Ant

Problem Description

The ant is on a board shaped like a convex polygon. It moves straight in the direction it is facing, but does not know which direction that is. If it reaches the edge of the board, it will fall off. Given the position of the ant and the positions of the vertices that make up the convex polygon of the board, determine the shortest distance it can travel before falling off the board. All positions are given in 2D coordinates.

Input

The first line contains two integers $x$ and $y$, representing the coordinates of the ant ($-100 \le x \le 100$, $-100 \le y \le 100$).

The second line contains an integer $N$, representing the number of vertices of the polygon ($3 \le N \le 10$).

The next $N$ lines contain integers $x_i$ and $y_i$ ($-100 \le x_i, y_i \le 100$), representing the coordinates of the vertices of the polygon, given in counterclockwise order.

All input values are integers. The point $(x,y)$ is guaranteed to be strictly inside the polygon (not on the boundary), and the polygon is guaranteed to be convex.

Output

Output the shortest distance that the ant can travel before falling off the board, on a single line. The output will be accepted if the absolute error or relative error does not exceed $10^{-6}$.

Scoring System

0 0
4
100 100
-100 100
-100 -100
100 -100

100

10 10
3
0 100
-100 -100
100 -100

31.3049516850

34 6
7
-43 -65
-23 -99
54 -68
65 92
16 83
-18 43
-39 2

25.0284205314