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.Collections.Generic;
using System.Linq;
using System.Text;
using System;
using System.IO;

public class Program
{
    private static int[] nums;
    private static int sum;
    private static int[] elem;

    public static void Main(string[] args)
    {
        Input();
        Method();
        System.Console.ReadLine();
    }

    private static void Input()
    {
        Console.ReadLine();
        nums = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
        sum = nums.Aggregate((s, el) => s + el);
        Console.ReadLine();
        elem = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
    }

    private static bool Solve(int p, int t)
    {
        if (t > sum)
        {
            return false;
        }
        if (p >= nums.Length)
        {
            return false;
        }
        if (t - nums[p] == 0)
        {
            return true;
        }
        return Solve(p + 1, t - nums[p]) || Solve(p + 1, t);
    }

    private static void Method()
    {
        var results = new StringBuilder();
        for (int i = 0; i < elem.Length; i++)
        {
            bool res = Solve(0, elem[i]);
            results.AppendLine(res ? "yes" : "no");
        }
        Console.Write(results.ToString());
    }
}