Two players take part in the game polygons. A convex polygon with n vertices divided by n-3 diagonals into n-2 triangles is necessary. These diagonals may intersect in vertices of the polygon only. One of the triangles is black and the remaining ones are white. Players proceed in alternate turns. Each player, when its turn comes, cuts away one triangle from the polygon. players are allowed to cut off triangles along the given diagonals. The winner is the player who cuts away the black triangle.
NOTE: We call a polygon convex if a segment joining any two points of the polygon is contained in the polygon.

Task

Write a program which: 

• reads from the text file GRA.IN the description of the polygon,
• verifies whether the player who starts the game has a winning strategy,
• writes the result into the file GRA.OUT.

Input

The first line of the input file GRA.IN contains an integer n, 4 <= n <= 50000. This is the number of vertices in the polygon. The vertices of the polygon are numbered, clockwise, from 0 to n-1.
The next n-2 lines comprise descriptions of triangles in the polygon. In the i+1-th line, 1 <= i <= n-2, there are three non-negative integers a, b, c separated by single spaces. Theses are numbers of vertices of the i-th triangle. The first triangle in a sequence is black.

Output

The output file GRA.OUT should have one line with the word:

• TAK (means "yes" in Polish), if the player, who starts the game has a winning strategy,
• NIE (means "no" in Polish), if he does not have a winning strategy.

Example

For the input file GRA.IN:

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

the correct answer is the text file GRA.OUT:

TAK

Your program should look for the file GRA.IN in the current directory and produce the output file GRA.OUT in current directory too. The file containing source code of your program should have a name GRA.???, whereas you should put three-letter abbreviation of used programming language name instead of ???. The same program in executable form should be written in file GRA.EXE