You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 4.0 seconds
Memory limit: 256.0 MB

# Problem
You like the card board game "Set". Each card contains $$$k$$$ features, each of which is equal to a value from the set $$$\{0, 1, 2\}$$$. The deck contains all possible variants of cards, that is, there are $$$3^k$$$ different cards in total.

A feature for three cards is called good if it is the same for these cards or pairwise distinct. Three cards are called a set if all $$$k$$$ features are good for them.

For example, the cards $$$(0, 0, 0)$$$, $$$(0, 2, 1)$$$, and $$$(0, 1, 2)$$$ form a set, but the cards $$$(0, 2, 2)$$$, $$$(2, 1, 2)$$$, and $$$(1, 2, 0)$$$ do not, as, for example, the last feature is not good.

A group of five cards is called a meta-set, if there is strictly more than one set among them. How many meta-sets there are among given $$$n$$$ distinct cards?

## Input Format
The first line of the input contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n \le 10^3$$$, $$$1 \le k \le 20$$$) — the number of cards on a table and the number of card features. The description of the cards follows in the next $$$n$$$ lines.

Each line describing a card contains $$$k$$$ integers $$$c_{i, 1}, c_{i, 2}, \ldots, c_{i, k}$$$ ($$$0 \le c_{i, j} \le 2$$$) — card features. It is guaranteed that all cards are distinct.

## Output Format
Output one integer — the number of meta-sets.

## Examples
```input
8 4
0 0 0 0
0 0 0 1
0 0 0 2
0 0 1 0
0 0 2 0
0 1 0 0
1 0 0 0
2 2 0 0
```
```output
1
```
-----
```input
7 4
0 0 0 0
0 0 0 1
0 0 0 2
0 0 1 0
0 0 2 0
0 1 0 0
0 2 0 0
```
```output
3
```
-----
```input
9 2
0 0
0 1
0 2
1 0
1 1
1 2
2 0
2 1
2 2
```
```output
54
```
-----
```input
20 4
0 2 0 0
0 2 2 2
0 2 2 1
0 2 0 1
1 2 2 0
1 2 1 0
1 2 2 1
1 2 0 1
1 1 2 2
1 1 0 2
1 1 2 1
1 1 1 1
2 1 2 0
2 1 1 2
2 1 2 1
2 1 1 1
0 1 1 2
0 0 1 0
2 2 0 0
2 0 0 2
```
```output
0
```

## Note
Let's draw the cards indicating the first four features. The first feature will indicate the number of objects on a card: $$$1$$$, $$$2$$$, $$$3$$$. The second one is the color: red, green, purple. The third is the shape: oval, diamond, squiggle. The fourth is filling: open, striped, solid.

You can see the first three tests below. For the first two tests, the meta-sets are highlighted.

In the first test, the only meta-set is the five cards $$$(0000,\ 0001,\ 0002,\ 0010,\ 0020)$$$. The sets in it are the triples $$$(0000,\ 0001,\ 0002)$$$ and $$$(0000,\ 0010,\ 0020)$$$. Also, a set is the triple $$$(0100,\ 1000,\ 2200)$$$ which does not belong to any meta-set.

In the second test, the following groups of five cards are meta-sets: $$$(0000,\ 0001,\ 0002,\ 0010,\ 0020)$$$, $$$(0000,\ 0001,\ 0002,\ 0100,\ 0200)$$$, $$$(0000,\ 0010,\ 0020,\ 0100,\ 0200)$$$.

In there third test, there are $$$54$$$ meta-sets.

Now solve the problem and return the code.