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;
const int N=2010;
int n,a[N],sum;
bitset<N*N> dp;
int main()
{
    scanf("%d",&n);
    for (int i=1;i<=n;i++) scanf("%d",&a[i]),sum+=a[i];
    dp[0]=1;
    for (int i=1;i<=n;i++) dp|=dp<<a[i];
    for (int i=(sum+1)>>1;;i++)
    if (dp[i]) printf("%d\n",i),exit(0);
    return 0;
}