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def expand_tuples(L):
    """
    >>> from sympy.multipledispatch.utils import expand_tuples
    >>> expand_tuples([1, (2, 3)])
    [(1, 2), (1, 3)]

    >>> expand_tuples([1, 2])
    [(1, 2)]
    """
    if not L:
        return [()]
    elif not isinstance(L[0], tuple):
        rest = expand_tuples(L[1:])
        return [(L[0],) + t for t in rest]
    else:
        rest = expand_tuples(L[1:])
        return [(item,) + t for t in rest for item in L[0]]


# Taken from theano/theano/gof/sched.py
# Avoids licensing issues because this was written by Matthew Rocklin
def _toposort(edges):
    """ Topological sort algorithm by Kahn [1] - O(nodes + vertices)

    inputs:
        edges - a dict of the form {a: {b, c}} where b and c depend on a
    outputs:
        L - an ordered list of nodes that satisfy the dependencies of edges

    >>> from sympy.multipledispatch.utils import _toposort
    >>> _toposort({1: (2, 3), 2: (3, )})
    [1, 2, 3]

    Closely follows the wikipedia page [2]

    [1] Kahn, Arthur B. (1962), "Topological sorting of large networks",
    Communications of the ACM
    [2] https://en.wikipedia.org/wiki/Toposort#Algorithms
    """
    incoming_edges = reverse_dict(edges)
    incoming_edges = {k: set(val) for k, val in incoming_edges.items()}
    S = {v for v in edges if v not in incoming_edges}
    L = []

    while S:
        n = S.pop()
        L.append(n)
        for m in edges.get(n, ()):
            assert n in incoming_edges[m]
            incoming_edges[m].remove(n)
            if not incoming_edges[m]:
                S.add(m)
    if any(incoming_edges.get(v, None) for v in edges):
        raise ValueError("Input has cycles")
    return L


def reverse_dict(d):
    """Reverses direction of dependence dict

    >>> d = {'a': (1, 2), 'b': (2, 3), 'c':()}
    >>> reverse_dict(d)  # doctest: +SKIP
    {1: ('a',), 2: ('a', 'b'), 3: ('b',)}

    :note: dict order are not deterministic. As we iterate on the
        input dict, it make the output of this function depend on the
        dict order. So this function output order should be considered
        as undeterministic.

    """
    result = {}
    for key in d:
        for val in d[key]:
            result[val] = result.get(val, tuple()) + (key, )
    return result


# Taken from toolz
# Avoids licensing issues because this version was authored by Matthew Rocklin
def groupby(func, seq):
    """ Group a collection by a key function

    >>> from sympy.multipledispatch.utils import groupby
    >>> names = ['Alice', 'Bob', 'Charlie', 'Dan', 'Edith', 'Frank']
    >>> groupby(len, names)  # doctest: +SKIP
    {3: ['Bob', 'Dan'], 5: ['Alice', 'Edith', 'Frank'], 7: ['Charlie']}

    >>> iseven = lambda x: x % 2 == 0
    >>> groupby(iseven, [1, 2, 3, 4, 5, 6, 7, 8])  # doctest: +SKIP
    {False: [1, 3, 5, 7], True: [2, 4, 6, 8]}

    See Also:
        ``countby``
    """

    d = dict()
    for item in seq:
        key = func(item)
        if key not in d:
            d[key] = list()
        d[key].append(item)
    return d