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>

int n,a,s;
std::bitset<2002005> b;

int main()
{
    for(b[0]=1,scanf("%d",&n);n--;)
        scanf("%d",&a),b|=b<<a,s+=a;
    for(int i=(s+1)>>1;true;++i)if(b[i])return printf("%d\n",i),0;
}