Problem:
Score : 400 points

Problem Statement

You are given a tree with N vertices.

Here, a tree is a kind of graph, and more specifically, a connected undirected graph with N-1 edges, where N is the number of its vertices.

The i-th edge (1≤i≤N-1) connects Vertices a_i and b_i, and has a length of c_i.

You are also given Q queries and an integer K. In the j-th query (1≤j≤Q):

find the length of the shortest path from Vertex x_j and Vertex y_j via Vertex K.

Constraints

3≤N≤10^5

1≤a_i,b_i≤N (1≤i≤N-1)

1≤c_i≤10^9 (1≤i≤N-1)

The given graph is a tree.

1≤Q≤10^5

1≤K≤N

1≤x_j,y_j≤N (1≤j≤Q)

x_j≠y_j (1≤j≤Q)

x_j≠K,y_j≠K (1≤j≤Q)

Input

Input is given from Standard Input in the following format:

N
a_1 b_1 c_1
:
a_{N-1} b_{N-1} c_{N-1}
Q K
x_1 y_1
:
x_{Q} y_{Q}

Output

Print the responses to the queries in Q lines.

In the j-th line j(1≤j≤Q), print the response to the j-th query.

Sample Input 1

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

Sample Output 1

3
2
4

The shortest paths for the three queries are as follows:

Query 1: Vertex 2 → Vertex 1 → Vertex 2 → Vertex 4 : Length 1+1+1=3

Query 2: Vertex 2 → Vertex 1 → Vertex 3 : Length 1+1=2

Query 3: Vertex 4 → Vertex 2 → Vertex 1 → Vertex 3 → Vertex 5 : Length 1+1+1+1=4

Sample Input 2

7
1 2 1
1 3 3
1 4 5
1 5 7
1 6 9
1 7 11
3 2
1 3
4 5
6 7

Sample Output 2

5
14
22

The path for each query must pass Vertex K=2.

Sample Input 3

10
1 2 1000000000
2 3 1000000000
3 4 1000000000
4 5 1000000000
5 6 1000000000
6 7 1000000000
7 8 1000000000
8 9 1000000000
9 10 1000000000
1 1
9 10

Sample Output 3

17000000000

Solution in Haskell (GHC 8.8.3) (judge verdict: Time Limit Exceeded)

{-# LANGUAGE BangPatterns #-}

import qualified Data.ByteString.Char8 as C
import Data.Maybe
import qualified Data.Vector as V
import qualified Data.Vector.Mutable as VM
import Data.Vector.Unboxed
import qualified Data.Vector.Unboxed.Mutable as UM
import Prelude hiding (drop, splitAt, tail, unfoldr)

main = C.interact $ put . sol . get

get = unfoldr (C.readInt . C.dropWhile (<'0'))

put = C.unlines . fmap (C.pack . show) . V.toList

sol v = fmap (\q -> ds!(q!0)+ds!(q!1)) qs
  where
  n = v!0
  (v0,v1) = splitAt (3*(n-1)) $! tail v
  es = V.unfoldrN (n-1) (Just . splitAt 3) v0
  q = v1!0
  k = v1!1
  qs = V.unfoldrN q (Just . splitAt 2) $! drop 2 v1
  tr = V.create $ do
    v <- VM.replicate (n+1) V.empty
    let add x (y,z) = VM.unsafeRead v x >>= VM.unsafeWrite v x . (V.cons (y,z)) 
    V.forM_ es $ \e -> do
      add (e!0) (e!1,e!2)
      add (e!1) (e!0,e!2)
    return v
  ds = create $ do
    ds <- UM.replicate (n+1) (-1)
    loop ds (k,0)
    return ds
  loop ds !(nd,d) = do
    UM.unsafeWrite ds nd d
    V.forM_ (tr V.! nd) $ \(nd',d') -> do
      x <- UM.unsafeRead ds nd'
      if x<0 then loop ds (nd',d+d') else return ()