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 qualified Data.Map as Map

main = do
    t <- readLn :: IO Int
    g <- replicateM (t - 1) (fmap (map read . words) getLine :: IO [Int])
    (t : k : _) <- fmap (map read . words) getLine :: IO [Int]
    q <- replicateM t (fmap (map read . words) getLine :: IO [Int])
    mapM_ print $ solve4 g k q

solve4 :: [[Int]] -> Int -> [[Int]] -> [Int]
solve4 g k q = foldr f [] q
  where
    f (from : to : _) acc = let Just d1 = Map.lookup from lst; Just d2 = Map.lookup to lst in (d1 + d2) : acc
      where lst = Map.fromList $ dfs k (-1) 0 (tree g)

dfs v p d g = (v, d) : (foldl dfs' [] (let Just ns = Map.lookup v g in ns))
  where
    dfs' acc (to, cost)
        | to == p   = acc
        | otherwise = acc ++ dfs to v (d + cost) g

tree = foldr (\(a : b : c : _) -> add (b, a, c) . add (a, b, c)) $ Map.fromList []
  where
    add (a, b, c) acc = case Map.lookup a acc of
        Nothing    -> Map.insert a [(b, c)] acc
        Just nodes -> Map.insert a ((b, c) : nodes) acc