Practice Trigonometry with the exercise "Number of triangles enclosing X"

Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Trigonometry

Statement

Goal

Given a point X in an orthonormal coordinate system, you must find the number of triangles formed by the other given points in which X is inside.



Example 1
INPUT  REPRESENTATION  OUTPUT  COMMENT
X 2;3  B(1;5)          1       X is inside the triangle ABC
3      |\
A 1;1  | \
B 1;5  |  \
C 5;1  | x(2;3)
       |    \
       |_____\
       A(1;1) C(5;1)


Example 2
INPUT  REPRESENTATION  OUTPUT  COMMENT
X 2;3  B(1;5)  D(5;5)  2       X is inside the triangles ABC and ABD
        _____
4      |\    /|
A 1;1  | \  / |
B 1;5  |  \/  |
C 5;1  | x(2;3)
D 5;5  | /  \ |
       |/____\|
       A(1;1) C(5;1)

Input

Line 1: X x;y string for the coordinates of point X. x and y are floats.
Line 2: an integer n for the number of points to read.
Next n Lines p x;y for the points with their coordinates used to build triangles, x and y are floats.

Output

c Number of triangles where X is inside.

Constraints

The triangles ABC, CBA, BCA... are considered as the same triangle.
All points are unique: they have different names and coordinates.
n <= 100

Example

Input

X 2;3
3
A 1;1
B 1;5
C 5;1

Output

Solve it

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