Hidden Camera
John wants to put a hidden camera in a room. For this problem, we ignore the vertical dimension and treat the room as a twodimensional object. The room has the shape of a convex polygon. The camera is placed on a wall, halfway between two corners. The camera has a limited view: the borders of the view are given by the two lines that intersect the wall at a 45 degree angle. John wants to know how much of the room is visible to the camera. Can you help him?
Input
On the first line one positive number: the number of test cases, at most 100. After that per test case:

one line with a single integer $n$ ($3 \leq n \leq 1\, 000$): the number of corners of the room.

$n$ lines with two spaceseparated integers $x$ and $y$ ($10\, 000 \leq x,y \leq 10\, 000$): the coordinates of the corners.
The corners are given in counterclockwise order. All angles are strictly between $0$ and $180$ degrees. The camera is placed exactly halfway between the first two corners in the input.
Output
Per test case:

one line with one floating point number: the ratio of the area that the camera can see and the total area of the room. This number should be accurate up to $10^{6}$ relative or absolute precision.
Sample Input 1  Sample Output 1 

2 5 3 0 3 0 4 5 2 8 5 3 4 0 2 2 0 3 1 1 3 
0.7125 0.5 