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.Linq;

namespace Competitive
{
    internal class Combination
    {
        public int[] A;
        public bool[] F;
        public int N;
        public bool Flag;
        public int Target;

        public Combination(int[] a, int target)
        {
            A = a;
            N = A.Length;
            F = new bool[N];
            Flag = false;
            Target = target;
        }

        public void Judge()
        {
            int ret = 0;

            for(int i = 0; i < N; i++)
                if (F[i])
                    ret += A[i];

            if (ret == Target)
                Flag = true;
        }

        public bool Run()
        {
            Run(0);
            return Flag;
        }

        private void Run(int i)
        {
            // 特定の条件時の処理
            if (i == N)
            {
                Judge(); return;
            }

            F[i] = false;
            Run(i + 1);

            F[i] = true;
            Run(i + 1);
        }
    }

    internal class Solution
    {
        public int n, q;
        public int[] A, M;

        public void Run()
        {
            n = Input.ReadInt();
            A = Input.ReadIntArray();
            q = Input.ReadInt();
            M = Input.ReadIntArray();

            for (int i = 0; i < q; i++)
            {
                var runner = new Combination(A, M[i]);
                Console.WriteLine(runner.Run() ? "yes" : "no");
            }
        }

    }

    
    internal static class Input
    {
        public static int ReadInt()
        {
            string line = Console.ReadLine();
            return int.Parse(line);
        }

        public static int[] ReadIntArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(int.Parse).ToArray();            
        }

        public static double[] ReadDoubleArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(double.Parse).ToArray();
        }
    }

    internal class Program
    {
        public static void Main(string[] args)
        {
            var s = new Solution();
            s.Run();
        }
    }
}