github.com/captn3m0/codechef.git

---
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---
<span class="solution-visible-txt">All submissions for this problem are available.</span><h3>Read problems statements in <a target="_blank" 
href="http://www.codechef.com/download/translated/JULY18/mandarin/SUBWAY.pdf">Mandarin chinese</a>, <a target="_blank" 
href="http://www.codechef.com/download/translated/JULY18/russian/SUBWAY.pdf">Russian</a> and <a target="_blank" 
href="http://www.codechef.com/download/translated/JULY18/vietnamese/SUBWAY.pdf">Vietnamese</a> as well.</h3>



Being a newcomer to Computopia, Chef is confused by the countless subway lines in the city. Help him!

You are given an undirected graph with $N$ vertices and $M$ edges. There are no self-loops and no simple cycles that contain more than 2 edges in the graph (i.e. if we replaced each set of multiple edges connecting the same pair of vertices by one edge, we would obtain a tree). Each edge also has a colour.

Consider a simple path with length $K$ in the graph that passes through edges with colours $A_1, A_2, \dots, A_K$ in this order. The *cost* of this path is defined as $(A_1 \neq A_2) + (A_2 \neq A_3) + \dots + (A_{K-1} \neq A_K)$, where the boolean value `true` is interpreted as the integer $1$ and `false` is interpreted as $0$. In other words, the cost of a simple path is the number of pairs of neighbouring (consecutive) edges on this path with different colours. The cost of a path with length $0$ is defined to be $0$.

You need to answer $Q$ queries. In each query, you are given vertices $u$ and $v$; you should find the maximum possible cost of some simple path connecting them.

Note that a simple path may not visit a vertex more than once.

### Input
- The first line of the input contains two space-separated integers $N$ and $M$.
- Each of the next $M$ lines contains three space-separated integers $u$, $v$ and $w$ denoting an edge between vertices $u$ and $v$ with colour $w$.
- The next line contains an integer $Q$.
- Each of the next $Q$ lines contains two space-separated integers $u$ and $v$ describing a query.

### Output
For each query, print a single line containing one integer — the maximum cost of a simple path.

### Constraints 
- $1 \le N, Q \le 500,000$
- $1 \le M \le 1,000,000$
- $1 \le u, v \le N$
- for each edge, $u \neq v$
- $1 \le w \le M$

### Subtasks
**Subtask #1 (20 points):**
- $1 \le N, Q \le 10$
- $1 \le M \le 100$

**Subtask #2 (20 points):**
- $1 \le N, Q \le 500$
- $1 \le M \le 10,000$

**Subtask #3 (20 points):**
- $1 \le N, Q \le 5,000$
- $1 \le M \le 100,000$

**Subtask #4 (20 points):**
- $1 \le N, Q \le 100,000$
- $1 \le M \le 300,000$

**Subtask #5 (20 points):** original constraints

### Example Input
```
8 10
1 2 1
1 2 2
1 3 2
1 3 3
2 4 2
2 5 1
3 6 3
3 7 1
3 8 1
3 8 3
5
2 3
5 6
4 6
4 8
4 7
```

### Example Output
```
1
2
3
3
3
```