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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.
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.
The output file should contain n lines of pairs of coordinates of the points
3 0 2 3 3 2 0 90 90 90
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