Polygons

Two players play the game of polygons. You are given a convex polygon with $n$ vertices that has been divided by $n-3$ pairwise non-crossing diagonals into $n-2$ triangles. The diagonals meet only at vertices of the polygon. One of the triangles is black and all of the others are white.

The players move in alternating turns. On a turn, the current player cuts exactly one triangle away from the current polygon along a diagonal. The only triangle that may be cut off is one that has a diagonal as one of its sides and two sides of the current polygon as its other two sides; cutting it removes that triangle from the polygon. The player who cuts away the black triangle wins.

A polygon is convex if the segment joining any two of its points lies entirely inside the polygon.

Write a program that reads the description of the polygon and decides whether the player who moves first has a winning strategy.

The first line contains an integer $n$, the number of vertices of the polygon ($4 \le n \le 50000$). The vertices are numbered clockwise from $0$ to $n-1$.

Each of the next $n-2$ lines describes one triangle. The $i$-th of these lines ($1 \le i \le n-2$) contains three non-negative integers $a$, $b$, $c$ separated by single spaces, the numbers of the vertices of the $i$-th triangle. The triangle given first is the black one.

Print a single line containing TAK if the player who moves first has a winning strategy, or NIE otherwise. (TAK and NIE mean 'yes' and 'no' in Polish.)