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: Time Limit Exceeded)

package main

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

func check(a []int, m int) bool {
	var i, j, n int
	n = len(a)
	max := int(math.Pow(2, float64(n)))
	for i = 1; i <= max; i++ {
		sum := 0
		for j = 0; j < n; j++ {
			if (i >> uint(j)) & 1 != 0 {
				sum += a[j]
				if sum > m {
					break
				}
			}
		}
		if m == sum {
			return true
		}
	}
	return false
}

func main() {
	sc := bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)

	sc.Scan()
	n, _ := strconv.Atoi(sc.Text())
	a := make([]int, n)
	for i := 0; i < n; i++ {
		sc.Scan()
		a[i], _ = strconv.Atoi(sc.Text())
	}

	sc.Scan()
	q, _ := strconv.Atoi(sc.Text())
	for i := 0; i < q; i++ {
		sc.Scan()
		m, _ := strconv.Atoi(sc.Text())

		if check(a, m) {
			fmt.Println("yes")
		} else {
			fmt.Println("no")
		}
	}
}