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 ALDS1_5_A
{
    class Program
    {
        static void Main(string[] args)
        {
            string input = Console.ReadLine();
            int N = int.Parse(input);

            string[] factor_st = Console.ReadLine().Split(' ');
            int[] factor = new int[N];
            for (int i = 0; i < N; i++)
            {
                factor[i] = int.Parse(factor_st[i]);
            }

            int k = int.Parse(Console.ReadLine());
            string[] analyte_st = Console.ReadLine().Split(' ');
            bool[] analyte = new bool[k];
            for (int i = 0; i < k; i++)
            {
                analyte[i] = solve(0, int.Parse(analyte_st[i]), factor);
                if (analyte[i])
                {
                    Console.WriteLine("yes");
                } else
                {
                    Console.WriteLine("no");
                }
            }
        }

        public static bool solve (int i, int m, int[] list)
        {
            if (m == 0) return true;
            if (i >= list.Length) return false;

            bool res = solve(i + 1, m, list) || solve(i + 1, m - list[i], list);
            return res;
        }
    }
}