## Problem Description

Recently, the term *Biometrics* been used to refer to the
emerging field of technology devoted to identification of individuals
using biological traits, such as those based on retinal or iris
scanning, fingerprints, or face recognition.

A simple biometric system translates a human image into a polygon
by considering certain features (eyes, nose, ears, etc.) to be vertices
and connecting them with line segments.
The polygon has distinct vertices
but may be degenerate in that the
line segments could intersect. Because these polygons are generally
created from remote images, there is some uncertainty as to their
scale and rotation. Your job is to determine whether or not
two polygons are similar; that is, can they be made equal
by repositioning, rotating and magnifying them?

Input consists of several test cases. Each test case consists
of three lines containing:

*f*, the number of features
*f* coordinate pairs giving the vertices of the first polygon
*f* coordinate pairs giving the vertices of the second polygon

The vertices for both polygons correspond to the same set of features
in the same order;
for example,

*right ear tip*,

*chin cleft*,

*right eye*,

*nose*,

*left eye*,

*left ear tip*,

*space between front teeth*.
Each polygon has

*f* distinct vertices;
each vertex is given
as an

*x* and

*y* coordinate pair. There are at least
three and no more than ten features. Coordinates are integers
between -1000 and 1000. A line containing 0 follows the last test
case.

For each case, output a line "similar" or "dissimilar" as appropriate.
The two polygons are similar if, after some combination of
translation, rotation, and scaling (but not reflection)
both vertices corresponding to each feature are in the same
position.

## Sample Input

4
0 0 0 1 1 1 1 0
0 1 1 0 0 -1 -1 0
3
0 0 10 0 10 10
0 0 -10 0 -10 10
3
0 0 10 10 20 20
0 0 11 11 22 22
3
0 0 10 10 20 20
0 0 11 11 20 20
0

## Sample Output

similar
dissimilar
similar
dissimilar

## Source

G. V. Cormack