Problem:
Exhaustive Search

Write a program which reads a sequence A of n elements and an integer M, and outputs "yes" if you can make M by adding elements in A, otherwise "no". You can use an element only once.

You are given the sequence A and q questions where each question contains Mi.

Input

In the first line n is given. In the second line, n integers are given. In the third line q is given. Then, in the fourth line, q integers (Mi) are given.

Output

For each question Mi, print yes or no.

Constraints

n ≤ 20

q ≤ 200

1 ≤ elements in A ≤ 2000

1 ≤ Mi ≤ 2000

Sample Input 1

5
1 5 7 10 21
8
2 4 17 8 22 21 100 35

Sample Output 1

no
no
yes
yes
yes
yes
no
no

Notes

You can solve this problem by a Burte Force approach. Suppose solve(p, t) is a function which checkes whether you can make t by selecting elements after p-th element (inclusive). Then you can recursively call the following functions:

solve(0, M)

solve(1, M-{sum created from elements before 1st element})

solve(2, M-{sum created from elements before 2nd element})

...

The recursive function has two choices: you selected p-th element and not. So, you can check solve(p+1, t-A[p]) and solve(p+1, t) in solve(p, t) to check the all combinations.

For example, the following figure shows that 8 can be made by A[0] + A[2].

Solution in C++ (judge verdict: Accepted)

#include <stdio.h>

int solve(int A[], int n, int i, int m)
{
  if (m == 0)
  {
    return true;
  }
  if (i >= n)
    return false;
  int res = solve(A, n, i + 1, m) || solve(A, n, i + 1, m - A[i]);
  return res;
}

int main()
{
  int n, q;
  int i;

  scanf("%d", &n);
  int A[n];
  for (i = 0; i < n; i++)
  {
    scanf("%d", &A[i]);
  }
  scanf("%d", &q);
  int m[q];
  for (int i = 0; i < q; i++)
  {
    scanf("%d", &m[i]);
  }

  for (int i = 0; i < q; i++)
  {
    if (solve(A, n, 0, m[i]))
    {
      printf("yes\n");
    }
    else
    {
      printf("no\n");
    }
  }
  return 0;
}