Krissh has gained stardom in India, and companies has tied up with him for their publicity and advertisement,
one such company named “X” has been organizing an advertisement campaign in which 2 people will get a chance
to meet Krissh.
Now, it is company’s policy that these two people should not be acquaintance. For this , company has asked people
to participate in lucky draw by which it will be able choose these 2 people. The company has asked Akshay Joshi,
Mani and KK to mine the info about these “n” people. Akshay, Mani and KK mined some pairs of acquaintance
relationship between these “n” people. Assume that you are provided enough pairs to let you identify the groups
of people even though you might not know their acquaintance status directly. For instance, if 1,2,3 are the
people who are acquainted to each other; it is sufficient to mention that (1,2) and (2,3) are pairs of people who
are acquainted to each other without providing information about a third pair (1,3).
The people are numbered from 0 to n - 1. Your task is to determine the number of ways the company can select pairs
of people such that they are not acquainted to each other.
NOTE : We can assume that just for the sake of question transitivity rule applies in acquaintance relationship
i.e. if 1,2 know each other and 2,3 know each other then 1,3 know each other.
Input
The first line contains two integers “n” and “m”, where “n” denotes the number of people and “m” denotes the pairs
which are mined by Akshay, Mani and KK. M lines follow. Each line contains 2 integers separated by a single space A and B
such that 0 ≤ A, B ≤ n -1 and A and B are people who are acquainted to each other.
Output
The number of ways to choose the above mentioned pair.
Constraint
1 <= n <= 10 ^ 5
1 <= m <= 10 ^ 4
Example
input
5 3
0 1
1 2
3 4
output
6
Explanation of Input
0,1 know each other , similarly 1,2 know each other, but it is not given that 0, 2 know each other(you have
to deduce it yourself).