Fast Fingers Thomas is delivering poutine to Wilson's restaurants!

Fast Fingers Thomas will drive a truck on a weighted tree with ~N~ vertices.

Each trip has two parameters, a source vertex ~s_i~ and a destination vertex ~t_i~. Thomas does not like driving along long edges, so he seeks to minimize the length of the second-longest edge that he travels on. Formally, if the weights of the edges that Thomas traverses are ~W_1, \dots, W_K~ in nondecreasing order, he seeks to minimize ~W_{K-1}~.

For each trip, compute this quantity.

Constraints

~2 \le N \le 10^5~

~1 \le a_i, b_i \le N~

~1 \le w_i \le 10^9~

~1 \le Q \le 10^5~

~1 \le s_i, t_i \le N~

~s_i \neq t_i~

Input Specification

The first line contains a single positive integer, ~N~.

The next ~N-1~ lines contain three space-separated integers, ~a_i~, ~b_i~, and ~w_i~, indicating an undirected edge between ~a_i~ and ~b_i~ of weight ~w_i~.

The next line contains a single positive integer, ~Q~.

The next ~Q~ lines contain two space-separated positive integers, ~s_i~ and ~t_i~, the parameters for query ~i~.

Output Specification

Output ~Q~ lines. On the ~i~th line, output the length of the second-longest edge that Thomas will take for the ~i~th trip. If Thomas can travel between ~s_i~ and ~t_i~ using strictly fewer than two edges, output -1.

Sample Input

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

Sample Output

2
3