Number of pairs

Input

The first line contains an integer $n$ ( $1 \leq n \leq 1 0^{5}$ 1 \le n \le 10^5). The second line contains $n$ integers, representing the $x$ -coordinates of the points, where each coordinate is between $0$ and $1 0^{5}$ 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 $k_{i}$ k_i ( $0 \leq k_{i} \leq 1 0^{9}$ 0 \le k_i \le 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

Example 1

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