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

$2\le N\le {10}^5$

$1\le a_i,b_i\le N$

$1\le w_i\le {10}^9$

$1\le Q\le {10}^5$

$1\le s_i,t_i\le N$

$s_i\ne t_i$

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