠⡇⠀⢸⣿⣄⣧⠀ ⣿⣿⣧⣿⠏⠀⣼⠏⠀⠀⠀⣰⣣⣾⣿⣿⡿⠋⣰⠟⠀⠀⠀⠀⠀⢀⣤⣀⠀⠈⢻⣿⣷⣿⠀⣿⡄⠀⢸⣿⣇⠀⠀⣿⡀⢸⣿⣿⣿⡆ ⣿⣿⡿⠁⠐⢴⣯⣀⡀⠂⢤⣿⣿⢟⠿⠋⠀⣴⠋⠀⠀⠀⠀⠀⠀⠌⠀⠀⠈⠑⠲⣇⠈⠛⣿⣿⣿⡄⢸⣿⣿⡄⠀⣿⣷⣸⣿⣿⣿⣿ ⣿⣿⣿⣶⠿⠿⠻⣿⢿⣿⣿⣿⡁⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢱⠀⠀⢹⣿⢿⣿⣄⣿⣿⣷⠀⢻⣿⣿⣿⣿⣿⣿ ⢿⣿⣿⣧⠀⠀⠀⠹⣾⡌⠛⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣭⣉⣉⡐⠒⠂⠈⠄⠀⠀⢿⠀⠻⣿⣿⠙⢿⣧⢸⣿⣿⣿⣿⣿⣿ ⢸⣿⡃⠉⠇⢤⣠⡤⣌⣻⣭⠽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⣿⣿⣿⢿⣿⣷⣶⣦⣤⣀⣇⠀⠙⣿⡆⣼⣿⣿⣿⣿⡿⠿⣿⣿ ⢸⣿⣷⠤⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⣉⣉⣩⣯⡿⠻⣿⣯⡀⠀⠈⣿⣿⣿⣿⣿⡁⠀⢄⠈⢿ ⠋⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠬⠭⣓⠒⠛⠁⠀⠀⠈⢻⣿⣷⣀⣯⠝⢻⣿⣿⠏⠀⠈⠀⢸ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠤⣄⣠⣴⠿⢿⣛⡿⣽⢀⡞⢱⡷⢲⠀⠀⠀⢸ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠄⠀⡀⠀⠈⠀⣿⠏⢀⡼⠀⢚⣤⠖⠁⣸ ⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠁⠀⠀⢰⠃⡴⠋⢀⣾⠕⠁⢀⣴⣿ ⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠈⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠞⠀⠐⠉⢀⣤⣾⣿⡿⠁ ⣄⡀⠀⠈⣧⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠉⠉⠒⠢⠤⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⣀⣀⣤⣾⣿⣿⣿⣿⠿⡄ ⠤⣙⣦⡀⠉⠛⣄⠀⠀⠀⠀⢸⣿⠼⡏⠀⠈⠁⠀⠀⠀⠂⠈⣉⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠉⠉⣼⠿⢿⣿⣿⢟⠝⠀⡇ ⠀⠀⠈⠛⢦⡀⠈⢣⡀⠀⠀⡀⣇⠀⣷⣄⠀⠀⠀⠀⠀⢀⣀⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⢀⡜⠋⠀⢸⣿⠟⠁⠀⠀⢹ ⠀⠀⠀⠀⠀⠱⡀⢀⠟⢆⣠⠃⠨⠦⡈⠛⢷⡆⣠⣖⣋⡭⠴⠻⠋⠀⠀⠀⠀⠀⣀⠤⠊⠁⠀⠀⠀⠀⢰⠀⣀⣀⣴⡟⠁⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠱⡎⠀⠈⢻⣇⠀⠀⠈⣇⢰⠿⠀⠂⠀⠈⠳⡀⠁⢀⡀⠤⠒⠋⠁⠀⠀⠢⡀⠀⠀⠀⠘⡆⢨⡧⠉⠀⠀⠀⠀⠀⢰⠟ ⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠘⢿⣶⣄⣀⣏⣀⣀⠤⣤⢴⣶⣮⡙⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠀⣀⣤⣽⢆⡥⡌⢧⣀⠀⣠⡔⠁⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢈⡿⢸⣠⠋⠀⢹⣠⣮⡻⡟⠛⠿⢷⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⢟⣋⡀⢊⡄⠘⠂⢹⣶⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠈⠢⢧⡀⠀⠀⢸⣷⠎⡘⠀⠀⠀⠻⡉⠁⣇⠀⣶⢤⣄⣉⣉⡙⡏⠉⠉⢻⣿⠿⠉⠉⡉⠉⠉⠉⠈⠱⠀⢘⡿⠛⠷⣄⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣙⣦⣄⣹⡟⢁⣼⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠛⣿⠀⣿⣿⣟⣻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢰⣿⡈⢿⣿⣏⣙⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⠈⠻⢍⣉⠉⠉⠉⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⢰⠋⠑⠾⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⡇⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠤⠴⠣⡀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠦⠤⢤⣀⢁⣀⠸⠉⢳⡲⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣀⢙⣦⠈⠉⡐⢺⠿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣰⣿⣼⠏⠀⠀⠈⠲⡄⠀⠉⠑⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⠀⣰⡿⣿⡏⠀⠀⠠⣤⠀⠈⣆⠀⠀⠀⢨⣶⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢠⠿⡇⢸⣷⡀⢀⡈⠛⠀⣠⣾⣦⠀⢀⣼⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢠⡞⠀⢳⠀⠙⢷⠦⠬⡤⠼⠛⠁⢹⡟⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡗⠒⠒⠚⠧⣀⠈⣇⠀⠈⡆⠀⠀⠀⠀⢠⡟⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠈⠹⢻⡦⣤⡃⠀⠀⠸⠀⣾⠃⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠛⣿⠶⠾⣧⠀⠸⢷⣤⡀⠀⣿⠀⠀⢿⡀⠀⠀⠀⠀ ⠀⣦⣄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣿⢧⣀⣸⣿⡋⢹⠿⣧⠀⠈⣧⠀⠀⠀⠀ ⠀⣿⡀⠉⠒⢢⣤⠤⢴⡞⠁⠀⠀⠀⠀⣧⢸⣿⣿⣿⡇⣸⠀⠘⢦⡀⠘⣆⠀⠀⠀ ⢰⠿⠻⢤⣄⣀⣀⣤⡿⠤⠀⠀⠀⠐⠒⠚⠛⠿⠿⠯⣬⣿⣄⠀⠀⠱⡄⠸⡄⠀⠀ ⠈⢷⣆⠀⢀⣩⠍⢸⡿⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⣀⣿⠀⣷⠀⠀ ⠀⠀⠰⢿⣉⣁⡤⢾⣷⠀⠙⠒⠶⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠯⣀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⡶⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠤⣤⣤⣤⣦⣤⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⣠⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠋⠀⠀⠀⠀⠀⠀⢀⣠⢿⡁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢚⡁⠀⠀⢀⣠⣤⡴⢾⣏⠀⠀⣧⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠈⢻⣿⣿⣷⣶⣦⣀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠿⠛⠋⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣤⣴⣿⣿⣦⣄⡀ ⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠉⠀ ⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⣠⣴⡶⠿⠿⠿⠷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡿⠁⠀⠀⢠⣾⡆⠀⢰⣶⠀⠀⢻⣧⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠛⠁⠀⠈⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⢻⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⡇⠀⣶⣤⣄⣀⣀⣀⣀⣀⣠⡄⢀⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⢃⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢿⣦⣈⠛⠻⠿⠿⠟⣛⣵⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠻⠿⠶⠾⠿⣛⣉⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢶⣶⣤⣤⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣯⠻⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⠉⠙⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⢀⡴⠶⣦⣴⠛⠉⠹⠏⠙⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣄⡀⠀⠀⠀⠀⠘⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣄⡀⠀⠀⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⣴⠇⠀⠀⠀⠀⠀⢠⡶⠶⢦⣀⠀⠀⠀⠙⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣽⣿⣴⣾⣿⣿⡻⠿⢷⣿⣧⣤⣤⣄⣀⣀⣀⣀⡀⠀⢻⣧⣸⠃⠀⠀⠀⣸⡟⠛⠛⠀⠀⠀⠈⠙⢦⡀⠀⠸⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠁⠀⠀⠀⠙⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⣰⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⣄⣀⣀⣠⣿⣟⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⣾⠋⠈⠛⠳⣆⠀⠀⠀⠀⠀⠀⠘⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠛⠛⠻⣿⡙⢿⣦⡀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢻⡁⠀⠀⠚⠳⠿⣷⡄⢀⣀⣤⠶⠦⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⣿⠀⠀⠀⠘⢿⣄⠈⠻⣦⣀⠀⠀⠀⠀⠉⠛⠿⣿⣷⠀⠀⠰⡿⣷⡀⠀⣀⣀⡀⠀⠀⠈⠉⠙⠷⢀⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⣿⠀⠀⠀⠀⠈⢻⣦⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢨⡿⣦⣛⠿⠿⠆⠀⠀⠀⠀⣠⣾⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠈⠹⣷⣄⠀⠀⠀⢿⠀⠀⠀⠀⢰⡟⠁⠈⠛⠿⣶⣤⣤⣤⣴⠾⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠸⣿⠀⠀⠀⣸⣿⠀⠀⠀⣴⣿⠀⠀⠀⣤⠗⠀⣨⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⠀⣿⠀⠀⠀⣻⣦⠀⢀⡀⢿⡏⠀⠀⠀⣻⡆⣐⣿⣹⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⣿⠀⠀⠰⣿⠋⣸⡾⢧⣾⠇⠀⠀⠸⣯⠙⣿⠛⢿⡉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⣿⡄⠀⢠⣾⣿⣏⣷⢈⣷⠀⠀⠀⣴⠟⢴⠛⢠⡾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⣿⡇⠀⠈⣿⣿⠛⠁⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⢹⡇⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⣼⡟⣀⣀⣤⣄⡀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⢀⣈⠻⣷⣤⡀⠀⠀⠀⢀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⠛⠛⠿⢷⣦⡄⠀⠀⣼⣿⡿⠟⠛⠉⠙⢿⣆⠀⣾⡇⠀⠀⠀⠀⠀⠀⠘⣿⣤⣶⡿⠿⠻⢿⣦⠙⠿⣶⣤⣶⠿⠛⠉⠉⠙⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠈⣿⠀⠀⠛⠿⣶⣤⣤⣀⣠⣾⠟⢰⣿⣶⣶⣶⣶⣤⡀⠀⠀⠻⢿⣧⣤⣀⣀⣼⣿⠀⠀⠈⠙⢷⣄⡀⠀⠀⣀⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢷⣾⠟⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠻⣿⣄⡀⠈⠉⣿⡄⠀⠀⠀⠈⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠙⠛⠿⠿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢸⠼⠋⠋⡉⠉⣠⠎⠉⠺⣄⠈⢒⢄⠀⠀⠀⢀⠐⠄⠐⡈⠔⠢⠈⠂⠀⠀ ⠀⠀⠀⠀⠀⠎⠀⠚⡌⡮⢒⠀⠈⠳⡀⢙⢶⠤⠀⠀⠢⠈⢦⠈⡌⢄⡀⠀⠀⠀ ⠀⠀⠸⢀⠌⠔⠁⠀⠘⡔⡀⢕⢄⠀⠈⠢⠀⢃⠓⢦⣀⢡⠀⢣⠐⡘⣯⠲⣄⡀ ⠀⠀⡠⠃⡪⠂⠉⠀⠀⠈⢴⡀⠐⠳⣄⠀⠑⡈⠄⠄⠦⡉⢲⠈⣧⢡⠘⠧⠈⢿ ⠀⢠⢡⢺⢦⠀⠀⠀⠀⠀⠀⠱⡄⠀⠈⠑⠄⠐⢌⣀⣀⣈⣂⣧⢸⢃⣧⡌⣥⠈ ⠀⢁⡺⡀⢊⢣⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⣴⠿⠶⠾⡏⠹⢿⡆⠈⣿⣿⡰⡇ ⠀⠢⡑⠋⢭⣣⠤⣒⣶⡾⡟⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⣿⠀⠘⣌⣣⠳ ⠀⠀⠀⣲⣿⠖⠛⠋⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⡆⠉⠆ ⠀⠀⠙⢍⠁⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡄⠀ ⠀⠀⣄⠀⠑⡀⡙⣆⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡶⢲⠀⠀⠀⠀⢀⠣⠀⠀⠀⠀ ⠀⠀⡹⠢⡀⠘⢮⡈⢆⠀⠀⠀⢴⣾⣿⢹⣿⣿⣿⣿⠀⠀⠀⢀⢾⠀⡇⡆⠀⣤ ⢀⠀⠓⡡⡈⢂⠈⢗⢌⠆⠀⠀⠈⢿⠛⠁⠀⠀⠀⠘⡄⠀⢀⢺⡈⡼⢀⣀⠈⡿ ⠀⠙⠻⣿⡵⣄⡡⠙⡌⢞⡀⠀⠀⠀⠕⠂⠀⠀⠀⠠⠁⢨⣿⡈⣧⠃⡌⣧⢐⡃ ⠀⠀⠠⢀⠙⠛⠯⠡⠰⢈⣇⠀⠀⢀⣀⣀⠀⠀⠀⠀⣰⡿⠃⡦⢍⢄⣤⡷⠉⠀ ⣀⣀⣂⡤⢈⡑⠂⢥⣂⠀⠩⠿⠿⠽⠿⢦⣉⣟⡛⡛⠁⡀⠤⠓⣶⣶⡜⠀⠀⠀

⠀⠀⠀⠀⠀⠈⠂⢵⢮⡯⣼⡿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡌⡸⣜⣿⣟⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⠇⠈⡔⠤⠠⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⣸⠀⠱⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠼⠠⢄⡁⣠⠑⣢⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⢀⣆⡇⠀⠢⡋⠛⠠⡀⠀⠀ ⠀⠀⠀⠀⠰⠁⢀⣞⢻⠀⠠⠆⠈⣄⠀⢸⠆⠀ ⠀⠀⠀⢠⠃⠀⡎⠰⡈⢳⠥⠤⠛⢹⡖⠉⠀⠀ ⠀⠀⠀⠘⣅⠀⠁⠂⢧⣀⠀⠀⠂⡇⢃⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⡩⠟⢺⡄⠓⡦⢠⣇⠘⡆⠀⠀ ⢸⡑⠂⠤⢄⠎⠀⠀⠸⣸⣿⡿⣸⠘⢆⠘⡀⠀ ⢯⠉⢒⡒⡯⠅⠀⠀⠀⠉⠉⠁⠛⠢⢀⣣⢡⠀ ⠀⠚⠁⠴⢿⡈⠁⠒⠂⠀⠀⠀⠀⠀⢀⡈⠙⢤ ⠀⠀⠀⠀⠀⠙⠠⠤⠤⢤⣤⠖⠉⠉⠈⠀⡠⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⠃⠀⣀⣀⣴⠊⢡⠀

⠀⠇⠇⠀⣠⣿⡟⣱⢪⣧⣸⣶⡄⡼⣿⣿⣿⣿⡉⣿⣿⣿⣯⣵⣷⡧⡄⠀⠀⠀ ⠳⢸⡠⢪⣾⡟⣰⡇⢸⣮⣿⡿⣿⣆⣿⣿⣿⣿⣇⣧⡤⣽⣿⣏⣿⣻⣿⢧⡀⠀ ⡶⡛⢁⣿⡿⢠⣿⠀⠘⡏⠉⠀⢹⢻⢸⣿⣿⡿⡸⠊⠀⠀⠀⣿⢿⢿⣟⣧⡘⠗ ⡞⢱⢺⡇⠇⣼⡇⠀⢸⢎⡀⠀⠀⠀⢡⢿⣿⣗⣧⠃⠀⠀⠀⠙⠉⢊⠻⡎⢿⡌ ⢇⡇⣼⡖⢀⣿⠇⠆⢸⠘⡀⢀⠀⠀⠀⢞⣿⣿⢸⡶⠀⠀⠀⠀⠀⠀⠣⠘⡌⡞ ⣼⡇⡏⣟⠀⣿⠀⠁⢸⠀⠈⠀⠀⠀⡀⠜⢼⡿⡎⣧⡦⠀⠀⠀⠀⠀⠀⢃⠰⣸ ⣿⡇⠇⡟⡀⣿⢸⠀⠈⠀⠀⠀⠒⠈⢀⢀⠜⢆⠹⣨⡘⠢⣀⠤⣤⣤⡆⠘⡄⠉ ⣿⣧⠀⡇⠀⣿⡄⠀⢠⣧⣒⣠⣀⣐⣢⠄⠀⠈⢢⣐⢻⣦⣶⣿⣿⡟⠿⣿⣿⡀ ⣹⣿⡄⢿⣀⢹⣩⣶⢽⠛⣿⣿⢿⣿⡿⠆⠀⠀⠀⠙⢦⢻⡿⠦⢿⠇⠀⡟⣿⣷ ⡟⣿⣷⣯⡆⠙⡿⣇⠸⠀⠿⣟⣚⡿⠃⠀⠀⠀⠀⠀⠀⢧⡹⡄⠥⣴⡢⠀⢻⡏ ⣧⢻⣿⣿⣟⡀⢁⠈⠠⡀⢺⠰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠘⠟⠻⣮⡲⠇⠀⢸⣿ ⣿⣧⢫⣿⣿⣄⠈⣆⡀⠈⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠢⠀⠘⣿ ⢻⣿⣎⢿⡝⢿⣆⢻⣇⠀⠈⠀⠀⠀⠀⠀⠀⢀⣔⠦⠭⢥⣢⠀⠀⠀⠀⠀⠀⣿ ⢸⣿⣿⡜⣿⣦⡙⢧⣿⣆⡸⠀⠀⠀⠀⠀⢠⠶⡇⠀⠀⠀⢹⡇⠀⠀⠀⠀⠠⠘ ⢸⣿⣿⣷⢹⣿⣿⡷⣝⢿⣧⡀⠀⠀⠀⠠⠉⢉⠇⠒⢢⠀⣽⡇⠀⠀⠀⡀⠀⠠ ⢸⣿⣿⡿⠎⣿⣿⡇⣿⠧⣻⡵⣄⠀⠀⠘⡄⠀⠀⢀⠴⠔⡱⠀⠀⢀⠔⠀⠀⠀ ⣼⢿⣇⢧⣿⡿⣿⣿⣿⣆⠈⠻⡈⢷⣤⢀⡈⠂⠔⠉⠉⠁⠀⡠⠔⠁⢀⠔⠀⠀ ⠥⢺⣾⠟⢸⣁⠀⣿⣿⣿⣷⣤⣜⣮⣿⣷⣾⣿⣳⣶⠀⠀⠊⠀⠀⢀⠂⢀⠀⢡

⠀⠀⠀⠒⠒⠒⠒⠒⣺⣟⣩⡩⠛⣻⣶⣖⡒⠒⠀⠀⠀⠀⠀⠄⠤⠀⠨⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢀⡸⣜⡹⣥⠶⣉⣍⢸⣷⡝⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿ ⢐⣆⠀⠀⠀⠤⢸⣿⣿⢋⣩⣿⡞⢻⣦⣿⣿⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⠘⠀⠁⠢⡠⠤⣼⢿⣧⠀⠙⠉⢳⣿⠿⠿⢿⣿⣷⡙⢄⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡆⠀⠀⠀⠈⠑⢥⣛⣿⣄⣠⠀⢨⠃⠀⠀⠀⢈⣻⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠈ ⠁⠀⢠⢀⡰⣿⢏⢈⣿⣷⣦⣴⣿⠆⠀⢠⡾⣋⣽⣿⣿⣿⣿⡿⠶⣤⣀⠀⠀⠀ ⢔⡟⠱⠈⢶⠡⣣⡾⠿⠿⠿⢻⠃⠀⢳⣼⣴⣧⣈⣿⣿⢿⣿⣿⣦⠆⠩⠉⠀⠄ ⠁⣇⠰⣀⠞⡉⠤⠒⠀⠀⠀⠸⣧⡀⠀⠉⢿⣿⣿⣿⣳⣿⣿⣿⣿⣷⣄⠂⢀⡀ ⠖⣊⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠬⠓⡄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄⢸⣤ ⢼⡏⠀⠀⠀⠀⠀⠀⠀⢀⣠⠊⢀⡸⢃⠆⠀⠈⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⣿⣿ ⢾⡀⠀⠀⠀⠀⠀⠀⣀⡼⠁⠀⠀⠀⠈⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⢼⣿⣿ ⠘⣧⡄⠀⠀⣠⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠈⢻⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⠀⠀⠀⠉⠙⠻⣟⣿⣿⡄⠀ ⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡀ ⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣼⡟⡆⠀⠀⠀⠀⠀⠀⠀⠛⢟⣧ ⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡵⣿⢙⡏⠹⣷⡂⡀⠀⠀⠀⠀⠀⠀⠘⠿ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢾⢿⡏⠇⢸⢀⣇⠘⣦⠈⠢⠀⠀⠀⠀⠀⠀⢰ ⣀⠀⠀⠀⠀⠀⠀⠀⣠⡮⠋⢡⣾⣿⢠⢣⠀⡾⠘⣄⣿⡄⠠⡀⠀⠀⠀⢀⣤⣼ ⣿⡄⠀⠀⠀⠀⢀⢮⠏⠠⠴⢿⣿⣿⠃⡸⠸⡇⠀⣼⣿⣷⡈⢗⣄⣀⣤⣾⣿⣿ ⣿⣷⣤⣄⡀⠀⠈⠊⠀⠀⢐⣿⣿⣿⢀⣇⣷⡇⢾⣟⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⢏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⠿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠙⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀ ⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠱⡀⠀⢀⢤⠎⠀⠀⠀⠀⠀⠀⣱⠠⠀⠀⠠⠂⠀⠀⠀⠀⠀⢀ ⢳⠀⠀⠀⠀⠀⠀⠐⠄⡌⠀⡕⡀⠀⠀⠀⠀⠀⡜⠀⠃⠠⠁⢀⠄⠀⠀⠀⠀⡄ ⠈⢣⠃⢀⡀⠀⠀⠀⠈⢂⠀⠈⣱⣴⠚⣿⣷⣦⡇⠀⡸⢃⠔⠁⠀⠀⠀⠀⡼⠁ ⠀⠀⠑⢄⣌⣀⠀⠀⠀⠀⠑⣄⣿⢿⠄⠱⠿⣿⡀⡔⠁⠀⠀⠀⠀⠀⣠⠞⠁⠀ ⠀⠀⠀⣀⣬⡿⠟⠛⠛⠓⠤⠸⡟⠆⡀⢀⡼⠛⡻⠀⡀⣈⡥⠴⠾⣯⢀⡀⠀⠀ ⡠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠁⣵⠀⠈⡎⠀⢠⠁⠂⠉⠀⠀⠀⠀⠀⠁⠈⠃⢢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡤⢶⣿⠶⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠈⠁⠀⠰⣿⠄⠀⠉⠢⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⣯⡄⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡘⠋⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠈⡿⠿⣾⢻⣛⣳⠀⠀⠀⠀⠀⠀⠀⠾⠇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠒⠁

⠀⣼⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⡏⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿ ⣿⣷⣾⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡗⢻⣿⠱⣽⢿⣿⡞⢿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠁⡎⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⠃⣸⣿⢐⣈⣦⣽⣿⣎⢻ ⣿⣿⣿⣿⣿⣿⣿⡇⢀⠕⢹⣟⣿⣿⣿⣿⣿⡿⠁⠸⠐⣴⣿⣿⡿⠟⡏⠙⠭⠉ ⣿⣿⣿⣿⢹⣿⡯⡗⠁⢀⡠⣿⣿⣿⣿⣿⣿⢁⡄⠆⠟⠹⣏⠕⢀⠐⠗⠋⠀⠀ ⣿⣿⣿⣏⣼⡟⢀⣻⣥⣬⣥⣼⣿⣿⣿⡟⣿⡠⠋⠀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⢁⣿⣿⣿⡿⠿⠛⢳⡀⣿⣿⣟⠐⢹⡀⡡⢪⢊⡕⢄⡐⠔⠀⠀⠀⠀⠀ ⣏⣿⡿⡿⠛⢀⣳⡤⢀⠔⠋⣸⠟⡱⢁⠴⢊⡎⠀⠀⠁⠈⠁⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣧⡀⠀⢋⠅⢸⠀⣰⠝⠁⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⡄⠀⡠⢸⡸⢣⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣿⡇⠀⠀⠀⠀⡀ ⢛⢿⣷⣿⣿⣾⠀⢗⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⣄⡽⠁⠀⠀⢀⠔⠀ ⠚⠺⣿⣿⢿⣿⣷⣄⢑⣄⠀⠀⠀⠀⠰⣦⢻⠋⠀⠀⠠⢊⡟⠀⠀⠀⣠⠋⠀⠀ ⠀⠀⠀⠉⠢⢿⡿⠌⠢⢀⠀⠀⠀⠀⠀⠈⠢⣉⠐⠒⠂⢱⡄⠀⢠⡞⢁⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠉⠒⢦⣤⣄⣀⣀⠐⡂⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⡤⣶⡾⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢠⢶⡰⠃⠃⠀⠀⠀⡆⣦⣄⠀⠑⣄⠠⡈⠢⣢⡐⢌⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠃⠜⢁⠔⢸⠀⠀⡸⢹⣷⣾⣷⢦⡹⡷⡈⢲⡬⢮⡢⡙⢷⡄⠀⠀⠀ ⠀⠀⠀⡆⡜⢠⠃⢻⣸⢧⠠⠁⠈⠐⠛⠁⠘⣽⣧⠳⡀⣷⠑⠕⢌⠘⢯⣳⣄⠀ ⠀⢀⢠⡿⡰⢋⡆⢠⣽⡿⡛⡀⠀⠀⠀⠀⠀⢃⣏⣵⣳⣷⡄⠈⠢⡑⢄⠙⢍⠧ ⢴⠁⡾⡕⡇⢆⢹⣄⠻⣶⡅⠀⠀⠀⠀⠀⡰⠉⠹⣿⣿⣿⣿⣆⠀⠈⠪⡳⣄⠳ ⠸⠠⣇⢰⢸⡄⡿⠝⣳⣿⣼⣶⣤⣤⡤⠊⠀⠀⠀⠟⡙⣿⠿⠛⠁⠐⢠⡀⠈⠣ ⠇⠀⠈⢻⠛⠉⢠⡎⠁⠀⠀⠈⠁⠁⠀⠀⠐⠀⠊⠉⠉⠀⠀⡀⠀⠀⠀⠐⡀⠀ ⢻⡀⠀⠀⠀⣠⢣⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠠⣠⡗⣄ ⢾⠋⠀⠀⢉⠯⣭⣶⣶⡦⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿ ⢸⣀⡀⠴⣉⣶⣇⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⠶⢥⡵⠶⠋⢹⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠈⠁⠀⠸⠀⣧⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢸⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⡀⢸ ⢀⡀⠀⠀⠀⠆⠘⣆⠀⠀⠀⠀⠀⠁⠀⠀⣀⣌⣀⣀⣉⡓⠢⠤⠤⠤⣴⠪⣄⢸

⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣟⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀ ⣿⣿⣿⡆⠀⠀⠀⠀⠀⣠⣤⣤⣾⣫⣽⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠒⠀⠀⠀⠀ ⢺⣿⣿⣿⡀⠀⠀⠀⢸⢞⣿⣿⣿⣼⣿⣿⣿⣿⠀⣿⡉⢻⣿⠿⣿⠀⠀⠀⠀⠀ ⠈⢿⣏⣿⣧⠀⠀⠀⢸⢻⣿⣿⣿⣿⠟⠛⠛⠋⠉⠙⣷⡼⠛⢊⣏⡀⠀⠀⠀⠀ ⡀⠈⣿⣼⣿⣆⠀⠀⠈⣻⢛⠿⢿⠃⠀⠀⡀⠀⣦⠀⢘⣿⢺⠇⠀⠀⠀⠀⠀⠀ ⡇⠀⠈⣿⣽⣿⣎⣫⠿⢃⠁⠀⢸⢂⠀⠀⠈⠳⡘⢦⡀⠈⢻⠀⣠⣆⣀⣀⣀⠀ ⣽⣆⠀⠘⣿⠿⠋⠀⠀⠌⠀⠀⠈⠀⢱⣤⠈⣇⣿⠢⣵⠀⠈⠂⡿⠛⠛⠛⠛⠀ ⡛⣟⣆⡸⠁⠀⠀⠀⢀⣄⠀⠀⠀⡇⠀⠹⡜⢮⣿⠀⠀⠠⡀⢰⣇⣀⣀⣀⣀⠀ ⢳⡸⣿⣧⣤⡤⠶⠾⡟⠀⡆⠀⠀⣡⠐⣄⠁⠀⣿⣇⠀⠀⣇⣼⠿⣟⡿⢟⣺⠀ ⠀⠙⢻⢯⠀⠀⢀⠔⠙⢄⣰⡀⠀⢻⡆⢘⣇⣀⣷⣿⠿⠟⠿⢉⡶⡉⠀⡘⣷⠂ ⠀⠰⣌⢌⢿⡴⢀⠁⢀⣀⠔⣷⣀⡼⠀⠈⠉⠻⣯⡙⠓⠲⠴⡺⣄⠀⠀⣷⣿⣹ ⠀⠀⢿⢿⣿⠟⣰⢔⡽⢚⡽⠛⠥⡉⠲⢀⠠⠂⠀⠉⠐⢦⠔⠚⣯⣳⣴⠿⠿⡗ ⠀⠀⢸⣆⣠⢞⡱⠋⡰⠋⠀⠀⠀⠘⣆⠧⡀⠀⠀⠀⠀⠈⣆⠀⠘⡙⢄⣀⡀⠀ ⠀⠀⡸⠋⡡⠋⠀⡸⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠁⠀⠈⠃⠀ ⠀⡜⢀⠞⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀ ⡜⠀⠊⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⢀⣠⡾⡇⠀⠀⠀⠀⣀⣾⠿⣄⢀⡀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣷⣿⣷⠖⠒⣋⡩⠽⠛⠛⠑⠺⠷⠶⠖⢶⡤⠞⢇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡷⡾⢯⠖⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡀⣤⠄⢀⠔⢀⠀⠀⠀⠸⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠂⠁⠌⠀⢀⠂⠀⢸⢀⠀⢀⣰⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠤⢀⢼⠀⣀⢀⣪⠗⣪⠦⠠⢀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢆⠀⡀⠄⠒⠒⠉⢀⠦⠬⠙⠃⠒⠠⡄⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡀⠔⠋⠀⠀⠀⠀⣰⣕⡀⠀⠀⠀⢀⣐⣴⠀⠀⠀⠈⠒⠢⢄⡀⠀⠀⠀ ⠈⠁⠀⠀⠀⠀⢀⠠⠄⢲⠁⢟⢟⡇⠀⠀⣿⣿⠃⢳⠤⠀⡀⠀⠀⠀⠈⠁⠂⠤ ⠀⠀⠀⠀⠀⢊⡣⠂⢒⠊⠐⢠⠵⠃⠊⠑⠷⢃⠔⠛⠒⠢⢔⠅⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⡣⠐⠒⢪⡄⠀⢄⢱⠤⣅⡠⢤⡡⠂⠀⡰⠀⣀⠧⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⠔⡙⠀⠀⠀⠀⠉⠂⢄⠹⡟⠈⠑⣼⠁⠀⣔⠕⠊⠀⠀⠑⡀⠀⠀⠀⠀ ⡠⠔⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⣀⣀⡹⡒⠈⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠠⠒⠁⠽⠻⠛⠻⠘⠑⠀⡀⠀⠀⠀⠀⠀⠀⡈⠢⡀ ⠀⠀⠀⠘⡄⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⡰⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⠴⠯⢥⣼⠛⠛⠀⢿⣿⠓⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠗⠋⠀⢀⠖⠀⢈⣷⣤⣤⡀⠰⡎⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢠⡏⠀⣰⠯⠤⢄⣉⠻⣖⣃⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠤⣄⡤⡄⠀⢰⢃⣴⠂⠀⠀⢠⣾⣿⡀⡇⠀⠀⠀⠀⢩⡚⡟⠻⣦⡀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢧⡈⢠⠃⠀⣿⢫⠇⠀⠀⣠⣿⣎⣀⡙⣿⠄⢀⣴⣿⣿⣿⡷⠀⢙⣟⣴⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣸⠀⠀⠀⢿⣿⣿⣿⠿⠃⠀⠈⠀⠉⠉⣹⡇⢀⠾⢛⣿⠟⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⣶⢿⡆⠀⠀⢻⠀⠀⠀⢸⣿⡆⠀⠀⠀⣠⠔⠋⡇⢴⣿⣴⢷⡦⠾⡏⠀⠀⠀⡼⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⣧⡀⠀⣿⢧⡼⣦⣀⠀⠀⠁⠜⢀⡠⠚⠣⠼⠃⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠉⠙⠷⢿⠀⢳⣏⡈⢉⡷⠶⢚⡇⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⢀⣰⠁⠀⠀⠙⠣⢄⠈⠷⠖⠢⢄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⢠⠎⢉⣿⡇⠀⡄⠀⠀⠀⠀⡄⠀⠈⠢⣌⠇⠀⣤⢄⡀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⢠⠏⢀⣴⢶⡇⠀⢳⠀⠆⠀⠀⢸⡀⠀⠀⠈⡇⢰⡬⣦⢷⡀⠀⠑⢤⡀⠀⠀⠀⢀⠴⣿⠀⠀ ⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠹⡄⠸⣿⡆⢳⡀⠈⣷⠤⠠⠴⠋⠙⠢⣤⣴⡁⠀⠉⢢⠀⢧⠀⠀⠀⠈⠙⠿⣉⡁⠔⠁⠀⠀ ⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠘⠿⣗⣷⣼⠛⣆⠀⠀⠀⠀⠀⠀⣿⣟⡦⠒⠉⢀⠼⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀ ⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠘⢿⣿⢠⠋⠀⠀⠀⠀⠀⠀⠹⡏⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀ ⢰⠃⠀⠀⢰⠀⠀⠀⠀⣠⠚⠀⠀⢀⡷⠙⣶⠾⣟⢇⡀⠀⠀⠀⠀⠀⠃⠀⡷⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠠⠸⡆ ⢸⠀⠀⠀⡇⠀⠀⠀⡜⠁⠀⠀⠀⠘⡶⠋⠁⠀⠈⠳⡵⡤⠄⠀⠀⠀⢀⡜⢁⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⡆⡇ ⢸⠀⠀⢸⡇⠀⠀⠰⠀⠀⠀⠀⠀⡼⠁⠀⠀⠈⠊⠷⣸⣿⣤⣀⣀⣰⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣿⡇ ⢸⡄⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠙⣿⠴⠟⠃⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀ ⠀⢳⠀⠸⡿⡆⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆ ⠀⠈⠣⡀⢣⡹⣄⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠘⣆⠀⠉⠲⢶⣖⠒⠒⠂⠈⠉⠉⠑⠒⢤⣷ ⠀⠀⠀⠈⠓⠳⠜⢦⡀⠀⠘⢄⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠘⡶⠤⠤⠤⠬⠽⠂⠀⠀⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⣀⣁⣀⡘⣦⡀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⢿⠧⣄⠀⠀⠀⠀⠀⠐⠋⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⡠⠤⠴⠶⠤⠶⠦⠦⠶⢖⣻⠽⠛⠩⡹⠿⢿⠿⣶⣔⡶⠤⠤⠤⠤⠄⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿ ⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣻⣿⣒⡬⠳⠛⣁⣴⢾⠿⣿⣿⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣼⢡⢏⡞⢿⣄⡾⠻⣅⢰⣆⠐⢮⣿⣷⡈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿ ⠰⣄⡆⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣟⣥⠖⠛⢦⣤⡽⣟⣿⡆⠸⣿⣿⣿⣤⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⣼⠳⣄⠀⠀⠴⠖⠊⠉⢹⣯⣷⣻⢩⢸⣴⣶⣽⡿⡇⠸⣹⣿⣼⣿⣿⣿⣿⣿⣟⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠛⠀⠈⠓⢤⡀⢀⣀⣀⣘⣿⣿⣿⣎⠀⠘⢛⠟⠁⢻⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿ ⢠⠀⠀⠀⠀⠀⠙⠻⣍⡉⠻⢁⣿⣿⡾⠃⠀⠀⠀⠀⠈⢿⡟⠉⠉⠉⠉⠙⠻⣿⣿⣿⣷⣌⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠀⠀⠀⠀⠀⠀⠀⠀⡹⠲⣼⣉⢿⣿⢦⣀⣤⠤⠀⠀⣾⠒⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⡇⠀⠀⠀⠀⠀⠀⣀⣶⣪⣾⠃⣿⢻⣿⣷⣭⣀⢀⣠⢾⣿⡄⠀⠀⠀⢀⣴⣾⠟⠛⣻⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⢀⣀⢰⠐⣤⠖⢩⡼⢃⠔⠀⣼⢿⣿⣿⣿⣿⣿⣿⡟⠃⡀⠀⢀⣮⠋⢤⣴⢿⣿⣿⣿⣿⣿⣿⣿⣍⡛⠛⠻⢿⣖⣦⣄⠀⠀⠀⠀ ⡴⢚⣽⠉⢴⠇⠘⣧⠞⢰⠏⣤⣾⣿⣮⣻⣿⣿⠟⢹⡏⠀⠀⠘⢦⣸⣧⣠⣿⣇⡀⠻⣿⣿⣿⣿⡿⣿⣿⣿⣦⣴⡦⠈⣉⠉⠁⢀⣈⠠ ⡴⢻⡂⠈⡈⠀⠀⣻⣠⠴⠚⠋⠉⣉⠉⠀⠀⠀⠀⣿⡄⠀⠀⠀⠘⠟⣿⣿⣿⣿⣿⣷⣾⣿⠟⣥⣾⣿⣿⣿⣷⣖⢍⡀⠂⠀⠀⠀⠀⠀ ⠀⢘⣗⠀⠘⣄⡴⠋⣀⡠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠸⣿⣦⡀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠙⠂⢠⡀⡀ ⣤⡤⠞⢧⣴⣿⠇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢯⣀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⣼⡇⢀ ⠋⣠⣔⡽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠉⠀⡎⣿⣿ ⣼⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⣘⡿⢀⡞⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠈⠀⠀⣿⣿⣿ ⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠈⠉⠁⠀⢸⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⡀⠀⢀⣾⣿⣿⣿ ⠋⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢟⠀⠀⠀⠀⠀⠀⠰⠤⠤⣄⣠⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⠿⢿⣿⡿ ⠀⢻⣧⣀⠀⠀⠀⠀⠀⠀⣀⡠⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⠀⠀⠈⠉ ⠀⠈⢿⣿⣄⣀⣠⣀⣼⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠈⠙⠛⠿⠿⠿⣿⣿⣿⣿⣿⢿⣧⣹⣿⡄⠀⠀⠀ ⠀⠀⠀⠙⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣳⡆⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣎⠻⣷⣿⣿⡄⠀⠀ ⠀⠀⠀⣠⣿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣿⣿⣿⣿⠀⠀ ⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⡄ ⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⡜⣿⣆ ⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣒⢶⣤⣤⣾⣿⣇⣬⠅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡸⣿ ⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⢛⡷⢸⢸⡀⠀⠯⡭⣍⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢻ ⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣺⣿⢷⡞⣿⠃⢸⠈⠀⣼⠀⠱⣿⡀⠉⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣾⠷⢋⣽⣡⡿⠘⢁⠀⢸⠀⢸⣿⡄⠀⣻⣷⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡥⠛⠁⢠⣾⣇⣿⠃⣠⠏⡀⠈⢰⡟⠀⢷⠀⣿⣿⡆⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼ ⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡵⠋⠀⠀⢰⣿⣿⣿⣿⣴⠃⠀⡇⢠⢻⡇⠀⠸⢸⣿⣿⣷⠈⠳⡝⣄⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿ ⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⡟⠡⠤⠖⠚⠿⣿⣿⣿⣿⡏⠀⢰⠇⢸⣾⡇⠀⢠⣾⣭⣿⣿⣧⠀⠹⣞⢧⡀⣠⣤⣾⣿⣿⣿⣿⣿ ⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠐⠣⠞⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⡇⠀⣾⢠⢇⣿⠀⢰⣿⡏⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⣶⣤⣂⡀⣀⣀⡀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣇⣼⠇⣾⣸⣿⢀⣅⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣨⣫⣽⣿⣾⣧⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⡿⠏⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠈⢙⣿⣿⣿⣿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿

⢠⠀⡇⢸⠀⠀⠀⢀⣼⣿⣷⡟⢁⡴⡏⣿⡀⠹⣷⣤⡀⢢⠸⣿⣿⣿⣿⣿⣿⣿⡍⢻⣿⣿⣿⣿⣿⣯⣛⢶⣾⣴⣅⠀⡠⠀⠀⠀⠀⠀ ⡜⢸⠀⡇⠀⠀⣠⣿⣿⣿⠏⢠⡿⠀⣿⡿⣿⣾⣿⣿⣿⡌⡆⣿⣿⣿⣿⣿⣿⣿⣇⢸⠛⠛⠿⢿⣿⣿⢿⣿⣿⣿⣭⣿⣇⡀⠀⠀⠀⠀ ⠃⡇⢸⢁⡤⠊⣽⣿⣿⠃⢠⣿⡇⠀⣿⣷⣼⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⢹⠸⣷⣶⡦⣴⣿⣷⣿⣫⣾⣿⣿⣿⣿⣷⣄⡀⠀⠀ ⣰⣤⣾⡟⠁⣼⣿⣿⠏⢀⣿⡿⠁⠀⣿⣿⠛⠟⠛⠃⢻⢿⣿⡈⣿⣿⣿⣿⣿⣿⡌⣷⡼⠋⠐⠋⠀⠀⢸⣿⣿⢯⣿⣿⣿⣧⡈⠻⡦⣄ ⠿⢫⡟⠀⢰⣿⡟⡟⠀⣼⣿⡇⠀⠀⢃⢻⡀⠀⠀⠀⠀⠶⠹⣇⢹⣿⣿⣿⣿⡿⣇⢻⠀⠀⠀⠀⠀⠀⢸⣿⢫⣿⢿⣿⣯⢻⣷⣄⠙⣄ ⣴⠏⢀⡷⣾⡿⢰⠃⢀⣿⣿⠀⠀⠀⣸⣦⠀⠀⠀⠀⠀⠀⠀⠘⡆⢿⣿⣿⣿⡧⢿⣜⠀⠀⠀⠀⠀⠀⢀⡵⠃⠘⢆⠿⢻⣆⠹⣿⣧⠈ ⡏⠀⣾⠀⣿⡇⠸⠀⣸⣿⡿⠀⠀⠀⣇⠈⡟⠀⠀⠀⠀⠀⠀⠀⠹⡜⣿⡿⣿⣷⢸⣇⣧⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢷⠀⢻⣆⠹⡌⣧ ⠇⣸⡏⢠⣿⢻⢁⢀⣿⣿⡇⠀⡟⠀⣿⠀⠱⡀⠀⡠⠀⠀⠀⠀⠀⠱⡽⣿⣿⣿⡈⣿⡜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⢻⡀⢻⡟ ⡀⣿⡇⢸⡟⣾⠏⠀⣿⣿⠁⢰⠁⠀⣿⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⢀⣷⣹⣿⣿⣇⢻⣧⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢱⡀⢿ ⢹⣿⡇⢸⡇⣿⡆⠀⣿⣿⠀⡸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠉⠀⢳⡹⠎⢿⡜⣿⡾⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢳⡼ ⣿⣿⣇⠸⡄⣿⠃⡀⣿⣿⠀⡇⠀⠀⠑⡀⠀⠀⠀⠀⠐⠉⠀⠀⠀⡀⢀⡼⠳⡀⠈⣷⢻⣆⢹⠦⢄⣀⣀⣀⣠⣤⣤⣴⣄⠀⢻⡀⠈⠙ ⣿⣿⣿⠀⡇⣿⠀⠁⣿⣿⢸⠁⠀⠀⠀⢧⢀⣀⡀⠤⠤⠤⠤⣀⠉⠀⠉⠀⠀⠹⣄⠈⢧⢿⡜⡄⠈⣡⣴⣾⣿⣿⣿⣿⣦⣤⣾⣷⡀⠀ ⣿⣿⣿⡆⠂⣿⠀⠀⢸⣿⡏⠀⠀⠀⣾⣿⣿⣶⣶⣶⣶⣶⣦⣄⠍⠒⠀⠀⠀⠀⠘⢦⣦⠀⢧⣳⣾⣿⣿⣿⣿⣿⣇⠈⠻⣿⣿⣿⣷⡖ ⢹⣿⣿⣇⠀⣹⡇⠀⠈⣿⡏⣑⣶⣯⣽⠟⢿⣿⣿⣿⣿⣿⣿⣿⢿⣶⠀⠀⠀⠀⠀⠀⠹⣷⡌⢿⣿⣿⣷⣄⣿⣿⡇⠀⠀⣿⠿⣿⣿⢳ ⡇⣿⣿⣯⢀⣿⢿⠲⠶⣿⣿⣿⡟⠃⢸⠀⠘⢿⣿⣧⣀⣿⣿⣽⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⢙⣯⣄⣀⡩⠟⠀⢀⠀⠋⠀⣿⣿⢸ ⡇⢻⣿⣿⣿⣿⣼⣆⠀⠘⡟⢿⣧⡀⠘⠀⠀⣿⢿⣉⣉⣉⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣆⠹⢶⡂⠶⣶⡾⣉⡇⠀⠀⣿⣿⡗ ⣧⠈⣿⣿⣿⣿⣿⣿⡄⠀⢳⠀⠈⠇⡇⠀⢀⣸⡀⣤⡽⠓⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⢄⣿⣤⠒⢭⣤⡈⠀⠀⣿⣿⣷ ⣿⣧⠘⣿⣿⣿⣿⣿⡳⡀⠘⣆⠀⠀⡇⠸⣀⣸⣗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠛⢷⣄⠉⠀⠀⠀⢸⣿⣿ ⣿⣿⣧⠘⣿⣿⣿⣿⣷⡁⠀⢹⣆⠀⠇⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠄⠀⠀⠈⣿⣿ ⣿⣿⣿⣧⠹⣿⡿⣿⣿⣷⡄⠘⡟⣾⡇⠀⠀⠬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠸⣿⣿⣿⣇⠹⣿⣌⠻⣿⣿⣄⢹⣞⣇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⡵⠒⠒⠒⠒⣆⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿ ⠀⣿⣿⣿⣿⡄⢿⣿⣷⣌⠻⢿⣦⣻⣾⢦⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⡏⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠿ ⠀⣿⣿⣿⣿⣿⠸⣿⣿⣿⣷⣄⡙⢿⣿⣿⣷⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣅⣀⢁⠀⠀⣀⡀⠀⢐⣸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈ ⢰⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⡹⣦⡙⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢠⠿⠒⠋⠉⢧⠀⢘⡬⢿⠃⠀⠀⠀⠀⠀⢀⠂⠀⠀⢠ ⢸⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⡇⢿⣿⣦⡹⣿⡿⣦⡀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⣸⣀⡸⢎⠏⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀ ⢸⣿⣿⣿⡿⢻⠋⣇⣿⣿⣿⣿⣷⢸⣿⡉⠳⢾⣿⡉⢳⣄⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⣠⣚⣛⣉⠠⠊⠀⠀⠀⢀⡤⠞⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⢃⡏⣰⣿⢻⢿⣿⣿⣿⢸⣿⣷⠀⠀⠙⢿⠀⠻⣷⣤⣀⡀⠀⠀⠑⠢⠤⠊⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⢀⡤⠲⢄⠀⠀ ⠟⠋⣠⢏⣾⣷⡿⢹⠸⡌⠉⢻⣿⢸⣿⣿⣷⣄⠀⠈⠳⣦⠹⣿⣷⣌⢉⣲⣶⣤⣤⣄⣀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⢀⠋⠀⠀⠀⠣⡀ ⠶⠚⣁⣿⣿⠟⠁⠘⣦⡇⠀⢈⣿⣿⣿⣿⣿⣿⣿⣷⣦⣽⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠀⠀⠀⠀⠀⢀⡘⠀⢀⣄⠀⠀⢳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣺⣵⣾⣿⣷⣮⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣽⣿⣿⣿⣿⣿⣿⣿⣦⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠲⢼⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢳⡘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠠⠾⠿⣿⣿⡿⣿⣿⣿⣾⣧⣿⣾⠇⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⡀⠀⡎⣁⠀⣼⣿⢏⡉⠙⣿⣿⣿⣿⣿⣿⠀⣠⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡉⠀⡿⠁⣠⠟⠃⠀⣙⣶⣾⣿⣿⣿⣿⢾⡀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⡀⠀⡟⣠⣶⠿⣗⣦⡀⠀⠀⠀⠀⣿⡷⣦⡞⠁⠀⠀⠀⠈⢉⣼⣿⣿⣯⢿⣶⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠟⢻⣿⡄⣿⣿⣿⣧⣦⢻⣷⠀⠀⠀⠀⢸⠛⡿⠐⠀⣀⡤⠴⠚⠁⣈⠻⣿⣿⣷⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⡟⣧⣿⣾⣹⣿⣿⢸⣿⠇⠀⠀⠀⢸⡤⠗⠂⠈⠀⠀⠀⠀⠀⠨⠀⠙⠿⠻⣷⣬⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⣷⣷⡟⣮⢿⣿⣻⣿⣿⣀⣀⢀⡴⣋⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣠⡾⠿⢿⣿⣿⣆⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⣿⣷⣧⠘⣷⣿⣟⣿⡯⡉⠉⡙⠛⣿⢟⡻⣯⣭⣿⣷⣿⣿⣿⣿⣿⡿⠀⣀⣭⣿⠛⢋⣉⠉⠉⠙⠓⠶⢤⣄⡀⠀⠀⠀⠀⠀ ⢿⣿⠀⠀⣿⡿⢿⣇⠘⣿⡇⠀⠙⣿⡁⣵⡿⠁⠀⣲⡿⣯⣹⣿⣾⣿⣿⣿⣿⣿⠟⠋⠀⠈⠉⠉⠉⠙⢧⡀⠀⠀⠀⠀⠙⠶⢤⣄⣀⠀ ⠾⣿⡄⠀⣿⠁⠈⣿⡆⠹⣬⡢⡀⢹⣿⠟⠁⣤⣴⣿⣀⣿⣿⣿⣿⣿⣿⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⣀⠀⠀⠀⠀⠀⠉⠛ ⠀⢻⣧⢀⣿⠃⠀⢘⣿⠀⢉⣿⣶⣬⠟⢀⣮⠿⢿⢿⣿⣿⣿⣿⣟⣯⡾⠟⠑⠒⠒⠒⠶⠤⠤⣤⣀⡀⠀⠀⠀⠈⢯⡀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⢿⣿⣴⣿⣿⣿⣿⣿⣿⠟⠁⢀⣾⣿⣀⡈⣼⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⣄⠀⠀⠹⣟⠶⣄⠀⠀⠀ ⠀⢀⣠⠞⣋⣾⢋⣼⣿⣿⡿⢻⣀⣤⣻⣟⣻⡿⣷⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣀⢹⣤⠈⠻⣦⡀ ⣠⠞⠁⢀⣿⡵⠟⠋⠉⠁⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠙⣿⡇⠀⠈⠳ ⠋⠀⡄⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠘⣿⠀⠁⠀ ⠀⠤⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡄⠀ ⠀⢈⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢳⡀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣉⣠⠤⢤⣈⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣶⣶⣿⣿⣿⡟⠻⣅⣶⢾⠉⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡟⠁⢸⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠼⡇⠀⠘⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠈⠑⠢⡀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠈⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣠⡖⣿⣏⣠⡟⠉⡟⠢⢄⡀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠙⠢⢤⣀⡀⠀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢠⣷⣿⣿⣿⣿⣾⣄⡀⡠⠏⣄⠀⢀⣤⠶⠋⡝⠁⠀⠀⠀⠀⠀⠀⠀⣽⠀⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡦⣤⣀⣀⣠⠋⠑⣴⡟⠻⡿⠋⢠⣶⣿⣿⣿⣅⣠⣼⡿⠋⢁⡠⡴⠁⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠉⠛⠯⣵⣶⣿⣿⣦⠀⠀⢸⣿⣿⣿⠛⣿⡴⢋⠤⠚⠁⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⢀⡿⣿⣿⠞⠀⠀⠈⡉⠉⠉⠀⡟⠉⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣉⣁⢧⡀⠀⠀⠤⣴⠶⢿⠀⢀⣠⡋⠉⢩⠗⠒⠃⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡠⠛⠀⢰⡶⠲⣶⠽⠟⣟⠛⠛⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣤⣤⣀⠊⣠⡾⠁⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠉⠀⠀⠀⠀⠀⣴⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠒⠒⠉⠈⠉⠀⠀⠀⠈⣹⠁⠀⢠⠏⢿⠆⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⣠⠃⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⢀⠎⠀⠘⣧⡀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀ ⠀⢀⣀⡀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⠒⠉⠀⠀⠀⢀⡴⡏⠀⠀⠀⠈⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀ ⠰⡟⠉⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠂⠀⠀⠒⠊⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠛⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣸⠓⣶⠲⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⣠⠃⠀⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠷⢄⡀⠀⠀⠀⠀⠀⢀⣠⢞⣁⠤⠚⠁⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠁⠒⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠓⠒⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣀⣤⠤⢴⠚⠉⠀⠀⢠⣴⠋⠀⢸⠀⡜⠀⡇⠀⢀⣿⡇⠀⠀⠀⠀⠀⣸⡹⢠⡞⡷⠞⠋⠁⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⠋⠀⢠⡏⠀⠀⠀⢠⣿⠇⠀⠀⠀⢿⠁⠀⢳⠀⢸⣿⡃⠀⠀⠻⣓⢦⡿⣷⡟⣽⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢦⣤⠀⠀⠀⠀⠀⠀ ⢀⡄⠀⣾⠀⠀⠄⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠘⣆⡞⢻⡇⠀⠀⠀⣾⣀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣀⢔⣿⠟⠁⠀⠙⠲⠤⣀⠀⠀⢠ ⠏⠀⣸⡏⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠘⡇⠀⠀⠀⢼⣿⣱⡿⠃⠀⠀⠀⠀⢀⡠⠞⣡⡾⠁⠀⠀⠀⠀⠀⠀⠀⣠⡠⠞ ⠀⢀⡟⡇⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢳⠀⠀⠀⣸⡟⡱⠁⠀⠀⢀⡠⠖⠉⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⢐ ⠀⢸⠇⣷⠀⣀⣏⣀⣀⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⢣⠀⣰⠋⡰⢁⡠⠔⠊⠁⢀⣠⠞⠋⠀⠀⠀⠀⢀⣀⠴⠒⠉⠀⠀⠀⠀⢸ ⠀⢸⠉⢹⡆⠙⡏⠉⠁⠀⠀⠀⠀⠉⠙⢿⡿⠻⠷⠂⠀⠀⠀⠳⢃⠼⠋⠁⠀⢀⣠⣶⣏⣀⠤⠤⠤⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⣸⡀⢸⣧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡆⠙⢿⣿⣬⣿⣧⣤⣶⣤⣒⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⢶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠱⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠋⠙⠛⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⣧⠀⠀⡇⢈⣿⠀⠘⣿⣿⣿⡟⢻⣿⣷⡙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄⠀⠀⠀⠀⠀⢸ ⣿⣆⠀⢹⡇⠘⣆⠀⠻⣯⡿⢿⣾⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀ ⣿⣿⣧⣜⡏⠀⠈⠳⣄⣙⠛⠚⠷⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠛⣉⣓⣲⣒⣦⠤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⣰ ⣿⣿⣿⠙⣻⣶⣶⡶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⢀⡴⠟ ⠙⢿⡇⠀⠀⠉⠀⠤⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⣿⣿⣿⣯⣙⣿⠿⣿⣿⣿⣿⣯⣍⡓⠐⠋⠀⢀ ⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣯⡷⠠⣼⡟⠉⠙⢻⣿⡿⠶⠒⢢⠏ ⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠞⠛⠉⢀⣠⡴⠋⠁⠀⢀⡴⠋⠠ ⠀⣼⣷⠴⠒⠋⠓⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢙⡶⠾⠍⠀⠈⠀⠀⠀⢠⠞⠁⢀⣹ ⡴⠋⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣠⣶⣿⣿ ⠀⣀⣧⠇⠀⠀⡴⠓⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠋⣿⣿⣿⣿ ⠀⠀⡇⠀⠀⡜⢀⡠⠄⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡴⠀⣼⣿⣿⡿⢋ ⠀⠀⢳⣀⣼⠟⠁⠀⠀⠘⡟⠓⠢⡀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢁⣴⣿⣿⣿⣷⣿ ⠀⠀⢀⡽⠃⠀⠀⠀⠀⡸⠁⠀⢀⣿⣿⣿⣿⠿⠛⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢋⡴⠛⠉⠁⠀⠀⠈⠙ ⠀⣰⠃⠀⠀⠀⣠⠴⠊⠁⠀⢀⡾⠼⠿⣿⡏⠀⠀⠀⡘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢇⠀⠀⡰⠋⠀⠀⠀⠀⡰⢋⠔⠀⠀⢨⡗⢦⡀⢸⣷⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⢤⣤⡾⠛⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⢘⡶⠋⠀⠀⢀⡠⠖⠛⢷⡇⠀⠀⠀⡼⠦⠤⠾⢟⠻⡏⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⣁⣤⠄⠉⠀⠁⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡜⠀⠀⠀⡷⠊⠀⠀⠀⣸⡇⠀⠘⢷⣿⡄⠀⠀⠈⠦⠙⡆⠀⠀⢀⣀⣤⣶⠏⠐⣿⠟⠁⠀⠀⣀⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠱⡀⢀⠞⠠⢄⣠⠴⢺⠁⠻⣄⠀⠈⢷⠘⣶⣤⠴⣯⡴⢿⣿⣿⣿⣿⣿⡟⠀⢘⣡⣤⣶⣾⣿⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠈⢁⣀⣴⣋⡤⠖⡟⠀⠀⢈⠟⠒⠋⠀⠘⢶⠶⡏⠿⠸⠹⢯⠛⢿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⠟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⠏⢆⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣄⡀⠀⠀⠀⠀⢸⠘⢠⣎⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡰⠛⠒⠒⠒⠦⠤⢄⣀⠀⠀⠀⠀⠈⠑⠢⡀⠀⠈⠣⣈⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡀⠀⠀⠀⠈⢦⢤⣠⡝⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⢰⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡀⠀⠀⢸⠀⠀⠀⠍⢉⣒⠒⠂⠤⢤⣤⠤⠀⠘⡄⣈ ⠀⠀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⠀⠀⠘⠁⠀⠀⠀⠀⠀⠈⠙⠳⢄⡀⠀⠀⠀⠉⠀ ⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣄⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⣈⠓⠦⣄⠀⠀ ⠀⠐⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠈⢱⡤⠤⠶⠖⠚⠉⠁⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠉⠁⠒⠻⠶ ⠀⠀⠀⠀⠀⠀⣶⣷⡿⠀⠀⠀⢠⠃⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠐⠒⠠⣈⠑⠦⡀⠀⠀⠀⠀⠀⠈⠑⢄⣀⡀⠠⠤⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⡴⡃⢀⠞⠀⠀⠀⠀⠀⠠⠤⣀⠀⠀⠀⠀⠀⠀⠉⠲⢬⣓⣄⠀⢀⡀⠀⠀⠀⠑⣬⡑⢦⣀⠀⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢠⡗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⣀⠀⠀⠀⣠⣯⣍⣷⣄⠑⢄⠀⠀⠀⢈⣻⣢⠹⣿⣷⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⠞⢈⣴⣿⢿⣯⡳⡈⢢⠀⠀⠀⠙⣽⡆⢿⣿⡿ ⠀⠈⠉⠉⠉⠉⠉⠉⢹⠁⡆⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡀⠀⠀⠀⢀⡠⢀⡴⠃⣰⣿⠛⠀⠀⠘⡇⢻⣦⢣⠀⠀⠀⠈⢿⡾⠋⠀ ⠀⠀⠐⠊⠉⠉⠁⠈⣏⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣀⠞⣧⠎⡔⣰⣟⣉⣀⠀⠀⠀⣣⠀⢻⢳⣷⡀⠀⢀⠞⠁⠀⠀ ⠀⠐⠒⠒⠤⠤⠤⣤⣯⠃⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣞⣛⣶⠏⠸⢁⣿⣿⣏⣹⢱⡤⠊⣹⣤⣾⡆⢻⠳⣀⠎⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⡹⠃⠀⠀⠀⠉⠀⠉⠓⠊⠀⢠⣿⣿⠃⢰⡀⡇⢹⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⡀⠀⠈⢦⡀⠀⠀⠀⢤⣄⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠙⡁⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠱⡀⠀⠀⠙⢦⡀⢠⠇⠈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢱⠘⣆⠀⠀⠀⠀ ⠐⢄⠀⠀⠀⠀⠀⠀⠀⢇⠀⣄⠀⠱⡀⠀⠀⠀⠙⢿⣏⣿⡥⢒⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣹⢦⡀⠈⢢⡀⠀⠀ ⠀⠈⠓⢤⣄⠀⠀⠀⠀⢘⡄⠘⣆⠀⠙⡄⠀⠀⠀⠀⢹⢓⣾⡿⠻⣟⣹⢳⠀⠀⣄⠀⠀⠀⠀⠀⣠⢖⣽⠿⠏⠀⠱⡀⠀⠃⠀⢀ ⠀⠀⠀⠀⣈⣛⣷⣾⣶⣾⣿⣇⠘⢆⠀⠈⢦⡀⠀⢀⣿⣿⠋⠀⠀⠈⠓⠟⠀⠀⠈⠑⠂⠀⢀⠔⣡⢺⡟⠂⠀⠀⠀⡇⠀⢰⠀⢘ ⠀⠀⠀⣠⢾⡛⢄⡀⠀⠉⠻⣿⣆⠈⠣⡀⠀⠙⢦⡼⠻⢿⣷⣤⡄⠤⠀⠀⠀⠀⠀⠀⠀⠀⣬⢼⣿⣿⠅⠀⠀⠀⠀⠙⠀⠀⡆⢸ ⠀⠀⠀⣇⡞⢱⠘⣄⠉⠉⠉⠉⠛⠓⠦⢽⣦⡀⢰⡇⠀⠀⠈⠑⠦⣤⣄⣀⠀⠀⣀⣀⡀⠤⠿⠿⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⠞ ⠀⠀⠀⣏⠃⣾⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠦⢄⣐⡢⢤⣀⣙⣻⡤⠮⣁⣀⢀⡠⠆⠀⠀⠈⠻⢯⣅⣀⣠⣤⣶⣿⠏⠀ ⠀⠀⠀⠈⠑⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⣀⣠⠄⢀⠤⠚⠉⢀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⠀⡀ ⠀⠀⠀⠀⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⣰⣃⣠⣴⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠈⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⡄⢦⡤⠠⠤⠤⠤⠶⡦⢤⡀⠀⠀⠀⣤⢴⡞⠚⣖⠒⠒⠒⠒⠒⠂⠠⠤⠄⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣺⡽⠛⠉⠙⢋⣼⣷⡾⢳⡀⠀⠀⠀⠀⢠⣦⣌⠳⡄⠀⣼⣿⢷⡶⠾⠆⣰⡾⠿⠻⠾⠟⠚⠓⡼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠁⡜⠁⣀⠄⢀⣴⠋⢰⣿⣍⡂⠁⠀⣠⠟⠀⠸⡌⠛⢟⣿⣷⠿⣇⢀⣤⣀⣀⣍⡉⠠⣄⣠⣤⣄⣍⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡃⠀⢸⡴⠊⠀⢠⠋⡇⠀⢠⡿⠳⡁⠀⠀⠻⢖⣠⠀⠹⠲⣈⣿⣯⠀⢸⠈⢙⡉⠉⠉⠉⠀⠈⠠⣤⠀⠠⠖ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡷⠀⠘⠀⠀⠀⠇⠀⠁⠀⠘⢿⣦⠀⠀⠀⠀⠀⣹⣦⣄⠀⠹⣿⠟⠠⢬⡇⠘⡷⠶⠆⠰⠟⠟⠛⠃⢀⣰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⠷⣄⠀⠀⠀⣈⡄⠀⠀⠀⠀⡸⢙⣦⣤⣤⣴⣚⡛⠙⠚⢷⣶⠁⠀⠀⠀⠙⠤⠒⠓⠓⠒⠒⠊⢉⣉⠥⠤⠂ ⠀⠀⠀⠀⠤⠀⠀⠀⣀⣬⣦⣼⡙⡆⠀⠙⡏⠀⠀⠀⣀⡴⠟⠛⠛⠛⠛⠻⠿⣿⣶⣬⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣴⣾⣿⠿⠛⠳⡇⠘⠦⣀⣈⣷⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⣿⠟⠋⠀⢀⡀⠤⠙⢛⣷⠾⠛⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀⠀⠀⣀⡤⢤⣀⣀⠘⡄⠀⣤⣀⣀ ⠀⠀⣴⣿⡿⠁⠀⢀⠔⠉⠀⠀⠀⣾⣃⣀⣀⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣟⣛⣿⡀⠘⠯⠽⠷⣿⣿⠋⠀⠉ ⠀⢸⣿⡟⠀⠀⢠⠎⠀⠀⠀⠀⠀⠻⣷⣿⣟⣹⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⠀⠙⡆⠀⠀⢾⠻⣏⠀⠀⠀ ⠀⣾⡿⠖⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡁⡄⠀⡇⠀⣰⡏⠀⣿⢆⠀⠀ ⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣀⣴⣷⣴⣿⠟⠉⠹⠾⠟⠛ ⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠭⠤⠤⠴⠒⠒⢒⠒⠋⠉ ⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠘⣆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣀⣀⣀⠤⠤⠤⢴⡶⠟⠒⠚⠛ ⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢬⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⢠⡖⠉⠀⠀⠀⠀⠀ ⠀⠀⠈⢷⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢧⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⣀⣀⣀⣀⠠⠼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⢦⡀⠀⠀⠀⠀⠀⠈⠒⠄⠀⠀⠀⣸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣈⡇⠙⢦⣀⠀⠀⠀⠀⠀⠀⢀⣠⠼⢻⢻⣟⠲⢤⣤⣤⣤⣤⡤⠤⠖⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡠⠔⠚⠉⠀⢱⠀⠈⣿⣷⡤⢤⡤⠴⠾⡛⠁⣴⠃⣸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠸⡄⠀⣿⠈⣷⣄⣀⠀⠀⠙⠞⠁⡼⣻⣿⣧⡰⡄⠀⠀⠀⢀⣤⣴⣟⣹⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⢤⣶⢛⣡⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣌⣵⣽⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣉⠟⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⢿⡿⣿⡻⣿⣟⡛⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢱⣭⣿⣿⣿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡑⢤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠶⣹⡿⢻⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⠏⢻⣿⣿⣿⡟⠃⠛⢿⣿⣷⡄⠙⢄⠀⠀ ⠀⠀⠀⠀⢀⣼⡟⣰⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢸⣿⣿⢹⣿⣿⠛⣿⣿⣿⠻⣿⣿⣷⡰⣀⣿⣿⣿⣿⣦⠱⣆⡈⡻⣿⡄⠀⢂⠀ ⣀⠀⠀⣠⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⡟⣿⠀⣿⣿⠀⣿⣿⣦⣸⣿⣿⣧⣀⣹⣿⣷⣿⡏⢿⠙⣿⠿⣧⡙⣷⣇⡌⠻⢦⣈⠀ ⠝⠻⣿⣙⣻⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⢻⣿⣷⡌⣿⡀⠉⢿⣉⣻⣯⣤⣴⣿⣿⣿⣿⠿⠻⣿⣿⠃⢸⣇⠙⠆⠉⠉⠛⡿⣷⣤⣤⣬⣽ ⠀⣴⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⡏⢹⣿⣥⣿⣷⣾⣿⠿⠿⠛⠋⠉⣹⠃⣠⡝⠀⠀⠿⠿⣶⣾⢿⡄⠀⠀⠀⢀⠐⠈⠁⠀⠀⠀ ⠀⢸⣿⠄⢸⣿⣿⣿⣿⣿⣿⣿⣬⣿⡿⠿⠛⠛⠉⡉⠀⠘⢿⠀⠰⡖⠀⢸⠏⠈⠟⠀⠀⠀⣶⣶⠿⣿⡀⢷⠀⠀⠀⠹⣷⡀⢀⣀⣠⣿ ⠀⢸⣿⠀⠀⣿⣿⣿⣿⣿⣿⠁⠸⡿⠃⠀⠂⠀⢉⣡⠀⢀⠀⠀⢸⣷⠀⠈⠀⣠⣦⣤⣤⣴⣿⡇⠀⣸⡆⢸⡆⠀⠀⠀⣻⣷⠀⠹⣧⡰ ⠀⠀⢹⡇⠀⣿⣿⣿⣿⣿⠟⠃⠀⣤⡄⠀⠀⠐⠛⠁⢀⣸⣷⣤⣴⣿⣾⣿⡿⠿⠿⠟⠛⠛⣻⣿⠀⣿⡁⠈⣿⡄⠀⠀⠈⣿⣧⠀⢹⣷ ⠀⠀⠈⢿⣀⣿⣿⣿⣿⣿⣷⣆⣠⣿⡧⠴⠶⠶⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⣧⣼⡟⡇⠀⢹⣷⡀⠀⠀⠈⢿⡆⠈⣿ ⠀⠀⠀⠈⣻⣿⣿⣿⣿⡏⢹⣿⡟⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⡞⣿⡿⠀⠿⣶⠸⣿⣷⣄⡀⠀⠈⢿⡀⣿ ⠀⠀⢀⡴⠃⣾⣿⣿⡉⢻⣿⠉⠉⠀⠈⠀⠀⠀⠀⢀⣖⣊⣭⣽⣿⣶⣦⡤⠀⠀⢀⣠⠟⠋⢸⣿⢃⣄⣴⠛⢾⣿⣿⡿⡇⠀⠀⠈⢳⣿ ⣤⠔⠋⡔⢠⣿⢻⣿⣷⣤⣿⣦⣤⡀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠛⠉⠙⡗⠀⣀⠭⠊⠀⢀⣿⢃⣿⡏⢉⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢻ ⠀⠀⢰⢣⣿⠁⠸⣿⣿⢸⣿⣿⣿⣿⠦⣀⠀⠀⠀⠀⢻⣿⡟⠀⠠⠚⢡⡷⠀⠀⠀⠀⠀⢸⠿⠾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⢸⣼⣿⠀⠀⢻⣿⠀⣿⣿⣿⣿⣷⡀⠀⢀⣀⣠⠤⠛⣋⠀⠀⢀⡾⠃⠀⠀⠀⠀⣠⣯⠀⡀⢠⣾⣧⣿⡼⣿⠿⠿⠟⣿⣆⠀⠀⠀ ⠀⠀⠘⣿⡟⡀⠀⠈⣷⡀⢿⣿⣿⣆⣻⡿⠖⠋⠀⢀⣶⣞⣁⡤⠴⠯⢤⡄⠀⢀⣤⣾⡿⡟⠀⠁⢺⣿⣿⣿⣷⡘⠂⠀⣄⢿⣿⠂⠀⠀ ⠀⠀⢀⡸⠷⠓⠒⠤⡌⠳⢼⣿⣁⠀⠀⠀⠀⠈⠉⠉⡉⠓⠒⠒⠠⠤⠤⠴⢲⣿⣿⡟⠁⢣⢸⡀⢾⣿⣿⣿⣿⣷⣄⠀⠈⢿⡇⠀⠀⠀ ⢀⡴⠋⠀⠀⢀⡠⠖⠂⠐⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠶⣶⣶⣶⣾⣿⣿⠋⠀⠀⠀⢸⣇⠀⢻⡏⠻⣿⣿⣿⣧⠀⠀⠻⣦⠀⠀ ⠉⢀⠖⡰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣦⣄⡀⠉⠛⠛⡭⠁⠀⠀⢠⠃⠘⣿⣆⠈⢣⡀⠘⢿⣿⡿⣤⡀⢀⠘⠇⠀ ⠀⢁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣉⣿⣯⣟⣛⠻⠭⣍⡀⠀⠀⡠⠃⠀⠀⠈⠛⢿⡿⣿⣶⣦⣿⣿⡟⢧⣼⣦⣤⠆ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣖⣚⣉⡴⠿⠿⠿⠶⠶⣽⣷⣦⣤⣀⣀⣀⣀⣀⣀⣈⣻⢿⣉⡽⠿⠧⠚⠛⠉⠉⠁ ⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠟⣛⠽⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠭⣙⠛⠛⠿⣗⢾⡋⠳⢤⣀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠋⡉⠉⠉⠛⠲⠤⣀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⣀⡤⠔⠒⠊⠉⠓⢲⡆⠀⠀⠀ ⠀⠀⠀⢸⡆⠈⠢⡀⠀⠀⠀⢸⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢙⡦⠊⠁⠀⠀⢀⠴⠂⢠⣾⡇⠀⠀⠀ ⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⡰⠛⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣄⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⣠⠏⠀⠀⠀⠀⠀⠀⣠⠞⠁⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⢿⡓⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢠⡞⠁⠀⠀⠀⠀⣀⡴⠊⢁⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⠖⠛⠓⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⣴⣿⣶⣶⣶⣶⣶⣾⣷⣲⣶⠯⢄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣴⡟⢿⣿⣿⣿⡍⢹⣿⠿⠿⠉⠁⠀⠀⠘⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢷⣤⠤⠤⠀⠈⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⠾⣅⠻⣝⣿⣿⣿⣠⣾⢯⡀⢀⢀⣀⣠⢤⣾⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠙⠒⢻⠟⠉⢿⣄⠀⠀⠀⠀⠀⢀⡴⠊⢁⡴⠃⡴⠈⠑⠓⠛⢲⡿⢿⡄⠀⠈⠻⡖⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣶⡾⡟⢧⡀⠀⠐⠚⠁⠀⣠⣯⣤⣞⣀⠀⠀⠀⠀⡞⠀⠈⢻⣆⣠⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣷⣀⣽⣦⡀⡀⢀⣴⣿⠷⠶⠶⢶⣿⡦⠔⠊⠹⣄⣀⣨⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡯⠚⠉⠁⠀⠀⠈⠉⠓⢾⣿⡧⠤⢀⣀⠘⠻⣿⠤⠤⠤⡖⠛⠉⠑⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⢏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠸⣧⣿⡂⠠⠤⠽⠦⢄⣀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠙⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢳⡄⠀⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠙⢢⣘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⡄⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⢸⠀⣷⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠻⣿⢦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠏⠀⣽⣄⡀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⡇⠀⣿⡼⠃⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⢰⠀⢹⡈⢣⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣏⠀⣾⠋⠁⠈⢹⣦⠀⠀⠈⠢⢄⡀⡠⠞⠀⢀⠏⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣠⠃⡠⢾⣇⠀⠳⡀⠀⠀⠀⠀⠀ ⠀⠀⣀⠜⠉⠙⢶⣿⡀⢀⡔⠉⣿⠀⠀⠀⠀⠀⠈⠓⠦⣀⣼⢀⡀⣀⣠⠴⠾⠁⠀⠀⠀⣠⠞⠁⢰⡇⠀⠙⣆⡀⢹⣄⠀⠀⠀⠀ ⠀⡴⠁⠀⠀⠀⠀⡟⠁⡏⠀⢀⣿⠤⠤⠤⠤⣤⣄⣀⣀⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢡⣖⠉⠉⠉⢆⠀⣸⡉⠉⠙⠦⡀⠀⠀ ⣸⠁⠀⠀⠀⠀⢀⡇⠀⠳⢴⣿⡟⠀⠀⠀⠀⠀⠙⠣⡀⢸⡏⠉⠙⠒⠒⠦⢤⣀⡀⠀⠀⠘⡏⠳⢄⠀⣸⣶⠟⠀⠀⠀⠀⠈⠆⠀ ⢇⠀⠀⠀⠀⢠⠎⠀⠀⠀⣰⠛⡄⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠒⢤⣧⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣄⠀⠀⡴⠃⠀⠀⣀⠔⠁⠀⠈⠦⣀⠀⠀⣀⠠⠚⠀⣼⡇⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⡿⠢⢤⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄ ⠀⠈⠓⠒⠒⠒⠂⠉⠀⠀⠀⠀⢀⠔⠛⠿⠟⠢⣤⡶⠟⠉⢿⣎⠒⠀⠀⠒⠊⠁⠀⠀⢀⡴⢅⠀⠀⠈⠒⠤⣀⡀⠀⢀⣀⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢹⠙⠢⢄⣀⣀⣀⠤⠖⠋⠀⠀⠑⢄⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⣀⣀⣀⣒⣀⡸⠄⠀⠀⠀⢸⣄⣀⣀⣇⣀⣀⣀⣀⡀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⡠⠤⠤⠒⠒⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠓⠚⠓⠦⠤⢤⣀⡀⠀⠀⠀⠀

⠀⠀⣼⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢠⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣸⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢳⣿⡟⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣼⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⡷⡘⢿⣿⣿⣿⣿⡿⣿⣿⣿⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⠛⠻⣿⣿⠛⠛⢶⡛⢿⣿⣿⣷⠙⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣿⠀⠀⣿⣿⣄⡤⠄⠛⣤⣈⣿⣿⣧⡈⢿⣿ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢱⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢠⡇⢀⡴⢻⣿⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣞⢻ ⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⡼⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢸⠁⠋⣤⣾⣿⣿⣿⣿⡿⠿⢿⠁⠉⠳⢤⡈⠀ ⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠟⣧⠴⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⡇⢠⣾⠿⣿⡇⠛⣛⠉⠀⣀⣸⣤⡴⠤⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⡿⠞⣯⠀⣀⣀⣀⡴⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣦⣸⠀⠈⠁⢀⣻⣦⣎⣀⣀⡌⠉⠉⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠁⣿⣿⡿⠄⠒⢿⡁⣀⣠⣌⣁⠀⣿⣿⣿⣿⣿⣿⣿⠏⣿⡇⢈⠟⠃⠀⠀⡰⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡿⢺⣿⣏⣠⣴⣶⣿⣿⣿⠿⣿⣟⠛⠛⣿⣿⣿⣿⣿⠃⡠⣿⡷⠃⡠⠀⣠⠊⡽⢄⠀⡰⠂⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣿⣿⣿⣿⢃⣼⣿⣿⣿⣿⣿⡿⠿⠿⠛⠉⢩⣇⢠⣿⣿⣿⣿⢇⠔⠁⢻⣤⠞⣡⠞⢡⠊⣠⣜⠛⢤⣠⠊⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⡝⢻⣿⣿⣿⣾⣿⡿⠋⠀⢯⣀⠀⡀⠀⠉⣩⠟⠉⣸⣿⠟⢡⠟⠋⢀⣤⠜⢁⠜⠁⠀⠁⠐⠁⠀⠑⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡼⣿⣿⡇⠘⠁⠀⢀⣤⣶⡿⢿⠁⡴⠋⢀⡄⣰⡿⠋⠰⠟⠀⠴⠙⠃⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣇⠀⠀⠀⠈⠉⡤⠀⢸⠀⠃⣠⣾⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⣿⣿⣷⡀⠀⠀⠈⠀⢀⢼⠀⣶⡿⠋⠔⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠰ ⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⡴⠁⢸⣬⠟⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠾⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⠃ ⠿⢿⣿⣿⣿⣿⣿⣿⣷⡎⠀⠰⡷⠁⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⡀⣨⣿⠃⠀⠀⠀⠀⠀⠀⡤⠁⠀ ⠙⣳⢹⣿⣿⣿⣿⣿⣿⣿⣆⠀⠁⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣠⣤⠞⠋⠀⠀⠀⠀⡼⣴⡟⠁⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀ ⠉⠁⠻⣿⣿⣿⡟⢿⣿⣿⣿⡷⡀⠀⢙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⢿⡏⠀⠀⠀⠀⠀⡠⠚⣴⡟⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠛⢿⣄⢻⣿⣿⣷⠈⠢⡈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡀⠙⠲⠤⠤⢀⠠⠤⢾⣽⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⡏⠋⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣦⠀⠀⠀⠀⠀⠀⠿⠆⠀⠀⣠⣾⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣤⣤⣀⣀⠀⠀⠀⠀⠙⡕⢄⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣶⣶⣾⡄⠀⣀⣀⣀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠻⢿⣿⣿⣿⣿⣿⠶⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⡸⠀⠀⠀⣴⡴⢸⢻⡿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⡜⠀⡃⡜⠀⣼⠏⡶⡏⢸⣧⣿⣿⣿⣿⣿⣷⣿⢿⣿⣷⣹⣿⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠵⣿⢠⢷⠃⣞⢇⢶⢁⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⢸⢰⣾⣼⣇⣾⣧⣿⣿⣿⣿⣿⢟⣹⣡⣿⣿⣿⣣⡟⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⣾⡿⣿⣧⣼⣿⡿⠛⠹⣿⣟⣛⣻⣿⣿⠟⣻⠁⡇⠀⠀⡠⠖⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⣿⣀⡇⠳⠛⠁⠀⠀⠀⠀⠈⠉⠉⠉⠀⣠⠇⣀⡤⠔⠋⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⠉⣿⣿⡻⡷⠤⣄⡀⠀⣀⣀⣀⡤⠄⢀⣼⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠳⢶⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣴⣿⣜⢷⣷⡀⣀⡭⣖⣤⣄⣀⡠⠔⠿⣿⣷⣬⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡤⠀⢬⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡁⣾⣵⡿⠿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⣿⡷⠦⠤⠤⢤⣤⡤⠒⠋⠁⠀⢀⣾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⠘⣿⡿⠋⠀⠀⠀⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠉⠳⢤⠄⠀⢩⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⢀⣾⡟⠀⠀⠀⠀⠀⠀⣀⠀⠑⢄⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣔⠛⣀⣠⣤⣄⠀ ⠀⠀⠀⠀⠀⠀⣼⢛⣵⠃⠁⢀⠀⡄⠀⣸⠋⠙⠢⣬⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣡⣿⠏⢸⣧ ⠀⠀⠀⠀⠀⡼⣡⠞⠈⢠⡀⢨⠀⡇⠀⣧⠀⠀⠀⠈⠃⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⠟⣶⣿⡿ ⣤⠄⠀⡀⡸⡿⠃⠀⢸⠈⡷⣼⣄⢸⠀⢹⠀⠀⢀⣠⠴⠒⠋⠉⠉⣻⠉⠉⠉⠓⠲⢤⣀⠀⠀⠀⠀⠀⣀⡠⠿⠛⠻⣷⣦⣿⡿⠁ ⠋⠀⠀⢰⡟⠳⣤⡀⠈⢦⠃⠘⠈⠓⠿⣺⠖⠚⠉⢀⣀⠤⠖⠛⠉⠹⠉⠉⠉⠉⠙⠒⢬⣑⢦⡀⠴⠊⠁⠀⠀⠀⠀⠈⢿⣿⠁⠀ ⡀⠀⠀⣸⠳⣀⣠⣿⠿⠋⠉⠉⠉⠙⠒⡻⢤⣒⠋⠁⠀⠀⠀⢐⠲⠤⣀⠀⠀⠀⠀⠀⠀⠈⠛⣷⡖⠢⣄⠀⠀⠀⠀⠀⢨⠀⠀⠀ ⠀⠀⣠⣿⠞⠉⠈⠁⠀⠀⠀⣀⡤⠖⠒⠋⠉⠉⠉⠑⠦⣄⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣿⠀⢠⠂⠆⠰⢸⠀⠀⠀ ⠀⢠⡟⢀⡀⠀⣀⡤⢀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣖⣒⠂⠀⠀⠀⠀⠀⠀⠀⣠⠤⠊⠀⣿⡋⢠⠇⢰⠁⡆⢸⡴⠀⠀ ⢰⡞⠀⡞⣠⠞⣡⠴⠃⠀⠀⠀⠀⠀⣀⣴⠾⠗⠒⠒⠒⠦⢤⣸⠁⠙⢦⣀⠀⠀⠀⣴⠋⠁⠀⠀⣰⠋⣧⢎⣠⡧⡴⠃⠀⢸⡀⠀ ⢿⠀⢸⣷⣣⠞⠁⠀⠀⠀⢀⣠⡴⣾⣿⠁⢀⣀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠈⠀⢀⡰⠃⠀⠀⠀⡼⠃⢀⡟⠉⠀⢀⣃⣤⠾⢻⡇⠀ ⣿⠀⠸⣿⠃⠀⠀⣠⣴⣾⡿⠉⣰⣿⠿⣄⣾⣿⣦⠘⣧⣤⣄⠀⠙⢿⣦⡀⠀⠀⠹⣆⠀⢀⡾⠳⠒⣶⡗⠊⠉⠉⠁⠀⠀⠰⡇⠀ ⡁⠀⣼⠁⣀⣤⢾⡋⢀⡾⠁⢠⣿⠏⠀⠨⡻⣿⣎⠳⢿⣿⡻⣿⡄⠈⢻⡿⣄⠀⠀⠈⢦⡞⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⢿⠀⣿⡞⡋⢀⣿⠀⣾⠃⠀⣼⠏⠀⠀⣀⣬⠆⠈⠙⠛⠓⠛⠋⣿⣦⠀⢻⡽⣆⠀⠀⣦⡇⠀⠠⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠘⣼⡿⣦⡟⣼⡇⣸⣿⡆⢀⣿⠀⠐⠛⢋⣁⠀⠀⠀⠀⣒⣲⣤⣬⣿⡄⠀⢻⡜⣆⠀⣼⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀ ⠖⢻⣧⣻⣇⣿⡇⣿⣿⡇⠸⣿⢀⣠⣤⣴⠼⡄⠀⠀⣾⠛⠋⢀⡿⣿⣧⠀⠈⣷⣼⣾⡏⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠂⠛⠛⠛⠿⢿⣧⣿⣿⡇⢠⣿⠋⠀⠉⣀⣠⠃⠀⢀⣈⠙⠉⠁⠀⢻⣿⡇⠀⢸⣿⣿⢻⡘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⢿⣿⡇⠀⣿⠉⠛⠁⠀⠀⠀⠀⣀⣡⣄⠀⠀⠀⢸⣿⡇⠀⠘⣿⣿⣾⡏⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⣯⣿⡇⠀⢹⣦⠀⠀⠀⠀⢠⣾⢷⣶⣿⠀⠀⢀⣾⣿⠀⠀⢸⡇⠸⠈⠳⣿⣄⠀⠀⢀⣀⡀⠀⢀⣰⠏⠀⠀⠀ ⣧⣀⣀⣀⣀⣵⠴⢿⣿⣧⠀⢻⣿⣆⡀⠀⠀⢸⣷⡀⠀⠈⢀⡴⠋⢀⡇⠀⢀⣸⡇⠀⠀⠀⠈⠛⢷⣦⣤⣤⣩⣿⠟⠛⠂⠀⠀⠀ ⢆⠉⠻⡉⠉⣿⡄⠀⣿⣿⣇⠈⢷⡎⠙⠒⠦⠤⣝⣿⣤⣀⣾⣁⡴⡋⠀⣴⠟⣻⣝⡲⠤⣄⠀⠀⠀⠉⠻⣯⣉⠓⠲⢤⡀⠀⠀⠀ ⠈⠣⠀⠙⠀⢹⠻⡄⠹⣿⣽⣆⠘⣿⠳⣄⣀⣀⠀⠀⣤⣘⠻⢿⡿⢣⣞⣡⠖⠋⢀⠉⢗⠢⢕⣤⣀⣀⣀⡀⠙⣝⠒⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣇⠙⢆⠈⠛⠿⣷⠮⣷⣄⡀⠉⠉⠉⠉⠉⠛⢶⣖⢿⡼⠁⣠⠖⠁⡠⠈⠢⡀⠙⠖⠋⠉⠉⠉⠺⢦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠘⠀⠈⢧⡀⠀⠈⠳⣄⡀⠀⠓⢤⡀⠀⠀⠀⠐⠪⣝⣷⡎⢀⡤⠊⠀⡤⠀⠀⠀⠀⢀⣀⣀⠀⠀⢈⢷⠄⠀⠀⠀

⢀⡿⠁⠀⠀⠀⢠⠏⠉⠹⣄⠀⠱⡴⠃⠀⢀⣾⣿⣿⡷⢫⡶⠋⠁⠟⠿⣿⠁⠀⣿⠀⢸⡞⡄⠀⢳⠀⢡⠀⠑⣆⠀⠀⠀⠈⠻⡧⡈⢆ ⢸⠁⠀⠀⠀⠀⡎⠀⠀⠀⠀⠑⢢⡄⠀⠀⡼⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣸⠀⢰⣿⠀⠀⡇⡇⠀⠈⡆⠀⡆⠀⠈⢷⡀⠀⠀⠀⠹⡌⠪ ⠆⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢸⠈⠢⣸⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡜⢿⠀⠀⡇⢧⠀⠀⢹⠀⢁⠀⠀⠀⠻⣄⠀⠀⠀⠹⣄ ⠀⠀⠀⠀⠀⠂⠀⢀⡆⠀⠀⡄⢸⠀⠀⠈⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢰⠃⢸⠀⢀⡇⣼⠖⠒⠺⡄⢸⠀⢱⡀⠀⢼⢷⣄⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡄⢸⠀⣀⣀⡀⣸⣀⣀⠀⠀⠀⠀⠀⠀⢸⢠⠇⠀⣸⠀⣸⠁⢸⠀⠀⠀⡇⠘⠀⢸⣧⠀⠸⣄⠈⠲⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢰⣧⣼⠿⠋⠉⠁⢸⠉⠙⠛⠄⠀⠀⠀⠀⣼⠏⠀⠀⡇⠀⠁⠀⢸⠀⠀⣀⡇⠀⠀⢸⠙⡄⠀⡿⡆⠀⠈⠑ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⢻⠸⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⢰⠃⠀⠀⠀⡾⠊⠉⣩⡇⠀⠀⣾⣙⣇⠀⣇⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⢧⠀⠀⣼⡄⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⡼⢁⣴⣿⣿⠃⠀⣸⣿⣿⣿⠀⣸⣽⡆⠀⠀ ⠆⠀⡀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠈⣣⡀⣿⣷⡀⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣠⣾⣴⢗⣿⣿⣿⣿⣏⣉⠉⠀⠈⣏⠀⣿⣿⣧⠀⠀ ⡆⠀⠀⠀⠀⠀⠀⣷⡄⡜⢻⣆⣬⣴⣿⣿⣿⣿⣿⣿⢷⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⣿⣿⣿⣿⣿⣷⡄⠀⠉⠙⠛⣿⣿⠀⠀ ⠘⠄⠀⠀⠀⠀⠀⣿⡷⢿⣿⣻⣿⡿⠛⠋⣩⣯⣿⣟⡛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠉⠙⠁⢸⣿⣿⠀⠀⠀⢀⣿⣿⠀⠀ ⠀⠀⢀⠀⠀⠀⠀⣟⣡⣾⣿⡿⠋⠀⢀⣾⣿⣿⣿⠿⣿⣦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠳⢄⣀⡾⠛⣿⠀⠀⠀⢸⡟⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡏⠀⠀⠀⣼⣿⡇⠈⠁⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣤⣴⠞⠁⠀⠀⠀⠉⠁⠈⠀⠠ ⡄⠀⠀⠀⠀⠀⢀⠈⣿⣿⡇⠀⠀⠀⠹⣇⠑⠤⣄⣠⢟⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷ ⠃⠀⠀⠀⡄⠀⠸⡄⠘⣿⣿⣆⠀⠀⠀⠙⠷⢦⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣷⠀⠸⣿⠿⣷⡄⠀⠀⠀⠀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃ ⠀⠀⠀⠀⠀⠀⢀⣿⣷⡀⠘⣆⠈⠁⠀⠀⠀⡠⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠠⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀ ⠀⠀⠰⠀⠀⠀⢸⠏⢻⡟⢦⠈⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⢠⠤⣔⣊⡡⠤⠖⠒⠒⠲⣀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠀⣾⣦⠀⠱⠘⣷⣔⠳⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀ ⠀⠀⠀⠀⠀⠀⣿⡎⢧⠀⠀⠘⣆⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣇⠀⠀⠀⠀⠀⢀⣀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⢠ ⠀⢀⠀⠀⠀⠀⡇⠙⢌⣣⠀⠀⠸⣆⠀⠀⠉⠓⠀⠀⡀⠀⠀⠀⠀⡄⡴⠉⠉⠉⠙⠋⠉⠉⠙⣇⠀⢸⠇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠠⠄ ⠤⠞⠀⠀⠀⢀⡇⠀⠀⠉⢇⠀⠀⡟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠈⠀⠀⠀⠀⢸⣄⡞⠀⠀⠀⠀⣠⠞⠁⡟⠀⠀⢀⠀ ⠀⠀⠰⠀⠀⢸⠀⠀⠀⠀⠈⣆⠀⣷⠀⢻⡷⣦⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠇⠀⢀⡴⠊⠀⠀⢸⠃⠀⡄⠠⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡀⣿⠀⠀⢻⣏⠻⣿⠶⣄⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⡼⠏⠀⣀⡴⠋⠀⠀⠀⠀⣾⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣇⠇⠀⠀⠀⠹⣷⣌⢱⡜⣄⣽⣛⣚⣷⠀⠀⠀⠀⠀⣠⠞⠀⠄⣸⠋⠀⠀⠀⠀⠀⠀⣿⠀⠆⠀⠀⠀

⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⣠⠤⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠲⡄⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⢰⠃⠈⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡇⠀⢻⡀⠀⢠⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡎ ⠈⣇⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡇⠀⠀⠸⣘⣆⠀⠀⠀⢀⣀⣀⠀⠀⠈⡾⠁⠀⠀⡇⢠⠃⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣴⠁ ⠀⠘⣧⠘⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⢈⢘⣆⣴⡾⠙⣷⡛⣻⣶⣆⡇⠀⠀⠀⣧⠏⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀ ⠀⠀⠈⢳⡀⠉⠓⠲⡤⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠨⣿⣿⣿⡦⠀⢹⠛⣿⣿⣿⡇⠀⢀⡴⠋⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀ ⠀⠀⠀⠀⠉⠢⣄⣄⣁⡀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣠⣿⡿⢿⡦⡄⠀⠛⠿⣿⣿⡇⢀⠎⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣷⡶⠶⠾⣯⣄⡀⠀⢿⣿⣿⠄⠀⠀⠀⠀⢰⣿⣿⣧⡏⠀⠀⡈⠉⠉⠉⠐⣐⣦⣶⠖⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⣴⠶⢭⠾⠛⠋⠀⠀⠀⠀⠀⠀⠉⢇⡘⣗⠀⠉⠰⣄⠀⡴⠋⠁⠀⣹⠃⠀⣰⣡⠶⠞⠛⠛⠛⠛⠻⠿⣗⡒⠤⢄⡀⠀⠀ ⠀⣠⠖⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢼⡆⠀⠀⢨⣿⠥⠀⠀⢠⠇⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠋⢗⢤ ⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⢬⣿⣄⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⢀⣸⠴⠞⢻⣿⡿⠭⠿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠘⠉⠑⠀⠀⣸⣿⣇⠀⠀⠀⠙⠢⠄⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⢥⣽⡇⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡷⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢷⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠰⣼⢿⣎⡆⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠹⠟⠋⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢠⣿⣿⣿⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡆⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢻⣿⣗⣶⣠⣤⣤⣦⣮⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠊ ⠀⢸⠝⢛⢻⣿⣿⢙⣯⣦⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠏⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠚⠉⠀⠀

⠀⠀⠀⠀⣿⣅⣿⠟⠷⠛⠋⡳⠋⠁⢀⡴⠚⠛⠺⣷⣄⠀⠈⢢⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠱⡀⠹⡖⠤⣀⠀⠑⠢⡀⠀⠀⠀ ⠀⠀⠀⠀⡟⠋⠀⠀⠀⢠⠊⠀⢀⡴⢯⠱⡄⢀⠀⢈⠻⣦⡀⠀⠑⣝⣄⠀⠀⠀⠀⠀⠑⡄⠀⠑⣄⠀⠙⡄⠙⡄⠀⠁⠀⠀⠈⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⡰⠃⠀⡠⠊⢆⠘⣷⡘⢎⠂⠀⠙⢬⡻⣄⠀⠈⢻⣵⠦⡴⠶⠤⠄⠘⢆⠀⠘⣦⠀⠘⡄⠘⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⠀⠀⡰⠁⢠⠞⠀⠀⠈⢆⠸⡌⠢⡳⡀⠀⠀⠙⢌⠣⡈⠁⠈⢷⠬⣳⢄⠀⠀⠀⠂⠀⠈⢷⡀⠘⡄⠸⣿⡶⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⡰⠁⡰⠁⠀⠀⢀⣀⠈⢆⠱⡀⠙⢿⣦⡀⠀⠀⠀⠙⢆⠀⠈⣆⠈⠑⣽⡢⣄⠈⠆⠀⠈⢷⡀⠸⡀⢹⣷⡙⢿⣶⣄⠀ ⠀⠀⠀⠀⢀⡟⠠⣞⡤⠖⠊⠉⠁⠀⠀⠈⠣⡱⡀⠀⠙⠿⣦⡀⠀⠀⠀⢢⡀⠘⡄⠀⠈⢳⣌⠉⠺⣤⣀⠘⣷⡀⢣⠀⠻⡷⡀⠙⢿⣧ ⠂⠀⠀⣰⠋⢀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠈⠻⣦⡀⠀⠀⠱⡄⠘⡈⠉⠉⠉⠣⡀⠸⣄⠀⢹⡷⡈⣇⠀⠹⡵⡀⠈⢿ ⠀⠀⢀⠇⢠⠛⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠉⠒⢄⠀⠘⢆⠀⠀⠀⠀⠀⠈⢆⢹⡄⠈⡗⢣⢹⡄⡄⠹⣷⠀⠀ ⠀⢀⠎⢠⣯⠀⢹⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⢀⣬⣓⣋⣉⣽⣿⢿⣿⣿⣿⡄⢹⠈⣿⣷⣿⡄⢻⣧⡀ ⠀⠀⢀⣎⠸⡆⠀⢣⠈⠱⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⣰⠿⠟⠛⠿⠛⠛⣻⡀⠸⠟⢿⣷⢸⠀⢹⡟⣿⣿⡈⣿⡉ ⠀⠀⣄⣈⡦⠽⠒⠉⢹⠀⢀⣠⡤⣴⣶⣶⣶⣿⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠀⠀⢳⠀⠙⢧⠸⣧ ⠀⠀⠀⠔⠊⠁⢈⣩⡾⠛⣉⣥⣾⣿⣿⣿⣛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠘⡟⠶⣬⡆⠘ ⠀⠀⠀⠀⠀⢲⣿⣷⡶⠟⠛⠗⠋⠑⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⡇⠀⠉⢳⠀ ⠀⠀⠀⠑⣴⡿⠿⠮⡳⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⡀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣗⠄⠀⠀⠣⣤⡲⡈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣥⣾⡇⠀⠀⠀⠀⠀⠀⢀⡟⠀⢀⠀⠀⠀⠐⠀⠀ ⠀⠀⠀⡀⢻⡳⡀⠀⠀⠙⢷⣌⠀⠻⡄⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡞⡇⠀⢸⠀⡇⠁⠀⢠⣤ ⠀⠀⠀⢻⣄⢣⠈⠳⣀⠀⠈⢿⡧⡀⢱⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡆⠛⠛⠉⠉⠉⠉⢿⡇⠀⠀⠀⠀⢀⣾⠁⠇⣸⡌⢈⡇⠀⠰⣿⣿ ⠤⣀⠀⠊⠉⢆⢣⠀⠈⢦⠀⢈⢷⠙⡄⢣⠀⠀⠀⠀⠀⠈⢿⡏⠀⡁⠀⠀⠀⠀⠀⠀⠀⢳⢢⡀⠀⢀⡎⣿⡆⠀⣧⠃⣸⣇⡀⠀⣿⡏ ⠀⠈⠻⣷⣶⣿⣦⢧⡀⠀⠡⡀⠩⣆⠘⡄⢇⠀⠀⠀⠀⠀⠀⠙⠲⠇⠀⠀⠀⠀⠀⠀⠀⡜⠈⠀⣠⣿⠇⡟⡇⣸⡏⢀⠏⣻⡁⢐⡿⠀ ⠀⠀⠀⠀⠙⠻⢿⣯⣿⣷⣤⣱⡀⠘⡀⠘⡜⡄⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣴⣿⡿⠦⢄⣻⡟⠀⡈⢀⣿⠇⣠⠖⠀ ⠀⠀⠀⠀⠠⣀⠀⠈⠛⠛⢿⡄⢱⠀⢣⣀⡸⣧⠀⠀⠀⠀⠀⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠁⢸⣦⣝⠢⣀⢁⣸⣿⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠢⢤⣇⡀⠘⡄⢃⠀⠈⠛⠿⣷⣶⢶⣤⣼⣿⣿⡉⠓⠦⢤⣤⣤⣤⣶⡿⠟⠁⠀⠀⢼⠀⣈⣑⣪⠙⡿⠃⠀⠀⠀⠀ ⣀⣠⣤⣦⣍⣓⠢⢤⣀⠀⠉⠙⢛⣈⡠⠤⠄⠠⠛⠛⠛⠛⠛⠻⠿⠿⢦⣤⣖⣦⣀⢩⣁⠀⠀⣠⠔⠒⠉⠉⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢻⠀⠀⠀⠀⠀⠘⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣤⠤⠀⠀⡰⠋⠀⣸⠀⠀⠀⠀⠀⠀⡇⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⡠⠊⠀⠀⠀⡜⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠸⠁⠀⠀⠀⡼⠀⠀⠀⠀⢷⠲⣄⠀⢀⣠⢶⠁⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠰⣄⠀⠀⡰⡇⠀⠀⠀⡀⠘⣄⣹⠗⠺⣍⣎⠤⣀⡀⠀⢸⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢉⠗⠁⣱⡤⠔⠋⡉⠑⠾⣦⣤⠶⠋⠀⡀⠀⠉⠁⠚⠚⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢇⠀⢀⣀⠤⠒⠋⠉⠉⠀⠀⠀⡠⠗⠒⠒⠒⠉⠙⠊⠉⠑⠢⣴⠂⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣈⡷⠋⠀⠀⠀⠀⠀⠀⠀⢀⡜⡡⠀⢠⠀⠀⠀⠀⠀⢠⠀⢢⡸⣄⠀⠀⠀⠀⠀⠑⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⠤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⣶⣤⣼⠀⠀⠀⠀⠀⣿⣤⣾⣿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⡿⠀⠸⡘⣿⣛⠀⠀⠀⠀⠀⣿⣿⣿⡏⠈⢷⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⢄ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡺⠅⣠⢤⣀⣠⡧⢄⡀⠑⢤⣈⡆⣠⠖⢦⡀⣏⡹⠋⢀⣠⣜⣃⣀⡀⠨⣉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠔⠋⠀⠀⢸⠃⠀⠀⠈⠲⡐⠋⠉⡁⠀⢀⡉⠛⢋⡴⠋⠀⠀⠀⢸⠈⠑⢦⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡜⣁⠤⠀⠀⠠⣜⡄⠀⠀⢤⡀⠱⣤⢤⡈⠀⠈⣀⣄⠎⢀⠔⠀⠀⠀⡸⠀⠀⠀⢙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⢏⠞⠁⠀⠀⠀⠀⠙⠿⣄⠀⠀⠙⢦⣿⣀⡞⠷⠎⡁⢸⣶⠃⠀⠀⠀⡰⠁⣀⠤⠖⠋⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠃⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⠀⢿⡟⠀⠀⠀⢹⣿⠇⠀⠀⢀⣼⠥⠚⠁⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠴⠋⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢾⠃⠀⠀⠀⠘⢻⣀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀ ⡴⠚⠁⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⣀⣶⣶⣦⣦⣄⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⣿⠿⢿⠿⠛⢿⠍⠋⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠦⡀⠀ ⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠈⠳ ⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣀⠎⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠁⣾⠏⠸⡄⠀⠀⠀⠀⠀⡆⢰⢦⡀⠀⠀⠈⢷⣄⠀⠀⠀⠈⠲⣄⢆⠀⠀⣄⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠋⢸⡼⠃⠀⠀⡇⠀⠀⠀⠀⢰⣿⣼⠿⠾⣶⣄⡀⠀⢻⣷⣄⠑⠦⣀⠈⠺⣷⢤⡀⠳⣽⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡜⠁⢰⠟⠃⢠⡎⠀⣷⠀⠀⠀⣐⡟⢨⣿⣶⣿⣿⣿⡿⣦⡀⠹⣿⣦⠀⠈⢻⡦⢬⣦⡙⠢⡈⠻⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠁⢠⠃⢀⡶⢹⣿⠀⣿⣗⠀⠀⡼⠁⠹⠋⠻⣽⣧⠟⠀⠘⡟⣦⣿⢸⣧⠀⠘⣧⣼⢪⡻⣄⠈⠳⣜⢿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢠⠏⢀⣾⠁⠈⠹⣧⡏⢹⣧⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡟⣻⣯⠀⢧⠀⣿⡇⠀⠑⢌⠳⣄⠈⠑⢿⣜⢿⡶⣄⠀ ⠀⠀⠀⠀⢀⣷⡏⢠⠿⢈⣷⠀⢰⣌⣿⡿⡟⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢁⣿⢈⣿⡘⣧⣿⣧⠀⠀⠈⠣⡈⠳⣦⡀⠙⢷⡉⢻⡁ ⠀⢀⡴⢃⣾⡟⢠⣏⣀⡞⢻⡄⠈⢿⣿⢻⠾⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⠢⡈⠻⣤⡀⠙⢦⡉ ⠖⡏⠀⢸⠛⢗⠻⡃⠙⢦⢠⣿⣦⠀⠻⣷⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠈⠢⡈⠻⣦⡈⠻ ⠀⡇⢀⣸⡀⠘⡄⢹⣆⠘⣿⣿⣻⣿⣦⣿⣏⣹⣶⣄⣀⣀⣀⠀⣀⠴⠋⠀⠀⠀⠀⢸⣿⠙⢿⣿⣿⣿⣿⠿⠷⠦⠤⣀⠀⠈⠂⠈⠻⡆ ⢠⠁⠈⠛⢳⣀⣇⣸⣿⣂⠷⠋⣀⣴⠯⠾⠿⠿⠻⣿⣿⢿⣿⠿⠁⠀⠀⠀⠀⠀⠀⣸⣁⣲⣤⠻⠛⠉⠀⠀⠀⠀⠀⠀⢳⢄⠀⠀⠀⠙ ⢾⠀⠀⠀⠈⠿⡿⠟⠉⠀⢀⣾⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠑⠦⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢣⠀⠀⠀ ⣼⡄⠀⠀⠀⠐⠁⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠤⢄⡀⠀⠀⠘⣆⠀⠀ ⠁⣿⡀⠀⠀⠀⠀⠀⣠⣾⣉⣷⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢶⣾⣟⠹⡦ ⣼⣯⠋⠓⠒⠒⢒⠋⣹⣟⡉⣹⣶⣶⣶⣤⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿ ⣈⣿⠀⠀⠃⠀⢸⡴⣁⣀⣽⠛⠛⠻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟ ⣩⣏⢀⣀⣤⠴⢯⣀⣸⣿⡏⣀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣄⣼⠋⠙⣧⣤⣾⣿⠟⢿⣽⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠉⠉⢻⣿⢛⡋⠁⢸⠀⠸⡏⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠯⡑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠈⠀⠀⠀⠀⠘⡀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⢹⡈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⡼⠀⠀⠈⠙⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⣿ ⠀⣄⡄⠀⠀⠀⠀⠀⠸⡀⠀⠸⣷⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣠⢾⠥⢤⣀⣤⣄⣀⣈⠙⡻⠶⠖⠒⠒⠒⢲⡟⠉⠲⣤⡀⡿

⡏⠉⠉⠉⠉⠉⠉⠉⠁⠀⣄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣻⣿⠿⣿⣿⣿⡍⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠈⢹ ⡇⣠⠶⠒⠲⠶⣿⣶⣦⣄⣈⣳⣀⠀⠀⠀⡠⣼⣟⣾⣾⣩⢷⣄⠀⣠⠤⢤⣧⣾⣿⣧⠀⢀⠀⠀⠀⠀⠀⠀⢀⣤⡖⣁⣀⣀⣠⣄⣀⣸ ⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠒⠻⢤⣿⣿⣿⣿⠁⣰⡟⠀⢹⣆⣠⣿⣸⣿⣿⡿⡁⠉⠒⠒⠒⠒⠈⠙⠛⠛⠿⠛⠋⠉⠉⠻⣿ ⣧⠀⠀⠀⠀⠀⢀⠀⠀⠒⠒⠶⠶⣶⣶⣶⣦⣀⣸⣿⣧⠀⠀⣠⣀⣤⡀⠀⣾⡏⣿⣿⣷⣈⣑⣶⠶⠶⠒⠉⠐⠀⢀⡠⠄⠀⠀⠀⠀⢹ ⡿⣧⣀⠀⠠⡀⠀⠉⠒⠒⠠⠤⢀⣀⠀⠉⠙⠫⣌⠻⣿⣧⣄⠉⠉⠋⣠⣾⣿⣿⣿⢿⠿⠋⠉⠀⣀⡠⠤⠒⠚⠉⠀⡀⠀⠀⠀⠀⠀⢸ ⡇⣿⣿⣧⡀⢱⡀⠀⠰⣤⣀⠀⠀⠀⠉⠓⠢⣄⠈⠑⢬⣉⣭⣭⣷⣿⣉⣉⠙⣫⠖⠁⣠⠔⠚⠉⠀⠀⠀⢀⣠⡴⠊⠀⢠⠀⢀⠀⣠⠃ ⡇⢹⣿⣿⣍⠙⣿⡄⠀⠹⣿⡿⠷⣶⣤⣄⣀⠈⠙⢶⣤⡈⣻⠁⢰⡏⠀⢀⣟⣱⠖⠉⠀⣀⣠⣤⣴⡶⣿⡿⠋⠀⣠⣶⡟⠀⣾⣴⣿⠀ ⡁⠀⠻⣿⡏⡀⣿⣿⣄⠀⠙⣦⠀⠈⣿⠉⠙⠳⢦⣤⣌⢻⡇⠀⡾⢳⠀⢀⣏⣡⣶⣴⣾⣿⠉⣼⣃⣤⠏⠀⣤⣾⣿⣿⠄⢰⣿⣿⡿⠀ ⡇⠀⢸⣿⡇⡇⢸⡟⠻⣦⡀⠈⠳⣆⡏⠀⠀⠀⠀⠙⢿⠙⠻⣖⠧⠼⣳⠟⠋⣹⠋⢀⣿⡇⣼⣿⠟⢁⣠⣼⠿⢻⣿⡟⠀⣿⣿⡇⡇⢀ ⡇⠀⢸⣿⡇⡇⢸⡇⠀⠈⠛⢦⡄⠘⡇⠀⠀⠀⠀⠀⠈⠳⡀⠈⠙⠚⠁⠀⣴⠁⠀⣸⠘⣿⣿⣧⣤⣾⠟⠁⠀⠘⣿⣡⣰⣿⣿⡇⢰⣸ ⡇⠀⢸⣿⣿⣷⠈⣧⠀⠀⠀⠈⠻⣶⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠃⠀⢠⡿⠀⢹⠿⠿⠋⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⡇⢸⣿ ⣇⣀⣼⣿⣿⣿⣴⣿⡆⠀⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⣾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠆⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⢰⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣄⣀⣇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠯⠁⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⢡⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡿⣡⣿⡍⠻⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣰⡾⣿⣿⣿⣿⣶⣶⣦⣤⣴⣶⣾⣿⣿⣿⣿⣿⣯⣾⣿⣿⡆⠀⢹ ⣿⣿⠟⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣄⠀⠀⠀⣀⣲⣿⣯⣠⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡄⢸ ⣿⣧⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⡥⣼⢿⠿⡿⡿⢿⣿⣿⣿⣿⣿⣧⣤⣵⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠠⢤⣴⠚⣹⠟⠉⠉⠀⠀⠘⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⣀⡀⠀⠀⣀⠤⠠⠭⢙⣉⣀⠤⠄⣀⢀⣀⣀⠀⢀⣠⠞⠃⣴⠇⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠈⠓⠉⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠙⢂⣤⡿⠟⠁⠀⠀⠋⠀⠀⠀⠀⠀⢀⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⢀⡾⠀⠀⠀⠀⠀⢀⣿⣿⣇⣀⣴⣞⣻⡭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣼⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢿⡇⠀⠀⠀⠀⢰⣾⣿⣿⣿⢛⣽⣿⣉⣀⣀⣀⣠⠴⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠱⣼⣧⠀⠀⠀⢠⡿⣿⣿⣿⣥⣬⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢻⣦⠀⠀⢸⣿⣇⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⡏⠀⠀ ⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣿⡷⣄⠘⣿⣿⣄⠀⠀⠀⢀⣀⢀⣀⣠⣤⣶⣿⣿⣿⣿⣿⠿⠟⠋⡇⠀⠀ ⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡏⠙⠉⠻⣿⣷⣾⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠁⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢿⣄⠀⠀⣼⠻⣿⣿⡏⠉⢁⣽⠃⠢⣀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣷⡟⠣⣄⢻⠀⠘⠃⢹⡴⣻⠃⠀⠀⠀⠙⢢⠀⠀⠀⣠⠞⢹⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢸⢸⡀⠈⠻⡄⠀⡠⠛⡰⠃⠀⠀⠀⠀⠀⢀⣧⠴⠋⠀⠀⡎⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢤⣀⡀⠀⠸⠀⠀⠀⣀⠜⠀⡇⠀⠀⠘⣶⠁⣰⣅⣀⣀⣀⠤⠔⠊⢩⡇⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠏⠉⠉⠀⠀⠀⠀⢽⠀⠀⠀⡇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣵⠀⠀⠀⠠⡇⠀⠀⠀

⢀⣀⡴⣋⠭⢁⣻⡿⠿⠛⠻⡿⠷⣾⣿⣿⣿⡷⢛⣧⣠⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁ ⣾⡅⣺⣤⡞⢓⣦⣀⣀⣾⣔⣷⣆⠈⠙⠾⢿⣿⣻⣿⣟⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀ ⡏⡜⢁⣾⡿⠉⠑⠢⣍⡑⢲⠤⣌⡓⠳⢼⣦⡈⠻⣿⣿⣝⢧⡀⡠⠖⠉⠁⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⠦⡤⢔⠁⠀⠀⠀⠀ ⡇⢹⡿⣏⠙⢄⡀⠀⠀⢹⠳⡄⠀⠙⠲⠤⣈⡙⠣⠸⢻⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⡌⠛⠳⣄⡀⠀⠀⠀⢠⢃⡖⠀⠀⠀⢻⠀⠀⠀⠀ ⠡⣾⢰⠼⠀⠀⠙⠢⢄⣀⡀⠘⢶⠳⠿⣷⣦⣬⣭⡝⢋⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠻⣦⣤⣀⡞⠋⠀⠀⠀⢰⡞⠀⣦⡀⠀ ⢠⣻⡌⠀⢀⠀⠰⡈⠀⠀⠙⢄⠈⣧⠀⡀⢈⣿⣄⡇⢸⣆⢻⣅⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⠀⠀⠘⢿⠿⡇⠀⠀⠀⣰⠟⢀⣾⠗⣳⡦ ⠀⢿⣧⠀⠸⡀⠀⠀⡄⢠⠀⢘⡦⣷⢋⣶⡿⠟⠘⣶⡄⣯⣿⡯⣆⡄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢲⣷⠃⠀⢀⣼⠋⠀⣉⣡⣴⣿⣿ ⣆⢧⢽⢣⠀⡇⠄⠡⢰⡀⠆⢸⠇⠣⠈⠁⠀⠀⠀⠻⣷⣹⡿⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠙⠲⢼⣷⣿⡋⠁⠀⠀⠒⠲ ⢸⣌⠫⡀⣣⣇⠘⣆⠀⡇⣸⣼⡀⠀⠀⠀⠀⠀⣠⡄⢻⣟⡇⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣋⠿⣦⠀⡀⠘⡇⠈⠙⠓⢦⣄⠀⠀ ⣿⣿⣆⢧⠞⢌⠑⠺⢶⣿⠛⠋⠀⠀⠀⠀⢠⣾⡿⢃⡷⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢠⡎⣰⡇⡠⣿⢀⡇⠀⠀⠈⠓⢦ ⠙⣿⣿⣮⠀⠀⠙⣷⣾⣿⣿⣶⣤⣄⠤⠤⠒⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢏⣾⡟⣸⡇⡏⣸⠀⠀⠀⠀⠀⠈ ⠐⠘⢿⣿⣧⡳⡀⠈⠻⣿⣽⣿⣿⠒⣚⡓⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠠⠴⣾⡵⠟⢩⣳⠏⣀⠿⡇⠀⠀⠀⠀⠀⠀ ⢀⠠⡈⠛⠉⠙⠺⣷⠤⢄⣻⡟⠿⠉⠁⠀⠀⠀⢸⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⠀⠀⠞⠁⢀⣤⢾⣯⡾⠃⢸⠀⠀⠀⠀⠀⠀⠀ ⡈⠳⢌⠲⢤⡀⠀⠀⠀⠠⢅⠙⢦⡀⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠙⢶⠤⣤⡭⠴⠚⠉⢀⣀⣸⠀⠀⠀⠀⠀⠀⠀ ⣧⡀⠈⠑⢄⠈⢆⠀⠀⠀⠈⠳⠀⠙⣦⠙⢦⡀⠀⡇⠀⠀⠀⠀⠀⡧⠀⢠⡈⠀⢸⡆⠀⠀⢀⡾⢇⠀⠀⠀⣙⣿⣿⡀⠀⠀⠀⠀⠀⠀ ⠻⣿⣦⡀⠀⠳⣌⢦⡀⠀⠀⠀⠀⠀⣝⣿⣆⡘⠀⣹⡀⠀⠀⠀⢠⡇⠀⢸⢿⢦⣞⣷⣴⡶⠿⠶⠚⠋⠉⠉⠁⠈⠙⢿⣆⠀⠀⠀⠀⠀ ⠀⠈⠻⣿⣦⡀⠈⠢⡑⢄⠀⠀⠀⠀⠈⣿⣿⣿⣄⡙⢿⣦⣄⣤⡟⠘⡶⠞⢸⣾⣿⣿⡟⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀ ⠀⠀⠀⠈⠻⣿⣦⡀⠘⢢⡁⠀⢀⣴⣾⣿⣿⣿⡿⣷⣤⡙⣿⣿⣷⣤⣿⣷⣿⣿⣿⣿⣇⠌⢧⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀

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⠀⠀⠀⠀⠀⠀⠀⠀⢾⡄⠀⠘⣷⣸⣷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠆⢀⢻⠓⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠘⠿⣿⣿⣧⡀⠀⠀⠀⠺⣏⠉⠀⠀⠈⣹⠗⠀⠀⠀⢀⣾⡿⡿⠀⠀⠀⡸⣼⠀⡜⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠹⠛⠉⠻⠷⣄⠀⠀⠈⠓⢤⡠⠞⠁⠀⠀⣠⣴⡿⠟⢠⠇⠀⠀⢀⣷⣿⣄⡇⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠐⠦⣿⣿⣶⣄⠀⠀⠀⠀⣀⣴⣾⠿⠋⠀⠀⣼⡀⠀⢀⣾⡟⠈⣿⣷⡀⢿⡄⠀⠀⢀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠀⠈⠙⠿⠿⣿⣶⡶⠾⠛⠋⠀⠀⠀⠀⢠⠏⠀⣠⠋⡿⠀⢠⣿⣿⢳⡘⣇⠀⠀⣸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⡔⠁⡼⠁⠀⠀⣿⢹⡀⣷⣹⣷⣯⢉⡛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⡴⠋⠀⡴⠁⠀⠀⠀⣿⣼⡇⠹⣿⣿⠈⠻⣭ ⠀⠀⠐⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⠈⠀⠀⠀⠀⠀⡿⢹⡇⠀⢿⣿⣧⠀⠖ ⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⣿⠁⠀⠀⢹⡇⣇⠀ ⣀⠀⢀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣿⠀⠀⠀⠀⢻⣿⠤ ⡉⡛⠉⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⣏⠀⠀⠀⠀⢸⢻⣁ ⡟⠁⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢁⢇⠃⠀⠀⠀⠀⠈⢿⠹ ⢷⣄⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣞⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠘⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣼⠏⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢣⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣖ ⡈⣧⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⡄⣻⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢃⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿ ⡇⠉⢿⡸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡜⣡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀ ⢿⡆⠈⢻⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⣠⢊⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⣴ ⣿⣿⠀⠈⡎⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⣠⢞⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⣼⢏ ⣬⣿⢿⣦⡸⡄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⡶⠚⣡⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⢇⡟⢡⡏ ⠙⢿⣄⡙⢷⣿⣄⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠛⢁⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⣠⠞⢀⠏⠁ ⠉⠉⠉⠉⠉⠙⠻⣦⡙⣿⣦⠀⠀⠀⠀⣀⣀⡠⢴⢒⣻⠿⠛⣉⠤⠾⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠞⠋⠉⠉⠉⠉⠉⠉⠉⠙ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠿⣷⡿⠿⠯⠴⠖⠒⣋⣩⣴⠶⠭⠤⠤⠴⠶⠾⠦⠤⠼⠶⢒⣒⣞⣉⣉⣁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙

⠀⠀⠀⠀⢀⠴⠗⠀⠀⠀⣸⣀⣤⣾⣧⣤⣶⡿⠟⣩⣷⣶⣭⣳⣄⠁⢀⣼⣛⠛⠒⠀⢸⣿⣧⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠏⠀⠀⢀⣤⣾⣿⣿⣿⣿⠿⠟⠛⠛⣋⣉⣉⠉⠉⢙⣿⣷⡟⠋⠛⠷⠄⠄⢈⣿⣿⣿⡟⠻⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡜⠀⣠⣾⣿⠟⠋⠉⠁⠀⠐⠀⠀⠉⢉⣀⡀⠀⠀⣹⣿⣿⡛⠛⠦⢤⣀⠀⠀⠀⠀⠉⠛⢿⡀⠘⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢃⣼⣿⢟⡟⠀⢀⣴⠾⠓⠒⠀⠉⠉⠉⠁⠀⠐⠚⠛⠛⠛⠛⠛⠻⠶⠮⠟⠷⠦⢤⣀⣀⡐⠻⢶⣬⡆⠀⠀⠀⠀⠀ ⠀⠀⢀⠏⣼⣿⠎⢀⣴⡟⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠛⠿⣄⠀⠀⠀⠀ ⠀⠀⢼⠀⣿⡇⠠⢺⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄⡀ ⠀⠀⠀⠀⣿⣷⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣷ ⠀⠀⢸⠀⢿⠹⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⠀⡸⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⡇⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟ ⠀⠀⡇⠀⠀⠀⠸⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃ ⠀⠀⠃⠀⠀⠀⠀⢻⣷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣤⣤⣤⣤⣤⡤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⣤⣤⣾⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢹⡿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡞⢠⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⡇⠀⠀⠀ ⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢖⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢄⣀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠉⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⡼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⢁⡄⠀⠀⠀⢀⡾⠁⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣰⡾⡿⠁⠀⢀⣴⠿⠇⠀⠀⠘⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠏⢀⡇⠀⠈⠉⠉⠉⠑⠒⡄⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⢸⣇⠁⠀⠀⢆⠀⠀⠀⠀⠀⠀⣼⢻⣿⠁⡠⠊⠀⠀⠀⠀⠀⣀⡴⠞⠁⢠⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⢸⡟⢹⡄⠀⠀⠘⡄⠀⠀⠀⠀⣸⠁⠉⠁⠈⠀⠀⠀⠐⠲⢶⡿⠟⠃⠀⠀⡸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⣿⡇⠀⢻⡄⠹⢄⠈⠄⠀⠀⢠⠇⠀⠀⢀⠀⠀⠀⢀⣀⣀⣀⡡⠄⠀⠀⢰⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢻⠃⠯⠈⣷⣄⣀⠙⠦⣀⠀⣸⣀⣀⣀⣸⠛⣯⣭⡭⠤⠤⠀⠀⠀⢀⡴⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠨⠀⠟⢿⡌⠛⠒⠚⠛⠉⠙⠋⠨⡽⠛⠉⠉⠙⢆⠀⣀⡠⠖⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⠀⢀⠀⣤⢨⡿⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡞⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣿⡆⠐⡰⣷⡞⠤⣀⡀⠀⠀⠀⠀⡠⠃⠐⡆⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣷⣴⡿⠋⠉⠑⠲⢍⠉⠒⠚⠉⠀⠀⣠⢇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢐⣿⠁⠀⢀⡤⠴⠦⠽⠶⠤⣀⣀⣀⠼⠁⠀⠘⣿⡟⠀⠀⠀⠀⣀⠀⠱⡀⠀⢀⣠⠞⠁⡏⠀⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⣽⡇⢀⣴⡥⠖⠒⠒⠒⠒⠶⠿⢿⡿⠛⠋⠉⠉⠉⠉⠒⠢⢤⣀⡊⠵⣶⣷⣴⣯⠀⠀⠀⡇⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡾⠁⠹⣋⡞⠀⠀⠀⣀⣀⣤⡴⣶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣭⣙⡻⠦⣀⣠⠁⠀⠀⠈⠉⠉⠳⡄⠀⠀⠀⠀⠀⠀ ⠀⠜⢀⣠⣤⡾⠀⠀⡴⠋⣩⣿⣿⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⡙⠳⢦⣌⡉⠒⢤⠀⠀⠀⢸⢿⡀⠀⠀⠀⠀⠀ ⠀⠸⣻⣿⡏⠀⠀⠀⣠⠎⢉⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣷⡲⡄⠀⠉⠓⢤⣣⠀⢀⣏⡼⠉⢢⡀⠀⠀⠀ ⠀⢠⠟⠻⠁⠀⠀⡴⠁⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠻⣿⡌⣶⣄⡀⠀⠉⡷⢿⡟⠁⠀⢸⣧⠀⠀⠀ ⢠⠂⠀⠀⠀⠀⣰⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡘⣯⡙⢶⡀⢹⣸⠀⠀⢀⣾⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣵⡄⠹⣖⠇⠈⣇⣀⣴⣿⡿⣄⠀⠀⠀ ⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⡦⣸⡀⢸⠟⡄⠀⠙⡄⠈⢆⠀⠀ ⠀⡀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣇⠈⠀⣧⠀⠀⠘⡆⠈⢆⠀ ⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢊⢆⠀⢸⡀⠀⠀⠘⠀⠘⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠞⣦⢸⡇⠀⠀⠀⠀⠀⠱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠘⣇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠹⡄⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣹⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣿⣿⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⢤⣤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠈⢢⡑⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠊⣠⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠱⡤⣀⠈⠑⠢⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⡀⠀⠀⠀⠀⠈⢣⡀⠀⢡⠀⠑⠢⣄⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⡀⠀⠀⠘⡄⠀⠀⢀⠀⠀⠱⡄⠀⡄⠀⠀⠀⠑⢄⠀⠉⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠢⣀⠀⠘⡄⠀⠘⡆⠀⢢⠘⡀⣷⣄⠀⠀⠀⠈⠳⡄⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⠔⠋⠳⣄⠘⡄⠀⢰⠀⠀⢧⢡⢸⠮⢷⣄⠀⠀⠀⠈⢆⠀⢏⠻⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠈⠣⣰⡀⠀⣇⠀⠈⣿⣮⡆⠀⠈⢏⢳⡀⠀⠈⢧⢸⣶⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⣠⡞⡏⠀⣀⣀⠀⠀⠀⠀⠘⢧⠀⣹⢆⠀⢿⣿⡇⢠⠒⠀⢳⣷⡄⠀⢹⡌⡿⢶⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⡤⠊⠹⢻⠗⠉⠀⠀⠉⣀⠀⠀⠀⠈⢇⢹⠈⣆⢸⡏⠧⣧⣶⣶⣦⣿⣿⡄⠀⣷⡷⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⠐⡇⠀⡇⠘⢀⣤⣤⣶⣾⣧⣤⣀⠀⠀⠈⣿⠀⠘⡄⠁⠀⣟⣟⠙⢫⡙⠿⢿⡀⢸⣇⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠣⡀⠀⠀⠘⡆⠀⣇⣸⣠⣾⣿⡿⠛⠉⠁⠈⢉⣧⠀⠀⠀⠈⠀⠀⢹⡆⠀⠈⠙⠏⠉⠛⠢⠜⢧⡜⠙⢿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⢆⠸⣿⡿⠉⠀⠀⢄⣀⡤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠈⠿⢿⣇⠀⠀⠀ ⣤⣴⡄⠀⠀⡀⠀⡀⡀⠀⠀⠀⠳⡿⠤⠤⠖⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠑⠢⢄ ⢟⠀⢡⠀⠀⠘⢆⠑⡜⢤⡀⠀⠀⠈⠲⣄⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠤⢠⡄⠀⠀⠀⠘⡉⠙⠢⡀⠀⠀⠀ ⠈⠀⡄⣆⢲⡀⠈⠢⣌⣆⠙⢦⡀⠀⠠⡈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣥⣶⣿⡅⠀⠀⠀⠀⣷⡀⠀⠙⢆⠀⠀ ⠀⠀⠀⠸⣸⡟⢦⡀⠀⠉⠣⡀⠉⠢⡀⠈⠲⣄⡚⠿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⡆⠑⠄⠀⠈⠆⠀ ⠀⠀⠀⠀⠹⣿⡀⢻⢷⣄⡀⠙⢆⠀⠈⢆⠀⠀⠙⣦⡀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⣿⣿⡿⠿⠿⠛⠻⣄⠀⠀⠀⢠⣷⠤⣄⢣⡀⠀⣆ ⠀⠀⠀⠀⢀⠟⠳⢼⡞⣿⣿⣷⣤⣷⣄⠠⣣⡀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣀⠀⠀⠀⠀⠈⣢⠀⠀⣼⣿⢆⠈⣷⣷⡄⠇ ⠀⠀⢠⠀⢇⠀⠀⠀⢳⢹⠛⠉⠉⠀⠹⡆⠱⣧⠀⠀⠀⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⢿⠿⡿⠁⠀⣰⣿⣿⣾⠀⢸⣿⠃⠀ ⠀⠀⠀⠀⠈⣦⣀⡤⠊⠘⣄⠀⠀⢀⣀⣹⣀⠽⠧⢄⡀⢣⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⣿⣿⣿⠇⠀⡼⠃⡜⠀ ⠀⠀⠇⠀⣼⢣⣼⠀⠀⠈⣿⡿⢿⣿⣿⡿⠁⠀⠀⠀⠹⣼⡆⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡤⢞⣡⡾⠴⠂ ⠀⠀⠀⣰⣿⢸⡇⠀⠀⠀⣿⣷⣬⣻⡏⠀⠀⡶⢤⣤⡄⠸⠿⡀⡇⠠⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣰⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⡰⠀⠀⠀⣸⡿⠛⠘⣿⡀⠀⠀⡏⠉⢯⠁⠀⠀⠙⡇⠀⠀⠉⠙⠛⠿⣿⣿⣿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡿⠁⠀⢀⣾⠏⠀⠀⠀⠸⠟⠢⣄⡇⠿⠷⠂⠀⠀⢀⣇⠀⣀⣀⣀⠠⠄⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡘⠁⠀⢠⢻⣿⠀⠀⡆⢓⡎⠀⢀⣀⠅⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠹⣿⣿⡻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⠹⣿⣷⡞⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠜⠿⣿⠿⡄⠀⠨⢿⣶⡟⠟⡿⢻⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣶⠄⠀⠀⠀⠀⠈⠓⠃⢠⡇⠀⣿⣿⣿⣿⣿⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣤⣿⣿⣿⣿⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡱⠦⣀⠀⠀⠀⠀⣠⠶⠳⠾⣿⣿⠟⠛⠏⣿⣷⡎⠀⠀⠐⣀⠤⠀⡀⠀⠀⠀ ⠻⠁⢀⡠⠉⠘⠳⡼⠁⢆⡀⠀⠀⠉⠲⠄⡀⠈⠢⠉⢆⡀⠀⠀⠀⠀⠈⠂⠀⠀ ⢀⠔⠉⠀⠀⡄⠀⠣⠤⠄⢉⠁⢐⠦⠀⠀⢬⡗⠀⠑⠌⢟⡒⠒⢄⡀⠀⠀⠀⠀ ⠉⠒⠤⢀⠀⢳⠢⠤⠤⡵⠋⣠⠁⠀⠀⢸⠉⠪⢣⣦⡀⠚⢏⠉⢩⠠⠈⠁⠀⠁ ⠀⠀⠀⠀⠉⠒⠧⡀⢎⡠⠊⣥⠘⡀⠀⠆⡠⣂⣉⠉⢺⡶⠼⡄⠀⠑⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠺⢄⠀⢹⠀⢁⣰⠪⠤⠤⠀⠱⠄⢱⡤⣸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠫⣉⢡⠆⠀⠀⠀⠀⠀⠀⠈⢷⣈⢇⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢣⢻⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠣⣦⡈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⣿⡜⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠟⠸⠿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⢀⠉⠁⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

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⠈⠱⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠘⣿⠙⠻⣍⠉⠙⠲⠦⣄⡀⠀⢻⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠹⣆⠀⠈⢳⡄⠀⠀⠀⠈⠓⢾⣽⣦⣄⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠘⢧⡀⠈⣙⢦⡀⠀⠀⠀⠀⠈⠛⠯⠷⣦⣄⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠄⠀⠀⠀⠻⣦⡉⢈⣻⣤⣀⣀⡀⣀⣀⣠⣦⡆⠉⢳⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠐⠀⠈⠙⢷⣦⣤⣍⣻⠿⣿⣾⣿⡇⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠉⠳⣾⣏⠀⠀⠉⠙⠃⠀⠸⡛⢻⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⠀⠀⠀⠀⠀⡿⢿⣦⡀⠀⠀⠀⠀⣠⣷⣼⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⠀⠀⠀⢹⡀⠉⠻⣶⣦⢤⣄⣨⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣏⠉⠉⠛⢦⣇⡀⠀⠈⠻⣽⣟⠿⣧⣀⡤⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⡷⠀⠀⠒⠫⠝⠒⠦⠀⠟⠛⠋⢁⣀⠀⠀⠘⣷⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣤⣾⡗⠀⠀⣰⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣤⡤⠖⠀⠀⠀⠀⠐⢤⣀⡀⠀⠀⣨⣿⠁⢰⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡉⣽⡇⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⠤⠠⠄⣀⣀⣀⠀⠈⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠉⠙⠺⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⣽⠂⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⣿⠃⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡶⢶⣾⡷⣶⣄⣤⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡷⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡑⢶⣛⣧⡿⢷⣭⣾⠛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⡞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠟⢿⣧⣶⢿⣿⣻⣿⠿⠿⠒⠒⠀⠀⢀⡀⠀⠀⠀⠀⢀⣴⠾⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⡄⠀⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⢼⣿⣥⡽⠟⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠲⢿⣟⣅⣰⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢧⣔⠀⠈⠉⠛⠲⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⠛⠁⠀⠀⠀⠀⢸⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠾⣯⣶⠂⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠉⢉⢉⢉⢉⠉⠉⠀⣀⡀⠀⡟⠙⡧⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢿⡶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⡛⠶⣄⣬⣷⣄⣬⣿⣷⠂⠄⠀⠀⠀⠰⠛⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⣤⣼⡿⢿⣿⣿⣿⣷⣦⣾⠢⡀⠀⠀⠣⣠⣷⣤⠄⠐⢢⣤⣀⠀⠀⠀ ⠀⡸⣿⣿⣖⠸⣿⣿⣿⣿⣿⣿⣄⡇⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⢻⠑⠄⠀ ⠀⣷⣿⣿⣿⣾⣿⡿⣿⣻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣾⠀ ⠀⣿⣿⡼⢻⡄⠉⢰⡻⢋⣿⣿⠅⡀⠀⠀⢀⠀⣠⣤⣤⣀⠀⠀⠀⡼⢿⠀ ⠀⠸⣿⣧⢈⠉⠀⣄⢠⣾⣏⠄⣀⠀⡉⠨⠶⠖⣻⢿⣿⠟⠛⢢⣼⣤⠎⠀ ⠀⠀⠈⠙⠂⠀⠀⠀⠈⠿⠁⠈⠳⠋⠀⠀⠀⠀⠀⢁⠟⠀⠀⢠⠯⠅⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡐⠁⠀⠀⠀⠀⠀⠀⠀⡎⡴⢠⠃⠀⠀⠈⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠟⡎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⡀⠀⠀⠀⣔⣊⡔⡠⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡔⣠⣤⣤⣅⣀⢜⠤⠤⣈⠀⠈⠢⣄⠠⠊⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⣋⡛⢇⠃⣰⣾⣿⣷⡂⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡵⢛⠃⣄⠙⠿⣿⠋⠀⣶⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠽⠟⠀⠀⠈⠑⢶⠾⠀⠀⠀⠀⠀

⠀⠀⠙⢻⣶⣶⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠂⢄⠜⠛⠻⡏⠀⠈⢢⠀⠀⠀⠀⠀⠀⢀⡾⢸⢰⠋⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠱⡠⠎⠢⡀⠀⠑⢤⣾⣧⠀⠀⠀⠀⢀⣾⣃⣸⡿⢀⡀⠀⢠⣄⣀⡀⠀⠀⠀ ⣀⠎⠀⠀⡇⠈⣶⢄⠀⢻⣿⢧⠀⠀⢠⣿⣿⣽⣋⣿⣓⣷⠀⡼⢿⠔⠦⠄⠀⠀ ⡇⠀⠀⣠⡑⢤⡿⠈⡄⠘⡄⠀⡀⠀⢘⠿⠿⣿⣟⡿⢿⣿⠇⠐⠀⠀⠀⠀⠀⠀ ⠓⠒⠊⠁⠀⠙⠛⡲⠅⠂⠣⡠⠓⠀⠈⠛⠒⣇⠉⢀⠈⣡⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠹⡉⢙⣜⢌⡢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠄⣄⢂⠀⠀⠀⠀⠀⠱⢰⡗⣉⠦⡄⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⢠⠀⠀⠀⠀⠀⢚⢺⣥⠋⠂⠀⠀⠀⠀⠀⢸⠀⠈⠒⠓⠂⠠⠄⠀⠀⡀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢡⡐⡈⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⡠⠤⠀⠰⠁ ⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠈⡇⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡰⠁⢀⢋⡔⠁⠀ ⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⢐⠀⠃⠀⠀⠀⠀⠀⢠⣴⣿⣷⣤⠅⢠⠃⡛⠀⠀⠀ ⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⡸⠐⠚⡄⠀⠀⠀⠀⠆⠀⠙⠿⡟⠀⠈⢲⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠀⠀⠀⢰⠁⠀⠀⢡⠀⠀⠀⢸⠀⠀⠀⠔⡁⠉⠉⠁⣀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣿⢁⡖⠀⡞⠀⠀⠀⢀⣾⠀⡄⠀⠀⡆⠀⠀⠀⡶⡀⠈⢧⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⠞⣠⣯⠞⢀⣼⢁⡎⠀⢀⡎⠘⡄⣳⠀⠀⢹⠀⠀⠀⢿⢧⠀⡌⢧⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⡇⡴⣽⠁⡴⠋⡟⢸⠀⠀⣼⠖⠒⢻⣿⣍⠀⢸⡆⠘⠒⢾⢼⣄⠸⡈⢻⣄⣇⢸⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⡿⠁⡇⢸⢱⢻⣹⢸⡀⣀⣧⣤⣭⣉⠉⠉⠛⠛⠓⠛⣙⣊⣀⡬⠥⠗⠛⢇⢼⢸⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠰⣖⣷⠸⣇⣸⠏⢸⠛⡿⣿⡿⡏⠀⠈⠹⣿⡀⠀⠀⢠⣾⠿⠉⠹⣻⣷⣖⡆⠸⡸⣸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⢏⠞⠛⣿⠴⡿⡀⢸⠢⠭⣧⡀⠤⠼⠁⠀⠀⠀⠈⢦⣀⣀⣰⡻⠛⠉⠀⣊⣷⡏⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠻⡤⣼⠞⢿⣠⢷⡇⠈⣆⠀⢡⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠈⠙⢡⢠⠃⢠⣿⢸⣄⣮⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣹⡟⣀⣞⡷⣀⣽⡀⠈⢦⡈⣆⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⣥⠏⠀⡼⢿⣀⠻⣯⣭⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⠁⣹⠉⠀⡏⢧⢳⠀⢀⡛⢮⢦⡀⠀⠀⠤⠀⠀⠀⢀⣴⣾⡿⠀⣰⣧⣼⠞⢳⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⡆⡿⡄⠀⣧⣈⡿⣧⠈⢧⡀⠙⢷⣄⣀⣀⣀⠤⣾⢻⡞⣿⠇⡼⢧⡟⠁⠠⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡙⢄⣻⠎⠑⡜⠱⣄⣏⣲⠏⠀⠈⠁⠀⡀⣿⣀⣁⣿⡮⠖⠋⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠛⠀⠀⡹⢧⢰⡀⠀⠀⠀⡇⠘⠀⠉⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡴⠊⠀⠀⠀⠱⡄⠀⠀⡇⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠂⠽⣄⠀⡼⠉⠀⠀⠀⠀⠀⠐⠦⢄⣀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠣⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠈⠙⠒⠢⠤⠤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣖⣀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣀⠔⠁⣀⡤⣤⠄⠀⠀⠀⢀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣤⡄⣠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡩⠛⠉⡀⠈⡱⢤⣌⠕⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⡀⢠⣋⠄⠀⣰⢇⡌⠉⠐⢊⠖⢤⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠥⠁⠚⡆⠀⢰⣿⣬⡗⠠⠺⠿⣟⢀⣧⣶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⣴⠀⠀⡇⠀⢸⢏⠁⠀⠄⠲⠰⣧⣧⢼⠁⠀⠴⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠘⠴⠜⢩⡗⢢⡤⢵⠊⠈⠈⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⠀⠀⠀⡠⣤⠃⠀⠈⠒⠘⠢⡒⠀⠀⠈⢆⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠠⠂⠀⠀⠀⡜⣠⣿⠀⢇⠀⠀⣣⠀⠈⡆⢼⠵⡀⠑⠄⣀⣀⠠⡏⠀ ⠀⠠⠁⠀⠀⠀⠀⠱⡘⢧⣧⡸⡅⠈⠀⠈⢻⣦⠤⢂⠁⠀⠀⠈⠐⠮⡀⠀ ⢠⠁⠀⠀⠀⠀⡠⠀⢸⣄⣹⢧⠃⠀⠀⢀⠈⣃⠔⠁⠀⠀⠀⠀⢀⠀⠑⡀ ⠘⠀⢰⠀⠀⠌⠀⠀⢺⠚⢁⢑⠥⡄⠀⢀⣰⡰⠀⠀⠀⠀⠀⠀⠀⠢⢰⡇ ⢸⠀⢸⠀⠀⠀⠀⢠⠃⠀⠀⠈⠘⢿⠲⠞⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃ ⠀⢆⠸⢇⠀⠀⠀⠸⡀⠀⠀⠀⠀⠈⡄⠀⠀⠑⡀⠠⣀⣀⣀⠀⠠⠄⣀⡇ ⠀⠀⠑⠃⠣⡀⠐⠄⠡⡀⠀⠀⠀⠀⢠⠀⠀⠀⠙⡤⠤⠡⠂⠀⠀⠀⠀⠃ ⠀⠀⠀⠀⠀⠀⠁⠒⠒⠓⢄⡀⠀⠀⠸⢆⠀⠀⠀⠁⢒⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⠰⠁⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠉⠣⡆⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠈⢢⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢝⣷⣄⠀⠀⠑⢄⠸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡳⠂⡷⢯⣥⣤⣶⣾⣷⣶⣦⣄⠀⠀⠀⠀⠀ ⠀⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⢁⡤⠷⠐⠋⣹⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀ ⠀⢀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠈⣐⡦⠚⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠈⠐⠦⢄⡀⠑⢄⠀⠀⠀⢸⡏⠀⠀⡇⠀⠘⣿⣿⣿⣿⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢈⣑⠤⡑⣄⠠⠘⠃⠀⠀⠂⠄⡀⠹⡏⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠔⠋⠁⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢧⠀⠀⡄⠀⠀⠀⠀⠀ ⠀⠀⡴⠁⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣄⠘⣄⡀⠄⠀⠀ ⠀⣸⠁⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⣀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠆ ⠀⢿⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀ ⠀⠈⢆⡀⠀⠀⠀⠀⠀⠙⠠⣀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀ ⠀⢀⣀⣯⡒⠤⠤⠤⠤⠐⠉⠱⡈⠉⠉⣁⣀⣀⣀⣀⠀⡠⠂⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢀⠘⢂⣾⣿⣿⣿⣿⣿⣿⣧⢄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢯⠒⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣆⠀⠀⠀⠢⣌⠉⠓⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣆⠀⠀⠀⠈⠳⣤⠀⠀⠈⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⡒⠋⠉⠉⠙⠣⣄⠀⠀⠀⠈⠳⣤⡀⠀⠀⠈⠳⢦⡤⣴⠲⣶⠶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⣠⠤⢽⣦⣄⡠⣄⠈⢿⡦⣄⡀⠀⠀⠹⠛⠛⠁⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠓⡾⠁⠀⠉⠀⠀⠙⠷⠦⣄⣹⢮⣙⠷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣿⠇⠀⠀⠀⠀⠀⠀⣠⣿⢻⡟⠉⠛⠚⠀⠀⠀⠀⠀⠀⠀⠶⣤⣄⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣸⢿⣀⣀⣿⡆⠀⠀⠀⠀⣐⣶⣿⠃⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣧⣍⣻⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣀⡴⠛⠛⠉⠈⠉⠛⠀⠀⠀⠀⠛⠛⠋⠒⠲⢸⣿⠷⢤⣀⣄⠀⠀⠀⠄⠈⠻⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡼⠋⠁⠀⠀⠀⠀⠀⠀⢠⣦⠄⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠈⠛⣧⡀⠀⢀⣀⠀⠈⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠤⠀⠀⠀⢤⣘⣿⡿⠃⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄⣯⡻⣄⢻⡹⣷⡤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠓⠊⠉⠀⠉⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⣿⠋⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠀⠀⢤⠀⠀⠀⡴⠻⢦⠀⠀⠀⠀⣠⠄⣰⣷⣿⠟⠉⠁⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⢀⠀⣻⣃⡙⠛⠂⣛⠛⢃⠀ ⠀⠀⠀⠘⠚⠀⠀⠀⠉⠀⠀⣸⠁⠀⣠⡥⣤⣶⣿⣶⣿⣿⣽⠃⢠⡞⠀⠘⣿⣷⣢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠸⣛⢛⡛⡛⣟⣙⡛⢃⣛⡛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⣠⠛⠁⠀⠀⢹⡍⡽⠡⠋⣿⣠⡾⠃⠀⠀⣿⠉⣿⣿⣿⡳⢤⣄⣀⠀⢀⣀⡴⠶⠒⠲⠤⡽⡄⠀⠀⠀⠉⣛⣯⡁⢉⢉⣁⣉⡉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⣾⠹⠃⠀⢠⡟⠹⠇⠀⠀⣄⣿⣼⣿⣿⣿⡇⠀⢀⣟⠛⠉⠁⠀⠀⠀⠀⢀⢼⡷⠀⠀⠀⠀⠉⠉⠉⠉⠈⠉⠉⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⢀⣠⡇⠀⠀⢀⢸⣇⠀⠀⢠⣿⣿⡟⣿⣿⡿⣿⠁⠀⢸⠀⠀⠀⠀⠀⠀⢀⣴⣡⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠤⢤⣀⣀⣀⠀⠀⡾⠁⠀⣀⣠⣴⣾⡟⠀⠀⢀⣴⠟⡿⠀⠀⠈⢹⣿⣶⣿⣿⡰⡟⠀⢠⣿⠀⠀⠀⠀⣰⠷⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⢾⣭⣉⠉⢽⠇⠀⠀⣼⠁⠀⠀⠀⠀⠈⠉⠈⣿⣧⡙⣿⠃⠀⡞⢘⡇⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠦⢤⣀⢿⣄⢀⣀⣰⣤⢀⡀⠀⣬⣿⠀⡝⠀⢰⠃⣼⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠟⠉⠿⠝⢛⣿⢤⡾⣿⣭⣷⡇⠀⡞⣀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠛⠛⢯⣧⣰⣇⠓⣾⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠿⣷⣄⠀⠀⠀⠈⠉⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠦⢤⣾⠀⠀⢰⣦⣤⣠⣄⣠⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⣠⠴⠶⠶⠖⠒⠲⠶⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢾⣯⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠇⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣮⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠆⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢷⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠈⠉⠓⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣿⠀⠀⠀⠀⠀⢀⡴⠋⠉⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣤⣤⠤⠴⠒⠒⠒⠛⠃⠀⠀⠀⠀⠀⠉⠙⠛⠓⠦⣤⣄⡀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⢸⡇⠈⣾⠀⠀⠀⠀⡴⠋⠀⣴⣷⣀⣀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀ ⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣤⣤⣈⣙⣳⣦⣀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠸⡇⣘⡟⠀⠀⠀⢸⠁⠀⣾⣿⣿⣷⣿⡇⠀⠘⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡟⠛⢻⣿⣿⣿⣿⣷⣅⠀⠹⣆⠀⠀⠀⠀⢰⡧⣼⠁⠀⠀⠀⠈⣆⠀⠛⠻⣷⣾⣿⠀⠀⠀⣯⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⢳⣦⣤⣤⠀⠀⠀⠀⠀⠀⢈⣿⣿⣶⣺⣿⣿⣿⣿⠛⢙⣧⣠⣝⣆⠀⠀⠀⣞⣸⠃⠀⠀⠀⠀⠀⠸⡆⠀⠀⢻⣟⠁⠀⠀⣸⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⠞⠉⠀⠀⠀⠀⠀⠀⠀⠐⠦⠒⠛⠿⣹⡋⠫⠉⠀⠀⠩⣿⣿⡿⠃⠀⢀⡾⠁⣠⡄⠀⠀⠀⠀⠀⣼⣄⡀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠛⣧⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⠀⠈⠀⠁⠹⣄⣠⡴⣿⣷⡞⢋⡇⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣇⣮⠉⠙⣍⡿⠁⠀⠀⠀⠀⠶⠀⠀⣀⣠⡄⠀⢠⠤⠤⠤⠀⠛⣁⣼⡿⠏⠡⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⢷⡀⡾⢁⣀⣠⠴⢖⡒⠒⡒⠋⠉⢩⣇⣀⣀⣀⣀⣤⢴⣾⠿⠋⣀⢠⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡈⠻⣯⡁⠀⠉⠙⠛⠛⣋⡥⠀⣰⠏⠉⢹⣿⠛⠦⣮⣭⣤⠴⠛⣹⢾⣧⣴⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⡉⣻⣶⠶⠶⠾⠥⣤⣞⣁⠀⠀⠈⣿⣿⡶⢤⠴⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠏⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠒⢿⣿⣷⡍⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⢺⣘⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠿⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠒⠫⢭⠑⢒⢤⣄⡀⠀⠀⠀⠀⠀⣴⣶⣿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡃⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠙⠳⢤⡀⠀⠀⠋⢠⣽⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠙⠲⡀⠀⠈⣭⢿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣝⣆⠀⢰⠿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣧⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⢿⣿⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⠒⢤⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⠒⠿⣯⣽⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠠⢿⠀⠀⠀⠠⠇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢸⡆⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣮⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠈⣧⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⢠⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡿⣿⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠛⠁⢀⣴⣯⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠙⢟⡲⠶⢤⣤⠤⠤⣴⣶⡶⠛⣿⣿⠀⢹⠳⢄⡀⠘⠻⠯⠭⠽⢿⠉⣿⡇⠀⠀⠀⠹⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡄⠀⠀⠀⠀⠀⠑⣦⠀⠉⠓⠚⡏⠀⠀⣰⡿⢹⠀⣾⠀⠈⠙⠳⢤⡀⠀⠀⠘⢧⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠚⠋⠉⠉⢁⣷⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⢻⠀⢀⣿⠁⠘⡀⣿⠀⠀⠀⠀⠀⠈⠓⢤⡀⢘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⢀⡴⠋⠹⡆⠀⠀⠀⠀⠀⠀⡀⠈⠑⢦⣈⣠⠟⠉⢷⡀⠂⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⡤⠋⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⢛⢁⠀⠀⢀⡀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⡴⠻⣿⡻⡉⣴⣏⣀⣴⣿⠿⠿⢓⠟⣿⣿⢟⢿⣿⠁⡀⡄⢰⠀⢳⡆⢒⡀⠀ ⣿⠏⢑⣮⢕⣜⣏⡴⣫⡟⠀⢀⣰⡏⣼⠟⡼⠋⠘⠏⠰⡀⡇⣇⠃⠘⣷⠈⣄⢀ ⣟⣴⡿⢩⣿⣿⡿⢿⡟⢀⣴⣿⣟⠜⠿⣶⣄⡀⠀⢧⢰⠁⠀⡏⡄⢀⠃⣧⢨⢢ ⣿⣟⡴⠛⡿⠃⠀⣞⣴⣿⡿⣻⠋⠀⠀⠀⠉⠻⣶⣍⡈⡆⠀⣿⡀⢸⡀⢺⣮⡆ ⣿⡟⢁⣼⣅⣀⣼⡿⠻⠋⡴⠁⠀⠀⠀⠈⠉⠐⢸⠙⢣⣿⡄⢿⣧⠘⣷⣸⣿⣿ ⣿⣿⡉⠉⢻⡟⠿⣦⡀⠈⠀⠀⠀⠀⡐⣒⡀⠤⠄⠂⠈⡏⢻⣾⠻⡆⣿⣿⣿⣿ ⢸⡇⢁⠂⠒⠹⠿⠉⠀⠀⠀⠀⠀⠀⠛⠻⣟⠿⠿⣷⣶⣼⠀⠹⣶⣿⣿⠟⠛⢿ ⠋⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⠟⡛⠋⠀⢙⣷⣄⡿⢻⢿⠂⠀⢸ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⢉⠉⠊⡧⢃⠏⢅⡤⢸ ⠀⠰⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠠⡱⠉⠜⢊⣤⡿ ⢄⠀⢡⡀⠀⠀⠈⣿⣿⠓⡐⠂⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣔⡀⣤⣾⣿⢿⠂ ⠁⠓⢤⠈⢄⠀⠀⠏⢹⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠔⠉⠀⡸⠉⣿⠟⠁⢸ ⠀⠀⠀⠡⡰⠱⣬⠘⠢⡙⡦⠒⠹⢖⠋⠀⢀⠠⠔⠊⡀⠀⠀⠆⢤⠾⠁⠀⠀⣨ ⠀⠀⠀⠀⡇⠀⠸⣦⡀⡇⢤⢤⣤⣶⡂⠋⠀⠀⠀⠀⠐⠄⣠⡼⡬⢔⢄⢀⠔⠁ ⠀⠀⠀⠠⢃⠀⠀⣧⢳⠀⠘⡞⢺⢨⣍⣒⣀⠄⠀⢠⡶⠛⠓⠂⠂⠀⠀⡿⢇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠦⠐⠲⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠎⠀⠀⠀⣀⢰⡌⢻⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠁⠀⢠⠇⣸⡿⣂⣴⣌⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢰⣶⣟⠉⠈⠀⣱⣿⣿⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠠⠤⣤⡇⣽⡝⡿⢷⠀⠀⣅⠉⠋⣞⡧⠄⡀⠀⠀⠀⠀⠀⠀⠀ ⣀⠤⠒⠈⠁⠀⠀⠰⠃⣇⣫⡌⠙⠀⢩⣶⡆⠀⢀⡿⡇⠀⠈⠁⠢⡀⠀⠀⠀⠀ ⠂⠀⠁⠢⢀⠀⠈⠆⡘⢿⠁⠈⢦⣀⠐⠹⢀⠴⢹⠁⣧⠀⡠⠂⡩⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⠄⣼⢈⠞⣷⠲⠯⠥⢈⢉⠯⠦⠼⡀⢸⢏⢀⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⢹⣿⠇⠻⡀⢠⣴⣶⣶⡶⠀⠒⠽⣼⡇⠃⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⢠⢃⣾⠁⡀⠀⠑⣸⣘⢨⡷⣿⡧⣀⠀⠿⣿⠜⡄⠀⠀⠀⠂⠀⠀ ⠠⠦⠤⣤⢠⠃⡮⠉⠀⠀⣴⠞⣩⠶⣿⡯⠰⣌⣸⡅⠀⠈⡇⠘⢄⠀⠤⠤⣦⣤ ⠀⠀⠀⠀⡏⠠⠧⢀⠀⣠⣏⠈⢐⣟⣓⣧⡰⠦⠈⢃⢀⣠⡁⠤⠬⢆⠀⠀⠀⠀ ⠄⢀⡀⡰⠋⠀⠀⠀⠉⠃⠀⢠⠞⠉⠉⠣⠴⢆⠀⠈⠉⠁⠀⠀⠀⠈⢆⠀⠀⠀ ⠉⠉⠉⠓⣤⣤⣄⣀⣠⠔⠂⠁⢀⣀⠀⠀⠀⠀⢁⠰⢢⠄⣀⣀⣀⣄⡴⠷⠄⢀ ⠲⣤⢀⡀⠀⠀⢀⠬⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⢀⠀⠀⢀⠤⢒⠾⠁ ⠀⠘⡀⠈⠁⠲⢅⠀⠀⠀⠀⢀⠀⠀⠀⠤⣀⠀⠀⠀⠀⢀⠠⠕⠈⠀⠀⡌⠀⠀ ⠀⠀⢁⠈⠢⠀⠀⠈⠀⠀⠞⠁⠀⢰⡄⠀⠈⢅⠀⠈⠁⠀⠀⠀⠐⠁⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠐⢄⠈⠀⠀⠀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠐⣿⡇⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⣿⠇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⡀⢲⣮⣵⣿⣿⣿⣿⣿⣷⣶⠤⡠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡻⣟⣻⣿⣿⣷⣧⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⣠⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡢⡀⠀⠀ ⠀⠀⠀⣪⢟⣿⣶⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣙⢻⣿⣿⢋⠻⢿⡌⠢⠀ ⣀⠀⣴⣯⣾⣿⣿⣿⣟⣻⡿⢻⢸⣿⢹⡧⠹⣿⣌⣻⣧⣾⢿⢿⢷⡳⣔⠙⠄⡂ ⢈⣿⣭⣿⣿⣿⣿⣷⣿⠽⣷⣹⣀⣥⣼⠷⠾⡟⢻⠏⢻⣏⣸⡌⠀⠈⠙⠳⠒⠚ ⠀⣯⠸⣿⣿⣿⣿⢴⡿⠛⠋⣉⠉⠻⠀⡆⢸⠁⠃⠀⢰⡞⢻⢱⠀⠀⢷⡀⣔⠴ ⠀⢹⠀⣿⣿⣿⠇⠈⡁⠈⠠⠖⢀⣆⣠⣧⣴⡾⠿⠾⢿⡇⢾⠘⣇⠀⠘⣧⠈⣦ ⠀⠈⢧⣿⣿⡿⣷⣴⠓⠒⠚⠋⠉⠉⠁⠀⠀⠀⠀⢠⢾⣷⢟⣀⢻⡆⠀⠘⣇⢹ ⠀⢀⠎⣿⣿⠳⡏⠁⠁⠀⠀⢀⣐⣢⣶⣦⡤⠀⣀⡞⢹⡟⣄⣞⣾⣿⣇⠀⠘⣼ ⠂⢡⣰⠋⣟⡷⣿⣶⣄⠀⠀⠈⢿⡿⢉⠄⡇⠐⠈⠀⣾⣼⣧⣾⣿⡿⣿⡄⠀⠈ ⠀⢸⣿⠀⢹⡇⣿⣿⢷⣌⡠⠤⢘⠡⢀⡰⠓⠀⢀⣴⡅⢄⣾⣼⡿⡛⠛⣷⡀⠀ ⠀⢀⠧⠦⢤⠳⢽⡋⠉⠉⠐⠒⡋⠀⠭⠭⠧⣴⡿⠃⢤⠠⣿⣿⣷⣄⠐⢿⠁⠀ ⠔⡁⡠⠔⠊⠈⠉⠀⠀⠀⠀⠀⢨⣉⠓⠾⠿⠟⠁⢀⠸⣇⠹⡈⢿⣿⣆⠈⠳⠀ ⠈⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣽⠯⣿⣂⠬⣀⠀⠂⠀⠙⠳⣻⡶⣽⡾⣧⣦⣄ ⠠⠀⠀⠀⠀⠀⠀⣀⠠⡖⠖⠛⠒⠉⠉⠉⠉⠙⠛⠒⠒⡲⠶⢾⢵⠮⣉⠀⠀⠀

⣀⣀⣀⡴⠮⠭⣷⡏⣁⣀⠉⠙⠻⣿⣢⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢣⣾⣯⠤⢤⣴⠚⠛⢧⣸⠒⠲⡾⢿⣯⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⣾⡄⢠⣿⠁⡀⠀⣸⣇⢱⡀⠘⣄⢻⣇⡏⣧⡀⠀⠀⠀⠀⢀⣀⡠⠀ ⣿⢸⣎⣿⢹⡀⣧⠘⣟⠸⣦⣷⣸⣿⢘⡟⢯⡀⠀⠉⠉⠉⠛⠒⠒⠀⠀ ⢫⢸⣿⡿⣼⣷⣼⠟⢿⣶⠧⣿⣿⣿⣿⢧⠀⠉⣳⣤⡀⠀⠀⠀⠀⠀⠀ ⢿⠞⣿⣧⣸⣏⣿⣯⠍⡟⠈⠉⠙⢈⢯⡆⣴⣟⣠⣈⠈⠁⢢⠄⣀⡀⡀ ⠈⢘⡧⠿⣿⣯⡛⠋⠀⠀⠀⠀⠀⢀⣾⢷⡟⠀⠀⠉⠑⢤⡒⠒⠈⠉⡇ ⠤⡎⡠⠊⠉⢛⢷⢤⡀⠀⠄⠒⢁⠚⠃⢸⠏⠀⠲⢲⣄⠀⠱⠤⣀⡸⠐ ⠀⠈⡵⢦⣤⣈⣾⡜⠀⢉⣁⡈⠀⠀⠀⡞⠀⠀⠀⠸⡀⠁⠀⢧⢄⡆⠀ ⠀⠀⠀⠀⢣⠹⣿⠀⠉⠀⠀⠀⠁⠀⢸⠃⠀⠀⠀⠀⢧⠀⠀⡎⣼⠀⠀ ⠀⠀⠀⠀⢼⠀⡿⢤⣀⣀⣀⣀⠀⠀⡾⠀⠀⠀⠀⠀⢸⠀⢰⠟⡍⠀⠀ ⠐⠊⣁⠵⡟⣠⠃⠀⠈⠉⠉⠈⠉⢺⡆⠀⠀⠀⣀⣀⣨⡆⣸⣦⠇⠀⠀ ⠐⠉⣴⡜⢁⣾⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠙⢄⢾⠀⠀⠀ ⣠⠞⠋⠀⡎⠸⡀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀ ⠁⠀⠀⡜⠀⠀⢃⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⠀⠀⡀⠀⠀⣀⣼⠀⠀⠀ ⠀⠀⡔⠓⢎⠉⠙⠠⢀⡀⠀⢀⣠⣂⡼⠁⠠⠂⠉⡠⠞⠉⠁⣼⠀⠀⠀ ⠀⡐⠀⠀⠀⠑⠦⣀⠀⣈⢭⣽⣿⡿⠁⢀⡠⠔⠊⠁⠀⠀⢰⢻⠀⠀⠀ ⠘⠀⠀⠀⠀⠀⠀⠀⠀⠲⡟⠉⢉⢃⡴⠃⠀⠀⠀⣇⢠⡔⠁⠈⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⠙⠓⠶⣖⠒⠉⠁⠑⠽⠀⠀⢥⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⢀⠀⠈⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠈⢆⠀⠘⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠁⢀⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⠅⠀⠀⠀⠀⠀⠀⢀⣔⣨⠄⠀⣠⡎⠀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⣠⡾⠋⡙⠀⠚⠛⠂⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⢰⢣⠀⠘⠄⠀⠀⢠⠻⠇⠂⠀⠀⣤⡴⠎⠀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⣿⠈⢇⠐⢄⠀⠀⠇⠀⣀⣀⠀⠤⠬⠄⠀⡐⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⣇⠂⠑⠒⠒⠒⡿⠛⠛⣄⣀⠠⠊⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣇⠀⣰⣜⠀⠀⠀⠀⡸⢀⠀⠀⡏⠀⠀⠀⠀⠀ ⠀⠀⢀⠖⠀⠒⢄⡀⠀⠀⢀⠜⣿⣤⠎⠁⠛⠄⠒⠈⢀⢼⠀⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⡟⢀⡖⠬⠥⠭⠴⣶⠯⠒⠚⠃⠄⢀⠐⢬⣄⣔⠀⢸⠀⠸⠀⠀⠀⠀⠀⠀ ⢀⠎⠘⡵⠀⣀⢤⣶⡲⠃⠀⠀⠀⠀⠀⠀⠉⠳⢿⢍⣢⠤⢀⠀⠈⢱⡀⠀⠀⠀ ⠀⢾⡟⠀⢀⠔⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣌⠁⠢⢥⣀⣎⠗⢆⠀⠀ ⠀⠋⠁⠀⠎⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢳⡢⡀⢏⠃⠀⡼⠀⠀ ⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡙⡄⢸⡤⠾⠷⡀⠀ ⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣣⠈⢇⠀⠣⠐⡀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢸⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢳⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀

⣿⡟⠁⠀⢀⡠⠄⠂⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⠟⠀⠀⢈⣠⠤⠴⣶⡚⠛⢋⣛⡍⢐⣌⡫⠑⣀⣀⠀⠀⠲⡈⢿⣿⣿⣿⣿⣿⡿ ⣤⣴⡾⠟⣃⠈⠁⠄⡀⠀⠀⠀⠈⠁⠒⠠⡁⠑⠠⢘⡤⢊⠃⠀⠙⣿⣿⣿⡇⠏ ⣿⡟⠀⠜⢰⠤⣁⠀⠀⠉⠀⠒⠀⠀⠤⠤⠤⠖⣂⣁⠔⣎⠁⠢⣀⠈⢿⣿⠁⠀ ⣿⠇⡘⢠⠀⠀⠀⠉⠙⠒⠠⡴⢀⠒⠐⡂⣭⣉⡁⠢⡂⢡⠓⢦⢌⢢⠈⢆⠉⠒ ⣿⢠⠁⢸⡇⠀⠀⠀⠀⠐⠈⠰⠉⣡⣾⡋⡹⠀⠈⢂⠈⡀⡇⠈⠛⣧⡇⠸⡄⠀ ⣿⡾⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠰⣯⠵⠛⠀⠀⠀⠀⠆⠃⡷⠀⡆⠟⣿⣦⡕⡄ ⣷⢸⠀⠀⢰⠀⠋⡦⠄⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⢰⠳⠻⡈⠢⠟⣧⠿⣿ ⢿⠀⡀⠀⣦⢃⠶⢡⣐⡢⠵⠄⠀⠀⠀⠀⠀⠀⠀⢀⢎⠂⡇⠡⠯⡯⢁⢌⠉⣇ ⢸⢃⢃⠀⣿⣧⣱⣿⣝⡞⠁⠀⠀⠀⠀⢀⢤⡴⢗⠁⠁⠀⠛⡄⠡⡘⡺⠯⢢⢝ ⡀⢸⣾⡀⢻⡻⢿⣄⡑⡄⠀⢀⠀⠀⢢⡖⠋⠀⠀⣇⠀⢸⠀⢁⠑⢹⠤⣌⠋⢪ ⢳⡈⣿⣏⢊⠢⡅⠶⡨⠔⠒⠈⠉⠢⡀⠑⠤⠀⠀⠋⢀⣿⣄⡞⣶⣤⣌⢩⢃⢧ ⠀⢋⣱⣾⣞⠦⠌⢲⣆⣀⣀⣀⠀⠀⠈⠲⡲⢖⡲⣶⣾⠿⡛⠀⠸⡟⠚⢺⢷⣁ ⠢⣤⣟⣿⠋⣹⡶⣤⠇⠀⠀⠉⢷⡦⣀⠀⠈⠑⠌⠙⠒⠾⠿⣤⣔⣩⣿⣓⡉⠀ ⠀⠀⠀⡎⠡⡞⠠⠋⠀⠀⠀⠀⠘⠾⡄⠑⠦⡀⠀⠀⠀⠉⠒⢲⢊⡿⠚⢦⣄⡉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⢐⠠⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠈⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⣿⣷⣿⣜⡈⡲⡀⢀⡠⢖⠂⠀⠀⠈⠐⡆⠇ ⠀⠀⠀⠀⠀⠀⠑⡲⢤⣌⣡⣾⡙⠁⣶⣿⣿⣤⠞⡋⠔⠆⠀⠀⠀⠀⢠⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠄⣈⡝⠻⠇⠀⢙⠙⠡⣃⣁⠀⠜⠀⠀⠀⠀⢀⡞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⡑⠄⢬⢭⣽⢶⠮⠤⠊⠀⠀⠀⠀⠀⣠⠟⠀⠀⡄ ⠀⠀⠀⠀⠀⠀⢀⡀⠀⠭⠖⠂⠥⡎⠀⣼⡀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⢰⠁ ⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⡀⠄⠊⠀⡜⠀⢧⣀⣀⣤⠞⠉⠀⠀⠀⠀⡠⠁⠀ ⢠⠲⠒⠁⠀⠀⠀⠀⠰⠯⠀⠠⠔⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠊⠀⠀⠀ ⠈⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⡰⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀ ⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⢀⠎⡑⢲⠰⠁⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠆⡀⠀⠀⠀⢀⠀⡀⠔⠁⢸⡆⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡋⠉⠉⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⣠⣊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢠⠔⡇⣃⢎⢂⣾⢊⢊⢆⠞⡡⢊⠱⡀⠀⠀⠀⢀⣀⠀⣠⠴⢦⣽⣷⡐⡄ ⠀⠀⠸⠀⠑⠥⢪⠘⣡⡱⣏⡠⣪⣞⠿⣣⠇⠀⠀⠀⠉⢈⡇⠻⠀⢀⣿⣿⣇⡇ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠒⢲⠖⠉⠀⣀⠠⣤⣤⣴⣿⣴⣶⣾⣿⣿⡿⠋⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣠⣔⣭⡶⠿⠿⠿⣿⣿⣿⣿⡿⠛⢉⣤⣾⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣤⣾⣿⠯⢄⠀⠀⠀⠢⡐⠀⢻⠿⣿⣿⣿⣿⡿⣿ ⠀⠀⠀⠀⠀⠀⢀⡾⠥⣿⣿⣿⣿⡗⣶⡷⠁⡼⠂⠀⠈⠂⠘⣽⣿⣿⣿⣿⣤⡀ ⠀⠀⠀⠀⠀⢀⠃⢃⢰⣿⣿⣿⣾⣾⢟⣡⣄⠀⠀⢀⠀⠀⠀⣿⣏⣿⣿⡃⠙⣿ ⠀⠀⠀⠀⠀⡈⠀⡤⣾⣿⣿⣿⣿⣿⣯⢟⣡⣴⣿⣿⢱⠀⣴⣿⡿⣡⣿⡇⢠⣿ ⠀⠀⠀⠀⠀⡇⢛⠀⣿⣿⣿⣿⣿⣿⣿⣿⡗⢻⣿⣛⣥⣾⣿⣿⣿⣿⣿⣿⣿⡷ ⠀⠀⠀⠀⠀⢃⢸⣴⣛⢿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⡿⠟⠉⠈⢹⣷ ⠀⠀⠀⠀⠀⠸⢺⣿⣿⣿⣹⣟⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢠⣿ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣻⠿⠉⣻⠃⠀⣠⡞⠀⡼⠃ ⠀⠀⠀⠈⠈⠉⠐⠻⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⡟⠛⠊⠉⣁⣴⠞⠉⢀⡜⠀⠀ ⠀⠀⠤⣄⡀⠀⠀⠀⠈⠉⠙⡻⢿⢾⡿⠥⠚⡱⠁⠀⠀⡠⡖⠁⠀⡠⠚⡿⢆⡀ ⠛⣳⣄⠈⠛⣭⣽⡧⢦⣖⣹⣿⠚⠰⡏⠈⣉⣀⡠⠒⢹⣵⠤⣠⣮⣤⡖⣹⣻⢥ ⢰⢻⣿⣿⡿⣌⠢⣌⠑⠒⠉⡙⠀⠰⠀⠈⠁⠀⠀⠀⠸⠸⡷⣿⣷⣿⡝⣵⡣⠋ ⠈⠺⣿⣿⣷⣿⣤⠤⠽⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⡟⠁⠉⠀⠀⠀⠀ ⠀⠀⡿⣿⣿⣿⣿⣷⡄⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠠⢠⠇⠀⠀⠀ ⠀⠀⠈⠘⢻⣿⣿⠏⠃⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠢⡀⠀⠀ ⢒⣤⣀⣀⣀⠈⠉⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀ ⠀⠀⠀⡀⠠⠉⣁⠒⢒⣤⣼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀ ⠀⠏⡩⢁⢄⠔⢈⢣⢏⢎⢣⠿⡝⣴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⠀

⣿⢢⡀⠀⠀⠀⠀⠀⠀⠌⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀ ⣿⣾⣷⣀⣠⠄⣠⠄⠚⠀⠀⠀⠂⠸⠀⠀⠀⢀⠤⣤⣀⣀⠠⠄⠐⠒⠓⠀⠀⠀ ⣼⣷⣿⡿⠓⠂⠁⠒⢄⠀⡀⠁⠀⡄⠀⢀⢌⣁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⢻⣿⣿⣃⢤⢲⡸⠆⢀⢁⠀⠀⠔⣀⠤⠊⠀⠀⠂⡀⣠⠲⠳⡒⠒⠒⣒⡒⠁⣀ ⣼⣿⡏⠈⣉⠤⢐⢖⡾⠓⠺⡉⠁⠀⠀⠠⣂⣈⢼⣾⢃⢠⡐⡒⠈⡀⡐⠁⢌⢀ ⠋⠙⣗⠰⠁⡀⠈⠘⠁⠀⠀⠁⢀⡠⠚⠈⠀⠀⠀⠘⣬⢦⡪⡚⠻⢁⣀⠚⠢⠏ ⢀⢔⠌⠀⠀⠠⣀⠀⠀⣀⣤⠛⢣⡀⠀⠀⠀⠀⠀⠀⠐⠓⡀⢀⠂⡌⡐⠠⠙⠴ ⠑⠁⠀⠀⣀⡤⣄⡟⠉⠀⠈⠔⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠐⣈⣉⣄⢀⠂⠀⢀ ⠀⠀⠀⠀⠀⠉⢻⡇⠠⠀⠀⠀⢀⡛⠀⠀⢀⠄⠀⠀⠀⠀⠀⢩⠉⣭⢄⠠⢂⠕ ⠛⠀⠀⠀⠀⠀⠀⠳⠀⡠⠀⢠⠞⣠⣪⡖⠁⠀⠀⠀⠀⠀⠀⠀⡭⣯⡕⠙⠇⠀ ⡀⢀⡄⠀⠀⠀⠀⢘⠛⠒⢺⣿⣿⣿⣿⠈⢢⠀⠀⠀⠀⠀⠀⠀⢸⣲⣇⠛⠀⠠ ⠈⢁⠀⠀⠀⠀⡀⠂⠀⠀⢈⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣦⣲⠂⠀⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⡿⠁⢠⡞⢡⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠋⠉⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠾⠃⢠⣿⠃⠈⠀⠀⠀ ⣿⡿⠋⠁⠈⢃⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣀⠄⠚⠿⡆⡾⠀⠀⠀ ⡿⠁⡜⢰⠀⢨⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣽⣿⢏⡴⣭⠟⠀⠀⠀⢹⠃⠀⠀⠀ ⣧⡘⠳⣯⣣⢾⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⢁⣿⠋⠁⠀⠀⠀⢠⠃⠀⠀⠀⠀ ⢻⡀⠀⠛⠙⣈⡈⠀⠀⠩⡟⠿⣿⠟⠻⠋⠀⠀⣯⠀⠠⠀⠀⠀⣧⡄⠀⠀⠀⠀ ⣾⣷⣶⣿⢰⠁⠀⠀⢄⡀⠘⡀⠀⠀⢠⠀⠀⠀⣉⠉⠁⠒⢿⣶⠘⠛⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣄⡀⢠⣿⡫⠓⠕⠂⢰⠒⠅⠀⡐⠒⠠⢽⣲⣤⠙⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠉⠩⡟⠿⡁⠀⠀⠀⠀⠀⠈⣾⡆⢐⣶⠌⣨⡿⢦⣄⣀⣴⠛⠁⢀ ⡿⠿⠿⡧⠧⠀⣠⠀⠀⣀⣁⣀⣀⣀⣘⠁⠙⢀⠈⠇⠀⠁⠀⡆⡌⠀⡏⡇⠐⠏ ⣅⡀⠀⠀⠀⠀⠈⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠒⠲⢷⣒⠒⠓⠃⠘⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⢒⠒⠢⡄⡀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⢀⠠⠤⠀⢤⡄⠀ ⠀⠀⠈⣄⠑⠄⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢨⠂⠀⠀⠔⢁⢾⠁⠀ ⠀⠀⠀⠹⣄⡀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡰⠁⠀⠀⢀⠔⢃⠎⠀⠀ ⠀⠀⠀⠀⣈⠶⢬⡇⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⣾⣤⣤⣤⡶⢥⢔⠁⠀⠀⠀ ⠀⠀⠀⢾⡀⠀⠈⢇⠀⠀⠀⠀⠀⠀⢀⢜⡴⡹⣿⡿⢹⡟⠛⠁⠀⣨⡆⠀⠀ ⠀⠀⠀⠀⠁⠒⡲⠘⣦⠀⠀⠀⡠⠒⡡⠣⠁⠚⠛⠟⣏⠉⠺⡋⠓⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⣛⣥⣑⣄⠀⢀⣾⠮⠵⣦⡠⠜⣄⢘⠗⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⠊⠁⠀⠀⠉⠺⣗⠂⠀⣝⡗⠒⢎⠉⠁⠢⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡌⠉⠢⠀⠀⠀⠀⠀⠘⠆⠀⣿⠋⠀⠀⠈⠁⠢⣣⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠞⢱⢀⠀⠈⢄⠀⠀⠀⡀⢸⡼⠁⠀⠀⢀⠄⠊⢩⠹⠡⡀⠀⠀⠀ ⠀⠀⢀⠾⣀⡏⢀⠼⡆⠀⠑⠠⢐⠀⡌⠀⠀⣀⠔⠁⠀⡠⢣⠒⢇⠑⡀⠀⠀ ⠀⡔⠁⠀⠈⠃⡊⣠⡧⠤⠤⢤⡀⢉⣁⡈⠉⠀⠀⠠⢪⣖⠈⢢⢈⡇⠙⠠⠀ ⠰⠀⠀⠀⡜⠀⠉⢿⠁⠀⠀⠀⢱⢸⠀⠀⠉⠁⠒⡠⢄⡄⠑⡜⠋⠀⠀⠀⠁ ⠀⠢⣀⣊⡀⠤⠊⠀⢑⣤⣠⣐⣁⠼⡄⡀⢀⡀⠔⠁⢀⠃⠒⢅⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⠸⠁⠀⢹⠂⢤⠀⠠⠔⠁⠁⢄⠀⠈⠁⠈⠁⠀ ⠀⠀⢀⡀⠀⠤⠇⠐⠒⠒⠒⠊⠀⠀⠈⠁⠘⠐⠒⠒⠒⠀⠤⠧⠀⢀⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡹⢦⠟⣢⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠸⠁⠁⡎⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⠀⠑⡀⠀⠀⠀⡄⠀⢀⢇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⡠⠃⢠⠀⢄⠸⡄⠀⢀⠃⠀⡌⠸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⠀⠀⠑⡞⠁⠀⢸⠀⠈⠀⢧⠀⢸⠀⠀⡇⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡀⠀⣰⠀⠀⠀⡜⠀⢀⠀⡆⠀⡄⠀⡠⡻⠀⠀⣠⠀ ⠀⠀⠀⠀⠀⠀⢰⠁⡔⠃⠀⠀⣴⠁⠠⠋⣸⣁⠸⠀⠰⣱⠁⠀⡞⠁⠀ ⠀⠀⠀⠀⠀⠀⢦⠊⠀⠀⠀⢈⢀⠈⠀⠑⠚⠻⣧⣀⡴⠃⠀⠀⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢰⣧⢴⡇⠀⠀⠀⠀⠃⢩⠃⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⣿⣿⡼⠀⠀⡌⢄⠀⡰⠇⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠸⢶⣦⣄⠨⠈⠙⠋⠂⠀⠀⠎⠟⡙⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⡷⠀⠀⠀⡆⠀⣼⠎⢠⠁⠀⠀⠀⠀⢀⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠽⣡⠀⢀⡼⢧⠎⡸⠀⡆⠀⠇⠀⠀⠀⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠿⠧⠔⢺⣇⡈⢠⠇⠀⠘⣄⠀⠀⠀⠸⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢠⠏⠀⠀⣸⡭⣵⡄⠀⠀⠀⠢⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⡠⡎⠀⠀⢠⠃⠀⠀⠈⠄⠀⠀⠀⠑⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠐⠈⡘⠀⠀⢠⠋⠀⠀⠀⠀⠀⡑⢄⠀⠀⠀ ⠀⠀⠀⠀⣠⠴⢆⠸⡀⠀⠀⡜⠀⠀⠠⡏⠀⠀⠀⡠⠐⠁⡀⠀⠈⠂⣠ ⢀⠴⢦⣿⣿⣀⠎⠲⡯⠖⢰⠀⠀⠀⡀⠁⠀⠀⠀⢀⠀⠄⠁⣀⠔⠊⠀ ⠘⡆⠀⠙⡿⠃⠀⠀⠙⡶⣞⢧⡀⠀⠈⠀⣀⡬⠤⠤⠶⢮⣅⣈⠉⠑⠒ ⣤⠞⠀⡀⠀⢀⣀⡀⡠⠀⠃⢀⡨⠝⠋⠁⠀⠀⠀⠀⠀⠀⠈⠳⣽⣷⣄ ⢻⠀⣰⣿⡆⠈⣿⠋⠀⢀⡼⠷⠂⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣗⡊⡟ ⠈⢇⠻⣻⣧⣶⠿⠳⠮⠤⠄⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⡴⠞⠛⠉⠀ ⠀⠉⠘⠒⠠⠤⠖⠂⠤⠤⠤⠀⠄⠀⠀⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢀⠤⠠⠄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠌⠀⠀⠀⠀⠀⠉⡂⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠐⡀⠡⠀⠀ ⠀⠀⠀⠀⠀⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀ ⠀⠀⠀⠀⠀⢸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠒⡆ ⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣂⠁⠀⠀⠀⡞⠀ ⠀⠀⠀⠀⠀⠀⠹⡠⣀⠀⢢⠀⢠⢺⢫⣽⡿⡿⠃⢀⡼⠇⠀ ⠀⠀⠀⠀⠀⢀⠔⢱⠆⠉⠒⠓⠁⠀⠈⠛⠃⠀⠀⢈⡖⠀⠀ ⠀⠀⠀⡠⠐⠁⠀⠀⢋⢃⢄⡀⠄⠀⠔⢀⣠⠴⠌⠔⢡⠀⠀ ⢀⡔⠉⠀⠀⠀⠐⡄⡀⡗⠢⡞⠛⠖⠞⠯⠤⠖⡁⢀⠄⠀⠀ ⠘⡆⠀⢔⠂⠉⠀⠠⠁⠃⠀⠀⠸⡿⠀⠀⠀⠆⡇⠆⠀⠀⠀ ⠀⠈⢄⠈⡄⠀⡀⢣⠀⠆⠀⠀⢀⠁⠤⠤⠤⠂⡏⠀⠀⠀⠀ ⠀⠀⠀⠑⢼⣹⢿⢿⠱⣢⠤⣤⡞⣦⣀⣀⠠⠰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠙⠀⠀⠁⢄⠀⣿⣽⠑⢺⢸⢀⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡄⠀⠀⠀⢀⡰⠛⠁⠀⢸⡿⢌⢒⠀⠀⠀⠀⠀

⠀⠀⠀⡍⢑⣛⡄⡮⠿⢆⠀⠀⠀⠘⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠈⡆⠀⠀⠀⠀ ⠀⠀⢠⢢⢜⠛⠀⠠⢄⠀⠀⠑⡧⠃⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀ ⠀⢨⡿⠋⠢⣌⡁⠻⣆⠢⡀⠀⢷⣀⠀⠀⠀⡰⠇⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀ ⠀⢸⠀⣇⠢⢀⠙⠢⢘⣄⠀⠐⠸⣿⣆⣠⡾⢣⡀⠀⠀⠀⠀⠀⢀⣔⢹⠀⠀⠀ ⢤⠊⠣⡈⢢⡀⠈⠉⠉⠀⢀⡀⣠⣩⣿⡍⠁⠄⠁⠀⠀⠀⠀⣴⠁⠀⡉⠀⠀⠸ ⠁⠀⠀⠀⣀⠠⠐⠂⠈⠭⠭⢁⠀⠑⢌⢻⣷⡘⡀⠀⠀⠀⠀⠈⣱⣰⠁⠀⠀⠀ ⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⢥⣧⣀⠀⠀⣀⠴⠃⢸⠀⠀⠀⡜ ⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢿⠻⣿⢧⣤⣄⣀⣼⠀⠀⠀⡁ ⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠂⠀⠈⠀⠈⠯⠃⠀⢰⠁⠀⠀⢘⡇ ⠀⠀⠀⠀⢳⢒⣒⠖⠒⠒⠀⠀⠁⢠⡏⠀⠀⠀⠈⠀⠀⠀⠀⣠⠚⠄⠀⠀⢸⡇

⠀⠀⠰⠀⣀⡀⠠⠤⠀⠀⠀⠀⠈⡄⠀⠀⠀⣼⣀⠁⢀⣘⣀⠀⣠⠄⠼⠗⢤⠀ ⠀⠀⠧⢊⠕⠀⠀⠀⠑⢆⠑⢄⢀⠳⢄⠀⡰⠋⠁⠀⣎⠀⠙⠀⠘⠒⡆⠀⠀⠇ ⠀⡐⠁⠀⠈⠀⠀⠀⢈⡠⠓⡘⠃⠉⠈⠛⢤⠔⠂⠀⠈⠐⡦⢀⠀⠀⡐⠧⢰⡄ ⠀⠀⠀⠀⡀⣤⠾⢑⠏⠀⠊⠀⠀⠀⠀⠀⠀⢵⡀⠀⢀⠎⠀⠀⠈⠢⣜⣀⠈⠏ ⠀⠀⡠⠐⠩⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡔⠉⢄⠀⠀⢀⠀⢠⠈⠒⣀ ⠀⠀⠀⢀⠀⢈⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⡤⠥⠶⠵⡈⢁⠐⢦⠈ ⠀⢠⡒⠅⠒⠙⡘⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣂⠁⠤⠬⠶⠑⠄⠀ ⢺⣿⣆⠀⢀⡐⠀⠀⠱⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⡉⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⠇⠁⠀⠀⠀⠀⢁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠁⢀⣀⣀⣀⠀⢢⠀⠀⠀⢠⣾⣿⡿⠛⠛⢟⣱⣆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢈ ⡔⠁⠀⠈⠉⠉⠘⠓⠀⠎⢿⣿⡏⠹⠀⠻⢨⣿⣿⡶⠐⠀⠀⢀⠚⠳⠞⠛⠛⢾ ⢧⡀⠀⠀⠂⠠⠀⣉⠛⠛⠖⠻⣧⡐⠒⠒⣠⣿⣿⡷⠚⠋⣀⠠⠀⠂⠀⠀⠀⠸ ⠸⣿⡦⢦⠀⢢⣤⣀⠈⠑⠢⣈⠫⡵⠿⠯⠭⡝⡉⠔⠊⠁⣀⣠⡴⠊⣠⢀⢀⡆ ⠀⠻⣗⢸⣧⡀⠻⡉⠿⠓⠢⣌⣻⡆⠸⢇⢀⣏⣤⣴⠞⣹⡹⠋⣠⣾⡏⢸⣻⠇ ⠀⢸⣧⢀⡏⠓⢄⠈⠇⠀⠀⠀⠋⠉⠒⠞⠋⠈⢁⢻⣼⣏⣠⠞⠋⣿⢁⣿⡏⡀ ⠀⢸⣿⡆⣇⠀⠀⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠁⡜⠀⠟⠛⠁⠀⠀⠘⠛⣿⡇⣿ ⣶⣿⣿⣿⣿⡀⠀⠀⢰⠀⠀⠀⠀⠀⣾⡦⠀⠰⠁⠀⠀⠀⠀⠀⠀⢀⣼⣿⢰⣿ ⣿⣿⣿⣿⣿⣿⣷⣶⣦⣆⠀⠀⠀⠀⠈⠋⢠⡆⠀⠀⠀⠀⠀⠀⣠⣾⣿⣧⡿⣿ ⣿⣿⢿⣿⣿⣿⣿⣟⣿⣿⣆⠀⠀⠀⣀⡴⣿⣿⣶⣶⣶⣴⣶⣿⣿⣿⣿⣿⣅⠸ ⣿⣁⣘⣿⣿⣿⣿⣿⣈⣿⣿⣦⣤⣶⣿⣷⣿⣿⡿⣿⣟⣹⣿⣿⣿⣿⣿⣿⣙⣤

⠀⠀⠀⠀⢐⡀⠆⠀⡴⣢⢻⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⡇⡚⣸⣱⣡⣸⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣇⣷⣟⣿⡿⠿⣿⠵⣿⣿⠿⢫⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣸⢿⣥⣜⠉⠀⠀⠀⠉⠉⣠⠧⠐⠊⠀⠀⠀⠀⠐⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠐⣿⣼⡿⣾⣈⠵⢤⠈⠡⠸⠿⣴⢄⡀⠀⠀⠀⠀⢀⡤⠈⡷⠀⠀ ⠀⠀⠀⠀⠀⢿⡼⠛⠉⠛⢄⠀⠀⠀⠀⠀⢈⠷⠛⠉⠁⠚⠫⢅⠀⢰⠃⠀⠀ ⠀⠀⠀⠀⣡⡿⠀⠀⠀⢠⢄⠢⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠳⣣⢤⡤⡄ ⠀⠀⠀⣜⠔⠁⡀⠀⡀⡅⠀⠉⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⣴⡿ ⠆⠀⣼⢇⠀⢃⠛⠧⢧⣅⠤⠐⢈⡡⠤⠇⠀⠈⠥⣂⢄⢀⠤⠂⠉⠙⢿⡿⠀ ⠀⢀⣗⠤⡿⠊⠉⠉⣐⣓⡖⢉⠀⠀⠖⠠⠀⠀⠀⠀⠙⢷⡒⡄⠀⠀⢸⠁⠀ ⠀⡞⡁⢀⡀⡠⠒⠉⠀⠀⠀⠀⠉⠪⣤⠀⠀⠀⠀⢀⡠⠂⢱⢃⢃⢂⠸⠄⠀ ⡞⢰⣵⡕⠊⠀⠀⣀⣴⠚⠉⠉⠉⠲⣧⠈⠂⠀⠰⠁⠀⡰⢻⠯⠚⡎⣠⣴⠀ ⡇⢸⠏⢀⡠⢶⠏⣹⡟⢴⣿⢄⣦⣄⠈⢷⣄⠈⠳⡀⡴⠒⣺⠂⠈⠉⠀⢸⠀ ⠆⣮⠖⢹⢃⡞⢠⡟⠀⣈⡏⠓⠽⠟⢳⡄⢻⣆⠀⢼⠀⠰⠃⠀⠀⠀⠀⢸⠀ ⣰⣿⡾⣿⣸⣷⢸⡆⢉⣡⡀⠀⡠⠾⢲⣷⠀⢯⣆⡞⣦⠀⠀⠀⠀⠀⠀⡈⠀ ⠚⠛⠛⢿⣿⡏⢸⣋⡉⠥⠃⠀⡁⠀⠁⢻⡇⠸⣿⣳⣾⠀⠀⠀⠀⠀⠀⠇⠀ ⠀⠀⠀⡀⢿⣇⠘⡆⠀⠀⢀⣴⣿⠄⢀⣾⠃⢀⠛⠟⢿⡀⠀⢀⠀⢀⡼⠀⠀ ⡢⢤⠤⡗⢻⣿⡈⣿⠦⢀⡘⢦⡀⣠⢊⡜⢀⢼⠄⡀⠀⠙⠷⣶⠿⣋⠁⠀⠀ ⠐⠀⠂⢛⢆⢻⣷⡘⡗⠄⢀⣉⣭⣛⠿⣲⡯⠊⡉⢒⠱⡤⣀⣈⣻⡂⠀⠀⠀ ⠀⠀⠀⠘⠈⢢⠈⠙⢝⠂⠀⡀⠀⠈⠿⣻⡔⢁⠔⠀⠁⠈⢀⡀⠀⢱⡄⠀⠀

⠈⢂⠀⠀⠀⡤⢄⠤⢄⡀⣇⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠑⢄⠀⠑⡈⠣⡀⠈⠙⠷⢤⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠣⡀⠈⠲⢮⢶⠶⣾⠁⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀ ⠀⠀⠀⠀⠀⠘⢄⠀⠀⡟⢄⡀⠀⣧⡇⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢋⡀⠒⡄⠙⢿⠯⠐⠢⡀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⡀⠀⠀⢀⠈⢰⡗⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⡀⡀⠙⣽⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢣⠈⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⣸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⣧⡤⣼⡇⠀⠀⠀⠀⠀⠀⢀⢴⠋⠀ ⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⡸⠘⣿⢾⠷⠓⠒⠀⠄⣀⣠⠔⡕⠁⠀⠀ ⠀⠑⠤⣉⠐⠀⠀⠀⠀⠒⠉⠀⢀⢿⠁⠀⠀⠀⠀⠀⠀⠈⠛⢌⠀⠀⠀ ⠀⠀⠀⠀⠉⠒⠂⠀⠀⠀⠀⠒⠻⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀

⠀⠀⠀⠀⠀⠀⡐⡉⠉⠁⠺⡹⢢⣀⠀⠀⠀⢀⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⠇⠀⣧⡦⣦⣠⡐⠒⠲⡥⠀⠀⠀⠈⠁⠂⠀⠀⠙⠲⢂⠀⠀⠀⠀ ⠀⠀⠘⢃⠂⠁⠠⠊⠀⠀⠉⠃⢌⠁⠀⠀⠀⠀⠀⠀⠈⢆⠀⠐⢸⡆⠀⠀⠀ ⠀⠀⢠⠇⠀⠀⠦⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣰⠃⠀⠀⠀ ⠀⠀⢸⢠⣺⠎⠲⠵⣶⠔⢠⠐⠤⠎⠀⠀⠀⡠⡰⠂⢉⢇⠠⠐⠚⣒⠢⢄⠀ ⠀⢠⠂⣿⣳⠀⢀⣾⠛⡷⠸⠇⠀⢌⣄⠀⢌⡞⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠡ ⠀⡇⠀⢸⠟⠗⠈⢛⠓⠁⡏⠀⢆⠈⣿⣰⠊⢄⡀⠀⢀⡠⠪⠁⠀⠀⠀⠀⠀ ⡄⢻⡀⡏⣲⣆⣂⡉⢱⢰⠄⠂⠨⢠⠃⠤⡙⠂⠒⠬⡀⠀⠃⠀⢰⠂⠀⠀⠀ ⠻⡂⠈⢩⠁⠈⠉⣽⣷⠖⢣⠠⢥⠗⠀⠀⠀⠁⠀⠀⠐⠄⡠⣔⠁⠀⠀⠀⠀ ⠢⡘⠦⡘⠀⣠⣾⠋⢙⡎⠃⠈⡆⠀⠀⠀⠀⠀⢀⡠⠂⠃⠀⡇⠉⠁⠀⠀⠀ ⠀⠈⢑⠒⠊⠉⢨⡆⠀⠀⢂⠀⠀⠀⠀⠀⢰⠔⠁⠀⢸⣀⡀⠅⠀⠀⠀⠀⠀ ⠀⠀⡎⠀⠀⢀⢧⠀⠀⠀⠈⠀⡄⠀⠀⠠⠛⠂⠄⡄⠓⠠⠄⣸⠀⠀⠀⠀⠀ ⠀⠰⠀⠀⠀⡘⠌⢄⣀⡀⣰⢀⠀⠀⠀⠸⢄⠀⠀⠀⠀⠐⠀⠺⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⢕⠠⣀⠑⣯⣡⡏⠀⠀⠀⣦⣀⠉⠑⠦⡀⠀⠀⠀⠈⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢰⡘⡁⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⠂⠠⠤⢀⡀⠈⠁⠂⢄⠈⢆⡓⡁⠀⠀⠀⠀⠄⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠈⠑⢀⠀⠀⡖⠒⠁⡤⠄⠀⣀⡀⢰⠘ ⠀⢠⣀⡄⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⣀⠅⠀⠁⠀⠀⠀⠉⠃⠥⡀⠀⠁ ⠀⠘⠿⠃⢀⡀⠀⠀⡠⠊⢂⠄⠤⠄⠒⠉⠄⡀⠀⠀⠀⠑⢄⠀⠀⠀⠒⠑⠦ ⠀⠀⠀⠰⠿⠃⠀⡰⢁⠀⠁⠀⢀⠀⠀⠈⠐⠨⢕⢄⠀⠀⠀⠑⢄⠔⡒⠀⠤ ⠀⠀⠀⠀⠀⠀⠜⠔⠁⠀⠀⠀⠀⠈⠁⠂⠤⣀⢀⡽⣵⣌⠢⠀⠀⢽⡎⣷⣶ ⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠁⠢⢀⠀⠀⢀⡀⡠⢡⡾⠉⠱⠱⡱⡀⠀⠻⡼⠋ ⠀⣀⣈⡁⠀⣧⠁⠀⠀⠀⠀⠀⠀⠑⡢⣊⢎⢢⣯⢤⡀⡠⡄⣋⢷⡀⡔⠁⠀ ⠀⠀⠀⠀⠙⡇⠀⠈⠢⠀⠀⠀⠀⠈⢛⠋⠀⠈⠉⠋⠊⢰⡿⠋⠜⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⠠⠀⠑⢄⠀⡘⢢⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡘⡀⠀⠀ ⠐⢄⠀⠀⠀⠘⡀⡄⠡⠀⠀⠙⢬⣗⣶⡤⣀⠀⠀⠀⠀⠀⢀⣤⡝⢄⠐⡄⠀ ⠀⠀⢉⣲⣤⣤⣗⡐⠄⠑⡀⠀⣖⡞⠁⠑⠹⠀⠐⠀⠀⠔⢵⡏⠁⠀⡆⢠⠐ ⠀⠀⣜⢋⠆⠬⠽⠷⢌⣢⡈⢲⠙⠻⢖⡒⠀⠀⠀⠀⣰⣾⣿⠂⠀⠀⠀⠀⣼ ⠀⠀⢟⣼⠎⠀⠀⠀⠀⠀⠉⠚⠢⠴⠂⠬⠿⠴⠭⣁⠔⠀⠉⠓⢤⣤⣴⣾⠁ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⣰⢈⡤⠂⠀⠀⠀⠀⠈⠛⠇⠒

⠀⠀⠀⠀⡄⠊⢡⠈⢆⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂⠀⠀ ⠀⠀⢠⠈⠀⠀⠀⠑⡤⢟⠭⣐⣒⣒⣒⣒⣒⣛⡉⠡⢒⠄⡀⠀⡘⠀⡇⡀⠀⠀ ⠀⠀⠀⢆⠀⠰⠔⡫⡪⣺⣷⣭⣤⣤⣤⣷⣤⣤⣉⠛⣅⡪⢜⢜⢄⢀⢁⠁⡀⠀ ⠀⠀⠀⠈⡄⢸⢸⣘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣄⢡⠁⡎⠈⠰⠀⠀ ⠄⠀⠀⢠⢣⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣤⣗⠃⠂⠀⠀ ⠀⣀⣠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣧⣸⠀⠀ ⣞⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⠗⢠ ⠤⡑⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣟⣻⣿⢿⣿⣿⣿⣿⣿⣿⣆⠳⠈⠀ ⣄⢨⣿⣿⣿⣿⣿⣿⣿⠀⠛⣿⡍⢿⣿⡿⢹⢣⠛⠚⣿⣿⣿⣿⣿⣿⣿⡆⢡⣤ ⣿⣿⣿⣿⣿⣿⡟⢻⣿⡟⣿⡶⠳⠈⢻⠁⠰⠶⢾⡟⢻⣿⡟⣿⣿⣿⠟⣣⣴⣿ ⣿⣿⣿⣿⣿⣿⣦⠀⠱⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠁⣿⣟⡵⢍⣿⣿⣿ ⣿⠟⠷⡿⡍⣿⣿⣷⡀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⣸⣿⣿⣄⠀⠈⠻⣿ ⠁⠀⠀⢻⢧⠈⢿⣿⣿⡅⣈⣢⣀⠻⣛⡻⠀⣀⣔⣋⣤⠊⣿⣿⡇⠊⠑⢄⠀⠈