# USACO Bronze division

# Cow Gymnastics

In order to improve their physical fitness, the cows have taken up gymnastics! Farmer John designates his favourite 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, Bessie ranks the **n** cows according to their performance. 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 contains two positive integers **k** (**1** ≤ **k** ≤ **10**) and **n** (**1** ≤ **n** ≤ **20**). The next **k** lines will each contain the integers **1** ... **n** in some order, indicating the rankings of the cows (cows are identified by the numbers **1**...**n**). If **A** appears before **B** in one of these lines, that means cow **A** did better than cow **B**.

#### Output

Print the number of consistent pairs.

#### Example

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

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

4