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

namespace aizu1
{
    public class Solution
    {
        public static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            int[] A = Array.ConvertAll<string, int>(Console.ReadLine().Split(' '), int.Parse);
            int q = int.Parse(Console.ReadLine());
            int[] M = Array.ConvertAll<string, int>(Console.ReadLine().Split(' '), int.Parse);
            string res = "";

            for(int j=0;j<q;j++)
            {
                if (CanSumUp(A, M[j], 0,n)) res += "yes\n";
                else res += "no\n";
            }

            Console.Write(res);
        }

        public static bool CanSumUp(int[] list, int sum, int index, int n)
        {
            if (sum == 0) return true;

            if (index == n) return false;

            return CanSumUp(list, sum - list[index], index + 1,n) || CanSumUp(list,sum,index+1,n); 
        }
    }
}