There is a polygon A_{1}A_{2}…A_{N} (the vertices
A_{i} are numbered in 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 (M_{i}A_{i} = M_{i}A_{i+1}). The angle A_{i}M_{i}A_{i+1} is equal to α_{i}. Here we assume that A_{N+1} = A_{1}.
The set of angles α_{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, coordinates of vertices M_{i} and angles α_{i} (measured in degrees). Write a program, which restores coordinates of the polygon vertices.
Input
The first line contains an integer N (3 ≤ N ≤ 50). The next N lines contain pairs of real numbers x_{i}, y_{i} which are coordinates of points M_{i} (–100 ≤ x_{i}, y_{i} ≤ 100). And the last N lines of the input consist of degree values of angles α_{i}. All real numbers in the input contain at most 2 digits after decimal point.
Output
Output N lines with points coordinates, ith line should contain the coordinates of A_{i}. Coordinates must be accurate to 2 digits after decimal point. You may assume that solution always exists.
Sample
input  output 

3
0 2
3 3
2 0
90
90
90
 1 1
1 3
3 1

Problem Author: Dmitry Filimonenkov
Problem Source: Ural State University collegiate programming contest (25.03.2000)