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 $S_n$.
<imgclass="img-responsive center-block"alt="diagram with squares under the hyperbola"src="https://cdn.freecodecamp.org/curriculum/project-euler/squares-under-a-hyperbola.gif"style="background-color: white; padding: 10px;">
The diagram shows some such squares labelled 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)?