I. Unrooted Trie
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Example
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
Output
2
0
Note

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.