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 Go (judge verdict: Accepted)

package main

import (
	"fmt"
	"strconv"
	"bufio"
	"os"
)

var sc = bufio.NewScanner(os.Stdin)

func nextInt() int {
	sc.Scan()
	v, _ := strconv.Atoi(sc.Text())
	return v
}

func exhaustiveSearch(A []int, n, i, m int) bool {
	// i-1を選んだときにもとのmが作れている
	if m == 0 {
		return true
	}

	if i >= n {
		return false
	}

	// i を選ばなかったときに残りの数で m　を作れるか: exhaustiveSearch(A, n, i+1, m)
	// i を選んだときに残りの数で m-i　を作れるか: exhaustiveSearch(A, n, i+1, m-A[i]
	return exhaustiveSearch(A, n, i+1, m) || exhaustiveSearch(A, n, i+1, m-A[i])
}

func main() {
	sc.Split(bufio.ScanWords)
	n := nextInt()
	A := make([]int, n)
	for i := 0; i < n; i++ {
		A[i] = nextInt()
	}

	q := nextInt()
	for i := 0; i < q; i++ {
		v := nextInt()
		if exhaustiveSearch(A, n, 0, v) {
			fmt.Println("yes")
		} else {
			fmt.Println("no")
		}
	}
}