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 7.10.3) (judge verdict: Accepted)

import Data.Bits
import Data.List
import Data.Foldable(foldlM)
import Data.Maybe(fromJust)
import Control.Monad
import Data.Array as A ((!),accumArray)
import Data.Graph
import qualified Data.Vector.Unboxed as V
import qualified Data.Vector.Unboxed.Mutable as VM
import Control.Monad.ST
import Data.Maybe (fromMaybe)
import qualified Data.ByteString.Char8 as BS

toTuple :: [a] -> (a,a)
toTuple (x:y:_) = (x,y)
toTuple _ = undefined

getInt :: IO Int
getInt = fst . fromJust. BS.readInt <$> BS.getLine

getIntList :: IO [Int]
getIntList = unfoldr (BS.readInt . BS.dropWhile (== ' ')) <$> BS.getLine

getLineB :: (Read a) => IO [a] --直接入力
getLineB = map (read.BS.unpack) . BS.words <$> BS.getLine

build :: Int -> Int -> [(Int,(Int,Int))] -> V.Vector Int
build s n ls = runST $ do
  vec <- VM.replicate (n+1) maxBound
  VM.write vec s 0
  sub vec s 0
  V.freeze vec
  where
    graph = A.accumArray (flip (:)) [] (1,n) ls
    sub vec s par = do
      forM_ (graph A.! s) $ \(vw,v) -> do
        d  <- VM.read vec v
        sd <- VM.read vec s
        if d > sd + vw && v /= par then VM.write vec v (sd+vw)
          else return ()
      --V.freeze vec >>= \vec -> traceShowM (graph A.! s, vec)
      forM_ (graph A.! s) $ \(_,v) -> if v == par then return () else sub vec v s

solve :: Int -> V.Vector Int -> IO ()
solve q vec = do
  replicateM_ q $ do
    [x,y] <- getIntList
    print $ (vec V.! x) + (vec V.! y)

main :: IO ()
main = do
  n <- readLn :: IO Int
  as <- fmap concat $ replicateM (n-1) $ do
    [a,b,c] <- getIntList
    return [(a,(c,b)),(b,(c,a))]
  [q,k] <- getIntList
  solve q $ build k n as