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)

using System;
using System.Linq;
class Program {
    static int n, x;
    static int[] a;
    static bool[,] vis; // solve(depth, sum) ????¨??????????????????????????????°
    static bool[,] dp; // solve(depth, sum) ??????
    public static bool solve(int depth, int sum) {
        if (depth == n) return (sum == x);
        if (sum > x) return false; // sum ??? x ????¶???????????????§?????????
        if (vis[depth, sum]) return dp[depth, sum];
        bool ret = false;
        if (solve(depth + 1, sum + a[depth]) == true) ret = true; // a[depth] ????????¶??´???
        if (solve(depth + 1, sum) == true) ret = true; // a[depth] ????????°????????´???
        vis[depth, sum] = true;
        dp[depth, sum] = ret;
        return ret;
    }
    public static void Main() {
        n = int.Parse(Console.ReadLine());
        a = Console.ReadLine().Split().Select(int.Parse).ToArray();
        int q = int.Parse(Console.ReadLine());
        int[] b = Console.ReadLine().Split().Select(int.Parse).ToArray();
        for (int i = 0; i < q; i++) {
            x = b[i];
            vis = new bool[n, x + 1];
            dp = new bool[n, x + 1];
            bool ret = solve(0, 0);
            Console.WriteLine(ret ? "yes" : "no");
        }
    }
}