graph

graph

Problem Statement

Takahashi found an undirected connected graph with N vertices and M edges. The vertices are numbered 1 through N. The i-th edge connects vertices a_i and b_i, and has a weight of c_i.

He will play Q rounds of a game using this graph. In the i-th round, two vertices S_i and T_i are specified, and he will choose a subset of the edges such that any vertex can be reached from at least one of the vertices S_i or T_i by traversing chosen edges.

For each round, find the minimum possible total weight of the edges chosen by Takahashi.

Constraints

• 1 ≦ N ≦ 4,000
• 1 ≦ M ≦ 400,000
• 1 ≦ Q ≦ 100,000
• 1 ≦ a_i,b_i,S_i,T_i ≦ N
• 1 ≦ c_i ≦ 10⁹
• a_i ≠ b_i
• S_i ≠ T_i
• The given graph is connected.

Partial Scores

• In the test set worth 28 points, Q = 1.
• In the test set worth another 43 points, Q ≦ 3000.

Input

The input is given from Standard Input in the following format:

N M
a1 b1 c1
a2 b2 c2
:
aM bM cM
Q
S1 T1
S2 T2
:
SQ TQ

Output

Print Q lines. The i-th line should contain the minimum possible total weight of the edges chosen by Takahashi.

Sample Input 1

4 3
1 2 3
2 3 4
3 4 5
2
2 3
1 4

Sample Output 1

8
7

We will examine each round:

• In the 1-st round, choosing edges 1 and 3 achieves the minimum total weight of 8.
• In the 2-nd round, choosing edges 1 and 2 achieves the minimum total weight of 7.

Sample Input 2

4 6
1 3 5
4 1 10
2 4 6
3 2 2
3 4 5
2 1 3
1
2 3

Sample Output 2

8

This input satisfies the additional constraints for both partial scores.