There is an SNS used by $N$ users, labeled with numbers from $1$ to $N$.

In this SNS, two users can become friends with each other.  
Friendship is bidirectional; if user X is a friend of user Y, user Y is always a friend of user X.

Currently, there are $M$ pairs of friendships on the SNS, with the $i$-th pair consisting of users $A_i$ and $B_i$.

Determine the maximum number of times the following operation can be performed:

-   Operation: Choose three users X, Y, and Z such that X and Y are friends, Y and Z are friends, but X and Z are not. Make X and Z friends.

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

```
$N$ $M$
$A_1$ $B_1$
$\vdots$
$A_M$ $B_M$
```

Print the answer.

-   $2 \leq N \leq 2 \times 10^5$
-   $0 \leq M \leq 2 \times 10^5$
-   $1 \leq A_i < B_i \leq N$
-   The pairs $(A_i, B_i)$ are distinct.
-   All input values are integers.

3

Three new friendships with a friend's friend can occur as follows:

• User 1 becomes friends with user 3, who is a friend of their friend (user 2)
• User 3 becomes friends with user 4, who is a friend of their friend (user 1)
• User 2 becomes friends with user 4, who is a friend of their friend (user 1)

There will not be four or more new friendships.

0

If there are no initial friendships, no new friendships can occur.