Given n natural numbers, find how to separate them into two sets so that the absolute value of the difference between the sums of the elements of the two sets is minimized.

Input

Input consists of several cases,
each with n followed by n natural numbers between 1 and 10^{6}.
Assume 1 ≤ n ≤ 23.

Output

For every case, print the minimum possible difference.

Public test cases

**Input**

5 18 10 19 14 3 4 1000 10 10 10 1 20 7 1 2 4 8 16 32 64

**Output**

0 970 20 1

Information

- Author
- Salvador Roura
- Language
- English
- Translator
- Salvador Roura
- Original language
- Catalan
- Other languages
- Catalan
- Official solutions
- C++ Python
- User solutions
- C++