Problem:
Weighted Union Find Trees

There is a sequence $A = a_0, a_1, ..., a_{n-1}$. You are given the following information and questions.

relate$(x, y, z)$: $a_y$ is greater than $a_x$ by $z$

diff$(x, y)$: report the difference between $a_x$ and $a_y$ $(a_y - a_x)$

Input

$n \; q$
$query_1$
$query_2$
:
$query_q$

In the first line, $n$ and $q$ are given. Then, $q$ information/questions are given in the following format.

0 $x \; y\; z$

or

1 $x \; y$

where '0' of the first digit denotes the relate information and '1' denotes the diff question.

Output

For each diff question, print the difference between $a_x$ and $a_y$ $(a_y - a_x)$.

Constraints

$2 \leq n \leq 100,000$

$1 \leq q \leq 200,000$

$0 \leq x, y < n$

$x \ne y$

$0 \leq z \leq 10000$

There are no inconsistency in the given information

Sample Input

5 6
0 0 2 5
0 1 2 3
1 0 1
1 1 3
0 1 4 8
1 0 4

Sample Output

2
?
10

Solution in Rust (judge verdict: Accepted)

use std::io;
use std::io::prelude::*;
use std::iter::repeat;

struct WeightedUnionFindTree(Vec<(usize, i64)>);
impl WeightedUnionFindTree {
    fn new(n: usize) -> WeightedUnionFindTree {
        WeightedUnionFindTree((0..n).zip(repeat(0)).collect())
    }

    fn diff(&mut self, n: usize) -> (usize, i64) {
        let p = self.0[n].0;
        if n != p {
            let (newp, d) = self.diff(p);
            self.0[n] = (newp, d + self.0[n].1);
        }
        self.0[n]
    }

    fn relate(&mut self, x: usize, y: usize, z: i64) {
        let (px, dx) = self.diff(x);
        let (py, dy) = self.diff(y);

        self.0[py] = (px, z - (dy - dx));
    }
}

fn main() {
    let stdin = io::stdin();
    let mut lines = stdin.lock().lines();

    let line0 = lines.next().unwrap().unwrap();
    let n = line0.split_whitespace().next().unwrap().parse().unwrap();

    let mut wuft = WeightedUnionFindTree::new(n);

    for l in lines.map(Result::unwrap) {
        let mut words = l.split_whitespace();
        let com = words.next().unwrap().parse().unwrap();
        let x = words.next().unwrap().parse().unwrap();
        let y = words.next().unwrap().parse().unwrap();
        match com {
            0 => {
                let z = words.next().unwrap().parse().unwrap();
                wuft.relate(x, y, z);
            }
            1 => {
                let (px, dx) = wuft.diff(x);
                let (py, dy) = wuft.diff(y);
                if px == py {
                    println!("{}", dy - dx);
                } else {
                    println!("?");
                }
            }
            _ => (),
        }
    }
}