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 CPP):

Solution:
#include<bits/stdc++.h>
#define rep(i,n) for(int i=0; i<(n); i++)
using namespace std;
int n, a, ac, m;
bitset<2000005> bt;
int main(){
	bt[0] = true;
	scanf("%d", &n);
	rep(i,n){
		scanf("%d", &a);
		ac += a;
		bt |= bt << a;
	}
	rep(i,ac/2+1) if(bt[i]) m = i;
	printf("%d\n", ac - m);
}