Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

3
1 2 1

Sample Output 1

2

In this case, S = (1, 1, 2, 2, 3, 3, 4). Its median is S_4 = 2.

Sample Input 2

1
58

Sample Output 2

58

In this case, S = (58).

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>

using namespace std;

typedef unsigned int ui;
typedef pair<int,int> pii;
typedef long long ll;
typedef vector<int> vi;
#define rep(i, n) for(int i = 0; i < n; ++i)
#define rInt(a) scanf("%d",&a);
#define MAXN 2001


main(){
    int n; rInt(n);
    int sum = 0;
    vi arr (n);
    rep(i,n) scanf("%d",&arr[i]);
    sort(arr.begin(),arr.end());
    if(n==1) cout << arr[0] << endl;
    else{
        rep(i,n-1) sum+= arr[i];
        cout << sum << endl;
    }
}