Problem Description

Given the coordinates of the three vertices of a triangle and the coordinates of $N$ points, calculate the area of the triangle and determine how many of these $N$ points lie inside the triangle (including the boundary).

Input Format

The first three lines, each containing two integers, represent the coordinates of a vertex of the triangle.

The next line contains an integer $N$.

The following $N$ lines, each containing two integers $x_i, y_i$, represent the coordinates of the $i$-th point.

Output Format

The first line contains a real number, representing the area of the triangle, rounded to one decimal place.

The second line contains an integer, representing the number of points inside the triangle and on its boundary.

Sample Input and Output

Sample Input #1

1 1
5 1
3 3
4
3 1
3 2
3 3
3 4

Sample Output #1

4.0
3

Sample Input #2

3 2
5 4
1 6
3
2 4
3 5
4 3

Sample Output #2

6.0
3

Sample Input #3

2 6
5 1
7 8
5
1 4
3 5
6 4
6 5
4 7

Sample Output #3

15.5
2

Notes

For $100\%$ of the data, $1 \le N \le 100$, and all coordinates $x, y$ are positive integers less than $10^3$.

Hint: The formula for the area of a triangle with vertices at $(x_A, y_A)$, $(x_B, y_B)$, and $(x_C, y_C)$ is as follows:

$\dfrac{|x_A(y_B-y_C)+x_B(y_C-y_A)+x_C(y_A-y_B)|}{2}$

This problem is scored according to the original competition settings, with a maximum of $30$ points.

见题面 Input 部分

见题面 Output 部分