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 JavaScript (judge verdict: Wrong Answer)

const line = require('fs').readFileSync('/dev/stdin', 'utf-8').split('\n');

let cnt = 0;

const merge = (arr, left, mid, right) => {
    const n1 = mid - left;
    const n2 = right - mid;
    const L = [];
    const R = [];

    for (let i = 0; i < n1; i++) {
        L[i] = arr[left + i];
    }
    for (let i = 0; i < n2; i++) {
        R[i] = arr[mid + i];
    }

    L[n1] = 1/0;
    R[n2] = 1/0;

    let i = 0;
    let j = 0;
    for (let k = left; k < right; k++) {
        cnt++;
        if (L[i] <= R[j]) {
            arr[k] = L[i];
            i++;
        } else {
            arr[k] = R[j];
            j++;
        }
    }
};

const msort = (arr, left, right) => {
    if (left + 1 < right) {
        const mid = Math.floor((left + right) / 2);
        msort(arr, left, mid);
        msort(arr, mid, right);
        merge(arr, left, mid, right);
    }
};

const data = line[1].split(' ').map(Number);
msort(data, 0, data.length);
console.log(data.join(' '));
console.log(cnt);