Online JudgeProblem SetAuthorsOnline ContestsUser
Web Board
Home Page
F.A.Qs
Statistical Charts
Problems
Submit Problem
Online Status
Prob.ID:
Register
Update your info
Authors ranklist
Current Contest
Past Contests
Scheduled Contests
Award Contest
User ID:
Password:
  Register
Language:
Telescope
Time Limit: 1000MSMemory Limit: 65536K
Total Submissions: 3643Accepted: 1023

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 xi and yi 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 ≤ xi, yi ≤ 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.

Sample Input

10
3
0 20
10 0
-10 0

Sample Output

144.35

Source

[Submit]   [Go Back]   [Status]   [Discuss]

Home Page   Go Back  To top


All Rights Reserved 2003-2013 Ying Fuchen,Xu Pengcheng,Xie Di
Any problem, Please Contact Administrator