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.Text;

class Program
{
    public void Proc()
    {
        int itemCount = int.Parse(Console.ReadLine());
        int[] items = new int[itemCount];
        string[] inpt = Console.ReadLine().Split(' ');
        for(int i=0; i<itemCount; i++)
        {
            items[i] = int.Parse(inpt[i]);
        }

        int targetCount = int.Parse(Console.ReadLine());
        int[] targetList = new int[targetCount];

        inpt = Console.ReadLine().Split(" "[0]);
        for(int i=0; i<targetCount; i++)
        {
            targetList[i] = int.Parse(inpt[i]);
        }

        // ?????????????????????
        Array.Sort(items);
        this.Parts = new int[itemCount];
        for(int i=0; i<itemCount; i++)
        {
            Parts[i] = items[itemCount - 1 - i];
        }


        for(int i=0; i<targetCount; i++)
        {
            bool ret = this.CanGet(0, targetList[i]);
            Console.WriteLine(ret ? "yes" : "no");
        }

    }

    private int[] Parts;

    private Dictionary<int, Dictionary<int, bool>> dic = new Dictionary<int, Dictionary<int, bool>>();
    private bool CanGet(int idx, int num)
    {
        if(dic.ContainsKey(idx) && dic[idx].ContainsKey(num))
        {
            return dic[idx][num];
        }
        bool isMatch = false;

        for(int i=idx; i<Parts.Length; i++)
        {
            if(Parts[i] > num)
            {
                // ???????????????
            } else if(Parts[i] == num)
            {
                isMatch = true;
                break;
            } else
            {
                bool ret = this.CanGet(i + 1, num - Parts[i]);
                if(ret)
                {
                    isMatch = true;
                    break;
                }
            }
        }
        if (!dic.ContainsKey(idx))
        {
            dic.Add(idx, new Dictionary<int, bool>());
        }
        dic[idx].Add(num, isMatch);
        return isMatch;
    }

    static void Main(string[] args)

    {

        Program prg = new Program();
        prg.Proc();

    }
}