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.ArrayList;
import java.util.Collections;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = Integer.parseInt(sc.next());
		ArrayList<Integer> A = new ArrayList<>();
		for(int i = 0; i < n; i++) {
			A.add(Integer.parseInt(sc.next()));
		}
		int q = Integer.parseInt(sc.next());
		ArrayList<Integer> m = new ArrayList<>();
		for(int i = 0; i < q; i++) {
			m.add(Integer.parseInt(sc.next()));
		}
		sc.close();
		
		Collections.sort(A);
		
		
		for(int i = 0; i < q; i++) {
			if(solve(A, 0, m.get(i))) {
				System.out.println("yes");
			}else {
				System.out.println("no");
			}
		}
	}

	public static boolean solve(ArrayList<Integer> data, int i, int m) {
		if(m == 0) return true;
		if(i == data.size() - 1) {
			if(data.get(i) == m) {
				return true;
			}else {
				return false;
			}
		}
		return solve(data, i + 1, m) || solve(data , i + 1 , m -data.get(i));
	}

}