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: Accepted)

import Data.List

cons a as = Just (a:as)

ans' _ [] = Nothing
ans' m (a:as) =
   if m < a
   then Nothing
   else if m == a
        then Just [a]
        else if a' /= Nothing
             then a' >>= (cons a)
             else b'
   where
        a' = ans' (m-a) as
        b' = ans' m as

ans m a =
   let o = ans' m a
   in
        case o of
            Nothing -> "no"
            Just _  -> "yes"

main = do
    _ <- getLine
    a <- getLine
    _ <- getLine
    m <- getLine
    let a' = sort $ map read $ words a :: [Int]
        m' = map read $ words m :: [Int]
        o  = map (\ m -> ans m a') m'
--    print o
    mapM_ putStrLn o