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 Ruby (judge verdict: Accepted)

class String
  def to_ia
    self.split(/\s/).map {|s| s.to_i}
  end
end

def create_memo(ary)
  memo = [Array.new(2001)] + ary.map {|i| Array.new(2001)}
  ary.each_with_index do |val, i|
    i += 1
    (1..2000).each do |j|
      res = false
      if val == j
        res = true
      elsif memo[i-1][j]
        res = true
      elsif j-val > 0 and memo[i-1][j-val]
        res = true
      end
      memo[i][j] = res
    end
  end
  memo
end

def solve(ary, dest)
  @memo ||= create_memo(ary)
  @memo.each do |row|
    return true if row[dest]
  end
  false
end

lines = STDIN.read.split(/\n/)
ary = lines[1].to_ia
lines[3].to_ia.each do |i|
  puts solve(ary, i) ? "yes" : "no"
end