Problem:
Score : 700 points

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 ≦ 10^{9}

a_i \neq b_i

S_i \neq T_i

The given graph is connected.

Partial Scores

In the test set worth 200 points, Q = 1.

In the test set worth another 300 points, Q ≦ 3000.

Input

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

N M
a_1 b_1 c_1
a_2 b_2 c_2
:
a_M b_M c_M
Q
S_1 T_1
S_2 T_2
:
S_Q T_Q

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.

Solution in Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

#!ruby -na
a,b,c=$F.map &:to_i;$.<2?(N,M,*P=a,b;R,*U=->x{U[x]?U[x]=R[U[x]]:x};Z=(G=1..N).map{[]};Q=G.map{[]};D=->i,q,r,v{Z[r][i]=v;Q[i].map{|j,c|j!=q&&D[j,i,r,[v,c].max]}}):$.<M+2?P<<[c,a-1,b-1]:$.<M+3?(s=0;P.sort.map{|c,a,b|R[a]==R[b]||(U[R[b]]=R[a];Q[a]<<[b,c];Q[b]<<[a,c];s+=c)};N.times{|i|D[i,i,i,0]}):p(s-Z[a-1][b-1])