--description--

$ABCD$ is a convex, integer sided quadrilateral with $1 ≤ AB < BC < CD < AD$.

$BD$ has integer length. $O$ is the midpoint of $BD$. $AO$ has integer length.

We'll call $ABCD$ a biclinic integral quadrilateral if $AO = CO ≤ BO = DO$.

For example, the following quadrilateral is a biclinic integral quadrilateral: $AB = 19$, $BC = 29$, $CD = 37$, $AD = 43$, $BD = 48$ and $AO = CO = 23$.

Let $B(N)$ be the number of distinct biclinic integral quadrilaterals $ABCD$ that satisfy ${AB}^2 + {BC}^2 + {CD}^2 + {AD}^2 ≤ N$. We can verify that $B(10\,000) = 49$ and $B(1\,000\,000) = 38239$.

Find $B(10\,000\,000\,000)$.

--hints--

biclinicIntegralQuadrilaterals() should return 2466018557.

assert.strictEqual(biclinicIntegralQuadrilaterals(), 2466018557);

--seed--

--seed-contents--

function biclinicIntegralQuadrilaterals() {

  return true;
}

biclinicIntegralQuadrilaterals();

--solutions--

// solution required