Let $S_i$ be an integer sequence produced with the following pseudo-random number generator:

• $S_0=290797$
• $S_{i+1}=S_i^{2}mod50515093$

Let $M(n)$ be the median of the pairwise products $S_i{S}_j$ for $0\le i<j<n$.

You are given $M(3)=3878983057768$ and $M(103)=492700616748525$.

Find $M(1000003)$.