P5831 [USACO19DEC] Cow Gymnastics B

To improve their health, the cows have started doing gymnastics training. Farmer John chose his favorite cow, Bessie, to coach the other $N$ cows, while also evaluating their progress in learning different gymnastics skills. In each of the $K$ training sessions, Bessie ranks the $N$ cows based on their performance. Later, she became curious about how consistent these rankings are. A pair of different cows is called **consistent** if one cow performs better than the other in every training session. Please help Bessie count the number of consistent cow pairs.

The first line contains two positive integers $K$ and $N$. The next $K$ lines each contain a permutation of the integers $1 \ldots N$, representing the rankings of the cows (the cows are identified by numbers $1 \ldots N$). If in a line $A$ appears before $B$, it means cow $A$ performed better than cow $B$.

Output one line containing the number of consistent cow pairs.

The consistent cow pairs are $(1,4)$, $(2,4)$, $(3,4)$, and $(1,3)$. $1 \leq K \leq 10$, $1 \leq N \leq 20$. Problem by: Nick Wu. Translated by ChatGPT 5