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:
Geometrical dreams
Time Limit: 1000MSMemory Limit: 65536K
Total Submissions: 540Accepted: 300

Description

There is a polygon A1A2...An (the vertices Ai are numbered in the clockwise order). On each side AiAi+1 an isosceles triangle AiMiAi+1 is built on the outer side of the polygon, and angle AiMiAi+1 = αi. Here An+1 = A1.
The set of angles ai satisfies a condition that the sum of angles in any of its nonempty subsets is not aliquot to 360 degrees.
You are given n <= 50, co-ordinates of vertices Mi and angles αi (measured in degrees). Write a program which restores co-ordinates of the polygon vertices.

Input

The first line of an input contains an integer n. The next n lines contain pairs of real numbers which are co-ordinates of points Mi. And the last n lines of the file consist of degree values of angles αi.

Output

The output file should contain n lines of pairs of coordinates of the points

Sample Input

3
0 2
3 3
2 0
90
90
90

Sample Output

Hint

1 1
1 3
3 1

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