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)

// ALDS1_5_A: Exhaustive Search

use std::str::FromStr;

fn scan() -> usize {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    let v = s.trim().parse().ok().unwrap();
    v
}

fn scan_vec() -> Vec<u32> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    let vec = s.split_whitespace().map(|n| u32::from_str(n).unwrap()).collect::<Vec<u32>>();
    vec
}

fn solve(a: &Vec<u32>, n: usize, i: usize, m: u32) -> bool {
    if m == 0 {
        return true;
    } 
    if i >= n {
        return false;
    }
    solve(a, n, i + 1, m) || solve(a, n, i+1, m - a[i])
}

fn main() {
    let n = scan();
    let a = scan_vec();
    let q = scan();
    let m = scan_vec();

    for i in 0..q {
        if solve(&a, n, 0, m[i]) {
            println!("yes");
        } else {
            println!("no");
        }
    }
}