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.Collections.Generic;
using System.Linq;
using System.Text;
namespace _20180305_AOJ
{
    class ALDS1_5A
    {
        static void Main(string[] args)
        {
            for (;;)
            {
                string line = Console.ReadLine();
                if (string.IsNullOrEmpty(line))
                {
                    break;
                }

                int[] A = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
                Console.ReadLine();
                int[] m = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();

                foreach (var v in m)
                {
                    bool solved = Solve(A, 0, v);
                    if (solved)
                    {
                        Console.WriteLine("yes");
                    }
                    else
                    {
                        Console.WriteLine("no");
                    }
                }
            }
        }

        static bool Solve(int[] A, int i, int m)
        {
            if (m == 0)
            {
                return true;
            }
            if (i >= A.Length)
            {
                return false;
            }

            return Solve(A, i + 1, m) || Solve(A, i + 1, m - A[i]);
        }
    }
}