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 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <stdio.h>

int a[2000];
int tab[4000001];

int main(){
    int n;
    scanf("%d", &n);
    tab[0] = 1;
    for(int i=0; i<n; i++){
        int a;
        scanf("%d", &a);
        for(int j=4000000; j>=0; j--){
            tab[j+a] += tab[j];
        }
    }
    int i = 1, j = 4000000;
    int diff = tab[j] - tab[i];
    while(i < j){
        //printf("%d %d %d\n", diff, i, j);
        if(diff > 0){
            diff -= tab[++i];
        }else if(diff < 0){
            diff += tab[--j];
        }else{
            diff = tab[--j] - tab[++i];
        }
    }
    printf("%d\n", i);
}