You are given an array A of n integers. Divide A into 2 sets of numbers so that the absolute difference in their sum is as small as possible.
### Input
- The first line contains an integer n.
- The second line contains n integers Ai.
### Output
- Print the minimum difference.
### Constraints
- 1≤n≤40.
- −109≤Ai≤109.
### Example
Input:
3124
Output:
1