Cow Gymnastics

Interview

Time limit1sMemory limit512 MB

Summary

Given K rankings of N cows, count the pairs where one cow beats the other in every ranking.

Level: Easy3 of 10
Topics: Brute force, Array, Implementation
Solved: No attempts yet

Problem

In order to improve their physical fitness, the cows have taken up gymnastics! Farmer John designates his favorite cow Bessie to coach the $N$ other cows and to assess their progress as they learn various gymnastic skills.

In each of $K$ practice sessions ( $1 \leq K \leq 10$ ), Bessie ranks the $N$ cows according to their performance ( $1 \leq N \leq 20$ ). Afterward, she is curious about the consistency in these rankings. A pair of two distinct cows is consistent if one cow did better than the other one in every practice session.

Help Bessie compute the total number of consistent pairs.

Input

The first line of the input file contains two positive integers $K$ and $N$ . The next $K$ lines will each contain the integers $1 \ldots N$ in some order, indicating the rankings of the cows (cows are identified by the numbers $1 \ldots N$ ). If $A$ appears before $B$ in one of these lines, that means cow $A$ did better than cow $B$ .

Output

Output, on a single line, the number of consistent pairs.

Hint

The consistent pairs of cows are $(1,4)$ , $(2,4)$ , $(3,4)$ , and $(1,3)$ .

Examples1

Example 1
Input
```
3 4
4 1 2 3
4 1 3 2
4 2 1 3
```
Expected output
```
4
```