You are given a weighted tree with N nodes. Now you are given q queries. In each query you are given three integers $x , y$ and z. Now you need to tell what will be the special distance between the two nodes x and y if you root the tree at node z.
Suppose that you want to calculate special distance between two nodes x and y and the tree is rooted at z then you start at node x and you will move towards the node y. Now if you are moving towards the root then add the weights on the edges or else subtract the weight of involved edges if you are moving away from the root.
Note: It is mandatory to view the image to understand the concept of special distance .
So for every query you have to provide the value of this distance.
Input
First line contains a number n as input denoting total number of nodes in the tree
Next $n-1$ lines contain a triplet of integers $u , v, w$ that denote there is an edge between the vertex u and v of the tree and its weight is w.
Next line contains a number q as input.
Next q lines contain a triplet of integers $x,y$ and z.
Output
For every query you need to find the absolute distance between the two nodes x and y if the root is z. Print the answer for each query in the new line.
Constraints
$1 \le n \le 10^5$
$1 \le u , v \le n$
$1 \le q \le 10^5$
$1 \le x , y , z \le n$
$-100 \le w \le 100$