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: Accepted)

use std::io;

fn is_combinable(vec: &Vec<u32>, target: u32) -> bool {
    dfs(0, vec, 0, target)
}

fn dfs(idx: usize, vec: &Vec<u32>, sum: u32, target: u32) -> bool {
    if idx < vec.len() {
        dfs(idx+1, vec, sum+vec[idx], target) 
            || dfs(idx+1, vec, sum, target)
    } else {
        sum == target
    }
}

fn main() {
    let sin = io::stdin();

    let mut buf = String::new();
    sin.read_line(&mut buf).ok();
    let _n: usize = buf.trim().parse().unwrap();

    let mut buf = String::new();
    sin.read_line(&mut buf).ok();
    let a: Vec<u32> = buf.split_whitespace()
        .map(|v| v.parse().unwrap())
        .collect::<Vec<u32>>();

    let mut buf = String::new();
    sin.read_line(&mut buf).ok();
    let _q: usize = buf.trim().parse().unwrap();

    let mut buf = String::new();
    sin.read_line(&mut buf).ok();
    let m: Vec<u32> = buf.split_whitespace()
        .map(|v| v.parse().unwrap())
        .collect::<Vec<u32>>();
    
    for v in m {
        if is_combinable(&a, v) {
            println!("yes");
        } else {
            println!("no");
        }
    }
    
}