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::str::FromStr;
use std::io::*;
use std::collections::*;

pub fn main() {
    let i = stdin();
    let mut o = Vec::new();
    run(&mut i.lock(), &mut o);
    stdout().write_all(&o).unwrap();
}

fn run<R: BufRead, W: Write>(i: &mut R, o: &mut W) {
    let mut i = AtRead::from(i);

    let (n, m) = i.read2::<usize, usize>();
    let mut lrds = Vec::new();
    for _ in 0..m {
        let (l, r, d) = i.read3::<usize, usize, isize>();
        lrds.push((l - 1, r - 1, d));
    }
    let r = if solve(n, &lrds) { "Yes" } else { "No" };
    writeln!(o, "{}", r).unwrap();
}
fn solve(n: usize, lrds: &[(usize, usize, isize)]) -> bool {
    let mut m = HashMap::new();
    for &lrd in lrds {
        insert(&mut m, lrd);
    }
    let mut x = vec![None; n];
    let mut q = Vec::new();
    while let Some(&k) = m.keys().next() {
        q.push(k);
        x[k] = Some(0);
        while let Some(l) = q.pop() {
            let rds = m.remove(&l).unwrap();
            let xl = x[l].unwrap();
            for &(r, d) in &rds {
                let xr_e = xl + d;
                if let Some(xr) = x[r] {
                    if xr != xr_e {
                        return false;
                    }
                } else {
                    x[r] = Some(xr_e);
                    q.push(r);
                }
            }
        }
    }
    true
}
fn insert(m: &mut HashMap<usize, Vec<(usize, isize)>>, (l, r, d): (usize, usize, isize)) {
    m.entry(l).or_insert(Vec::new()).push((r, d));
    m.entry(r).or_insert(Vec::new()).push((l, -d));
}

struct AtRead<'a, R: BufRead + 'a> {
    r: &'a mut R,
    s: String,
}

macro_rules! fn_read {
        {$f:ident($($v:ident: $t:ident),*)} => {
            fn $f<$($t: FromStr),*>(&mut self) -> ($($t),*) {
                let i = &mut self.next().split(' ');
                $(
                    let $v = next(i);
                )*
                ($($v),*)
            }
        };
    }

impl<'a, R: BufRead + 'a> AtRead<'a, R> {
    fn from(r: &'a mut R) -> Self {
        AtRead {
            r: r,
            s: String::new(),
        }
    }
    fn next(&mut self) -> &str {
        self.s.clear();
        self.r.read_line(&mut self.s).unwrap();
        self.s.trim()
    }

    fn_read! { read2(v1: T1, v2: T2) }
    fn_read! { read3(v1: T1, v2: T2, v3: T3) }
}

fn next<'a, T: FromStr, I: std::iter::Iterator<Item = &'a str>>(i: &mut I) -> T {
    i.next().unwrap().parse().ok().unwrap()
}