Problem Statement

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.

Input

The input is given from Standard Input in the following format:
N M
A_1 B_1
$\vdots$
A_M B_M

Output

Print the answer.

Constraints

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

Sample Input 1

4 3
1 2
2 3
1 4

Sample Output 1

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.

Sample Input 2

3 0

Sample Output 2

0

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

Sample Input 3

10 8
1 2
2 3
3 4
4 5
6 7
7 8
8 9
9 10

Sample Output 3

12

见题面 Input 部分

见题面 Output 部分