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>
std::bitset<2000010>v;
int main(){
	int N,A,S=0;
	scanf("%d",&N);
	v[0]=1;
	for(int i=N;i--;){
		scanf("%d",&A);
		S+=A;
		v|=v<<A;
	}
	for(int i=S/2;;i--)if(v[i])return printf("%d\n",S-i),0;
}