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 Rust (judge verdict: Time Limit Exceeded)

fn search_recursive(i: u32, target: i32, arr: &mut Vec<i32>, a: &Vec<i32>) -> bool {
    let sum = arr.iter()
        .zip(a.iter())
//        .cloned()
        .filter(|&(&u, &_)| u == 1)
        .map(|(&_u, &a)| a)
        .fold(0, |s, n| s + n);

    if sum == target {
        return true;
    } else if sum > target {
        return false;
    }

    if i >= arr.len() as u32 {
        return false;
    }

    let res1 = search_recursive(i + 1, target, arr, &a);
    arr[i as usize] = 1;

    let res2 = search_recursive(i + 1, target, arr, &a);
    arr[i as usize] = 0;

    res1 || res2
}

fn search(target: i32, arr: &Vec<i32>) -> () {
    let mut v: Vec<i32> = vec![0; arr.len()];
    if search_recursive(0, target, &mut v, arr) {
        println!("yes");
    } else {
        println!("no");
    }
}

fn main() {
    let mut line = String::new();
    std::io::stdin().read_line(&mut line).ok();

    let mut line = String::new();
    std::io::stdin().read_line(&mut line).ok();
    let mut inputs_a: Vec<i32> = line.split_whitespace()
        .map(|e| e.parse::<i32>().ok().unwrap())
        .collect();

    inputs_a.sort();
    inputs_a.reverse();

    let mut line = String::new();
    std::io::stdin().read_line(&mut line).ok();

    let mut line = String::new();
    std::io::stdin().read_line(&mut line).ok();
    let inputs_t: Vec<i32> = line.split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect();

    // println!("{:?}", inputs_a);
    // println!("{:?}", inputs_t);

    for t in inputs_t {
        search(t, &inputs_a);
    }
}