--description--

In a sliding game a counter may slide horizontally or vertically into an empty space. The objective of the game is to move the red counter from the top left corner of a grid to the bottom right corner; the space always starts in the bottom right corner. For example, the following sequence of pictures show how the game can be completed in five moves on a 2 by 2 grid.

Let $S(m, n)$ represent the minimum number of moves to complete the game on an $m$ by $n$ grid. For example, it can be verified that $S(5, 4) = 25$.

There are exactly 5482 grids for which $S(m, n) = p^2$, where $p < 100$ is prime.

How many grids does $S(m, n) = p^2$, where $p < {10}^6$ is prime?

--hints--

slidingGame() should return 2057774861813004.

assert.strictEqual(slidingGame(), 2057774861813004);

--seed--

--seed-contents--

function slidingGame() {

  return true;
}

slidingGame();

--solutions--

// solution required