class Coord:
    def __init__(self, array, coord, check= True):
        self._array= array
        self._list=  coord
        assert(len(self) == len(self.array.dimension_list()))
        assert(check and array.min() <= self)
        assert(check and self < array.max())

    def __len__(self):
        return len(self._list)

    def __str__(self):
        return ','.join(map(str, self._list))

    def __iter__(self):
        return iter(self._list)

    def __lt__(self, right):
        return all([left < right for (left, right) in zip(self._coord, right._coord)])

    def __le__(self, right):
        return all([left <= right for (left, right) in zip(self._coord, right._coord)])

    def __eq__(self, right):
        return all([left == right for (left, right) in zip(self._coord, right._coord)])

    def __gt__(self, right):
        return all([left > right for (left, right) in zip(self._coord, right._coord)])

    def __ge__(self, right):
        return all([left >= right for (left, right) in zip(self._coord, right._coord)])

    def __add__(self, right):
        return Coord(self._array, [ (left + right) for (left,right) in zip(self._coord, right.coord) ])

    def __sub__(self, right):
        return Coord(self._array, [ (left - right) for (left,right) in zip(self._coord, right.coord) ])

class Value:
    def __init__(self, array, attribute_value_list):
        self._list= attribute_value_list
        assert(len(array.attribute_list()) == len(attribute_value_list))

    def __str__(self):
        return ','.join(map(str, self._list))


class Box:
    def __init__(self, array, begin, end):
        self._begin= begin
        self._end=   end
        assert(begin < end)

    def begin(self):
        return self._begin

    def end(self):
        return self._end

    def include(self, coord):
        return self._begin <= coord and coord < self._end

    def __len__(self):
        return self.end() - self.begin()

    def __iter__(self):
        return itertools.iproduct(xrange(minimum, maximum - minimum) for (minimum, maximum) itertools.izip(self.begin(), self.end()))