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39 - ZOJ Monthly, September 2005 - 1005
Restore the Polygon

Time Limit: 2 Seconds      Memory Limit: 65536 KB

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 = ai. 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(which is not greater than 50) co-ordinates of vertices Mi and angles ai(measured in degrees). Write a program which restores co-ordinates of the polygon vertices.

Input

The input consists of multiple test cases. In each test case, the first line is 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 ai. Input ends with EOF.

Output

The output file should contain n lines of pairs of coordinates of the points with value rounded to two digitis after the decimal point. Print a blank line between two test cases.

Sample Input

3
0 2
3 3
2 0
90
90
90

Sample Output:

1.00 1.00
1.00 3.00
3.00 1.00


Author: DAI, Wenbin


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