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<cstdio>
#include<bitset>
using namespace std;
bitset<2100*2100>f;

int main() {
	int N,A,sum=0;
	scanf("%d",&N);
	f[0]=1;
	for(int i=0; i<N; i++) {
		scanf("%d",&A);
		f|=f<<A;
		sum+=A;
	}
	//for(;p<cnt;)if(f[p]==1)p++;
	for(int i=(sum+1)/2;; i++)if(f[i]) {
			printf("%d\n",i);
			break;
		}

	return 0;
}