Intransitive

Peter has some unconventional dice. A number can appear multiple times on their faces, and the numbers are not necessarily between 1 and 6. For example, he has three dice ( $A,B,C$ ), with the following numbers on their faces:

A: 2, 2, 4, 4, 9, 9
B: 1, 1, 6, 6, 8, 8
C: 3, 3, 5, 5, 7, 7

If Panna uses die

A

and Peter uses die

B

in a game where the winner is the one who rolls a higher number (neither wins in the case of a tie), then Panna has an advantage. This can be shown by considering the 36 possible

A−B

roll pairs and counting how many times the number rolled on

A

is greater than the number rolled on

B

. In our case:

(2,1),(2,1)
(2,1),(2,1)
(4,1),(4,1)
(4,1),(4,1)
(9,1),(9,1),(9,6),(9,6),(9,8),(9,8)
(9,1),(9,1),(9,6),(9,6),(9,8),(9,8)

Here, we went through the numbers on die $A$ one by one and paired them with numbers from die $B$ that they are greater than. We see that in 20 out of 36 cases, die $A$ rolls higher numbers than die $B$ , meaning Panna wins in more than half the cases. Similarly, the same is true for $B$ versus $C$ : $B$ wins in more than half the cases. And most surprisingly, the same holds for $C$ versus $A$ . In everyday terms, $A$ is stronger than $B$ , $B$ is stronger than $C$ , and $C$ is stronger than $A$ !

Peter calls such a set of three dice with this property interesting, and now he wants to know how many interesting triples of dice exist in a set of

N

unconventional dice.

Input specification

The first line contains the number of dice, $N$ . Then $N$ lines follow each of with 6 numbers: $f_{i,1}\le f_{i,2}\le \ldots \le f_{i,6}\ \ i=1\ldots N$ . The dice are pairwise different.