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;
use std::collections::HashMap;

fn main() {
    let _ = read_vec::<i32>();
    let a = read_vec::<i32>();
    let _ = read_vec::<i32>();
    let m = read_vec::<i32>();

    let mut map = HashMap::new();
    let len = a.len();

    for s in 0..1 << len {
        let mut sum = 0;
        for i in 0..len {
            if s >> i & 1 == 1 {
                sum = sum + a[i];
            }
        }
        map.insert(sum, 0);
    }

    for num in m {
        if map.contains_key(&num) {
            println!("yes");
        } else {
            println!("no");
        }
    }
}


/// 標準入力から一行を読み取り、空白文字で分割し、各要素を指定の型に変換する関数
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut line = String::new();
    io::stdin().read_line(&mut line)
        .ok()
        .expect("Faild to read Vec");
    line.trim().split_whitespace()
        .map(|i| i.parse().ok().unwrap()).collect()
}