Alice is buying Christmas trees! The shopkeeper, for some reason, keeps the trees arranged in a weird layout. Each of the trees covers a triangular region in a coordinate plane where one side of the triangle is parallel to the x-axis and another side is parallel to the y-axis. The shop offers special Christmas offers, where the -th offer allows the customer to buy all trees covering the point . Alice wonders: for each offer, how many trees is she able to buy?
The first line contains integers and .
The next lines each contain integers , describing the coordinates of the vertices of the -th tree. Specifically, the -th tree covers the area bounded by the triangle with vertices .
The next lines each contain integers , the point included in the -th offer.
For each offer, output the answer on a new line.
2 5 -2 -3 -2 3 7 -3 -4 1 -4 -6 3 1 2 2 -4 1 1 -2 -2 -1 3 -5
0 1 1 2 0
A diagram of the sample case is provided below: