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: Time Limit Exceeded)

#include <stdio.h>

void rec(int);

int n,q;
int A[20];
int M;

int flag=0;
int B[20];

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

void rec(int a){
  if(flag==1)return;
  if(a==n){
    int i;
    int sum=0;
    for(i=0;i<n;i++){
      if(B[i]==1){
	sum=sum+A[i];
      } 
    }
    if(sum==M){
      flag=1;
    }
    
  }else{
    B[a]=1;
    rec(a+1);
    B[a]=0;
    rec(a+1);
  }
  
}