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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def all_casings(input_string):
 """ Permute all casings of a given string. A pretty algorithm, via @Amber http://stackoverflow.com/questions/6792803/finding-all-possible-case-permutations-in-python """

    if not input_string:
        yield ""
    else:
        first = input_string[:1]
        if first.lower() == first.upper():
            for sub_casing in all_casings(input_string[1:]):
                yield first + sub_casing
        else:
            for sub_casing in all_casings(input_string[1:]):
                yield first.lower() + sub_casing
                yield first.upper() + sub_casing