Algorithms and Data Structures

Divide the weights

Given n weights , you are asked to split those weights into 2 groups so that the difference between those weights is minimal.

Input

The first line of the input contains a single integer n (1 ≤ n ≤ 20).
The next line contains n space-separated integers (1 ≤ ≤ ).

Output

The program should print the minimal possible difference between the two groups.

Examples

Input
Output
3 3 2 1
0
5 1 2 3 4 7
1

Explanation

  1. First group → 3, second group → 1 + 2 = 3
  1. First group → 1 + 7 = 8, second group → 2 + 3 + 4 = 9
 
Hint
You can try to split the weights in all the possible ways and calculate the minimum possible difference.

Constraints

Time limit: 2 seconds

Memory limit: 512 MB

Output limit: 1 MB

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