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>

// found = 1: みつかった
// found = 0: まだみつかっていない
int found;

main(){
  int n,A[20],q,M[200];
    int i;
  scanf("%d", &n);
  for(i=0; i<n; i++)
    scanf("%d", &A[i]);
  scanf("%d", &q);
  for(i=0; i<q; i++)
    scanf("%d", &M[i]);
  
  for(i=0;i<q;i++){
    found = 0;
    solve(A, 0, M[i], n);
    if(found==0)
      printf("no\n");
    else if(found==1)
      printf("yes\n");
  }
  return 0;
}

int solve(int A[], int p, int t, int n){

  if(p<n){
    solve(A, p+1, t-A[p], n); //A[p]番目を使うとき
    solve(A, p+1, t, n); //使わないとき  
  }

  if(t==0)
    found=1;  

}