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>

using namespace std;

bitset<4000010>b;
int N;

int main(){
	int N;
	scanf("%d",&N); 
	b.reset();
	b.set(0);
	int S=0;
	while(N--){
		int A;
		scanf("%d",&A);
		S+=A;
		b|=(b << A);
	}		
	for (int i=(S+1)/2;i<=S;i++)
	if (b.test(i)){
		printf("%d\n",i);
		break;
	}		
}