--description--

Define:

$$\begin{align} & x_n = ({1248}^n\bmod 32323) - 16161 \\ & y_n = ({8421}^n\bmod 30103) - 15051 \\ & P_n = \{(x_1, y_1), (x_2, y_2), \ldots, (x_n, y_n)\} \end{align}$$

For example, $$P_8 = \{(-14913, -6630), (-10161, 5625), (5226, 11896), (8340, -10778), (15852, -5203), (-15165, 11295), (-1427, -14495), (12407, 1060)\}$$

Let $C(n)$ be the number of triangles whose vertices are in $P_n$ which contain the origin in the interior.

Examples:

$$\begin{align} & C(8) = 20 \\ & C(600) = 8\,950\,634 \\ & C(40\,000) = 2\,666\,610\,948\,988 \end{align}$$

Find $C(2\,000\,000)$.

--hints--

trianglesContainingOriginTwo() should return 333333208685971500.

assert.strictEqual(trianglesContainingOriginTwo(), 333333208685971500);

--seed--

--seed-contents--

function trianglesContainingOriginTwo() {

  return true;
}

trianglesContainingOriginTwo();

--solutions--

// solution required