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: Memory Limit Exceeded)

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

namespace ALDS1_5_A_ExhaustiveSearch
{
	class Program
	{
		static void Main ( string[] args )
		{
			int arraySize = int.Parse (Console.ReadLine ());
			int[] elementArray = new int[arraySize];
			elementArray = Console.ReadLine ().Split (' ').Select (int.Parse).ToArray ();

			arraySize = int.Parse (Console.ReadLine ());
			int[] searchArray = new int[arraySize];
			searchArray = Console.ReadLine ().Split (' ').Select (int.Parse).ToArray ();

			Pattern pattern = new Pattern (elementArray);

			foreach (var item in searchArray)
			{
				bool isCreate = pattern.IsCreate (item);

				if (isCreate)
					Console.WriteLine ("yes");
				else
					Console.WriteLine ("no");
			}

		}
	}

	class Pattern
	{
		public Pattern ( int[] numArray )
		{
			this.NumArray = numArray;
			hashTable = new Dictionary<Pair, bool> (numArray.Length * numArray.Length);
		}

		private int[] NumArray { set; get; }
		Dictionary<Pair, bool> hashTable { set; get; }

		public bool IsCreate ( int num, int index = 0 )
		{
			//???????????¶
			if (num == 0)
			{
				return true;
			}
			else if (NumArray.Length <= index)
			{
				Pair p = new Pair (num, index);
				hashTable.Add (p, false);

				return false;
			}

			Pair p2 = new Pair (num, index);

			if (hashTable.ContainsKey (p2))
			{
				return false;
			}

			//?¶??????´?????¨?¶????????????´???
			bool isCreate = IsCreate (num, index + 1) || IsCreate (num - NumArray[index], index + 1);

			return isCreate;
		}
	}

	class Pair
	{
		public Pair ( int num, int index )
		{
			this.Num = num;
			this.Index = index;
		}

		public int Num { set; get; }
		public int Index { set; get; }
	}
}