--description--

In the classic "Crossing Ladders" problem, we are given the lengths $x$ and $y$ of two ladders resting on the opposite walls of a narrow, level street. We are also given the height $h$ above the street where the two ladders cross and we are asked to find the width of the street ($w$).

Here, we are only concerned with instances where all four variables are positive integers. For example, if $x = 70$, $y = 119$ and $h = 30$, we can calculate that $w = 56$.

In fact, for integer values $x$, $y$, $h$ and $0 < x < y < 200$, there are only five triplets ($x$, $y$, $h$) producing integer solutions for $w$: (70, 119, 30), (74, 182, 21), (87, 105, 35), (100, 116, 35) and (119, 175, 40).

For integer values $x$, $y$, $h$ and $0 < x < y < 1\,000\,000$, how many triplets ($x$, $y$, $h$) produce integer solutions for $w$?

--hints--

integerLadders() should return 210139.

assert.strictEqual(integerLadders(), 210139);

--seed--

--seed-contents--

function integerLadders() {

  return true;
}

integerLadders();

--solutions--

// solution required