There are four lists of increasing primes that sum to $20$:

$(2,5,13);(2,7,11);(3,17);(7,13)$

The median prime list is defined to be the median of these lists when they are written in lexicographic order (as shown in the example above).
If there are an even number of lists then disregard the last one and find the median of the rest.

Therefore the median prime list of $20$ is $(2,7,11)$.

Find the median prime list of $2026$. Give the last nine digits of the product of the primes.