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

$1\le N,Q\le 3\times {10}^3$

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

$x_{i1}=x_{i2}$

$x_{i1}\ne x_{i3}$

$y_{i1}\ne y_{i2}$

$y_{i1}=y_{i3}$

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: