4 - Collapse The Array

Ayush has an array $a$ of $n$ integers. He wants to collapse the entire array into a single element. To do this, he can perform the operation described below any number of times. Each operation grants some points, and Ayush's total score will be the sum of the points granted over all operations he performs. Let $a[i..j]$ denote the subarray of $a$ starting at index $i$ and ending at $j$. Define