def triangulation(points):
    vertices = wrapPoints(points)

    vertices = sorted(vertices, key=lambda vertex : vertex.y, reverse=True)
    divideToChains(vertices)

    LC, RC = showChains(vertices)

    stack = []

    stack.append(vertices[0])
    stack.append(vertices[1])


    for vertex in vertices[2:]:
        #print("ver: ", vertex.x, " ", vertex.y)
        top = stack.pop()
        #print("top: ", top.x, " ", top.y)

        if vertex.chain != top.chain:
            top.otherPoints.append(vertex)
            vertex.otherPoints.append(top)

            while stack:
                    v = stack.pop()

                    if not vertex.preceding == v and not vertex.following == v:
                        v.otherPoints.append(vertex)
                        vertex.otherPoints.append(v)

            stack.append(top)
            stack.append(vertex)

        else:
            second = stack.pop()
            if vertex.chain == ChainType.LEFT and detSgn(det(vertex, top, second)) == 1:
                stack.append(second)
                stack.append(top)
                stack.append(vertex)
            elif vertex.chain == ChainType.RIGHT and detSgn(det(vertex, top, second)) == -1:
                stack.append(second)
                stack.append(top)
                stack.append(vertex)
            else:
                vertex.otherPoints.append(second)
                second.otherPoints.append(vertex)
                stack.append(second)
                stack.append(vertex)

    return vertices, LC, RC