19. Let $p=p_{1} p_{2} \ldots p_{6}$ be a permutation of the integers from 1 to 6 . For any such permutation $p$, we count how many integers there are which have nothing bigger on its left. We let $f(p)$ be the number of these integers for the permutation $p$. For example, $f(612345)=1$ because only 6 has nothing to its left which is bigger. On the other hand, $f(135462)=4$ because only $1,3,5$, and 6 satisfy the condition.
Let $S$ be the sum of $f(p)$ over all the 6 ! different permutations. Find the sum of the digits of $S$.
19. 18 (1764)