Minimum Partition Difference

You are given an array of integers. Your task is to partition the array into two non-empty subsets such that the absolute difference between the sum of the elements in the two subsets is minimized. Formally, if the two subsets are denoted by S₁ and S₂, you need to minimize the value:

\( |\sum_{i \in S_1} a_i - \sum_{j \in S_2} a_j| \)

This is a classic partition problem that can be solved using dynamic programming. Note that the whole array must be partitioned into exactly two subsets and both subsets should be non-empty.

inputFormat

The first line of input consists of a single integer n (the number of elements in the array). The second line contains n space-separated integers representing the elements of the array.

outputFormat

Output a single integer which is the minimum absolute difference between the sums of the two subsets.

4
1 6 11 5

1