|시간 제한||메모리 제한||제출||정답||맞은 사람||정답 비율|
|1 초||128 MB||182||36||31||25.833%|
The Bytean cross spider (Araneida baitoida) is known to have an amazing ability. Namely, it can instantly build an arbitrarily large spiderweb as long as it is contained in a single plane. This ability gives the spider an opportunity to use a fancy hunting strategy. It does not need to wait until a fly is caught in an already built spiderweb; if only the spider knows the current position of a fly, it can instantly build a spiderweb to catch the fly.
A cross spider has just spotted n flies in Byteasar’s garden. Each fly is flying still in some point of a 3D space. The spider is wondering if it can catch all the flies with a single spiderweb. Write a program that answers the spider’s question.
The first line of the input contains an integer n (1 ≤ n ≤ 100 000). The following n lines contain a description of the flies in a 3D space: the i-th line contains three integers xi, yi, zi (−1 000 000 , xi, yi, zi , 1 000 000) giving the coordinates of the i-th fly (a point in a 3-dimensional Euclidean space). No two flies are located in the same point.
Your program should output a single word TAK (i.e., yes in Polish) if the spider can catch all the flies with a single spiderweb. Otherwise your program should output the word NIE (no in Polish).
4 0 0 0 -1 0 -100 100 0 231 5 0 15
4 0 1 0 -1 0 -100 100 0 231 5 0 15