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>
#define N 20//the maximum number of first elements
int solve(int[],int,int,int);
int main(void)
{
  int i;//counter
  int n;//the number of elements that can be used
  int arr[N];//input of second line
  int q;//the number of elements judged
  int x;//input of forth line
  scanf("%d",&n);
  for(i=0;i<n;i++) scanf("%d",&arr[i]);
  scanf("%d",&q);
  for(i=0;i<q;i++)
    {
      scanf("%d",&x);
      if(solve(arr,n,0,x)==1) printf("yes\n");
      else printf("no\n");
    }
  return 0;
}
int solve(int arr[],int n,int p,int t)//checks whether we can make t by selecting after p-th element (inclusive)
{
  //printf("solve(arr,%d,%d,%d)\n",n,p,t); //debugging
  if(p>=n||t<0) return 0;
  if(t==arr[p]) return 1;
  if(solve(arr,n,p+1,t-arr[p])==1) return 1;
  if(solve(arr,n,p+1,t)==1) return 1;
  return 0;
}