--description--

$E_a$ is an ellipse with an equation of the form $x^2 + 4y^2 = 4a^2$.

$E_a'$ is the rotated image of $E_a$ by $θ$ degrees counterclockwise around the origin $O(0, 0)$ for $0° < θ < 90°$.

$b$ is the distance to the origin of the two intersection points closest to the origin and $c$ is the distance of the two other intersection points.

We call an ordered triplet ($a$, $b$, $c$) a canonical ellipsoidal triplet if $a$, $b$ and $c$ are positive integers.

For example, (209, 247, 286) is a canonical ellipsoidal triplet.

Let $C(N)$ be the number of distinct canonical ellipsoidal triplets ($a$, $b$, $c$) for $a ≤ N$.

It can be verified that $C({10}^3) = 7$, $C({10}^4) = 106$ and $C({10}^6) = 11\,845$.

Find $C({10}^{17})$.

--hints--

crisscrossEllipses() should return 1199215615081353.

assert.strictEqual(crisscrossEllipses(), 1199215615081353);

--seed--

--seed-contents--

function crisscrossEllipses() {

  return true;
}

crisscrossEllipses();

--solutions--

// solution required