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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 group_dict_by_value(d: dict) -> dict: """ Group a dictionary by values. Parameters d : dict Input dictionary Returns ------- dict Output dictionary. The keys are the values of the initial dictionary and the values ae given by a list of keys corresponding to the value. {3: [2], 2: [1], 1: [3]} {3: [2, 12], 2: [1], 1: [3, 10]} """

    d_out = {}
    for k, v in d.items():
        if v in d_out:
            d_out[v].append(k)
        else:
            d_out[v] = [k]
    return d_out