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ZOJ Problem Set - 4134
Unrooted Trie

Time Limit: 1 Second      Memory Limit: 65536 KB

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?

#### Input

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 $10^6$.

#### Output

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.

#### Sample Input

2
6
3 1 a
3 2 a
3 4 b
4 5 c
4 6 d
6
3 1 a
3 2 a
3 4 b
5 4 c
6 4 c


#### Sample Output

2
0


Author: CHEN, Jingbang
Source: The 2019 ICPC China Shaanxi Provincial Programming Contest
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