P9648 [SNCPC2019] Unrooted Trie

Recall the definition of a trie: - A trie of size $n$ is a rooted tree with $n$ vertices and $(n-1)$ edges, where each edge is marked with a character; - Each vertex in a trie represents a string. Let $s(x)$ be the string vertex $x$ represents; - The root of the trie represents an empty string. Let vertex $u$ be the parent of vertex $v$, and let $c$ be the character marked on the edge connecting vertex $u$ and $v$, we have $s(v)$ = $s(u) + c$. Here $+$ indicates string concatenation, not the normal addition operation. We say a trie is valid, if the string each vertex represents is distinct. Given an unrooted tree with $n$ vertices and $(n-1)$ edges, where each edge is marked with a character, how many different vertices can be selected as the root of the tree so that the tree becomes a valid trie?

There are multiple test cases. The first line of the input contains an integer $T$, indicating the number of test cases. For each test case: The first line contains an integer $n$ ($1 \le n \le 10^5$), indicating the size of the tree. For the following $(n-1)$ lines, the $i$-th line contains two integers $u_i$, $v_i$ ($1 \le u_i, v_i \le n$) and a character $c_i$ separated by a space, indicating that there is an edge marked with a character $c_i$ connecting vertex $u_i$ and $v_i$. It's guaranteed that $c_i$ will only be lower-case English letters. It's guaranteed that the given graph is a tree, and the sum of $n$ of all test cases will not exceed $10^6$.

For each test case output one line containing one integer, indicating the number of different vertices that can be selected as the root of the tree to make it a valid trie.

For the first sample test case, we can only select vertex 1 or vertex 2 as the root, otherwise $s(1)$ and $s(2)$ will be the same. For the second sample test case, no matter which vertex we select as the root, $s(1)$ and $s(2)$, or $s(5)$ and $s(6)$ will be the same.