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 :

$1 \le N \le 10^5$

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

$1 \le q \le 10^5$

$0 \le r_{i} \le 10^{18}$