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: Time Limit Exceeded)

import Control.Monad
import Data.Maybe
import Data.List
import qualified Data.IntMap as M

main :: IO ()
main = do
    n <- readLn
    ts <- replicateM (n-1) $ do
        [a,b,c] <- getInts
        return ((a,b),c)
    [q,k] <- getInts
    xys <- replicateM q $ do
        [x,y] <- getInts
        return (x,y)
    let t = build k ts
    mapM_ (print . solve t) xys

type Tree = M.IntMap Int

getInts :: IO [Int]
getInts = map read . words <$> getLine

build :: Int -> [((Int,Int),Int)] -> Tree
build k = worker M.empty [(k,0)]

worker :: Tree -> [(Int,Int)] -> [((Int,Int),Int)] -> Tree
worker acc [] ts = acc
worker acc ((p,w):stk) ts = let (ps,ch) = foldr (classify p w) ([],[]) ts
                                acc' = foldr (\(k,v) t -> M.insert k v t) acc ps
                                stk' = ps ++ stk
                            in worker acc' stk' ch

classify :: Int -> Int -> ((Int,Int),Int) -> ([(Int,Int)],[((Int,Int),Int)]) -> ([(Int,Int)],[((Int,Int),Int)])
classify p w ch@((a,b),c) (ps,cs) | p == a = ((b,w+c):ps,cs)
                                  | p == b = ((a,w+c):ps,cs)
                                  | otherwise = (ps,ch:cs)

solve :: Tree -> (Int, Int) -> Int
solve t (x,y) = fromJust $ (+) <$> M.lookup x t <*> M.lookup y t