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 Rust (1.15.1) (judge verdict: Accepted)

#![allow(unused_imports, unused_macros, dead_code)]

macro_rules! min {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| min!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = min!($($ys),*);
        if $x < t { $x } else { t }
    }}
}
macro_rules! max {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| max!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = max!($($ys),*);
        if $x > t { $x } else { t }
    }}
}
macro_rules! ewriteln {
    ($($args:expr),*) => { let _ = writeln!(&mut std::io::stderr(), $($args),*); };
}
macro_rules! trace {
    ($x:expr) => { ewriteln!(">>> {} = {:?}", stringify!($x), $x) };
    ($($xs:expr),*) => { trace!(($($xs),*)) }
}
macro_rules! put {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        if let Some(x) = it.next() { print!("{}", x); }
        for x in it { print!(" {}", x); }
        println!("");
    }};
    ($x:expr) => { println!("{}", $x) };
    ($x:expr, $($xs:expr),*) => { print!("{} ", $x); put!($($xs),*) }
}

const M: i64 = 1_000_000_007;

trait Group: std::ops::Add<Output=Self> + std::ops::Sub<Output=Self> + std::ops::Neg<Output=Self>
    + std::iter::Sum + Clone + Copy {
    fn zero() -> Self;
}
impl Group for i32 { fn zero() -> Self { 0 }}
impl Group for i64 { fn zero() -> Self { 0 }}
impl Group for f32 { fn zero() -> Self { 0.0 }}
impl Group for f64 { fn zero() -> Self { 0.0 }}

trait Ring: Group + std::ops::Mul<Output=Self> + std::ops::Div<Output=Self> {
    fn one() -> Self;
}
impl Ring for i32 { fn one() -> Self { 1 }}
impl Ring for i64 { fn one() -> Self { 1 }}
impl Ring for f32 { fn one() -> Self { 1.0 }}
impl Ring for f64 { fn one() -> Self { 1.0 }}

#[derive(PartialEq, Eq, PartialOrd, Ord, Clone, Copy, Debug)]
enum Hyper<X> { NegInf, Real(X), Inf }
use Hyper::{Real, NegInf, Inf};
impl<X> Hyper<X> {
    fn unwrap(self) -> X { if let Hyper::Real(x) = self { x } else { panic!() } }
}
impl<X: Ring> std::ops::Add for Hyper<X> {
    type Output = Self;
    fn add(self, rhs: Hyper<X>) -> Hyper<X> {
        match (self, rhs) {
            (Real(x), Real(y)) => Real(x + y),
            (Inf, _) => Inf,
            (_, Inf) => Inf,
            _ => NegInf,
        }
    }
}
impl<X: Ring> std::ops::Sub for Hyper<X> {
    type Output = Self;
    fn sub(self, rhs: Hyper<X>) -> Hyper<X> { self + (-rhs) }
}
impl<X: Ring> std::ops::Neg for Hyper<X> {
    type Output = Self;
    fn neg(self) -> Hyper<X> {
        match self {
            Inf => NegInf,
            NegInf => Inf,
            Real(x) => Real(-x),
        }
    }
}

fn main() {
    let mut sc = Scanner::new();
    let n: usize = sc.cin();
    let mut g = vec![vec![]; n];
    for _ in 1..n {
        let a = sc.cin::<usize>() - 1;
        let b = sc.cin::<usize>() - 1;
        let c: i64 = sc.cin();
        g[a].push((b, c));
        g[b].push((a, c));
    }
    let q: usize = sc.cin();

    let k = sc.cin::<usize>() - 1;
    let mut memo = vec![Inf; n];
    memo[k] = Real(0);
    {
        let mut stack = vec![k];
        while let Some(u) = stack.pop() {
            for &(v, c) in g[u].iter() {
                if memo[v] >= memo[u] + Real(c) {
                    memo[v] = memo[u] + Real(c);
                    stack.push(v);
                }
            }
        }
    }

    for _ in 0..q {
        let a = sc.cin::<usize>() - 1;
        let b = sc.cin::<usize>() - 1;
        put!((memo[a] + memo[b]).unwrap());
    }
}

use std::io::{self, Write};
use std::str::FromStr;
use std::collections::VecDeque;

struct Scanner { stdin: io::Stdin, buffer: VecDeque<String>, }
impl Scanner {
    fn new() -> Self { Scanner { stdin: io::stdin(), buffer: VecDeque::new() } }
    fn cin<T: FromStr>(&mut self) -> T {
        while self.buffer.len() == 0 {
            let mut line = String::new();
            let _ = self.stdin.read_line(&mut line);
            for w in line.split_whitespace() {
                self.buffer.push_back(String::from(w));
            }
        }
        self.buffer.pop_front().unwrap().parse::<T>().ok().unwrap()
    }
    fn chars(&mut self) -> Vec<char> { self.cin::<String>().chars().collect() }
    fn vec<T: FromStr>(&mut self, n: usize) -> Vec<T> { (0..n).map(|_| self.cin()).collect() }
}