You are given the coordinates of $n$ points and a set of $m$ isosceles right triangles. The legs (shortest sides) of the triangles are parallel to the coordinate axes.

For each triangle, you have to find how many of the given points it contains.

First line contains two positive integers $n$ and $m$ $(1 \leq n,m \leq 10^5)$, the numbers of points and the number of triangles respectively.

Next $n$ lines contain two integers $x$ $y$ $(-10^9\le x,y \le 10^9)$, the coordinates of each of the given points.

Next $m$ lines contain six integers $x_1\ y_1\ x_2\ y_2\ x_3\ y_3$ $(-10^9\le x_1,y_1,x_2,y_2,x_3,y_3 \le 10^9)$, the coordinates of the vertices of the given triangles.

Print $m$ numbers in separated lines, the number of points on each triangle.

Input

3 2
1 1
-8 -4
-8 -4
0 0 -100 0 0 -100
2 3 3 3 2 4

Output

2
0

Input

9 5
0 0
10 0
20 0
0 10
10 10
20 10
0 20
10 20
20 20
20 0 20 20 0 0
0 20 0 -20 40 20
0 20 0 -19 39 20
9 9 12 9 9 12
-10 -10 -15 -10 -10 -15

Output

6
9
8
1
0

Input

5 4
1000000000 1000000000
-1000000000 1000000000
1000000000 -1000000000
-1000000000 -1000000000
0 0
1000000000 1000000000 -1000000000 1000000000 1000000000 -1000000000
1000000000 -1000000000 1000000000 1000000000 -1000000000 -1000000000
-1000000000 1000000000 -1000000000 -1000000000 1000000000 1000000000
-1000000000 -1000000000 1000000000 -1000000000 -1000000000 1000000000

Output

4
4
4
4