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.Linq;

namespace _5
{
    class Program
    {
        static int n, x;
        static int[] a;
        static bool[,] vis;//solve[depth,sum]????¨??????????????????????????????°
        static bool[,] dp;//solve[depth,sum]??????
        public static bool solve(int depth, int sum)//depth=??±???,sum=???????????§???????¨?
        {
            if (depth == n)
            {
                return (sum == x);
            }
            if (sum > x)
            {
                return false;//sum???x????¶???????????????§?????????
            }
            bool ret = false;
            if (solve(depth + 1, sum + a[depth]) == true)
            {
                ret = true;//a[depth]????????¶??´???
            }
            if (solve(depth + 1, sum) == true)
            {
                ret = true;//a[depth]????????°????????´???
            }
            vis[depth, sum] = true;
            dp[depth, sum] = ret;
            return ret;
        }
        public static void Main()
        {
            n = int.Parse(Console.ReadLine());
            a = Console.ReadLine().Split().Select(int.Parse).ToArray();
            int q = int.Parse(Console.ReadLine());
            int[] b = Console.ReadLine().Split().Select(int.Parse).ToArray();
            for (int i = 0; i < q; i++)
            {
                x = b[i];
                vis = new bool[n, x + 1];
                dp = new bool[n, x + 1];
                bool ret = solve(0, 0);
                Console.WriteLine(ret ? "yes" : "no");
            }
            Console.ReadLine();
        }
    }
}