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)

fn main() {
    let (n,m) = {
        let s = rv::<usize>();
        (s[0],s[1])
    };
    let mut c = vec![true;n];
    let mut g = vec![vec![];n];
    for _ in 0..m {
        let s = rv::<usize>();
        let (l,r,d) = (s[0]-1,s[1]-1,s[2]as i32);
        g[l].push((r,d));
        c[r]=false;
    }
    let mut a = vec![-1;n];
    let mut r = true;
    for i in 0..n { if r && c[i] {
        a[i]=0;
        r = f(i,&g,&mut a);
    }}
    r = r && a.into_iter().all(|a|a>=0);
    println!("{}",if r {"Yes"} else {"No"});
}
fn f(v:usize, g:&Vec<Vec<(usize,i32)>>, a: &mut Vec<i32>) -> bool {
    for &(u,d) in &g[v] {
        let d=a[v]+d;
        if a[u]<0 {
            a[u]=d;
            if d>1000000000 || !f(u,g,a) {
                return false;
            }
        }
        else if a[u]!=d {
            return false;
        }
    }
    true
}
fn rl() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s
}
fn rv<T>() -> Vec<T> where T: std::str::FromStr, T::Err: std::fmt::Debug, {
    rl().split_whitespace().map(|x|x.parse::<T>().unwrap()).collect()
}