def __missing__(self, key):
        if self.default_factory is None:
            raise KeyError(key)
        else:
            ret = self[key] = self.default_factory(name=key)
            return ret
def split(root, minRight):
    if root is None:
        return None, None
    if root.key >= minRight:
        left, right = split(root.left, minRight)
        root.left = right
        root.update()
        return left, root
    else:
        left, right = split(root.right, minRight)
        root.right = left
        root.update()
        return root, right