Summing the values

For an array $B$ of length $M$, we define its *value* $f(B)$ as follows: $$ f(B) = \sum_{i=1}^{M-1} \left( \left( \sum_{j=1}^i B_j\right) - \left( \sum_{j=i+1}^M B_j \right) \right) $$ In particular, if $M = 1$ then $f(B) = 0$. You're given an array $A$ of length $N$. Find the sum of *values* of all of its subarrays. That is, compute $$ \sum_{L=1}^N \sum_{R=L}^N f(A[L\ldots R]) $$ where $A[L