Number of pairs - 2

Input

The first line contains one integer $n$ ( $1 \leq n \leq 1 0^{6}$ 1 \leq n \leq 10^6) — the number of points. Each of the next $n$ lines contains two integers $x_{i}$ x_i and $y_{i}$ y_i ( $0 \leq x_{i}, y_{i} < 1 0^{3}$ 0 \leq x_i, y_i < 10^3) — the coordinates of the $i$ -th point. It is guaranteed that all points are distinct.

The next line contains one integer $q$ ( $1 \leq q \leq 1 0^{6}$ 1 \leq q \leq 10^6) — the number of queries. Each of the next $q$ lines contains one integer $k_{i}$ k_i ( $0 \leq k_{i} \leq 1 0^{9}$ 0 \leq k_i \leq 10^9) — the queried distance value.

Output

For each query, output on a separate line the number of unordered pairs of points with distance exactly equal to $k_{i}$ k_i.

Examples

Example 1

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