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)

module Main
  extend self

  @@memo = {}
  def can_assemble?(elements, index, sum, raw_elements_length)
    unless @@memo[index].nil?
      return @@memo[index][sum] unless @@memo[index][sum].nil?
    else
      @@memo[index] = {}
    end

    if sum == 0
      true
    elsif index >= raw_elements_length
      false
    else
      @@memo[index][sum] = can_assemble?(elements, index + 1, sum, raw_elements_length) || can_assemble?(elements, index + 1, sum - elements[index], raw_elements_length)
      @@memo[index][sum]
    end
  end

  def main
    lines = STDIN.read.split(/\n/)
    lines.shift

    elements = lines.shift.split(' ').map{|s|s.to_i}
    lines.shift

    sums = lines.shift.split(' ').map{|s|s.to_i}
    sums.each{ |sum|
      puts can_assemble?(elements, 0, sum, elements.size) ? 'yes' : 'no'
    }

  end
end

Main::main