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 Haskell (judge verdict: Time Limit Exceeded)

import Control.Applicative ((<$>), (<*>))
import Data.ByteString.Char8 (ByteString)
import qualified Data.ByteString.Char8 as B
import Data.Bool (bool)
import Data.List (unfoldr)
import Data.Char (isSpace)

main :: IO ()
main = solve <$> f <*> f >>= mapM_ putStrLn
  where f = B.getLine >> readil B.readInt <$> B.getLine

solve :: [Int] -> [Int] -> [String]
solve as = map (bool "no" "yes" . search as)

search xs m | m == 0 = True
            | m < 0 = False
            | null xs = False
            | otherwise = let (y:ys) = xs
                          in search ys m || search ys (m - y)

readil :: Integral a =>  (ByteString -> Maybe (a, ByteString)) -> ByteString -> [a]
readil f = unfoldr g
  where
    g s = do
      (n, s') <- f s
      return (n, B.dropWhile isSpace s')