Points

Time limit1sMemory limit128 MB

Summary

Count triangles formed by white points that have no black point strictly inside them.

Level: Medium7 of 10
Topics: Geometry, Combinatorics, Sorting, Two pointers
Solved: No attempts yet

Problem

There are $n + m$ points on the plane. Exactly $n$ of them are white and the remaining $m$ are black.

Count the number of triangles whose three vertices are white points and that contain no black point in their interior.

You may assume that no three points are collinear.

Input

The first line contains two integers $n$ and $m$ ( $0 \le n, m \le 500$ ), the number of white points and the number of black points, respectively.

The next $n$ lines describe the white points, and the following $m$ lines describe the black points. Each line contains two integers $x$ and $y$ ( $-10^9 \le x, y \le 10^9$ ), the coordinates of a point.

Output

Print, on a single line, the number of triangles with white vertices that contain no black point inside.

Hint

The figure above illustrates the first example.

Examples3

Example 1
Input
```
4 1
6 0
3 6
3 3
0 0
2 1
```
Expected output
```
2
```
Example 2
Input
```
3 1
0 0
10 0
0 10
1 1
```
Expected output
```
0
```
Example 3
Input
```
3 1
0 0
10 0
0 10
100 100
```
Expected output
```
1
```