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

func main() {
	sc := bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)
	n, err := nextInt(sc)
	if err != nil {
		panic(err)
	}
	as, err := nextInts(n, sc)
	if err != nil {
		panic(err)
	}
	q, err := nextInt(sc)
	if err != nil {
		panic(err)
	}
	ms, err := nextInts(q, sc)
	if err != nil {
		panic(err)
	}
	for _, v := range ms {
		if exhaustiveSearch(v, as) {
			fmt.Println("yes")
		} else {
			fmt.Println("no")
		}
	}
}

func exhaustiveSearch(x int, elements []int) bool {
	return solve(x, 0, elements)
}

func solve(target int, index int, elements []int) bool {
	if target == 0 {
		return true
	} else if target < 0 || index >= len(elements) {
		return false
	} else {
		return solve(target-elements[index], index+1, elements) ||
			solve(target, index+1, elements)
	}
}

func nextInt(sc *bufio.Scanner) (int, error) {
	sc.Scan()
	return strconv.Atoi(sc.Text())
}

func nextInts(n int, sc *bufio.Scanner) ([]int, error) {
	rs := make([]int, n)
	for i, _ := range rs {
		x, err := nextInt(sc)
		if err != nil {
			return nil, err
		}
		rs[i] = x
	}
	return rs, nil
}