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

\(1 \leq N \leq 10^6 \\ 1 \leq A_i \leq 10^6 \\ 1 \leq Q \leq 10^6 \\ 1 \leq X \leq 10^6\)