--description--

Consider the region constrained by $1 ≤ x$ and $0 ≤ y ≤ \frac{1}{x}$.

Let $S_1$ be the largest square that can fit under the curve.

Let $S_2$ be the largest square that fits in the remaining area, and so on.

Let the index of $S_n$ be the pair (left, below) indicating the number of squares to the left of $S_n$ and the number of squares below $S_n$.

The diagram shows some such squares labeled by number.

$S_2$ has one square to its left and none below, so the index of $S_2$ is (1, 0).

It can be seen that the index of $S_{32}$ is (1,1) as is the index of $S_{50}$.

50 is the largest $n$ for which the index of $S_n$ is (1, 1).

What is the largest $n$ for which the index of $S_n$ is (3, 3)?

--hints--

squaresUnderAHyperbola() should return 782252.

assert.strictEqual(squaresUnderAHyperbola(), 782252);

--seed--

--seed-contents--

function squaresUnderAHyperbola() {

  return true;
}

squaresUnderAHyperbola();

--solutions--

// solution required