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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 multigrad_dict(fun):
    "Takes gradients wrt all arguments simultaneously,"
    "returns a dict mapping 'argname' to 'gradval'"

    import funcsigs
    sig = funcsigs.signature(fun)

    def select(preds, lst):
        idx = lambda item: next(
            (i for i, pred in enumerate(preds) if pred(item)), len(preds))
        results = [[] for _ in preds] + [[]]
        for item in lst:
            results[idx(item)].append(item)
        return results

    is_var_pos = lambda name: sig.parameters[name].kind == sig.parameters[name].VAR_POSITIONAL
    is_var_kwd = lambda name: sig.parameters[name].kind == sig.parameters[name].VAR_KEYWORD
    var_pos, var_kwd, argnames = select([is_var_pos, is_var_kwd], sig.parameters)

    todict = lambda dct: {key:dct[key] for key in dct}

    def apply_defaults(arguments):
        defaults = {name: param.default for name, param in sig.parameters.items()
                    if param.default is not param.empty}
        return OrderedDict((name, arguments[name] if name in arguments else defaults[name])
                           for name in sig.parameters)

    def gradfun(*args, **kwargs):
        bindings = sig.bind(*args, **kwargs)

        args = lambda dct: tuple(dct[var_pos[0]]) if var_pos else ()
        kwargs = lambda dct: todict(dct[var_kwd[0]]) if var_kwd else {}
        others = lambda dct: tuple(dct[argname] for argname in argnames
                                   if argname not in var_kwd + var_pos)

        newfun = lambda dct: fun(*(others(dct) + args(dct)), **kwargs(dct))

        argdict = apply_defaults(bindings.arguments)
        grad_dict = grad(newfun)(dict(argdict))
        return OrderedDict((argname, grad_dict[argname]) for argname in argdict)

    return gradfun