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: Runtime Error)

#include<stdio.h>
#include<math.h>
#include<stdlib.h>

int Psum(int *A,int t,int N){
  int f=0;
  int i;
  for(i=0;i<N;i++){
    if(t%2==1) f+=A[i];
    t/=2;
  }
  return f;
}

int comp(const void *a,const void *b){
  return *(int *)a-*(int *)b;
}

int main(){
  int N;
  int n;
  int i;
  scanf("%d",&N);
  if(N==1){
    scanf("%d",&N);
    printf("%d",N);
    return 0;
  }
  int A[N];
  n=pow(2,N)-1;
  int S[n];
  for(i=0;i<N;i++){
    scanf("%d",&A[i]);
  }
  for(i=1;i<=n;i++){
    S[i-1]=Psum(A,i,N);
  }
  qsort(S,n,sizeof(int),comp);
  n/=2;
  printf("%d",S[n]);

}