We have an undirected graph with N vertices and M edges. The vertices are numbered 1 through N, and the edges are numbered 1 through M. Edge i connects vertices a_i and b_i. The graph is connected.
On this graph, Q pairs of brothers are participating in an activity called Stamp Rally. The Stamp Rally for the i-th pair will be as follows:
Find the minimum possible score for each pair.
The input is given from Standard Input in the following format:
N M a_1 b_1 a_2 b_2 : a_M b_M Q x_1 y_1 z_1 x_2 y_2 z_2 : x_Q y_Q z_Q
Print Q lines. The i-th line should contain the minimum possible score for the i-th pair of brothers.
5 6 2 3 4 5 1 2 1 3 1 4 1 5 6 2 4 3 2 4 4 2 4 5 1 3 3 1 3 4 1 3 5
1 2 3 1 5 5