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<html lang="en">
<head>
    <meta charset="UTF-8">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <title>C///</title>
</head>
class Graph:
    def __init__(self, objects, arrows):
        self.objects = objects  # Sequence of objects
        self.arrows = arrows    # Map[name] ->pair(object, object)

    def source(self, x):
        return self.arrows[x][0]

    def target(self, x):
        return self.arrows[x][1]

    def get_dual(self):
        objects = self.objects
        arrows = dict([(arrow, (tgt, src))
                       for (arrow, (src, tgt)) in list(self.arrows.items())])
        return self.__class__(objects, arrows)


class Cat:
    # Category presented by a graph (with objects and generators) and relations.
    def __init__(self, graph, relations):
        # category is defined by the parameters:
        #    graph.objects: sequenceof(O)
        #    graph.arrows: dict mapping(A, pairof(O in objects))
        #    relations: sequence(pairof(sequence(A), sequence(A)))
        self.graph = graph
        self.relations = relations

    def get_dual(self):
        graph = self.graph.get_dual()
        relations = dual_relations(self.relations)
        return self.__class__(graph, relations)


class Functor:
    def __init__(self, fo, fa, src=None, tgt=None):
        self.fo = adapt_function(fo)
        self.fa = adapt_function(fa)
        self.src = src
        self.tgt = tgt


class Function:
    def __init__(self, map, src, tgt):
        f = getattr(map, '__getitem__', None)
        if callable(f):
            pass
        else:
            f = map
            if not callable(f):
                raise TypeError(
                    'Function: map is neither callable or indexable')
        self.f = f
        self.src = src
        self.tgt = tgt

    def __getitem__(self, *args):
        return self.f(*args)

    def __call__(self, *args, **kwargs):
        return self.f(*args, **kwargs)

    def __str__(self):
        return '%s(%s, %s, %s)' % (self.__class__, self.src, self.tgt, self.f)

    def asdict(self):
        return dict([(x, self[x]) for x in self.src])

    def items(self):
        return [(x, self[x]) for x in self.src]

    def keys(self):
        return list(self.src)

    def values(self):
        return [v for (k, v) in list(self.items())]


class Identity(Function):
    def __init__(self, src):
        Function.__init__(lambda x: x, src, src)


def check_graph(G):
    # Check t