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;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleTest
{
    class Program
    {
        static void Main(string[] args)
        {
            Console.ReadLine();
            var from = Console.ReadLine().Split().Select(int.Parse).ToArray();
            Console.ReadLine();
            var targets = Console.ReadLine().Split().Select(int.Parse).ToArray();
            var max = targets.Max();

            var IsCompleted = new bool[targets.Length];

            IsComputable(targets, from, 0, 0, max, ref IsCompleted);
            foreach(var v in IsCompleted)
            {
                Console.WriteLine(v ? "yes" : "no");
            }
        }

        private static void IsComputable(int[] targets, int[] from, int beginIndex, int nowSum, int max, ref bool[] IsCompleted)
        {
            if (beginIndex >= from.Length) return;

            var nextSum = nowSum + from[beginIndex];

            if (nextSum <= max)
            {
                for (var k = 0; k < targets.Length; ++k)
                    if (targets[k] == nextSum) IsCompleted[k] = true;
                IsComputable(targets, from, beginIndex + 1, nextSum, max, ref IsCompleted);
            }
            IsComputable(targets, from, beginIndex + 1, nowSum, max, ref IsCompleted);
        }
    }
}