Subarray Sum

Chef has a sequence of $N$ integers $A_1, A_2,\dots, A_N$. He defines a function $f(i, j)$ as follows: $f(i, j) = A_i + max(A_i, A_{i + 1}) + max(A_i, A_{i + 1}, A_{i + 2}) + \dots + max(A_i, A_{i + 1}, \dots, A_j)$ Chef tries to find the sum of $f(i, j)$ over all $(i, j)$ such that $1 \leq i \leq j \leq N$ $(i.e \sum\limits_{i=1}^n \sum\limits_{j=i}^nf(i, j))$, but fails. Can you help him find