A9582. Strongly Connected City 2

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.

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.

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

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: ${(1,1),(2,2),(3,3),(4,4),(5,5),(2,1),(3,1),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)}$