$N$ participants, numbered $1$ to $N$, will participate in a contest with $M$ problems, numbered $1$ to $M$.

For an integer $i$ between $1$ and $N$ and an integer $j$ between $1$ and $M$, participant $i$ can solve problem $j$ if the $j$-th character of $S_i$ is `o`, and cannot solve it if that character is `x`.

The participants must be in pairs. Print the number of ways to form a pair of participants who can collectively solve all the $M$ problems.

More formally, print the number of pairs $(x,y)$ of integers satisfying $1\leq x < y\leq N$ such that for any integer $j$ between $1$ and $M$, at least one of participant $x$ and participant $y$ can solve problem $j$.

The input is given from Standard Input in the following format:

```
$N$ $M$
$S_1$
$S_2$
$\vdots$
$S_N$
```

Print the answer.

-   $N$ is an integer between $2$ and $30$, inclusive.
-   $M$ is an integer between $1$ and $30$, inclusive.
-   $S_i$ is a string of length $M$ consisting of `o` and `x`.

5

The following five pairs satisfy the condition: participants 1 and 2, participants 1 and 3, participants 1 and 4, participants 1 and 5, and participants 2 and 3.
On the other hand, the pair of participants 2 and 4, for instance, does not satisfy the condition because they cannot solve problem 4.