Pastries

A bakery has baked $N$ triangular pastries. Every pastry can be described as a triangle whose three vertices have integer coordinates on the 2D plane.

A child wants to cut the pastries with a large knife. Each cut is made along a vertical line $x = c$ or a horizontal line $y = c$. For a single cut, we want to know how many pastries in total get cut. A pastry is considered cut if the cut divides it into two parts and both parts have area greater than $0$.

Given the positions of the pastries and the list of cuts, write a program that determines how many pastries each cut slices through.

The first line contains the number of pastries $N$. ($2 \le N \le 100{,}000$)

Each of the next $N$ lines contains six non-negative integers, each smaller than $10^6$. In order they are $(x_1, y_1)$, $(x_2, y_2)$, $(x_3, y_3)$, the three vertices of a triangular pastry. No three of these points are collinear. Different pastries may overlap or touch each other.

The next line contains the number of cuts $M$. ($2 \le M \le 100{,}000$)

Each of the next $M$ lines describes one cut in the form x = c or y = c, where $c$ is a non-negative integer smaller than $10^6$.

Print, one per line and in the given order, how many pastries each cut slices through. Treat every cut independently; that is, assume the pastry magically becomes whole again after each cut.