Its time for yet another challenge, and this time it has been prepared by none other than Monk himself for Super-Hardworking Programmers like you. So, this is how it goes:

Given N points located on the co-ordinate plane, where the \(i^{th}\) point is located at co-ordinate \((x_{i}\), \(y_{i})\), you need to answer q queries.

In the \(i^{th}\) query, you shall be given an integer \(r_{i}\), and considering you draw a circle centered at the origin \((0,0)\) with radius \(r_{i}\), you need to report the number of points lying inside or on the circumference of this circle.

For each query, you need to print the answer on a new line.

Input Format :

The first line contains a single integer N denoting the number of points lying on the co-ordinate plane. Each of the next N lines contains 2 space separated integers \(x_{i}\) and \(y_{i}\), denoting the x and y co-ordintaes of the \(i^{th}\) point.

The next line contains a single integer q, denoting the number of queries. Each of the next q lines contains a single integer, where the integer on the \(i^{th}\) line denotes the parameters of the \(i^{th}\) query \(r_{i}\).

Output Format :

For each query, print the answer on a new line.

Constraints :

\( 1 \le N \le 10^5 \)

\( -10^9 \le x_{i} , y_{i} \le 10^9 \)

\( 1 \le q \le 10^5 \)

\( 0 \le r_{i} \le 10^{18} \)