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)

#[test]
fn test_solve() {
   assert_eq!(solve("3 3\n1 2 1\n2 3 1\n1 3 2\n"), "Yes\n");
   assert_eq!(solve("3 3\n1 2 1\n2 3 1\n1 3 5\n"), "No\n");
   assert_eq!(solve("4 3\n2 1 1\n2 3 5\n3 4 2\n"), "Yes\n");
   assert_eq!(solve("10 3\n8 7 100\n7 9 100\n9 8 100\n"), "No\n");
   assert_eq!(solve("100 0\n"), "Yes\n");
}
fn solve(src: &str) -> String {
    let mut sc = Scanner::from_str(src);

    let n: usize = sc.read();
    let m: usize = sc.read();
    let mut frm = vec![Vec::new(); n];
    for _ in 0..m {
        let l: usize = sc.read();
        let r: usize = sc.read();
        let d: isize = sc.read();
        frm[l-1].push((r-1, d));
        frm[r-1].push((l-1, -d));
    }

    let mut x = vec![None; n];
    for v in 0..n {
        if x[v].is_none() {
            x[v] = Some(0);
            if !dfs(v, &mut x, &frm) {
                return "No\n".to_string();
            };
        }
    }

    "Yes\n".to_string()
}
fn dfs(v: usize, x: &mut Vec<Option<isize>>, frm: &Vec<Vec<(usize, isize)>>) -> bool {
    let xv = x[v].unwrap();
    for &(w, d) in &frm[v] {
        if let Some(xw) = x[w] {
            if xv + d != xw {
                return false;
            }
        } else {
            x[w] = Some(xv + d);
            if !dfs(w, x, frm) {
                return false;
            }
        }
    }
    true
}

fn main() {
    let mut buf = String::new();
    use std::io::{Read, Write};
    std::io::stdin().read_to_string(&mut buf).unwrap();
    std::io::stdout().write_all(solve(&buf).as_bytes()).unwrap();
}
struct Scanner<'a>(std::str::SplitWhitespace<'a>);
impl<'a> Scanner<'a> {
    fn from_str(src: &str) -> Scanner {
        Scanner(src.split_whitespace())
    }
    fn get(&mut self) -> &str {
        self.0.next().unwrap()
    }
    fn read<T: std::str::FromStr>(&mut self) -> T {
        self.get().parse().ok().unwrap()
    }
}