A weighted tree is given. You must find the distance between two given nodes.
Input
The first line contains the number of nodes of the tree n (1 ≤ n ≤ 50000). The nodes are numbered from 0 to n – 1.
Each of the next n – 1 lines contains three integers
u, v, w, which correspond to an edge
with weight w (0 ≤ w ≤ 1000) connecting nodes u and v.
The next line contains the number of queries m (1 ≤ m ≤ 75000).
In each of the next m lines there are two integers.
Output
For each query, output the distance between the nodes with the given numbers.
Sample
input  output 

3
1 0 1
2 0 1
3
0 1
0 2
1 2
 1
1
2

Problem Author: Dmitry Zhukov
Problem Source: Ural SU and Orel STU Contest. Petrozavodsk Summer Session, August 2006