Description

Updog is watching a plane object with a telescope. The field of vision in the telescope can be described as a circle. The center is at the origin and the radius is R. The object can be seen as a simple polygon of N vertexes. Updog wants to know the area of the part of the object that can be seen in the telescope.

Input

The input will contain several test cases. For each case:
The first line contains only one real number R.
The second line contains an integer N. The following N lines contain two real numbers x_i and y_i each, which describe the coordinates of a vertex. Two vertexes in adjacent lines are also adjacent on the polygon.
Constraints: 3 ≤ N ≤50, 0.1 ≤ R ≤1000, -1000 ≤ x_i, y_i ≤ 1000

Output

For each test case, output one real number on a separate line, which is the area of the part that can be seen. The result should be rounded to two decimal places.

10
3
0 20
10 0
-10 0

144.35

Source

POJ Founder Monthly Contest – 2008.07.27, Updog