Points

In a planar square bounded whose opposite corners are (-20,000,
-20,000) and (20,000, 20,000), consider a particular set of K (1
<= K <= 25,000) x,y points whose cartesian coordinates are both
integers which we will call a `pattern'.

In that same planar portion, consider as well a N (1 <= N <= 20)
other sets of planar points, also with integer coordinates. We would
like to know which of these sets is similar to the pattern, i.e.,
which of them can be transformed by rotations, translations,
reflections and dilations (scaling) 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)}.

Write a program which:

* reads the description of the pattern and the family of the
  investigated sets of points,

* determines which of the investigated sets of points are similar
  to the pattern,

PROBLEM NAME: points

INPUT FORMAT:

* Line 1: A single integer: K

* Lines 2..K+1: Line i describes point i of the pattern with two
        space-separated integers: x_i and y_i

* Lines K+2.....: A single integer: N

* Lines K+3.. and on: N descriptions of these sets follows. In the
        intuitive way, 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). Each of the
        subsequent L lines contains a pair of space separated
        integers, x_j,y_j.  The points which belong to the same set
        are pairwise different.

SAMPLE INPUT:

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

OUTPUT FORMAT:

* Lines 1..N: Line i contains 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.

SAMPLE OUTPUT:

TAK
NIE