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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠛⠛⢛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠃⢈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠘⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣽⣿⣿⣷⡟⣿⣦⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣇⠀⠀⠀⠠⣿⣿⡁⢀⣠⣄⡀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣖⣿⣆⠀⠀⠀⢹⣿⣷⣾⠉⠹⣧⢰⣿⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣷⡏⠀⠀⠀⠀⠀⣿⡿⠀⠀⣯⣀⣿⣷⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⡧⣿⡿⣿⣿⣿⣿⢻⣿⠁⠀⠀⠀⠀⢸⣿⡇⠠⠀⠀⠉⢹⣿⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⡇⢻⡇⠀⠻⣿⡿⠂⢿⡆⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠈⢹⣷⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣷⣼⣿⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢿⣿⡿⢐⠀⠀⠀⠀⠀⢿⣇⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⢸⠀⠀⠀⠀⢠⠘⣿⡀⠀⣸⣿⡿⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⢸⠀⢿⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⡇⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⡘⣿⣠⣿⣿⠇⠀⠀⠀⠀⠀⡇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇⢹⣿⣿⡏⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣷⣶⣤⡄⠀ ⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⣻⡿⠀⠀⠀⠀⠀⠀⠀⠁⢀⢿⣆⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⠉⠀⠈⠙⢷⡀ ⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢘⠘⠿⢿⣷⣶⣶⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠈⡇ ⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢈⠳⣦⡀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣠⢸⡇ ⠀⠀⠐⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣸⣇⠀⢰⣾⣿⣧⠃ ⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡾⣻⣿⣿⡄⣼⠉⠀⠀⠀ ⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡟⢀⣿⣿⡿⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠘⢿⣷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡾⠋⠀⠈⢻⣿⣧⣀⡰⠃⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣿⣧⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣽⠟⠋⠀⠀⠀⠀⠀⠙⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣶⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⣆⠂⠀⠀⠀⢀⢀⣀⣲⣶⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣷⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⣦⢠⣴⡶⣖⠲⣄⠀⠀ ⠀⠀⠀⣼⣿⢻⡆⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣿⣿⣿⣠⣤⡅⡌⣿⡆ ⠀⠀⠐⣿⠬⣆⠛⣦⡀⠀⠀⢸⣿⣿⣿⠋⠻⣿⣿⣿⠀⠘⢦⣶⠏⠀ ⠀⠀⠀⢿⣶⠛⢢⣿⡇⠀⠀⠀⠙⣿⣧⠤⢴⣏⣾⣿⣉⣲⡾⠁⠀⠀ ⠀⠀⠀⠀⠙⣿⣭⣟⢿⡄⠀⠀⠀⣿⣿⣷⣾⣾⣿⣿⣿⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣿⣞⣷⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⡞⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣽⣷⣀⣿⣿⣿⣿⣿⣿⡿⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⠟⠛⠛⠻⣿⣿⣿⠟⠋⠁⠀⠀⠀⠈⠹⣆⠀⠀⠀ ⠀⠀⠀⢀⣾⡟⠁⠀⠀⢈⣲⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠀⠀⠀ ⠀⠀⠀⣼⡿⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠟⠍⠻⣦⠀ ⠀⠀⢰⣿⠃⠀⠀⡘⡾⠀⠀⠀⠀⢀⣠⡤⠞⠛⠁⠀⠀⠀⠀⠀⠈⡄ ⠀⢀⣿⠇⠀⠀⠀⠀⠑⣦⣤⣴⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧ ⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠘⣏⠀⠀⠀⠀⢀⣀⣀⡤⣤⡤⠴⠒⠋⠀ ⣾⣿⠣⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⢄⡿⠀⠀⠀⠀⠀ ⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣐⡾⠁⠀⠀⠀⠀⠀ ⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣟⡉⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⢲⣿⣿⣿⡿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣧⠀⠀⠀⠀⣷⣿⣿⠉⠀⢸⣿⣿⣿⣷⢹⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⣿⡏⠉⠉⠉⣿⡏⣿⠹⠷⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠀⠀⠀⠀⠿⠧⠿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢚⣿⡷⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡿⢫⣽⣽⣛⠛⠻⢿⠿⠛⣉⣥⠤⢼⣿⣿⣿⡿⣽⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⢱⣶⣶⢬⣟⢶⠙⣷⠞⣩⣶⣿⢳⢹⣾⣿⡀⣽⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣎⢿⣿⡿⢏⣼⠀⠻⣆⠻⢿⣿⠟⣿⣿⣿⣷⣟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣯⡓⠒⠒⠋⠀⠀⢀⠈⠙⠒⢚⣿⣿⣿⣿⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣷⡄⠺⢷⠆⠼⠿⠇⣴⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢻⣿⣿⢿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⣤⣀⣤⣤⣀⣠⢾⣿⣿⣾⣿⣿⣿⣿⣷⣄⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡀⠀⠀⠈⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀ ⠀⣠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⣄⢂⡉⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠄⢡⠀⠏⠿⣦⡈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⠅⠨⠄⣈⠡⢉⠝⢭⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⡿⣽⣻⢾⡿⣿⣦⠀⠀⠀⠀⠀⢸⣿⣿⢈⠐⠂⡄⠂⡅⡈⠜⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⣿⣿⣿⣽⣻⣽⢿⣽⣿⡼⣧⠀⠀⠀⠀⣾⣿⣿⠀⣸⣥⣤⠡⠐⡐⡈⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣟⣧⣿⣻⡿⣼⣻⣿⣿⣇⠀⠀⠀⠛⣿⣿⣼⡿⢻⣿⡄⢻⣧⠠⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⣻⣽⡷⣿⣻⣯⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⡃⢒⣻⣇⠘⣿⡇⡘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣯⣿⣿⣷⡿⣿⣻⣟⠃⠀⠀⠀⠀⠀⣾⣿⡁⠀⠈⠛⠛⣿⣷⢀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣻⣿⡹⣿⣿⣿⢳⣿⡄⠀⠀⠀⠀⢠⣿⣿⠀⠁⠀⠀⠀⠘⢿⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣟⣷⠁⠈⠉⠁⠀⠻⣧⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠟⣿⡀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡧⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⣸⣿⣏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣿⣿⠃⠀⠀⠀⠀⠀⠐⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⠟⠛⠿⢷⡀⠀ ⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⢻⣦⣤⣀⣀⣀⣀⣠⣴⣾⣿⡿⠛⠀⡀⠂⠄⠂⣳⡀ ⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠛⢻⣟⡁⢀⠂⠁⠄⡈⠐⡐⣺⠇ ⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⡁⢂⠀⡁⠀⣿⠀ ⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠠⠀⢢⣴⡟⣽⡆ ⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⡆⢰⡿⠿⠷⠋⠀ ⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⣿⣿⡇⠘⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⠟⠀⢸⣿⣿⠇⠀⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣧⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠋⠀⠀⠙⣿⣿⣀⣶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⡷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣒⣼⠟⠉⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡼⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣥⡤⠤⠄⠀⠀⠀⠀⠀⢀⣲⣶⣶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠻⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀🦍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⣄⢂⡉⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠄⢡⠀⠏⠿⣦⡈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⠅⠨⠄⣈⠡⢉⠝⢭⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⡿⣽⣻⢾⡿⣿⣦⠀⠀⠀⠀⠀⢸⣿⣿⢈⠐⠂⡄⠂⡅⡈⠜⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⣿⣿⣿⣽⣻⣽⢿⣽⣿⡼⣧⠀⠀⠀⠀⣾⣿⣿⠀⣸⣥⣤⠡⠐⡐⡈⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣟⣧⣿⣻⡿⣼⣻⣿⣿⣇⠀⠀⠀⠛⣿⣿⣼⡿⢻⣿⡄⢻⣧⠠⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⣻⣽⡷⣿⣻⣯⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⡃⢒⣻⣇⠘⣿⡇⡘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣯⣿⣿⣷⡿⣿⣻⣟⠃⠀⠀⠀⠀⠀⣾⣿⡁⠀⠈⠛⠛⣿⣷⢀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣻⣿⡹⣿⣿⣿⢳⣿⡄⠀⠀⠀⠀⢠⣿⣿⠀⠁⠀⠀⠀⠘⢿⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣟⣷⠁⠈⠉⠁⠀⠻⣧⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠟⣿⡀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡧⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⣸⣿⣏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣿⣿⠃⠀⠀⠀⠀⠀⠐⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⠟⠛⠿⢷⡀⠀ ⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⢻⣦⣤⣀⣀⣀⣀⣠⣴⣾⣿⡿⠛⠀⡀⠂⠄⠂⣳⡀ ⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠛⢻⣟⡁⢀⠂⠁⠄⡈⠐⡐⣺⠇ ⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⡁⢂⠀⡁⠀⣿⠀ ⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠠⠀⢢⣴⡟⣽⡆ ⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⡆⢰⡿⠿⠷⠋⠀ ⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⣿⣿⡇⠘⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⠟⠀⢸⣿⣿⠇⠀⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣧⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠋⠀⠀⠙⣿⣿⣀⣶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⡷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣒⣼⠟⠉⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡼⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣥⡤⠤⠄⠀⠀⠀⠀⠀⢀⣲⣶⣶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠻⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⢿⢿⣿⣿⣷⣾⣿⣶⢶⣷⣤⢤⣀⠠⣾⣿⡿⣿⣏⣿⣿⣿⣷⣶⣤⣾⣯⣿⣶⣶⣮⡻⣿⣿⣿⢿⣿⣿⣶⣶⣿⣿⣿⣿⣏⢻⣿⣦⠀⡀⠉⠉⠑⠒⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⢺⣿⣿⣿⡟⢻⣿⡵⣛⣒⣓⣾⢟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣭⣿⣷⣽⣿⣟⡻⢧⣄⣐⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠄⣸⣿⣿⣿⡇⠽⢏⣾⣿⣿⣿⣷⣿⡿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣟⣿⣏⣵⣿⣿⣿⣿⣿⣿⣟⠧⣍⣿⣿⣟⣭⣷⣾⣿⣷⡌⡸⢉⡟⣆⡀⠄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⡿⢛⡾⣿⣤⢸⣿⣿⣿⡿⠟⢛⣛⠿⣿⣮⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣯⣿⣴⢋⡳⣦⣄⡉⡕⠀⠀⠀⠀⠀ ⣀⠀⠠⣶⣶⡿⢿⡽⣿⣿⠿⣿⣿⣿⣿⣟⣴⣾⣿⣡⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠙⣛⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣽⣿⣳⢈⣿⠀⠀⠀⠀⠀ ⠈⠉⠉⠙⡛⡲⠿⣯⠁⣠⣴⣿⣽⣟⠚⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣟⡅⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣦⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢣⠀⠲⣠⢿⢡⠾⢤⣿⣷⣦⣄⢻⣿⣯⣿⣿⣿⣽⣿⣿⡟⣿⣿⣿⣿⠉⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⣠⣼⢶⣄⢽⣿⡇⣰⣿⣿⣿⣿⣿⣦⣝⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀ ⠀⠀⣿⢙⡷⣟⣻⢿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢀⠀⠀⠀⠀ ⠀⠀⢷⡘⣇⢫⡟⠍⠻⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣏⣵⣿⣇⡈⣻⣷⣾⣿⣿⣷⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠁⠀⠈⡆⠀⠀⠀ ⠀⠀⠈⠙⠚⠛⣼⣿⡾⠿⣿⣿⣿⣿⣿⣷⣿⢻⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣷⣤⣶⣿⣿⣿⣿⣿⠏⣡⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⡀⠀⠀⠀⢣⠀⠀⠀ ⠀⠀⠀⠀⠀⠺⢿⣿⣤⣴⣿⣿⣿⣿⣿⡿⢟⣛⣿⣾⣿⣟⡟⠿⢿⡿⢟⣿⣿⢉⣿⣿⣿⣿⣽⣿⣿⣿⣿⠃⣠⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢛⣻⣿⣿⣿⣯⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠿⣿⣿⣿⣿⡄⠉⠉⠛⠻⢿⣿⣿⡿⠅⠁⠀⠀⣹⠻⣿⣿⣿⣿⣾⣿⣿⣿⣧⣾⠟⣡⣿⣿⣿⡏⠛⠉⢙⣿⣿⣟⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣢⣾⣿⣿⣿⣷⣷⣠⣤⣶⣋⣉⣀⣀⣄⣀⡀⢺⠁⡀⠉⠛⠧⣉⠛⠛⣉⣥⢿⣿⣿⣭⣥⣆⣉⣿⣦⣀⠀⠈⣿⣿⣿⣿⣿⣿⡿⢿⣿⢇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣿⣿⣿⣿⣿⡿⣹⣿⡿⠿⠿⣿⣿⣿⣿⣿⢿⣶⣇⣠⠀⣀⠸⡄⢤⡹⣾⣾⣿⣿⣿⣟⣿⣿⣿⢿⠿⢿⡄⢻⣿⣿⣿⣿⣿⣶⠿⠋⠸⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡗⠋⠀⠀⣀⣀⣀⣩⣭⣍⣁⢤⣈⠩⠍⠀⠀⠀⠀⠁⢀⣥⢀⣈⣿⣿⣿⣿⣿⣟⠋⠀⠀⠉⢸⣿⣿⣿⣿⡯⠘⠀⠀⠀⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠃⠀⠀⣾⣿⣟⣿⣿⣿⣿⠙⣿⣿⢷⠀⠀⠀⠀⠀⢰⣿⣵⡿⢻⣿⣿⣿⡟⢿⣿⣷⣄⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠻⣿⣿⠀⠀⠀⠈⠙⣿⣿⣿⠿⠛⠚⠛⣫⠀⠀⠀⠀⠀⠀⢸⠳⣟⠓⡺⠿⢿⠟⣵⣿⣟⠋⠈⠀⠀⠸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⡏⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠘⣆⠙⠷⣌⠙⠛⠻⠿⠉⠀⠀⠀⠀⠀⠀⢻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠦⣄⣀⣀⣠⣴⣖⣴⠿⠀⠀⠀⠀⠀⠀⠀⠠⡿⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣧⡆⠀⠀⠁⠀⠀⠀⠀⠀⣀⣠⣾⣧⣄⡐⠋⢡⣼⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⢀⣤⠀⣠⣼⡿⣿⣿⣿⣿⠂⢸⣾⣿⣿⠀⣠⣠⠀⠀⠀⠀⠀⣄⣻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡆⢀⣾⣿⢟⡛⠉⣁⣙⠋⣈⠁⠀⠀⣙⢟⡃⢸⣿⣿⣿⣿⣿⠂⠀⣸⣿⣿⣿⣿⣷⣾⡛⠋⠉⠛⠓⠒⠤⠤⠤⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡾⠋⠁⠈⠹⣏⠉⠙⠓⣿⠿⠶⠿⠽⠟⠉⢻⡿⠛⠀⠸⣿⣦⣿⣿⣿⣿⣿⣟⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣽⣿⠁⠀⠀⠀⠀⠈⠃⠀⠀⠈⠁⠂⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠛⣿⣿⣿⣿⣷⡂⠤⠀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⣠⠀⠀⠀⠀⠀⠐⡿⠿⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠋⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⠿⢟⠓⠀⣠⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⣿⣿⡀⣀⡀⠀⠀⠀⡀⠀⡌⣏⢿⠋⠃⠀⠀⠀⢀⠀⣼⣿⣿⣿⣿⠃⠀⠀⠈⣿⣿⣿⡟⡇⠂⠀⠀⢰⣾⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣿⠿⣿⣿⣿⣿⣿⣧⣇⡆⡀⠀⠞⡀⠆⢳⠸⡈⠀⠀⠀⠀⢤⣿⣷⣿⣿⣿⣿⡿⠀⢀⡆⠀⣿⣿⣿⣇⡇⠀⠀⠁⢠⢻⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣾⣁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⢸⢹⠀⠸⡅⠳⠀⢀⢠⡆⢹⣬⣿⣿⣿⣿⡯⠁⠀⠈⠀⠀⣿⣿⣿⣿⠠⠀⠀⠉⠍⢸⣿⣦⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠞⠛⠛⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⢀⣠⠤⠴⠤⣀⡀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⣤⠾⠋⠉⠀⠀⠀⠀⠀⠉⠳⡦⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⠁⠀⣼⠏⢀⣤⣤⡀⠀⢰⣿⣶⡄⠀⣷⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠂⠀⣼⡃⠀⢸⣿⣿⣿⠀⢸⣿⣿⣷⠀⢹⡇⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡀⠀⢸⣇⠀⠀⠻⠿⢟⣀⡈⠛⠛⠃⠀⠈⣧⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡇⠀⠀⢿⠀⠀⠀⠀⠈⠉⠃⠀⠀⢀⡀⠀⣿⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⠀⠀⠘⡆⠀⠠⠤⢤⣀⣠⠤⠖⠋⠁⠀⣸⠃⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡿⣦⡀⠀⠈⠑⠢⢤⣤⠤⠤⠤⠖⠚⠉⠀⢀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⠁⠛⠿⣦⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠃⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠈⠙⠛⠓⠛⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⡏⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡟⠀⠀⠀⠀⠀⡼⠀⠀⠀⢀⡴⠒⠛⠉⠉⠙⠢⢤⣀⠈⣆⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀ ⠀⠀⣼⠁⠀⠀⠀⠀⠀⡇⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠘⣆⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀ ⠀⢰⡏⠀⠀⠀⠀⠀⢸⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠸⡆⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀ ⠀⣾⠃⠀⠀⠀⠀⠀⢸⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢹⡀⠀⠀⠀⠀⠹⣇⠀⠀⠀ ⢀⡿⠀⠀⠀⠀⠀⠀⣸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢧⠀⠀⠀⠀⠀⣿⡆⠀⠀ ⢸⠇⠀⠀⠀⠀⠀⠀⡿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠘⣆⠀⠀⠀⠀⢸⣿⡀⠀ ⣾⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠘⢦⠀⠀⠀⠀⢻⣧⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠈⢧⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠋⣀⡤⠔⠒⠂⠤⣀⠉⠳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⠁⡼⢁⣤⡄⢠⣖⡄⢰⠀⠀⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠈⡆⠀⠿⢟⡘⠿⠇⠈⡇⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢣⠀⢱⠀⢀⠈⠉⢀⡠⠀⡣⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡄⠈⠦⡀⠈⠉⠀⠀⣰⠁⢀⡾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠻⢦⣀⠈⠉⠉⠉⠁⠀⣠⠏⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⡴⠁⠀⠀⠈⠉⠉⠀⠀⠀⠉⠀⠀⠀⠹⣄⠀⠀⠀⠀ ⠀⣸⠁⠀⠀⡈⠀⢀⠔⠒⠀⠐⠤⠀⢂⠀⠀⠈⢧⠀⠀⠀ ⢀⡇⠀⠀⠀⡇⠀⠂⠀⠀⠀⠀⠀⠘⡌⠆⠀⠀⠘⡆⠀⠀ ⢸⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢡⠘⡀⠀⠀⢹⡀⠀ ⡇⠀⠀⠀⢸⠂⢸⠀⠀⠀⠀⠀⠀⠀⠈⡄⠱⡀⠀⠈⣧⠀ ⡇⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠱⡀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠾⠿⠛⠛⠻⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⣀⣠⡴⠶⠗⠛⠶⣄⣀⠀⠀⠀⠀⠉⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⢀⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⡤⠀⠀⠀⠘⢻⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⢠⣿⠋⠀⣀⣀⠀⠀⠀⠀⣤⣶⣤⡀⠀⢸⣇⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⢠⡿⠑⠀⣼⣿⣏⣿⡄⠀⢰⣿⣧⡾⣷⡀⠘⣿⡄⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⣿⡅⠀⠀⢹⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⡇⠀⢸⣷⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢸⡇⠀⠀⠘⣧⠀⠀⠀⠹⠿⠿⢏⢀⡀⠙⠿⠿⠋⠀⠀⠘⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠸⠃⠿⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠠⠄⢹⣧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⢿⠀⠀⠈⠓⠒⠶⠤⠴⠖⠚⠋⠁⠀⠀⠀⣾⠁⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣄⠀⠀⠀⠙⠳⣤⣀⣀⣀⣀⣀⣀⣀⣠⠤⠶⠛⠀⠀⢀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢫⣿⣧⣄⠄⡀⠀⠀⠉⠙⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⢀⣾⠏⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠁⠙⠿⣷⣦⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣦⣾⠟⠀⠀⠙⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠤⢤⣄⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠈⢻⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢀⡼⠋⠁⠀⠀⠀⠀⠀⠈⠛⠲⢤⡄⠈⣧⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠃⠄⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠹⡆⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢻⡄⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀ ⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⢷⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀ ⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀ ⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢻⡆⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀ ⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠻⣄⠀⠀⠀⠀⠀⢸⣿⡆⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢿⣿⡀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠹⣆⠀⠀⠀⠀⠈⢿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠿⣿⣿⢿⡿⣿⢿⡿⣿⢿ ⡷⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣷⣻⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣳⣟⣾⣳⣟⡾⣧⡄⠀⠀⠙⢞⣯⣟⢧⡟⣾⣱⢯ ⣟⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⡻⢾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡷⣯⣟⢷⡻⣦⡄⠀⠀⠁⠻⣏⡾⢧⣛⡾ ⣟⣮⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣽⣞⣷⣻⢾⣽⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠻⣿⣿⣿⣽⣳⢯⡷⣻⣼⣻⢶⣀⠀⠀⠈⠻⣽⣹⣞ ⣟⡾⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⣧⢿⡾⣽⣻⢺⣿⣿⠡⢒⣚⠂⢤⣄⠈⠉⢉⣠⠔⢂⣍⡙⠦⣹⣿⡷⣯⡟⣾⣱⣳⢯⡿⡽⣶⡄⠀⠀⠈⢳⡾ ⣯⢿⡽⣯⢷⣻⣞⣷⣻⣞⡷⣯⣟⣷⣻⡼⣯⣟⣷⣻⢸⣿⣟⢠⢺⣿⣭⣵⡌⣓⠀⣏⢰⣾⣿⣧⣼⠀⣿⣿⣟⣷⣻⡵⣣⣟⡿⣼⣻⢶⣻⢧⡀⠀⠀⠙ ⣟⣯⢿⣽⣻⣽⢾⣽⣳⢯⣟⣷⣻⣞⣷⢻⣷⣻⢾⣽⣻⣿⣿⣎⣄⡛⠛⠉⠰⠛⠀⠙⠦⡈⠛⠋⢡⣺⣿⣿⣽⣞⣧⢟⡵⣾⣽⢳⣯⢾⡽⣞⡽⣦⣀⠀ ⡿⣞⡿⣞⡷⣯⢿⡾⣽⣻⣞⣷⣻⢾⣽⣛⣾⣿⣿⡾⣿⣿⣿⣿⣷⣤⣀⠀⣀⣀⠀⣠⣠⡀⣠⣴⣿⣿⣿⣿⣷⣻⡞⣯⢞⣳⢯⣟⣮⢻⡷⣭⢿⣱⣟⣶ ⡿⣝⡿⣽⣻⡽⣯⣟⣷⣻⣞⡷⣯⣿⡾⠛⠓⠲⠂⠡⢾⣿⣿⣿⣿⣿⣿⠆⠉⠛⠁⠉⠉⢰⣿⣿⣿⣿⣿⣿⣟⣷⣻⡵⣯⣻⢿⣼⢳⣯⠷⣯⣞⣧⣟⣾ ⡿⣽⣻⢷⣯⣟⣷⣻⣞⡷⣯⣿⣿⣿⡳⠆⠀⢀⠄⠁⣼⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣿⣞⣷⣻⢷⣯⣟⣾⣻⡼⣟⣷⣻⢮⣟⣾ ⠻⣳⣯⣟⣾⡽⣞⣷⢯⣿⣿⣿⣿⠻⣿⢦⡀⠃⢀⣾⢹⡙⠻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣳⡟⣾⣳⢯⡿⣽⢾⣽⣻⢾⣽ ⠀⠈⠳⣟⣾⡽⣟⣾⣟⣯⠙⣿⣿⣿⡜⣾⡅⣠⡞⣼⣿⣷⡄⠘⠻⣿⣧⡘⠖⠒⠋⠓⠒⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣳⢯⡿⣽⢯⣟⡾⣽⣻⢾ ⣆⠀⠀⠈⠳⣟⣯⣷⣻⣧⢾⣻⢿⣻⣝⣽⠇⣰⣯⣿⣿⡿⠁⠀⠀⢸⣿⣷⣶⣤⣠⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣯⢷⡯⣟⡾⣽⣳⢯⣿ ⣿⣳⣄⠀⠀⠈⠳⣯⢷⣯⡄⣮⣍⢅⣾⠃⣼⠁⠀⠈⢿⡇⠀⠀⠠⠾⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⡾⣽⣳⢯⣟⡿⣾ ⣿⣳⢯⣷⣄⠀⠀⠈⠻⣞⣿⢿⣿⢏⡛⡾⣩⠶⠢⠤⠘⠧⡀⠀⠀⠀⠂⠀⠀⠀⠉⠀⠉⠀⠈⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡽⣷⣻⢯⡿⣽⣻ ⡿⣽⣻⢾⣽⣳⣄⠀⠀⠈⠻⣜⣒⣫⣿⠥⠃⠀⠀⠀⠀⢠⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢷⣯⢿⣽⣳⢿ ⣿⣷⣯⣿⣾⣷⣯⣷⣤⣤⣤⣼⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣬⣷⣤⣤⣤⣤⣤⣤⣴⣶⣤⣤⣶⣶⣴⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣽⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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