$F(i,j)$ = sum of positive integers ( in base $10$ ) having an identical representation in both base $i$ and base $j$.

$F(2,3)=1$

Let $S(N)$ be the sum of all values of $F(i,j)$ for $2 \leq i < j \leq N$

Find $S(N)$ mod $22011663$ for $N = 10^{18}$