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 JAVA (judge verdict: Accepted)

import java.util.*;
import java.io.*;

class Main{
    static boolean solve(int i,int m, int n, int[] array){
        boolean res;

        if(m == 0){
            return true;
        }

        if(i >= n){
            return false;
        }

        if((res = solve(i + 1, m, n, array)) == true ||
           (res = solve(i + 1, m - array[i], n, array)) == true){
            return true;
        }

        return false;
    }

    public static void main(String[] args){
        int count1;
        int count2;
        int[] array1;
        int[] array2;
        int flag = 0;

        try{
            Scanner scan = new Scanner(System.in);
            String str;

            str= scan.next();
            count1 = Integer.parseInt(str);
            array1 = new int[count1];

            for(int i = 0; i < array1.length; i++){
                str = scan.next();
                array1[i] = Integer.parseInt(str);
            }

            str = scan.next();
            count2 = Integer.parseInt(str);
            array2 = new int[count2];

            for(int i = 0; i < array2.length; i++){
                str = scan.next();
                array2[i] = Integer.parseInt(str);
            }

            for(int i = 0; i < array2.length; i++){
                if(solve(0, array2[i], array1.length, array1) == true){
                    System.out.println("yes");
                }else{
                    System.out.println("no");
                }
            }

        }catch(Exception e){
            System.out.println("ERROR");
        }

    }
}