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.
7 5 1 2 1 4 2 3 4 1 2 5 3 6 1 6 4 7 2 2 4 3 3 2
18 11
3 1 2 1000000000 2 3 1000000000 1 2 1000000000
2000000000000000000
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 $$$11$$$.
