Strongly Connected City 2
Description
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.
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.
5 4<br>1 2<br>1 3<br>1 4<br>1 5<br>
4 5<br>1 2<br>2 3<br>3 4<br>4 1<br>1 3<br>
2 1<br>1 2<br>
6 7<br>1 2<br>2 3<br>1 3<br>1 4<br>4 5<br>5 6<br>6 4<br>
13<br>
16<br>
3<br>
27<br>
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)}