A Pythagorean triangle is called supernatural if two of its three sides are consecutive integers.

Let $S(N)$ be the sum of the perimeters of all distinct supernatural triangles with perimeters less than or equal to $N$.
For example, $S(100)=258$ and $S(10000)=172004$.

Find $S({10}^{{10}^{10}})$. Give your answer modulo $1234567891$.