Imagine a city with $*n*$ junctions and $*m*$ streets. Junctions are numbered from $1$ to $*n*$.

In order to increase the traffic flow, mayor of the city has decided to make each street one-way. This means in the street between junctions $*u*$ and $*v*$, the traffic moves only from $*u*$ to $*v*$ or only from $*v*$ to $*u*$.

The problem is to direct the traffic flow of streets in a way that maximizes the number of pairs $(*u*, *v*)$ where $1 ≤ *u*, *v* ≤ *n*$ and it is possible to reach junction $*v*$ from $*u*$ by passing the streets in their specified direction. Your task is to find out maximal possible number of such pairs.

Input

The first line of input contains integers $*n*$ and $*m*$, (), denoting the number of junctions and streets of the city.

Each of the following $*m*$ lines contains two integers $*u*$ and $*v*$, ($*u* ≠ *v*$), denoting endpoints of a street in the city.

Between every two junctions there will be at most one street. It is guaranteed that before mayor decision (when all streets were two-way) it was possible to reach each junction from any other junction.

Output

Print the maximal number of pairs $(*u*, *v*)$ such that that it is possible to reach junction $*v*$ from $*u*$ after directing the streets.

Note

In the first sample, if the mayor makes first and second streets one-way towards the junction $1$ and third and fourth streets in opposite direction, there would be 13 pairs of reachable junctions: ${(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (2, 1), (3, 1), (1, 4), (1, 5), (2, 4), (2, 5), (3, 4), (3, 5)}$