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
