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 A[20];
int n;

int solve(int p, int t);
int sort(void *a, void *b);

int main(void) {
	int i, q, M, j;
	
	scanf("%d", &n);
	for (i = 0; i < n; ++i) {
		scanf("%d", &A[i]);
	}
	
	qsort(A, n, sizeof(A[0]), sort);
	
	scanf("%d", &q);
	for (i = 0; i < q; ++i) {
		scanf("%d", &M);
		for (j = 0; A[j] > M; ++j);
		if (solve(j - 1, M)) {
			printf("yes\n");
		} else {
			printf("no\n");
		}
	}
	
	return 0;
}

int solve(int p, int t) {
	if ((p == n) || (t == 0)) return t == 0;
	if ((t >= A[p + 1]) && (solve(p + 1, t - A[p + 1]))) return 1;
	return solve(p + 1, t);
}

int sort(void *a, void *b) {
	return *(int*)b - *(int*)a;
}