## USACO 2019 December Contest, Bronze

## Problem 1. Cow Gymnastics

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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.

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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 FORMAT (file gymnastics.in):

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 FORMAT (file gymnastics.out):

Output, on a single line, the number of consistent pairs.#### SAMPLE INPUT:

3 4 4 1 2 3 4 1 3 2 4 2 1 3

#### SAMPLE OUTPUT:

4

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

Problem credits: Nick Wu