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E. Strongly Connected City 2

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputImagine 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.

Examples

Input

5 4

1 2

1 3

1 4

1 5

Output

13

Input

4 5

1 2

2 3

3 4

4 1

1 3

Output

16

Input

2 1

1 2

Output

3

Input

6 7

1 2

2 3

1 3

1 4

4 5

5 6

6 4

Output

27

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)}

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

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