Description

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

= α

_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 <= 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

</p>1 3 3 1

Source

Ural State University collegiate programming contest 2000