F. Hide and seek

**单点时限: **5.0 sec

**内存限制: **512 MB

`lbromine`

,`Komorebi`

and`Amuzi`

like to play hide-and-seek in the teaching building. The teaching building is very large and its structure is very strange. It is composed of $n$ classrooms numbered from $1$ to $n$ and $n-1$ two-way passages, and any two classrooms can reach each other.

`lbromine`

is responsible for finding and `Komorebi`

and`Amuzi`

are responsible for hiding.But the teaching building is too big, so`lbromine`

makes a rule that the `Komorebi`

and`Amuzi`

can only hide in the classroom with the classroom number in the range of $[l, r] $.

At the beginning,`lbromine`

can use his transmission device to transmit to any classroom in the teaching building with $0$ seconds, and then search for `Komorebi`

and `Amuzi`

along the passages of the classrooms. In order to evaluate whether the selected interval $[l, r] $is reasonable, `lbromine`

wants to know the shortest possible time he needs to find `Komorebi`

and `Amuzi`

for some intervals.

The first line of input contains a positive integer $n $ ($1 \leq n\leq1 \times10 ^ 5 $) , indicating the number of classrooms in the teaching building.

The next $n-1 $ line has three integers $u, v, w $ in each line, indicating that there is a passage between classroom $u$ and classroom $v$ , and `lbromine`

needs $w$ seconds to pass through the passage $(1 \leq u, v \leq n, 1 \leq w \leq 10 ^ 9)$

An integer $q$ in line $n+1$ represents the number of queries $(1 \leq q \leq1 \times 10 ^ 4)$

The next $q$ line has two integers $l,r $ per line,indicating the query interval $(1 \leq l<r \leq n)$

For each query output one line contains one integer indicating the shortest possible time for him to find `Komorebi`

and `Amuzi`

.

Input

5 1 5 1 5 4 2 2 4 3 3 4 4 3 1 3 3 5 2 3

Output

6 2 7

The structure of the teaching building in the sample is as follows

So for the interval $[1,3]$ ,if `Komorebi`

hides in classroom $1$ and `Amuzi`

hides in classroom $2$,`lbromine`

can transmit to classroom $1$ and go through classroom $5$ and $4$ to classroom $2$ using $6$ secends.It can be proved that this is the shortest possible time for `lbromine`

to find `Komorebi`

and `Amuzi`

.

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