Problem:
Score : 400 points

Problem Statement

There are N people standing on the x-axis.
Let the coordinate of Person i be x_i.
For every i, x_i is an integer between 0 and 10^9 (inclusive).
It is possible that more than one person is standing at the same coordinate.

You will given M pieces of information regarding the positions of these people.
The i-th piece of information has the form (L_i, R_i, D_i).
This means that Person R_i is to the right of Person L_i by D_i units of distance, that is, x_{R_i} - x_{L_i} = D_i holds.

It turns out that some of these M pieces of information may be incorrect.
Determine if there exists a set of values (x_1, x_2, ..., x_N) that is consistent with the given pieces of information.

Constraints

1 \leq N \leq 100 000

0 \leq M \leq 200 000

1 \leq L_i, R_i \leq N (1 \leq i \leq M)

0 \leq D_i \leq 10 000 (1 \leq i \leq M)

L_i \neq R_i (1 \leq i \leq M)

If i \neq j, then (L_i, R_i) \neq (L_j, R_j) and (L_i, R_i) \neq (R_j, L_j).

D_i are integers.

Input

Input is given from Standard Input in the following format:

N M
L_1 R_1 D_1
L_2 R_2 D_2
:
L_M R_M D_M

Output

If there exists a set of values (x_1, x_2, ..., x_N) that is consistent with all given pieces of information, print Yes; if it does not exist, print No.

Sample Input 1

3 3
1 2 1
2 3 1
1 3 2

Sample Output 1

Yes

Some possible sets of values (x_1, x_2, x_3) are (0, 1, 2) and (101, 102, 103).

Sample Input 2

3 3
1 2 1
2 3 1
1 3 5

Sample Output 2

No

If the first two pieces of information are correct, x_3 - x_1 = 2 holds, which is contradictory to the last piece of information.

Sample Input 3

4 3
2 1 1
2 3 5
3 4 2

Sample Output 3

Yes

Sample Input 4

10 3
8 7 100
7 9 100
9 8 100

Sample Output 4

No

Sample Input 5

100 0

Sample Output 5

Yes

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::cmp;
use std::collections::VecDeque;

fn main() {
    let (n, m) = {
        let v = read_values::<usize>();
        (v[0], v[1])
    };

    let mut map: Vec<Vec<(usize, i64)>> = (0..n).map(|_| Vec::new()).collect::<Vec<_>>();
    for _ in 0..m {
        let v: Vec<usize> = read_values::<usize>();
        let l = v[0] - 1;
        let r: usize = v[1] - 1;
        let d = v[2] as i64;
        map[l].push((r, d));
        map[r].push((l, -d));
    }


    let mut x = vec![0; n];
    let mut checked = vec![false; n];
    let mut queue = VecDeque::new();

    for v in 0..n {
        if !checked[v] {
            queue.push_back(v);
            checked[v] = true;
        }

        while !queue.is_empty() {
            let i = queue.pop_front().unwrap();
            for t in &map[i] {
                let (to, d) = *t;
                if checked[to] {
                    if x[to] != x[i] + d {
                        println!("No");
                        return;
                    }
                } else {
                    checked[to] = true;
                    x[to] = x[i] + d;
                    queue.push_back(to);
                }
            }
        }
    }


    let mut min = 0;
    let mut max = 0;
    for d in &x {
        min = cmp::min(min, *d);
        max = cmp::max(max, *d);
    }
    if max - min > 1000000000 {
        println!("No");
    } else {
        println!("Yes");
    }
}

fn read_line() -> String {
    let stdin = std::io::stdin();
    let mut buf = String::new();
    stdin.read_line(&mut buf).unwrap();
    buf
}

fn read_values<T>() -> Vec<T> where T: std::str::FromStr, T::Err: std::fmt::Debug {
    read_line()
        .split(' ')
        .map(|a| a.trim().parse().unwrap())
        .collect()
}