Any integer $A$ is said to be compatible with  another integer $B$ if $A|B=A+B$ where $A|B$ is the Bitwise OR of $A$ and $B$.

You are given an array $A$ of $N$ integers. You are also given $Q$ queries where each query has a single integer $X$. For each query find the sum of all the array elements which are compatible with $X$.

Input format

• The first line contains a single integer $N$.
• The second line, contains $N$ space-separated integers, the array elements. 
• The third line contains a single integer $Q$.
• The next $Q$ lines contain a single integer each, the value of $X$.

Output format

Print the answer for each query in a separate line — the sum of all the array elements which are compatible with $X$.

Constraints

$1 \leq N \leq 10^6 \\ 1 \leq A_i \leq 10^6 \\ 1 \leq Q \leq 10^6 \\ 1 \leq X \leq 10^6$