Subset Sum Queries

Given a set of n integers, and q queries where each query consists of an integer . For each query, you are asked to determine whether there exists a subset of the numbers that sum up to .

Input

The first line of the input contains a single integer n (1 ≤ n ≤ 500).
The second line contains n space-separated integers (1 ≤ ≤ 100 000), the elements of the set.
The third line of the input contains a single integer q (1 ≤ q ≤ 100 000), the number of queries. Each of the next q lines contains a single integer (1 ≤ ≤ 100 000), representing the target sum for the i-th query.

Output

Output q lines, each containing either Yes or No, depending on whether there exists a subset of the numbers whose sum is equal to the corresponding query.

Examples

Input
Output
4 1 2 5 7 5 4 3 10 14 11
No Yes Yes Yes No

Constraints

Time limit: 10 seconds

Memory limit: 512 MB

Output limit: 1 MB

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