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;
using System.Collections;
using System.Collections.Generic;

class Program
{
    public static void Main(string[] args)
    {
        int n = int.Parse(Console.ReadLine());
        int[] ns = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
        int q = int.Parse(Console.ReadLine());
        int[] qs = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();

        bool[,] res = new bool[n + 1, qs.Max() + 1];
        for (int i = 0; i <= n; i++) res[i, 0] = true;
        for (int i = 1; i <= qs.Max(); i++) res[n, i] = false;
        for (int i = n - 1; i >= 0; i--)
        {
            for (int j = 1; j < qs.Max() + 1; j++)
            {
                bool r = res[i + 1, j];
                r = (j - ns[i] >= 0)? (r || res[i + 1, j - ns[i]]): r;
                res[i, j] = r;
            }
        }
        for (int i = 0; i < q; i++) Console.WriteLine((res[0, qs[i]])? "yes": "no");
    }
}