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 Ruby (2.3.3) (judge verdict: Accepted)

class Heap
    attr_reader :size
    def initialize
        @heap = []
        @size = 0
    end

    def length
        @size
    end

    def push(x)
        i = @size
        @size += 1
        while i > 0 do
            p = (i - 1) / 2
            break if @heap[p] <= x
            @heap[i] = @heap[p]
            i = p
        end
        @heap[i] = x
        self
    end

    def pop
        return nil if @size == 0
        ret = @heap[0]
        @size -= 1
        x = @heap[@size]
        i = 0
        while i * 2 + 1 < @size do
            a = i * 2 + 1
            b = a + 1
            if b < @size && @heap[b] < @heap[a]
                a = b
            end
            break if @heap[a] >= x
            @heap[i] = @heap[a]
            i = a
        end
        @heap[i] = x
        @heap.pop
        return ret
    end
end

class Dpair
    attr_reader :dist, :vertex
    include Comparable
    def initialize(dist, vertex)
        @dist = dist
        @vertex = vertex
    end
    def <=>(other)
        @dist <=> other.dist
    end
end

# edges[src][dst] = cost
def dijkstra(start, n, edges)
    queue = Heap.new
    dist = Array.new(n+1, Float::INFINITY)
    prev = Array.new(n+1)
    dist[start] = 0
    queue.push(Dpair.new(0, start))
    while queue.size > 0 do
        dpair = queue.pop
        v = dpair.vertex
        next if dist[v] < dpair.dist
        edges[v].each do |dst, cost|
            if dist[dst] > dist[v] + cost
                dist[dst] = dist[v] + cost
                queue.push(Dpair.new(dist[dst], dst))
                prev[dst] = v
            end
        end
    end
    return dist, prev
end

def prev2path(start, goal, prev)
    path = [goal]
    pt = goal
    loop do
        break if pt == start
        pt = prev[pt]
        path.unshift(pt)
    end
    return path
end


N = gets.to_i
edges = Array.new(N){{}}
(N-1).times do |i|
    a, b, c = gets.split.map(&:to_i)
    edges[a-1][b-1] = c
    edges[b-1][a-1] = c
end

Q, K = gets.split.map(&:to_i)

dist, _ = dijkstra(K-1, N, edges)

Q.times do |i|
    x, y = gets.split.map(&:to_i)
    puts dist[x-1] + dist[y-1]
end