Number of pairs

You are given n points on the line y = 0. Your task is to answer queries regarding the number of pairs of points that have a distance equal to k.

Input

The first line contains an integer n (1 ≤ n ≤ 10^5). The second line contains n integers, representing the x-coordinates of the points, where each coordinate is between 0 and 10^5. All points have distinct coordinates. The third line contains an integer q, the number of queries. Each of the following q lines contains a single integer k[i] (0 ≤ k[i] ≤ 10^9).

Output

For each query, output the number of pairs of points that have a distance equal to the given k, with each result on a new line.

Examples