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,int);
int A[2000],n;
 
int solve(int x,int y) {
  if(A[x] == y)
    return 1;
  if(x+1 == n)
    return 0;
  if(solve(x+1,y-A[x]) || solve(x+1,y)) 
    return 1;
  return 0;  
  }
int main(void) {
 
  int S[2000],i,m;
 
  scanf("%d",&n);
   
  for(i=0;i<n;i++) 
    scanf("%d",&A[i]);
   
  scanf("%d",&m);
  for(i=0;i<m;i++) 
    scanf("%d",&S[i]);
   
  for(i=0;i<m;i++) {
    if(solve(0,S[i])) 
      printf("yes\n");
    else printf("no\n");
     
  }
  return 0; 
}