Let’s define a term “Powerful Pair” as pair of two integer numbers, say A and B such that bitwise xor of these integers ( say, A xor B ) is a power of 2.

You are given a tree rooted at vertex 1 and total N vertices where each node contains a value in it. You have to answer Q queries. In each query, you will be given two vertices U and V, your task is to count the number of pairs of vertices (X, Y) (not necessarily distinct) such that X belongs to the subtree rooted at U and Y belongs to the subtree rooted at V and values in these vertices form a Power Pair.

Input:

Input starts with an integer N (1<=N<=100000), denoting the total number of nodes in tree. Next line contain N space separated integers denoting the values in node starting from 1 to N, which is nonnegative integer having value at most 100000. Next N-1 line contain two space separated integers, denoting an edge in tree. Next line will contain a single integer Q (1<=Q<=100000), denoting total number of quires. Following Q lines will contain two integers U and V separated by space between them.

Output:

For each query, output an integer denoting total number of ways of forming powerful pairing in between the values of subtrees given in each query.