--description--

Consider the triangle with sides $\sqrt{5}$, $\sqrt{65}$ and $\sqrt{68}$. It can be shown that this triangle has area 9.

$S(n)$ is the sum of the areas of all triangles with sides $\sqrt{1 + b^2}$, $\sqrt{1 + c^2}$ and $\sqrt{b^2 + c^2}$ (for positive integers $b$ and $c$) that have an integral area not exceeding $n$.

The example triangle has $b = 2$ and $c = 8$.

$S({10}^6) = 18\,018\,206$.

Find $S({10}^{10})$.

--hints--

nonRationalSidesAndIntegralArea() should return 2919133642971.

assert.strictEqual(nonRationalSidesAndIntegralArea(), 2919133642971);

--seed--

--seed-contents--

function nonRationalSidesAndIntegralArea() {

  return true;
}

nonRationalSidesAndIntegralArea();

--solutions--

// solution required