CF1866K.Keen Tree Calculation

There is a tree of $N$ vertices and $N-1$ edges. The $i$ -th edge connects vertices $U_i$ and $V_i$ and has a length of $W_i$ .

Chaneka, the owner of the tree, asks you $Q$ times. For the $j$ -th question, the following is the question format:

• $X_j$ $K_j$ – If each edge that contains vertex $X_j$ has its length multiplied by $K_j$ , what is the diameter of the tree?

Notes:

• Each of Chaneka's question is independent, which means the changes in edge length do not influence the next questions.
• The diameter of a tree is the maximum possible distance between two different vertices in the tree.

The first line contains a single integer $N$ ( $2\leq N\leq10^5$ ) — the number of vertices in the tree.

The $i$ -th of the next $N-1$ lines contains three integers $U_i$ , $V_i$ , and $W_i$ ( $1 \leq U_i,V_i \leq N$ ; $1\leq W_i\leq10^9$ ) — an edge that connects vertices $U_i$ and $V_i$ with a length of $W_i$ . The edges form a tree.

The $(N+1)$ -th line contains a single integer $Q$ ( $1\leq Q\leq10^5$ ) — the number of questions.

The $j$ -th of the next $Q$ lines contains two integers $X_j$ and $K_j$ as described ( $1 \leq X_j \leq N$ ; $1 \leq K_j \leq 10^9$ ).

Output $Q$ lines with an integer in each line. The integer in the $j$ -th line represents the diameter of the tree on the $j$ -th question.

In the first example, the following is the tree without any changes.

The following is the tree on the $1$ -st question.

The maximum distance is between vertices $6$ and $7$ , which is $6+6+6=18$ , so the diameter is $18$ .

The following is the tree on the $2$ -nd question.

The maximum distance is between vertices $2$ and $6$ , which is $3+2+6=11$ , so the diameter is $11$ .