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;

namespace Aizu
{
	class Program
	{
		static void Main(string[] args)
		{
			var n = int.Parse(Console.ReadLine());
			var aList = Console.ReadLine().Split(' ').Select(value => int.Parse(value)).ToList();
			var q = int.Parse(Console.ReadLine());
			var mList = Console.ReadLine().Split(' ').Select(value => int.Parse(value)).ToList();
			var mDictionary = new Dictionary<int, bool>();

			foreach(var m in mList)
			{
				if(!mDictionary.ContainsKey(m))
				{
					mDictionary.Add(m, false);
				}
			}

			for(var i = 0; i < Math.Pow(2, aList.Count); i++)
			{
				var sum = 0;

				for(var j = 0; j < aList.Count; j++)
				{
					if(((i >> j) & 1) == 1)
					{
						sum += aList[j];
					}
				}

				if(mDictionary.ContainsKey(sum))
				{
					mDictionary[sum] = true;
				}
			}

			foreach(var value in mList)
			{
				Console.WriteLine(mDictionary[value] ? "yes" : "no");
			}
		}
	}
}