Problem: You are given N integers A_1, A_2, ..., A_N.

Consider the sums of all non-empty subsequences of A. There are 2^N - 1 such sums, an odd number.

Let the list of these sums in non-decreasing order be S_1, S_2, ..., S_{2^N - 1}.

Find the median of this list, S_{2^{N-1}}.

Constraints

* 1 \leq N \leq 2000
* 1 \leq A_i \leq 2000
* All input values are integers.

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 ... A_N


Output

Print the median of the sorted list of the sums of all non-empty subsequences of A.

Examples

Input

3
1 2 1


Output

2


Input

1
58


Output

58

Solution (in JAVA):

Solution:
import java.util.*;

class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] a = new int[n];
        int sum= 0;
        //int len = 4000000;
        for(int i=0;i<n;i++) {
            a[i] = sc.nextInt();
            sum += a[i];
        }
        BitSet bs = new BitSet(sum+1);
        bs.set(sum);
        for(int i=0;i<n;i++){
            BitSet cur = bs.get(a[i],sum+1);
            bs.or(cur);
        }
        int ini = sum%2==0?sum/2:(sum+1)/2;
        for(int i=ini;i<=sum;i++){
            if(bs.get(i)){
                System.out.println(i);
                break;
            }
        }
    }
}