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D. Mr. Kitayuta's Colorful Graph
time limit per test
4 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Mr. Kitayuta has just bought an undirected graph with n vertices and m edges. The vertices of the graph are numbered from 1 to n. Each edge, namely edge i, has a color c i, connecting vertex a i and b i.

Mr. Kitayuta wants you to process the following q queries.

In the i-th query, he gives you two integers - u i and v i.

Find the number of the colors that satisfy the following condition: the edges of that color connect vertex u i and vertex v i directly or indirectly.

Input

The first line of the input contains space-separated two integers - n and m(2 ≤ n ≤ 105, 1 ≤ m ≤ 105), denoting the number of the vertices and the number of the edges, respectively.

The next m lines contain space-separated three integers - a i, b i(1 ≤ a i < b i ≤ n) and c i(1 ≤ c i ≤ m). Note that there can be multiple edges between two vertices. However, there are no multiple edges of the same color between two vertices, that is, if i ≠ j, (a i, b i, c i) ≠ (a j, b j, c j).

The next line contains a integer- q(1 ≤ q ≤ 105), denoting the number of the queries.

Then follows q lines, containing space-separated two integers - u i and v i(1 ≤ u i, v i ≤ n). It is guaranteed that u i ≠ v i.

Output

For each query, print the answer in a separate line.

Examples
Input
4 51 2 11 2 22 3 12 3 32 4 331 23 41 4
Output
210
Input
5 71 5 12 5 13 5 14 5 11 2 22 3 23 4 251 55 12 51 51 4
Output
11112
Note

Let's consider the first sample.

The figure above shows the first sample.
• Vertex 1 and vertex 2 are connected by color 1 and 2.
• Vertex 3 and vertex 4 are connected by color 3.
• Vertex 1 and vertex 4 are not connected by any single color.