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 = 2e3+5;
bitset<N*N> B;
int n, sm, rt;
int main(){
    B.set(0);
    scanf("%d", &n);
    for(int i=0;i<n;i++){
        int a; scanf("%d", &a);
        B |= B<<a;
        sm+=a;
    }
    for(int i=((sm+1)>>1);;i++) if(B[i]) return !printf("%d", i);
}