Alice is buying Christmas trees! The shopkeeper, for some reason, keeps the trees arranged in a weird layout. Each of the ~N~ 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 ~Q~ special Christmas offers, where the ~i~-th offer allows the customer to buy all trees covering the point ~(x_i, y_i)~. Alice wonders: for each offer, how many trees is she able to buy?

Constraints

~1 \le N, Q \le 3 \times 10^3~

~-10^9 \le x_{i1}, y_{i1}, x_{i2}, y_{i2}, x_{i3}, y_{i3}, x_i, y_i \le 10^9~

~x_{i1} = x_{i2}~

~x_{i1} \neq x_{i3}~

~y_{i1} \neq y_{i2}~

~y_{i1} = y_{i3}~

Input Specification

The first line contains ~2~ integers ~N~ and ~Q~.

The next ~N~ lines each contain ~6~ integers ~x_{i1}, y_{i1}, x_{i2}, y_{i2}, x_{i3}, y_{i3}~, describing the coordinates of the vertices of the ~i~-th tree. Specifically, the ~i~-th tree covers the area bounded by the triangle with vertices ~(x_{i1}, y_{i1}), (x_{i2}, y_{i2}), (x_{i3}, y_{i3})~.

The next ~Q~ lines each contain ~2~ integers ~x_i, y_i~, the point included in the ~i~-th offer.

Output Specification

For each offer, output the answer on a new line.

Sample Input

2 5
-2 -3 -2 3 7 -3
-4 1 -4 -6 3 1
2 2
-4 1
1 -2
-2 -1
3 -5

Sample Output

0
1
1
2
0

Explanation

A diagram of the sample case is provided below: