--description--

Given two points ($x_1$, $y_1$, $z_1$) and ($x_2$, $y_2$, $z_2$) in three dimensional space, the Manhattan distance between those points is defined as $|x_1 - x_2| + |y_1 - y_2| + |z_1 - z_2|$.

Let $C(r)$ be a sphere with radius $r$ and center in the origin $O(0, 0, 0)$.

Let $I(r)$ be the set of all points with integer coordinates on the surface of $C(r)$.

Let $S(r)$ be the sum of the Manhattan distances of all elements of $I(r)$ to the origin $O$.

E.g. $S(45)=34518$.

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

--hints--

scarySphere() should return 878825614395267100.

assert.strictEqual(scarySphere(), 878825614395267100);

--seed--

--seed-contents--

function scarySphere() {

  return true;
}

scarySphere();

--solutions--

// solution required