Description

There is a polygon A₁A₂...A_n (the vertices A_i are numbered in the clockwise order). On each side A_iA_i+1 an isosceles triangle A_iM_iA_i+1 is built on the outer side of the polygon, and angle A_iM_iA_i+1 = α_i. Here A_n+1 = A₁.

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 <= 50, co-ordinates of vertices M_i and angles α_i (measured in degrees). Write a program which restores co-ordinates of the polygon vertices.

Input

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 M_i. And the last n lines of the file consist of degree values of angles α_i.

Output

The output file should contain n lines of pairs of coordinates of the points

3
0 2
3 3
2 0
90
90
90

Hint

1 1

1 3

3 1

Source

Ural State University collegiate programming contest 2000