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: Runtime Error)

fn get_line() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().to_string()
}

fn reads<T>() -> Vec<T>
    where
        T: std::str::FromStr,
        <T as std::str::FromStr>::Err: std::fmt::Debug {
    get_line().split(' ').map(|x| x.parse().unwrap()).collect()
}

fn main() {
    let nm = reads();
    let inf = 10001;
    let mut xs = vec![vec![inf; nm[0]]; nm[0]];
    let mut bs = vec![vec![false; nm[0]]; nm[0]];

    for _ in 0..nm[1] {
        let lrd: Vec<usize> = reads();
        let l = lrd[0] - 1;
        let r = lrd[1] - 1;
        let d = lrd[2];

        xs[l][r] = d;
        bs[l][r] = true;
    }
    let ys = xs.clone();

    let mut res = true;

    'outer:
    for i in 0..nm[0] {
        for j in 0..nm[0] {
            for k in 0..nm[0] {
                if xs[i][j] > xs[i][k] + xs[k][j] {
                    if bs[i][j] {
                        res = false;
                        break 'outer;
                    }
                    
                    xs[i][j] = xs[i][k] + xs[k][j];
                }
            }
        }
    }

    if res {
        let mut cs = vec![0; nm[0]];

        for i in 0..nm[0] {
            if cs[i] == 0 {
                res = visit(i, &ys, &mut cs);
                if !res {
                    break;
                }
            }
        }
    }

    println!("{}",
    if res {
        "Yes"
    }
    else {
        "No"
    });
}

fn visit(i: usize, ys: &Vec<Vec<usize>>, cs: &mut Vec<u64>) -> bool {
    let inf = 10001;
    let mut res = true;

    if cs[i] == 1 {
        return false;
    }
    else if cs[i] == 0 {
        cs[i] = 1;

        for j in 0..cs.len() {
            if inf > ys[i][j] && !visit(j, ys, cs) {
                res = false;
                break;
            }
        }

        cs[i] = 2;
    }

    res
}