| Recently, Melody built a little boat, as cute as it could be. And she put a | |
| number of animals, two-by-two, on her little boat on the sea! | |
| Melody's boat features **N** rooms, numbered from 1 to **N**. The contents of | |
| the _i_th room are described by the string **Ai**. If **Ai** = "-", then the | |
| room is empty, while otherwise the room contains an animal of species **Ai** | |
| (where **Ai** is a case-sensitive alphanumeric string made up of lowercase | |
| letters "a"..."z", uppercase letters "A"..."Z", and digits "0"..."9"). There | |
| are **at most two animals of any given species** on the boat. | |
| There are **N**-1 corridors in the boat, the _i_th of which allows Melody and | |
| the animals to travel in either direction between rooms **Xi** and **Yi**. | |
| Each room is reachable from each other room by following a sequence of | |
| corridors. | |
| It's time for Melody's daily walk through her boat! She'd like to choose one | |
| room to start in and a different room to end in, and walk from the former to | |
| the latter. She'll take the unique path which allows her to do so without | |
| visiting any room multiple times. Along the way, any time she finds herself in | |
| a room containing an animal (including the starting or ending room), that | |
| animal will join her for the remainder of her walk. Normally, both Melody and | |
| the animals will keep quiet, which is just how she likes it. However, if two | |
| animals of any given species ever end up joining her, they'll promptly make a | |
| racket talking to one another, which is no good! As such, she'll refuse to | |
| take a walk which would result in encountering two of any species of animal. | |
| For how many of the **N***(**N**-1) possible ordered pairs of starting/ending | |
| rooms would it be possible for Melody to enjoy a quiet walk from one to the | |
| other? | |
| ### Input | |
| Input begins with an integer **T**, the number of boats. | |
| For each boat, there is first a line containing the integer **N**. | |
| Then, **N** lines follow, the _i_th of which contains the string **Ai**. | |
| Then, **N** \- 1 lines follow, the _i_th of which contains the space-separated | |
| integers **Xi** and **Yi**. | |
| ### Output | |
| For the _i_th boat, print a line containing "Case #_i_: " followed by one | |
| integer, the number of valid ordered pairs of starting and ending rooms for | |
| Melody's walk. | |
| ### Constraints | |
| 1 ≤ **T** ≤ 95 | |
| 2 ≤ **N** ≤ 800,000 | |
| 1 ≤ **Xi**, **Yi** ≤ **N** | |
| 1 ≤ |**Ai**| ≤ 10 | |
| The sum of **N** across all **T** test cases is no greater than 4,000,000. | |
| ### Explanation of Sample | |
| In the first case, the 4 starting/ending room pairs (1, 2), (2, 1), (2, 3), | |
| and (3, 2) are valid. On the other hand, the pairs (1, 3) and (3, 1) are not. | |
| For example, on the way from room 1 to room 3, a Fox would begin following | |
| Melody around in room 1, and upon being joined by another Fox in room 3, the | |
| two Foxen would begin making strange noises towards one another. | |
| In the second case, both possible starting/ending room pairs ((1, 2) and (2, | |
| 1)) are no good, as they would involve encountering two talkative Turtles. | |
| In the third case, both possible starting/ending room pairs will do, as no two | |
| animals of any given species can be encountered. | |