Split It Again

Given an array $A$ of $N$ integers, the task is to split the array into 3 non-empty subarrays, such that the difference between the subarray having maximum sum and the subarray having minimum sum is minimized. More formally, let $s1$, $s2$ and $s3$ be the sums of the first, second and third subarrays respectively. Then you need to calculate the minimum value of $max({s1, s2, s3})$ - $min({s1, s2,