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;

int main() {
    int n; cin >> n;
    int sum = 0;
    bitset<4004000> dp; dp[0] = 1;
    for (int i = 0; i < n; i++) {
        int a; cin >> a;
        sum += a;
        dp |= (dp << a);
    }
    int ans = (sum + 1) / 2;
    while (!dp[ans]) ans++;
    cout << ans << endl;
    return 0;
}