2015/round3/gentrification.html

<p>
The residents of Townsville have made it clear to the mayor that they're greatly concerned about gentrification,
a process by which wealthy people move into the city in large numbers, displacing the people who currently
live there. The mayor of Townsville knows a thing or two about this, and she would like to put the people's
minds at ease by determining the worst-case scenario.
</p>

<p>
Townsville is made up of <strong>N</strong> neighbourhoods, with <strong>M</strong> one-way roads running
between them. The <strong>i</strong>th road runs from neighbourhood
<strong>A<sub>i</sub></strong> to neighbourhood <strong>B<sub>i</sub></strong>. A swarm of rich migrants will
move to the city all at once, immediately gentrifying any neighbourhood they decide to move into.
</p>

<p>
The mayor knows the following facts about these new affluent residents: 
First, they like to visit other gentrified neighbourhoods.
If there's a way of getting from their home neighbourhood to another gentrified neighbourhood, they will
surely go visit. Second, they never walk anywhere; they only drive. Consequently, they'll get very angry if they end
up in some neighbourhood with no way to drive back home.
</p>

<p>
Putting these facts together, it means that
if rich migrants move into and gentrify any two neighbourhoods <strong>u</strong> and <strong>v</strong>, 
then it must be the case that there is a series of roads connecting <strong>u</strong> to <strong>v</strong> 
if and only if there is a series of roads connecting <strong>v</strong> to <strong>u</strong>. 
</p>

<p>
Given this self-imposed constraint, and the layout of the roads in Townsville, what is the maximum number of neighbourhoods 
that can be gentrified?
</p>


<h3>Input</h3>
<p>
Input begins with an integer <strong>T</strong>, the number of test cases.
For each test case, there is first a line containing the space-separated integers 
<strong>N</strong> and <strong>M</strong>.
</p>

<p>
Then, <strong>M</strong> lines follow, the <strong>i</strong>th of which contains the space-separated integers
<strong>A<sub>i</sub></strong> and <strong>B<sub>i</sub></strong>.
</p>


<h3>Output</h3>
<p>
For the <strong>i</strong>th test case, print a line containing "Case #<strong>i</strong>: " followed by
the maximum possible number of gentrified neighbourhoods.
</p>


<h3>Constraints</h3>
<p>
1 &le; <strong>T</strong> &le; 20 <br />
1 &le; <strong>N</strong> &le; 500 <br />
1 &le; <strong>M</strong> &le; 20,000 <br />
0 &le; <strong>A<sub>i</sub></strong>, <strong>B<sub>i</sub></strong> &lt; <strong>N</strong>
for all 1 &le; <strong>i</strong> &le; <strong>N</strong> <br />
<strong>A<sub>i</sub></strong> &ne; <strong>B<sub>i</sub></strong>
for all 1 &le; <strong>i</strong> &le; <strong>N</strong> <br />
</p>


<h3>Explanation of Sample</h3>
<p>
In the first test case, you can get from any neighbourhood to any other neighbourhood, so they can all be gentrified.
<p>

<p>
In the second test case, any single neighbourhood can be gentrified, but that's it. If any two neighbourhoods are gentrified,
there would be a path from one to the other, but no path back.
</p>