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)

{-# OPTIONS_GHC -Wall #-}

readInt :: String -> Int
readInt = read

isOk :: [Int] -> Int -> Bool
isOk _ 0  = True
isOk [] _ = False
isOk (a:as) m
    | a > m     = isOk as m
    | otherwise = (isOk as (m-a)) || (isOk as m)

yesno :: Bool -> String
yesno True  = "yes"
yesno False = "no"

main :: IO ()
main = do
    _  <- fmap readInt getLine
    as <- fmap (map readInt . words) getLine
    _  <- fmap readInt getLine
    ms <- fmap (map readInt . words) getLine
    let ans = map (isOk as) ms
    mapM_ (putStrLn . yesno) ans