| 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. |
|
|
| Townsville is made up of **N** neighbourhoods, with **M** one-way roads |
| running between them. The **i**th road runs from neighbourhood **Ai** to |
| neighbourhood **Bi**. A swarm of rich migrants will move to the city all at |
| once, immediately gentrifying any neighbourhood they decide to move into. |
|
|
| 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. |
|
|
| Putting these facts together, it means that if rich migrants move into and |
| gentrify any two neighbourhoods **u** and **v**, then it must be the case that |
| there is a series of roads connecting **u** to **v** if and only if there is a |
| series of roads connecting **v** to **u**. |
|
|
| Given this self-imposed constraint, and the layout of the roads in Townsville, |
| what is the maximum number of neighbourhoods that can be gentrified? |
|
|
| ### Input |
|
|
| Input begins with an integer **T**, the number of test cases. For each test |
| case, there is first a line containing the space-separated integers **N** and |
| **M**. |
|
|
| Then, **M** lines follow, the **i**th of which contains the space-separated |
| integers **Ai** and **Bi**. |
|
|
| ### Output |
|
|
| For the **i**th test case, print a line containing "Case #**i**: " followed by |
| the maximum possible number of gentrified neighbourhoods. |
|
|
| ### Constraints |
|
|
| 1 ≤ **T** ≤ 20 |
| 1 ≤ **N** ≤ 500 |
| 1 ≤ **M** ≤ 20,000 |
| 0 ≤ **Ai**, **Bi** < **N** for all 1 ≤ **i** ≤ **N** |
| **Ai** ≠ **Bi** for all 1 ≤ **i** ≤ **N** |
|
|
| ### Explanation of Sample |
|
|
| In the first test case, you can get from any neighbourhood to any other |
| neighbourhood, so they can all be gentrified. |
|
|
| 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. |
|
|
|
|
