Consider the region constrained by 1 ≤ x and 0 ≤ y ≤ ¹/_x.

Let S₁ be the largest square that can fit under the curve.
Let S₂ 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 labelled by number.
S₂ has one square to its left and none below, so the index of S₂ is (1,0).
It can be seen that the index of S₃₂ is (1,1) as is the index of S₅₀.
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)?