Polish version    English version  
  History of OI


 News
 About Olympic
 History of OI
XVII OI 2009/2010
XVI OI 2008/2009
XV OI 2007/2008
XIV OI 2006/2007
XIII OI 2005/2006
XII OI 2004/2005
XI OI 2003/2004
X OI 2002/2003
IX OI 2001/2002
VIII OI 2000/2001
VII OI 1999/2000
VI OI 1998/1999
V OI 1997/1998
IV OI 1996/1997
III OI 1995/1996
II OI 1994/1995
I OI 1993/1994
 OI books
 National team
 Olympic camps
 Photo gallery
 Links
 SIO
 MAIN

Task: pun


Points


I stage competition  
Source file: pun.xxx (xxx=pas,c,cpp)
Memory limit: 32 MB

Alternative formats: PostScript | PDF

A set of integer points on a plane (points whose both cartesian coordinates are integers) which we shall refer to as the pattern, as well as a group of other sets of integer points on the plane are given. We would like to know which of the sets are similar to the pattern, i.e. which of them can be transformed by rotations, translations, reflections and dilations so that they are identical to the pattern. For instance: the set of points {(0,0), (2,0), (2,1)} is similar to the set {(6,1), (6,5), (4,5)}, it is however not similar to the set {(4,0),(6,0), (5,-1)}.

Task

Write a programme which:

  • reads from the standard input the description of the pattern and the familly of the investigated sets of points,
  • determines which of the investigated sets of points are similar to the pattern,
  • writes the outcome to the standard output.

Input

In the first line of the standard input there is a single integer k (1 <= k <= 25.000) - the number of points the pattern consists of. In the following k lines there are pairs of integers, separated by single spaces. The i+1st line containts the coordinates of ith point belonging to the pattern: x_i i y_i (-20.000 <= x_i, y_i <= 20.000). The points forming the pattern are pairwise different. In the next line there is the number of sets to be investigated: n (1 <= n <= 20). Next, there are n descriptions of these sets. The description of each set begins with a line containing a single integer l - the number of points belonging to that particular set (1 <= l <= 25.000). These points are described in the following lines, a single point per line. The description of a point consists of two integers separated by a single space - its coordinates x i y (-20.000 <= x, y <= 20.000). The points which belong to the same set are pairwise different.

Output

Your programme should write to the standard output n lines - one for each of the investigated sets of points. The ith line should contain the word TAK (YES in Polish), if the ith of the given sets of points is similar to the pattern, or the word NIE (NO in Polish) if the set does not satisfy this condition.

Example

For the input data:

3
0 0
2 0
2 1
2
3
4 1
6 5
4 5
3
4 0
6 0
5 -1

the correct outcome is:

TAK
NIE



Print friendly version