Restore the Polygon

Time Limit: 2 Seconds
Memory Limit: 65536 KB

There is a polygon A_{1}A_{2}...A_{n}(the vertices A_{i} are numbered in the clockwise order). On each side A_{i}A_{i+1} an isosceles triangle A_{i}M_{i}A_{i+1} is built on the outer side of the polygon, and angle A_{i}M_{i}A_{i+1} = a_{i}. Here A_{n+1} = A_{1}.

The set of angles a_{i} 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 M_{i} and angles a_{i}(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 M_{i}. And the last n lines of the file consist of degree values of angles a_{i}. 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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