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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 parse_expr(expr, local_dict=None):
 """ Parses a json-object created with 'expr_to_json' into a Sympy expression. If a local_dict argument is passed, symbols with be looked up by name, and a new symbol will be created only if the name is not in local_dict. """

    if local_dict is None:
        local_dict = {}
    if expr["type"] == "Add":
        return add([parse_expr(arg, local_dict) for arg in expr["args"]])
    elif expr["type"] == "Mul":
        return mul([parse_expr(arg, local_dict) for arg in expr["args"]])
    elif expr["type"] == "Pow":
        return Pow(parse_expr(arg, local_dict) for arg in expr["args"])
    elif expr["type"] == "Symbol":
        try:
            return local_dict[expr["name"]]
        except KeyError:
            return symbolics.Symbol(expr["name"])
    elif expr["type"] == "Number":
        return symbolics.sympify(expr["value"])
    else:
        raise NotImplementedError(expr["type"] + " is not implemented")