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;

namespace AOJ.ALDS
{
    public class ExhaustiveSearch
    {
        private static int length;
        private static int[] items;

        private static bool Solve(int i, int m)
        {
            if (m == 0) { return true; }
            if (i == length) { return false; }

            // 再帰呼び出し
            bool res1 = Solve(i + 1, m);            // i番目の要素を使用しない
            bool res2 = Solve(i + 1, m - items[i]); // i番目の要素を使用する

            return res1 || res2;
        }

        public static void Main()
        {
            length = int.Parse(Console.ReadLine());
            var input = Console.ReadLine().Split(' ');
            items = new int[length];
            for (int i = 0; i < length; i++) { items[i] = int.Parse(input[i]); }

            int q_cnt = int.Parse(Console.ReadLine());
            input = Console.ReadLine().Split(' ');
            for (int i = 0; i < q_cnt; i++)
            {
                bool ans = Solve(0, int.Parse(input[i]));
                Console.WriteLine(ans ? "yes" : "no");
            }
        }
    }
}