Geometers Anonymous Club

Description:

Input:

The first line of the input contains one integer $$$n$$$ — the number of convex polygons Denis prepared ($$$1 \le n \le 100\,000$$$).

Then $$$n$$$ convex polygons follow. The description of the $$$i$$$-th polygon starts with one integer $$$k_i$$$ — the number of vertices in the $$$i$$$-th polygon ($$$3 \le k_i$$$). The next $$$k_i$$$ lines contain two integers $$$x_{ij}$$$, $$$y_{ij}$$$ each — coordinates of vertices of the $$$i$$$-th polygon in counterclockwise order ($$$|x_{ij}|, |y_{ij}| \le 10 ^ 9$$$).

It is guaranteed, that there are no three consecutive vertices lying on the same line. The total number of vertices over all polygons does not exceed $$$300\,000$$$.

The following line contains one integer $$$q$$$ — the number of tasks ($$$1 \le q \le 100\,000$$$). The next $$$q$$$ lines contain descriptions of tasks. Description of the $$$i$$$-th task contains two integers $$$l_i$$$ and $$$r_i$$$ ($$$1 \le l_i \le r_i \le n$$$).

Output:

For each task print a single integer — the number of vertices in the sum of Minkowski of polygons with indices from $$$l_i$$$ to $$$r_i$$$.

Sample Input:

3
3
0 0
1 0
0 1
4
1 1
1 2
0 2
0 1
3
2 2
1 2
2 1
3
1 2
2 3
1 3

Sample Output:

5
5
6

Note:

Description of the example:

First, second and third polygons from the example Minkowski sums of the first and second, the second and third and all polygons correspondingly