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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠄⠄⠄⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠑⠁⠅⠁⠁⠁⠁⠁⠁⠅⠁⠁⠁⠁⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠑⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠅⠁⠁⠅⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠁⠁⠅⠅⠕⠕⠕⠅⠅⠅⠅⠁⠁⠁⠁⠁⠁⠅⠑⠅⠁⠁⠁⠁⠁⠁⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠅⠕⠑⠁⠁⠁⠀⠁⠁⠁⠁⠅⠅⠕⠕⠕⠁⠅⠅⠅⠁⠁⠁⠁⠅⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠁⠁⠕⠅⠁⠁⠀⠁⠁⠀⠁⠁⠁⠁⠁⠁⠅⠁⠑⠑⠑⠕⠕⠅⠁⠁⠁⠁⠁⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠅⠅⠁⠁⠁⠀⠀⠁⠀⠀⠀⠀⠁⠀⠁⠁⠀⠁⠁⠁⠁⠁⠁⠑⠕⠅⠅⠁⠁⠁⠁⠁⠁⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠁⠅⠁⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠁⠀⠁⠁⠁⠁⠕⠅⠁⠁⠅⠅⠑⠅⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠁⠁⠀⠁⠁⠁⠁⠁⠀⠁⠁⠀⠁⠁⠁⠁⠁⠅⠁⠅⠁⠁⠁⠁⠁⠁⠁⠅⠕⠅⠁⠕⠕⠅⠁⠁⠁⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠁⠁⠅⠁⠑⠅⠅⠁⠅⠅⠅⠅⠅⠅⠕⠕⠕⢕⢕⢕⢕⢕⠕⠅⠁⠅⠁⠁⠅⠁⠁⠁⠁⠁⠁⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠀⠁⠅⠕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢝⢝⢕⢕⠕⠕⠅⠁⠁⠁⠅⠁⠁⠅⠁⠁⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠅⠕⢕⢕⢕⢝⢽⢽⢽⢽⢽⢽⢽⢽⢽⢿⢿⢿⢿⢽⢽⢽⢽⢝⢕⢕⠕⠕⠅⠁⠅⠅⠁⠁⠑⠅⠁⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠁⢕⢕⢝⢽⢿⢽⢿⢿⢿⢿⢿⢿⣿⣿⣿⣿⢿⢿⢿⢿⢿⢿⢽⢽⢝⠕⠕⠅⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠁⠁⢕⢝⢽⢽⢿⢿⢿⢿⢿⢿⢿⢿⣿⣿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢝⢕⢕⠕⠅⠅⠁⠅⠁⠁⠁⠁⠁⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠁⠁⢝⢝⢽⢽⢿⢿⢿⢿⢽⢿⢿⣿⣿⣿⣿⣿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢝⢝⢕⠅⠅⠁⠁⠕⠅⠅⠅⠁⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠑⢝⢽⢽⢿⢿⢿⢿⢿⢿⢿⢿⣿⣿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢝⢝⢕⠅⠅⠅⠅⠅⠁⠁⠅⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⢕⢝⢽⢽⢽⢿⢿⢿⢿⢿⢿⢿⢿⣿⣿⢿⢿⢿⢿⢿⢿⢿⣿⢿⢿⢿⢿⢿⢿⢝⢝⢕⠅⠅⠁⠁⠁⠅⠁⠁⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⢕⢝⢽⢽⢿⢿⢿⢿⢿⢿⣿⣿⣿⢿⢿⢿⢿⢿⣿⣿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢝⢝⢕⠅⠅⠅⠁⠁⠅⠁⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠑⢝⢝⢽⢿⢿⢿⢿⢿⢿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⢿⣿⣿⢿⣿⢿⢿⢿⢿⢿⢽⢝⢕⠅⠅⠅⠅⠅⠕⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⢕⢝⢽⢽⢿⢿⢿⢿⢿⢿⢿⢿⣿⣿⣿⢿⣿⢿⢿⢿⢟⠟⢟⠟⢝⢟⢟⠝⢟⢿⢿⢿⢿⢿⢿⢕⠅⠁⠅⠕⠅⠕⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⢝⢽⠝⠝⠝⠝⠑⠑⠑⠕⠝⢽⢿⢿⢿⢿⢿⢿⠕⢝⠕⠕⠁⠁⠁⠁⠑⠕⠕⠝⢝⢿⢿⢿⢿⢿⢕⠅⠕⠕⠕⠑⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠑⢝⠅⠕⢁⢅⢅⢅⢅⢅⢅⢕⢝⢝⢽⢿⢿⢿⢝⢕⢕⢕⢕⢵⢵⢽⢷⢽⢷⢵⢕⠕⠝⢿⢿⢿⢿⢿⠅⠕⠅⠅⢕⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢑⠕⢅⢵⢿⢿⢿⢿⢟⠟⠿⢽⢝⢝⢽⢽⣿⢿⢽⢽⢽⢽⠝⢟⢝⢝⢟⢿⢿⢿⢿⢷⢕⢽⢿⢿⢿⢿⠕⠅⠁⠕⠑⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢙⢕⢝⢽⠟⢝⠕⠝⠉⠙⠑⠕⢝⢽⢽⢿⢿⢿⢽⢿⢽⠝⠕⢉⠅⠁⠍⠙⠝⢝⢿⢿⢿⢿⢿⢿⢿⢽⠕⠅⠅⠅⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢙⢝⢝⠝⠕⠁⠕⢅⢄⢅⢝⢵⢝⢽⢽⢿⢿⢿⢿⢿⢿⢵⢵⢝⢕⢕⢅⢝⢅⠅⠑⢝⢽⢽⢽⢿⢿⢿⢕⠅⠅⠅⠁⢅⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠕⢝⢝⢝⢅⢕⢕⢵⢵⢽⢟⢽⢿⢟⢝⢽⢿⣿⢿⢽⢿⢿⢿⢿⣽⢝⢿⢿⢿⢿⢿⢿⣽⢿⣿⣿⣿⢿⢿⢟⠅⠕⢕⢽⢟⢝⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⢗⢽⢿⢿⢝⢽⢽⢽⢽⢿⢿⢿⢿⢟⢽⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⣿⣿⣿⣿⣿⢿⢿⢿⢿⢿⠅⢑⢽⢟⢕⢝⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠕⢽⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢝⢽⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⣿⢿⢿⣿⣿⣿⢿⢿⢿⢿⢿⠅⢝⢝⢽⢽⢟⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠕⢽⢿⢿⢿⢿⢿⢿⢿⣿⣿⢿⢟⢝⢽⢿⢿⢿⢿⢿⢽⢿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⢿⢿⠅⠝⢽⣿⢽⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⢽⢿⢿⢿⢿⢿⣿⣿⢿⢿⢿⢽⢽⢿⢿⣿⣿⢿⢿⢿⢿⢿⢽⢿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⢿⢿⢿⢿⢿⠅⢕⢽⢿⣿⢿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢽⢽⢿⢿⢿⢿⣿⢿⢿⢿⢽⢝⢝⢽⢿⢿⢿⢿⢽⢿⢿⢿⢟⢿⢿⢽⢿⢿⢿⣿⣿⣿⣿⣿⢿⢿⢿⢿⢽⢕⢝⢽⢿⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢝⢿⢿⢿⢿⢿⢿⢿⢿⢿⠝⠝⠝⠙⢝⢝⢽⠝⠉⢉⢝⠝⢽⢿⢿⢿⢿⢿⢿⣿⢿⢿⣿⣿⢿⢿⢿⢿⢝⢝⠝⢝⣿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢝⢽⢿⢟⢿⢿⢿⢽⢿⢿⢕⢕⢕⢕⢝⠕⠝⢑⢕⢝⢝⢽⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢝⢝⢕⢽⢿⢿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢝⢝⢿⢿⢿⢿⢿⢿⢿⢝⠝⢝⢕⢕⢝⢝⢝⢝⢝⢝⢝⢝⢽⢝⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢝⢝⢝⢿⢿⢿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⢝⢝⢽⢟⢽⢝⢝⢝⢝⢕⠕⠝⢝⢝⠕⢕⢝⢽⢝⢝⢽⢝⢝⢝⢝⢝⢽⢝⢿⢿⢽⢿⢿⢿⢿⢽⢝⢝⢝⢿⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢝⢽⢝⢽⢽⢝⢝⠝⢕⠕⢕⢕⢵⢽⢽⢿⢽⢽⢿⢿⢿⢿⢝⢕⢝⢝⢝⢝⢽⢽⢿⢿⢿⢿⢿⢿⢟⢽⠝⢽⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢽⢿⢝⢿⢝⠕⠕⠕⠕⠝⠝⢕⢕⢕⢝⢝⣝⣝⣵⢵⣵⢕⠅⠝⠙⠕⢕⢝⢽⢿⢿⢿⣿⢿⢿⢽⢝⠕⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢝⢽⢝⢿⢿⢕⢽⢅⠅⢕⢽⢿⢿⣿⣿⣿⣿⣿⣿⢿⣿⢿⢿⠕⢕⢵⢽⢽⢽⢿⢟⢿⣿⢿⢿⢿⢝⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢝⢝⢟⢝⢿⢿⢽⢿⢕⢅⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢕⢽⢽⢽⢿⢿⢽⢿⢽⢿⢿⢿⢿⢽⠝⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢝⢟⠝⢽⢿⢿⢿⢝⢕⢝⢕⢝⢝⢝⢝⢽⢽⢽⢝⢝⢽⢽⢿⢿⢿⢿⢿⢿⢟⢽⢿⢿⢿⢽⢝⢕⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢝⢝⢝⢝⢽⢿⢿⢿⢝⢝⢝⢝⢽⢽⢿⢿⢿⢟⢝⢽⢽⢿⢿⢿⢿⢽⢿⢿⢽⢿⢿⢿⢿⢝⢝⢝⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢝⢕⢝⢝⢝⢽⢽⢽⢕⢝⢕⢝⢝⢝⢝⢽⢽⢽⢽⢿⢿⢿⢿⢿⢿⢽⢟⢽⢽⢿⢝⢝⠕⢕⢝⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢕⢕⠝⢝⢝⢽⢿⢿⢿⢽⢽⢝⢝⢽⢽⢿⢿⢿⢿⢿⢿⢿⢿⢿⢽⢽⢝⢿⢽⢿⢝⠝⢕⢝⢝⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢝⠕⢝⢝⢽⢿⢽⢿⢿⢿⢽⢽⢿⣿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢟⢽⢝⢝⢝⢝⢕⢝⢝⢝⠅⠁⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠕⢝⢝⢝⢝⢿⢿⢽⢟⢽⢿⣿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢟⢝⢝⢝⢝⠝⠝⢕⢝⢝⢝⢝⠅⠁⠁⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠕⢝⢽⢝⢽⢿⢽⢿⢿⢿⢟⢿⢿⢿⢿⢿⢿⢟⢽⢟⢝⢝⠝⠕⠕⠕⢕⢝⢝⢝⢝⠅⠁⠁⠁⠁⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠕⠕⢽⢝⢝⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢿⢽⢽⠝⢝⠕⠕⠕⠕⢕⠕⠕⢝⢝⢝⢝⠅⠁⠑⠁⠅⠁⠁⠅⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠁⠁⠀⠀⠁⠕⠅⠝⢝⢝⢝⢿⢽⢝⠝⢝⢝⢝⢝⢝⢝⠝⠝⠕⠕⢕⠕⠕⠕⠕⠕⢕⢝⢝⠝⠁⠁⠁⠁⠅⠁⠑⠕⠅⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠁⠁⠁⠑⠕⠕⠕⠕⠝⠝⢝⠕⠕⠕⠝⠕⠝⠕⠕⠅⠕⠕⢕⠕⠕⠕⢕⢕⢕⢕⠝⠅⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠅⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠁⠁⠁⠑⢕⢕⠕⠅⠕⠅⠕⠅⠅⠅⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⢕⢕⢝⢝⠝⠁⠁⠀⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠁⠁⠁⠁⠐⢝⢝⢕⠕⠅⠅⠕⠕⠕⠕⠕⠕⠕⠕⢕⠕⢕⢕⠕⢕⢕⢝⢝⢝⠝⠁⠁⠁⠁⠁⠁⠀⠁⠁⠁⠁⠁⠅⠁⠁⠁⠁⠁⠁⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠁⠁⠑⠅⠀⠀⢕⢝⢝⢕⠕⠕⠕⠕⠕⢕⢕⢕⠕⢕⠕⠕⠕⢕⢕⢕⢝⢝⢽⠅⠁⠁⠁⠁⠀⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⢅⢕⢕⠕⢕⢕⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠁⠁⠀⠁⠁⠄⠁⠕⢝⢝⢝⢕⠕⠕⠕⢕⢝⢝⢝⢕⢕⢕⢕⢕⢝⢝⢝⢝⢝⠅⠁⠁⠁⠁⠀⠁⠁⠁⠁⠁⠁⢁⢅⢕⠕⠕⢕⢕⢝⢝⢕⢝⢅⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠁⠁⠁⠁⠁⠁⠑⠕⢝⢝⢝⢝⠕⠕⠕⢕⢝⢝⢝⢕⢝⢝⢝⢝⢝⢝⢝⢽⠅⠁⠁⠁⠁⠁⠁⠁⠁⠁⢁⢕⠕⢕⢕⠕⢕⢕⢝⢝⢕⢕⠝⢝⢝⢝⢕⢄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠕⠕⠅⠁⠁⠁⠁⠁⠁⠁⠁⠁⠑⢕⢝⢝⢝⢕⢕⢕⢕⠝⢝⢝⢝⢝⢝⢝⢝⢽⢽⢽⠝⠁⠁⠁⠁⠁⠁⠁⠁⢁⢕⢕⢕⠕⢕⠕⢕⠕⢝⢝⢕⢝⢕⢕⢝⢕⢕⢕⢝⢝⢕⢄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠕⠕⠕⠕⠕⠅⠁⠁⠁⠁⠁⠁⠁⠁⠁⠑⢕⢝⢝⢝⢕⢕⢝⢕⢕⢝⢝⢝⢽⢽⢽⢽⢿⠝⠁⠁⠁⠁⠁⠀⠁⠁⠐⢕⠝⢝⢕⢕⠝⢝⢕⢕⢕⢕⢕⢝⢝⢕⢕⢕⢝⠕⢝⢝⢝⢝⢝⢝⢕⢄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⢔⠝⢕⠕⠕⢕⠕⢕⠕⠕⠅⠁⠁⠁⠁⠁⠁⠁⠁⠁⢕⢝⢝⢝⢕⢝⢝⢝⢝⢝⢽⢽⢽⢝⢽⢿⠟⠁⠁⠁⠁⠁⠀⠁⠁⠁⢕⢕⢕⠝⢝⠕⢝⢝⢕⢝⢕⢝⢝⢕⢕⠝⢕⢕⢕⠕⠝⠝⢝⢝⢕⢝⢝⢝⢝⢝⢕⢄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⢔⢝⢕⠕⢕⢕⠕⢕⢕⠕⢕⠕⠕⠕⠕⠁⠁⠁⠁⠁⠁⠁⠁⠁⠑⢝⢝⢝⢝⢕⢝⢝⢝⢝⢝⢝⢝⢽⢽⢝⠅⠁⠁⠁⠁⠁⠁⠁⠁⢐⢕⠕⢕⠕⢕⢕⢝⢝⢝⠝⢝⢝⢕⢕⢝⢕⢝⢕⢕⢕⢕⠝⢕⠝⠕⢝⢝⠕⢝⢝⢝⢝⢝⢝⢕⢄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠝⢕⠕⠕⠕⠕⢕⠕⠕⠕⠕⠕⢕⢕⠕⠕⠕⠕⠅⠁⠁⠁⠁⠁⠁⠁⠁⠁⢝⢝⢝⢝⢕⢕⢝⢝⢝⢝⢝⢝⢝⢝⠕⠁⠁⠁⠁⠁⠁⠁⠁⠁⢕⢝⢝⢕⢕⢕⢝⠝⢕⢝⢝⢕⢕⢕⢕⢕⢝⢕⢝⢕⢝⢝⠕⢕⢕⢕⢝⢕⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢵⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢔⠝⠕⢝⢕⢕⢕⠕⠕⠕⠕⠕⠕⢕⠕⠕⠕⢕⠕⢕⠕⠕⠅⠀⠁⠁⠁⠁⠁⠁⠁⠁⠕⢕⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⠝⠁⠁⠁⠁⠁⠁⠁⠁⠁⢐⠕⢕⠕⢝⢝⠝⠕⢕⢕⢝⢝⢝⢝⢕⢕⢕⢕⢝⠝⠕⢕⢕⠕⢝⢕⢕⢝⢕⢝⢝⢕⢕⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢵⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⢝⢕⢕⢕⠕⢕⠝⢕⠕⠕⠕⢕⠕⠕⢕⢕⢕⢕⠕⠕⢕⠕⠕⠕⠁⠀⠀⠁⠁⠁⠁⠁⠁⠁⠑⢝⢕⢝⢝⢝⢝⢝⢝⢝⢝⢝⠝⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⢕⢕⠕⢕⢝⢝⢕⢝⢝⢝⢕⢕⢕⠕⢕⢕⢝⢕⢝⢕⢝⠕⢕⢝⢕⠝⢕⢝⢕⢝⢝⢕⢝⢝⢝⢝⢕⢝⢝⢝⢝⢝⢝⢝⢝⢕⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⢝⠕⠕⢕⢕⢕⠕⠕⢕⠕⠕⠕⠕⠕⠕⠕⢕⢕⠕⠕⠝⠕⠕⠕⠕⠕⠁⠁⠁⠀⠁⠁⠁⠁⠁⠁⠁⠁⠙⠙⠝⠝⠝⠝⠝⠝⠝⠟⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⢕⢕⠕⢝⠕⢕⢝⢕⢝⢕⢝⢕⢝⢝⢕⠝⢝⢕⢝⢝⢕⢕⢕⢕⢕⠕⢝⢕⢝⠝⢝⢝⠝⢝⢝⢝⢝⢝⢝⢝⢝⢕⢝⢝⢝⢝⢝⢝⢝⢵⢄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⢝⢕⢝⢕⢕⠕⠕⢕⢕⠕⠕⠕⢕⠕⠕⠕⠕⢕⠕⠕⢕⠕⢕⢕⢕⠕⠕⠕⠁⠁⠁⠁⠀⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠀⠁⠁⠁⠁⠁⠁⠕⢕⢕⢝⢝⢕⠕⢕⢝⢝⢕⢝⠕⢝⢕⢕⢝⢝⢕⢝⠕⢕⢝⠕⢕⢕⠕⢕⢝⢕⢝⢝⢕⢝⢝⢝⢝⢝⢝⢝⢕⢝⢝⢝⢝⢝⢝⢝⢕⢝⢝⢵⢤⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠕⢕⢕⢕⢕⢕⢕⢕⢕⢕⠕⠕⠕⢕⠕⠕⠕⠕⢕⠕⠕⠕⢕⠕⢝⢝⠕⢕⠕⠕⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠅⠁⠁⠁⠁⠁⠁⠁⠁⠁⠕⠕⢕⢕⢕⢝⠕⠕⢝⢝⢝⠝⢝⢕⢕⠝⢕⢕⢝⠕⠝⠕⠕⢝⢝⢝⢕⢕⢝⢝⢝⢝⢝⢝⢕⢝⢝⢝⢝⢝⢕⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⠅⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠕⢝⢕⢕⢕⠕⢕⠕⠕⢝⠕⢕⠕⠕⠕⠅⠑⠕⠕⠕⠕⠕⢕⢝⠕⢝⢕⢕⠕⠝⢕⠅⠀⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠅⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠀⠁⠁⠁⢕⢕⠕⢕⢕⢕⢕⢝⢕⢝⠝⢝⢝⠝⠕⠕⠝⠑⢁⠅⢕⢕⢝⢝⢕⢕⢕⢕⢕⢝⢕⢝⢕⢝⢝⢝⢝⢝⢕⢝⢕⢝⢝⢝⢝⢝⢝⢕⢝⢝⢝⢝⢝⢝⢝⢝⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠕⢕⢕⠕⢕⢕⠕⠕⢕⠕⠕⠕⢕⠕⠕⠕⠕⠕⠅⠑⠕⠕⠕⠕⢕⠕⢕⠕⢕⢕⢕⠕⠅⠀⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⢕⠅⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⢕⠕⢕⢕⢕⢕⢝⢝⢝⢝⢕⢕⠕⠕⠁⠁⠅⠕⠕⢕⢝⠕⢕⢝⢝⢕⢝⠝⢕⢕⢝⢕⢕⢝⢝⢝⢝⢝⢝⢕⢝⢕⢕⢕⢝⢝⢕⢝⢝⢝⢵⢝⢝⢝⢝⢝⢝⢅⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠕⢕⠕⠕⢕⠕⢕⠕⠕⠕⠕⢕⠕⢕⠕⠕⠕⠕⠕⠕⠅⠑⠕⢕⠕⢕⠕⠕⠕⢕⠕⠕⠅⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⢝⢕⢅⠕⠅⠁⠁⠅⠁⠁⠁⠁⠁⠁⠁⠁⠁⠑⠕⢕⢝⢝⢕⢝⢝⢕⢕⠝⠕⢝⢕⢕⢕⠕⢕⢕⢕⢝⢝⢝⢝⢝⢕⢝⠝⢕⢕⢕⢝⢝⢝⢕⢝⢝⢝⢝⢕⢝⢝⢝⢝⢝⢝⢽⢝⢕⢝⢕⢝⢕⢝⢝⢝⢝⢝⢝⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠕⠕⠕⠕⢕⢕⢕⠕⠕⠕⠕⠕⠕⠕⠕⠕⢕⢕⠕⠕⠕⠕⠕⠕⢕⢝⠕⢕⢕⠕⠕⢕⢕⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠑⢝⢝⠅⠁⠅⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠕⠕⢕⢝⠕⢕⢕⢝⢝⢝⢝⢕⢕⢝⢝⢝⠕⢕⢕⢕⢕⢕⢝⠕⢕⠝⢝⢝⢝⢕⢝⢕⢕⢝⢝⠝⢕⢕⢝⢕⢝⢝⢝⢝⢝⢝⠝⢕⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⠅⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢕⢕⠕⠕⢕⠕⠕⠝⠕⠕⠕⢕⢕⢕⠕⢕⢕⢕⢕⢕⠕⢕⢕⠕⠕⢕⢕⢕⠕⢕⠕⠕⢕⠕⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⢝⢝⢕⠅⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⢑⠕⠕⢕⢕⢕⠝⢕⢝⠕⢕⢝⢝⢝⠕⢝⢝⢝⢝⢝⢕⢝⢝⠝⢕⠝⢕⢕⢝⢝⢝⢕⢝⢝⢕⢝⢕⢕⢝⢝⢝⢝⢝⢝⢝⢝⢝⠕⢕⢝⢝⢝⢕⢕⢝⢝⢝⢝⢝⢝⠅⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠕⢕⠕⢕⢕⢕⠕⢕⠕⠕⠕⢕⠕⠕⢕⠕⢝⠕⢕⢕⢕⢕⠕⢕⠕⠕⠕⠕⢕⢕⠕⠕⠕⠀⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠑⢝⢝⠕⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⢝⠕⢕⢝⠝⢝⢝⢕⢝⢝⢝⢝⢝⠝⢕⢝⢝⢕⠝⢕⢝⢝⢝⠕⠝⢕⢕⢝⢝⢝⢕⢕⢕⢝⢝⢝⢕⢝⢝⢝⢝⢝⢕⢝⢝⢝⢕⢕⢝⢝⢝⠝⢝⢝⢝⢕⢝⢝⢝⢝⠅⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⢕⠕⠕⠕⠕⢕⠕⠕⠕⠕⢕⠕⢕⠕⠕⠕⠕⢕⠕⠕⠕⢝⢕⢕⢕⢕⠕⢕⢕⠕⠕⠕⠅⠀⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⢝⠝⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⢕⠕⢝⢝⢕⢕⢕⢝⠕⢝⢝⠝⢕⢝⢝⢕⢝⢝⢝⢝⢕⢝⠝⠅⠕⢕⢕⠝⢕⢝⢝⢝⢝⢕⢝⢝⢝⢕⢝⢝⢝⢝⢝⢕⢝⢝⢕⢝⢝⢝⢝⢕⢝⢝⢝⢝⢝⢝⢝⢝⠕⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠕⢕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⢕⢕⠕⢕⢕⠕⢝⠕⠕⢕⢕⠕⠕⠕⢕⢕⢝⢕⢕⢕⠕⠅⠀⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠑⢝⢑⠅⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⢕⢝⢕⢕⢕⢕⢝⢕⢝⢝⢕⢝⢕⠕⠕⢕⠝⢝⠝⢝⢝⢝⠝⠅⢕⢕⠝⠕⢕⢕⢕⢝⢕⢕⢝⠕⢝⢕⢕⢕⢝⢝⢕⢝⢕⢝⢝⢕⢝⢕⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢕⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢕⠕⠕⠕⠕⠕⠕⠕⠕⢕⢕⠕⠕⠕⢕⠕⠕⢕⢕⠕⢕⢕⢕⠕⢕⢕⠕⠕⢕⢕⠕⢕⢕⠕⠅⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠑⠕⠕⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠕⠕⢕⠝⢝⢝⢝⢕⢕⢝⢝⢝⢕⢝⢕⢕⢝⢝⢕⢕⢝⢝⠅⢕⢕⢝⠕⢝⢕⢕⢕⢝⢝⠕⢝⢕⢝⢕⢕⢝⢕⢝⢕⢝⢝⢕⢝⢝⢝⢝⢝⢕⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠕⠕⠕⠕⠕⢕⢕⠕⠕⢕⠕⠕⢕⠕⠕⠕⠕⢕⢕⠕⠕⢝⢕⠕⠕⠕⠕⢕⠕⢕⠕⢕⠕⠅⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠐⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⢕⢕⢕⠕⢕⢕⠕⢝⢝⢕⢝⢝⢕⢝⢝⢝⢝⢕⢝⢕⢝⢝⠕⢕⠕⠝⠕⠕⢕⠕⢝⢝⢝⢝⢝⢝⠝⢝⢝⢕⢝⢝⢽⢕⢝⢕⢕⢝⢝⢕⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠕⠕⠕⠕⠕⠕⢕⢕⠕⠕⠕⠕⢝⠕⠕⠕⠕⢕⠕⢝⢕⢕⢕⠕⠕⠕⠝⠕⢕⠕⢕⢕⠕⠅⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠅⠅⠀⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠕⢕⠕⢕⢕⢝⢝⢝⢝⢕⢝⢕⢝⢝⢝⢕⢝⢝⢵⢝⢝⠕⢕⢝⢕⢝⢕⠕⠕⢕⢝⢝⠕⢝⠝⢕⢝⢕⢝⢝⢝⠝⢝⢕⢕⢝⢕⢝⢝⢕⢕⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⢕⠕⠕⠕⢕⢕⢝⢕⠕⠕⢕⠕⠕⠕⠕⢕⢕⠕⠕⠕⠅⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠕⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⢑⢕⠕⢕⢝⢕⢕⠝⢝⢕⢝⢕⢝⢝⢕⢝⢝⢕⢝⢕⢝⠕⢕⢝⢕⢝⢕⠕⢕⢕⢝⢝⢕⢕⠝⢕⢝⢝⢝⢕⢝⢝⢝⢝⢝⢕⠕⢝⢝⢕⢝⢝⢝⢕⢝⢝⢝⢝⢕⢝⢝⢝⢝⢝⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢝⠕⠕⠕⠕⠕⠕⠝⠕⢕⠕⠕⠕⠕⠕⢕⠕⢕⠕⢕⢕⠕⢕⠕⢕⠕⢕⠕⢕⠕⠕⢕⢕⢕⠕⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⢁⠕⠁⠀⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⢕⠝⢝⢕⢕⢕⢝⢝⢕⢕⢝⢝⢕⢝⢕⢝⢕⠕⢕⢕⠕⠑⢝⢝⢝⢝⢕⠕⠕⢝⢝⢝⢝⠕⢝⢕⢝⢕⢝⢝⢝⢝⢝⢝⢕⢝⠕⠝⢝⢕⢝⠝⢕⢝⢝⢝⢝⢝⢕⢝⢝⢝⢝⢝⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⢕⠕⢕⠕⠕⢝⠕⠕⢕⠕⠕⢕⢕⢕⠕⠕⢕⢕⢕⢝⠕⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠅⠁⠁⠁⠁⠁⠁⠁⠁⠁⢑⢕⢕⢕⢕⠕⢝⠝⢕⢝⢝⢕⢝⢝⢝⢝⢝⢕⢝⢝⠝⢅⢕⢝⢕⢕⢝⢕⢕⢕⢝⢝⢝⠕⢕⢕⢝⠕⢕⢝⢝⢝⠕⢝⢝⠕⢝⢕⢝⢕⢝⢝⢕⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢽⢝⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢕⠕⠕⠕⠕⠕⢕⢕⠕⠕⠕⠕⠕⢕⠕⢕⢝⠕⢕⠕⠕⢕⢕⠕⠕⢕⢕⠕⠕⢕⢕⢝⠕⢕⠕⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠀⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠕⢕⠝⢕⢕⢝⢕⢕⢝⢕⢝⢕⢝⢕⢕⢕⢕⢕⢝⠝⠅⢝⢕⢝⢝⢕⠕⢕⠕⢕⢕⢝⢕⠕⢕⠝⢝⢕⢝⢝⢝⠝⢕⢕⢕⠕⠝⢕⢝⢝⠕⢕⢝⢝⢝⢕⢝⢝⢝⢝⢝⢝⢝⢝⢝⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢕⠕⢕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⢕⠕⢕⠕⢕⠕⢕⠕⠕⢕⢕⢕⠝⢕⢝⢕⠕⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠀⠁⠁⠁⠁⢑⠕⠕⢕⠕⢕⢕⢕⠝⢕⢝⢕⢕⢕⢝⠝⢕⢕⢕⠝⠅⠕⢕⢕⢝⠕⢝⢕⠕⠕⢕⢝⢝⢝⠕⠝⢝⢝⢝⢕⢕⢝⢕⢝⠝⢝⢕⠕⢝⢝⢕⢝⠝⢽⢝⢝⢝⢝⢝⢝⢵⢕⢝⢝⢝⢝⢕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠕⢕⢕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⢕⠕⢕⢕⠕⢕⠕⢕⠕⢕⠕⢕⢕⠕⢕⠕⠕⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠅⠁⠁⠁⠁⠁⠁⠁⠁⠁⢕⠕⠝⠝⢝⢝⢕⠕⢕⢕⠝⠕⢝⢝⢝⢝⠝⢝⠕⠅⠕⢕⠕⢝⢝⢕⢕⢝⠕⢕⢕⢝⢕⠝⢕⢕⢝⢕⢕⢝⢕⢕⠝⢕⢕⠕⢕⢕⢕⢕⢕⢕⢝⢝⢝⢝⢝⢝⢝⢕⢝⢝⢝⢝⢝⢝⢝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠕⠕⢕⠕⠕⠕⠕⠕⠕⠕⠕⠕⢕⠕⠕⠕⢕⢕⠕⠕⠕⠕⢕⢕⠕⠝⠕⠕⠕⠕⠕⠕⢝⠕⠕⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠅⠅⠁⠁⠁⠁⠁⠁⠁⠁⠁⢕⢕⢕⠕⢝⠕⢕⢕⢕⢝⢕⢝⢝⠝⢝⢝⢕⠝⠅⠕⢕⢝⢕⢕⢕⢕⠝⠕⠕⢕⢕⢝⢝⢕⢕⢕⢕⢕⠝⠝⢕⢕⢝⢕⢝⠕⠕⠕⢝⢝⢕⢝⢝⢝⢕⢕⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⢕⢕⢝⠕⠕⠕⢕⢝⠕⢕⠕⠕⠕⠕⠕⠕⢕⢝⠕⠕⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⢕⠝⢕⢕⢝⠕⢕⢝⢝⢕⢕⢝⢝⢕⢝⢝⢝⢝⠅⢕⢝⢝⠝⢕⢝⢝⢝⢕⢝⢕⢕⢝⢕⢝⠕⢕⢝⢝⢕⠕⢝⢕⢕⢕⢝⢝⠕⢕⢕⢕⠝⢕⢝⢕⢝⢝⢝⢝⢕⢝⢝⢝⢝⢝⢝⢝⢝⢝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢕⠕⠕⠕⠕⢕⠕⠕⠕⠕⠕⠕⠕⠕⠕⢕⠕⠕⢕⢕⠕⠕⢝⢕⢕⢕⠕⢕⠕⠕⠕⢕⠕⢕⠕⠅⠀⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⢕⠕⢕⢝⠝⢕⢝⢕⢝⢕⢝⢝⢕⢝⢝⢕⢕⠅⢕⢕⠝⢕⢕⢝⢝⢝⢕⢝⠕⢕⢕⢕⢝⢕⠕⢕⢕⢝⢕⢕⢕⠕⢝⢕⢝⢝⠅⢝⢝⠝⢕⢝⢝⢝⢝⢝⢝⢝⢝⢝⢕⢽⢝⢝⢝⢝⢝⢝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠕⠕⠕⢕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠝⢕⠕⢕⠕⢕⢕⠕⢝⠕⢕⠕⢕⠕⠝⢕⠅⠀⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⢑⠝⢕⢕⢕⠕⢝⢝⢕⢝⢕⢝⢕⢝⢝⢝⢝⠕⢕⢝⢝⢕⢝⠕⢕⢕⢝⢝⠝⢕⠕⢝⢕⢕⠕⠕⢝⢕⠝⢕⠕⢕⢕⢝⢕⢕⢕⠕⠕⢕⢕⠕⢝⢕⢝⠝⠝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠕⠕⠕⠕⢕⠕⠕⠕⠕⠕⠕⠕⠕⠕⢕⢕⠕⠕⠕⠕⠕⠕⠕⠝⢕⢕⠕⢕⠕⠕⠕⢕⠕⢕⠕⠅⠀⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠅⠁⠁⠁⠁⠁⠁⠁⠁⢕⠕⢝⢕⠕⠝⢕⢕⢝⢕⢕⢝⢕⢝⢝⢝⠝⢁⠝⢝⠝⢝⢝⢝⢕⢝⢕⢝⠝⢕⢕⢕⢝⢕⠕⠕⠝⢝⢝⢝⠕⠝⢕⢕⢕⢕⠝⢕⢕⠕⢝⢕⢝⢕⢝⢝⢕⢝⢝⢕⢝⢝⢽⢝⢝⢝⢝⢝⢝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢕⠕⢕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⢕⠕⠕⢕⢕⠝⢕⠕⠕⠕⢕⠕⠕⠕⢕⠅⠀⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠅⠅⠁⠁⠁⠁⠁⠁⠁⠁⠕⢕⢕⢕⢕⠕⢕⢕⢕⠕⢕⢝⢝⢝⢝⠕⠁⠕⠕⢕⢕⢝⢕⢕⢕⢝⢝⢕⠕⠕⢝⢕⢕⢝⢕⢕⢕⠕⠕⠕⠝⢕⢕⢕⠕⠕⠕⢕⢕⢕⢝⢝⢝⢝⢝⢝⢕⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⢕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⢕⠕⢕⠕⠕⠕⠕⠕⢝⢕⠕⢕⠕⠕⢕⠕⠕⢕⢕⠕⠅⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⢑⠕⢕⢕⢕⠕⢕⢝⢕⢝⢕⠕⢝⢝⢕⠕⠁⠕⢝⢝⢝⢝⢕⢝⢝⢝⢝⢝⠕⠕⢕⢝⢝⢝⢝⠕⢕⢕⢕⢕⠕⢕⢕⠕⢕⠕⢕⠕⠝⢝⢕⢝⢝⢝⢝⢝⢕⢝⢝⢝⢕⢝⢕⢝⢝⢝⢝⢝⢝⢝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠕⠕⢕⠕⠕⢕⠕⠕⠕⠕⠕⠕⠕⠕⠕⢕⢕⠕⠕⠕⢕⠕⠕⠕⢝⢝⠕⢕⠕⢕⠕⠕⠕⢕⢝⠕⠕⠀⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⢕⠕⢕⢕⢝⢕⢕⢕⢝⢕⢝⢕⢝⢝⠕⠁⠕⢕⠝⢝⢝⢕⢕⠝⢕⢕⢝⢝⠝⢝⠕⢝⢕⢕⠝⢕⢕⢝⢕⠕⠕⠝⢕⢕⢝⠕⠕⠕⢕⢕⢝⠕⢝⠝⢕⢕⢝⢝⢕⢝⢝⢝⢝⢝⢝⢝⢝⢝⢕⢝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠕⠕⠕⠕⢕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⢕⠕⠕⠕⠕⠕⠕⠕⠝⢝⢕⠕⢕⠕⠕⠕⢕⢕⠕⠕⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠑⠕⢕⠕⢕⢝⠕⠝⢝⢝⢕⢝⢝⢕⠝⠅⢕⢕⠝⢕⢕⢝⢕⢝⢕⢕⢕⢕⢝⢕⢕⢕⢝⢝⢕⢕⠕⠕⢕⢕⠕⠕⢕⠕⢕⠕⢝⢕⠕⢝⠕⠝⠕⢝⢝⢕⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⠝⢝⢝⢝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢝⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⢕⠕⠕⠕⠕⠕⠕⠕⠝⢕⢝⢕⢕⢕⠕⠕⢕⠕⠕⠕⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⢕⢕⠕⢕⢕⢕⠕⢕⢝⢝⢝⢝⢝⠕⠅⢕⢕⢕⢕⢕⢝⢕⠕⠝⢕⢝⢕⢝⠝⠕⢕⢕⢝⢝⢝⢝⢕⢕⢕⢝⢝⢕⠕⠕⢕⠕⢕⢝⠕⠕⢕⠕⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢕⢝⢝⢝⢝⢝⢝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢕⢕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠅⢕⢕⢕⠝⢕⢕⠕⠕⠕⠕⢕⠅⠀⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⢕⠕⠝⢝⢝⢕⢕⠝⢝⢝⢕⢝⢝⠅⠑⠕⢕⠕⢝⢕⢕⢕⢕⢝⢝⢕⠕⢝⢕⠕⢝⢕⢝⢕⢕⢕⠕⢕⢕⢕⢕⢕⠕⢕⢕⢝⢕⠕⠕⠕⢕⢕⢝⢝⢝⢝⢝⢝⢕⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⢝⠕⠕⢕⢕⢕⠕⢕⠕⢕⠕⠅⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⢑⠕⠝⢕⢝⢕⢝⠕⠕⢕⢝⢕⢝⠅⠁⢕⠕⠝⢕⢕⢕⢝⢕⢝⢕⢕⠕⢝⢕⢕⢕⢕⢝⢝⢕⢝⠕⢕⢕⢕⢝⠕⢕⢕⢝⢕⠕⢝⢕⠅⢕⠕⢕⢝⠝⢕⢝⠕⠕⢝⢝⢕⢕⢝⢝⢝⢽⢝⢝⢝⢝⢝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠕⢕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠅⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⠕⢕⠕⢕⠕⠕⢕⢕⢕⠕⠕⠕⠀⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⢕⠝⢕⢝⢕⠕⢕⢕⢕⢝⢝⢕⠕⠁⠕⢕⠕⠕⢝⢕⢝⠕⢕⢝⠕⢕⢕⢕⢝⢕⢕⢝⢝⢕⠕⢕⠕⢕⠕⢕⢝⢕⢕⢕⠝⠝⢕⢕⢕⠕⢕⠕⢕⢕⢕⢕⢕⢕⠝⢝⢕⢕⢝⢝⢝⢝⢝⢝⢝⢝⢝⢝