Extend the definition of $f$ to apply for any permutation of $1,2, \ldots, n$, for any positive integer $n$. For positive integer $n$, let $g(n)$ denote the number of permutations \pi$of$1,2, \ldots, n$such that$f(\pi)=n$. We have$g(1)=1$. For fixed$n, k$(with$k \leq n$), the number of permutations \pi$ of $1,2, \ldots, n$ such that $f(\pi)=k$ is $g(k)(n-k)$ !. This gives us the recursive formula $g(n)=$ $n!-\sum_{k=1}^{n-1} g(k)(n-k)$ !. Using this formula, we find that the first 7 values of $g$ are $1,1,3,13,71,461,3447$. Our sum is then equal to \sum_{k=1}^{7} k \cdot g(k)(7-k)$!. Using our computed values of$g$, we get that the sum evaluates to 29093 .