--description--

Let $C$ be the circle with radius $r$, $x^2 + y^2 = r^2$. We choose two points $P(a, b)$ and $Q(-a, c)$ so that the line passing through $P$ and $Q$ is tangent to $C$.

For example, the quadruplet $(r, a, b, c) = (2, 6, 2, -7)$ satisfies this property.

Let $F(R, X)$ be the number of the integer quadruplets $(r, a, b, c)$ with this property, and with $0 < r ≤ R$ and $0 < a ≤ X$.

We can verify that $F(1, 5) = 10$, $F(2, 10) = 52$ and $F(10, 100) = 3384$.

Find $F({10}^8, {10}^9) + F({10}^9, {10}^8)$.

--hints--

circleAndTangentLine() should return 799999783589946600.

assert.strictEqual(circleAndTangentLine(), 799999783589946600);

--seed--

--seed-contents--

function circleAndTangentLine() {

  return true;
}

circleAndTangentLine();

--solutions--

// solution required