Points

You are given a set of grid points in the plane (points whose two Cartesian coordinates are both integers); we call this set the pattern. You are also given a family of other sets of grid points in the plane.

For each set, decide whether it is similar to the pattern, i.e. whether it can be turned into a set identical to the pattern by some combination of rotations, translations, reflections and dilations (scalings).

For example, the set $\{(0,0),(2,0),(2,1)\}$ is similar to the set $\{(6,1),(6,5),(4,5)\}$, but it is not similar to the set $\{(4,0),(6,0),(5,-1)\}$.

Write a program that:

• reads the pattern and the family of investigated sets from standard input,
• determines which of the investigated sets are similar to the pattern,
• writes the result to standard output.

The first line contains a single integer $k$ ($1 \le k \le 25\,000$) — the number of points in the pattern. Each of the next $k$ lines contains two integers separated by a single space; the $i$-th of them holds the coordinates $x_i$ and $y_i$ ($-20\,000 \le x_i, y_i \le 20\,000$) of the $i$-th pattern point. The points of the pattern are pairwise distinct.

The next line contains the number of sets to investigate, $n$ ($1 \le n \le 20$). Then follow the descriptions of the $n$ sets. Each description begins with a line containing a single integer $l$ ($1 \le l \le 25\,000$) — the number of points in that set. Each of the next $l$ lines contains two integers $x$ and $y$ ($-20\,000 \le x, y \le 20\,000$), the coordinates of one point. The points belonging to the same set are pairwise distinct.

Print $n$ lines, one for each investigated set. On the $i$-th line print TAK (Polish for “yes”) if the $i$-th set is similar to the pattern, or NIE (Polish for “no”) otherwise.