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 <stdio.h>
#include <bitset>
#define reg register
std::bitset<4000005> f;
int n,m,a;
int main() {
	reg int i;
	scanf("%d",&n);m=0;
	f[0]=1;
	for(i=0;i<n;++i) {
		scanf("%d",&a);
		f|=f<<a;m+=a;
	}
	for(i=(m+1)>>1;;++i) if(f[i]) {
		printf("%d",i);
		break;
	}
	return 0;
}