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: Time Limit Exceeded)

#[allow(unused_imports)]
use std::io::*;
#[allow(unused_imports)]
use std::str::*;
#[allow(unused_imports)]
use std::mem::*;
#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::HashMap;

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let mut line = String::new();
    stdin().read_line(&mut line).unwrap();
    line.trim().to_string().parse().ok().unwrap()
}

#[allow(dead_code)]
fn read_cols<T: FromStr>() -> Vec<T> {
    let mut line = String::new();
    stdin().read_line(&mut line).unwrap();

    line.trim()
        .split_whitespace()
        .map(|s| s.parse().ok().unwrap())
        .collect()
}

fn execute() -> bool {
    let header = read_cols::<usize>();
    let n_variables = header[0];
    let n_info = header[1];

    let mut mat = Vec::new();
    mat.resize(n_variables, Vec::<(usize, i32)>::new());
    let mut num_ins = Vec::new();
    num_ins.resize(n_variables, 0);

    for _ in 0..n_info {
        let info = read_cols::<i32>();
        let i_left = (info[0] - 1) as usize;
        let i_right = (info[1] - 1) as usize;
        let diff = info[2];
        mat[i_left].push((i_right, diff));
        num_ins[i_right] += 1;
    }
    let mat = mat;

    let mut stack = Vec::new();
    for i in 0..n_variables {
        if num_ins[i] == 0 {
            stack.push(i);
        }
    }
    let mut tp_sorted = Vec::new();
    let mut full_mat = mat.clone();
    while let Some(n) = stack.pop() {
        tp_sorted.push(n);

        for &(m, diff) in &mat[n] {
            full_mat[m].push((n, -diff));
            num_ins[m] -= 1;
            if num_ins[m] == 0 {
                stack.push(m);
            }
        }
    }

    if tp_sorted.len() != n_variables {
        // has loop ( = inconsisetent info)
        return false;
    }

    let mut visited = Vec::new();
    visited.resize(n_variables, false);
    for i in tp_sorted {
        if visited[i] {
            continue;
        }

        let mut positions = Vec::<Option<i32>>::new();
        positions.resize(n_variables, None);
        let mut stack = Vec::new();
        stack.push(i);

        positions[i] = Some(0);
        while let Some(n) = stack.pop() {
            if visited[n] {
                continue;
            }

            visited[n] = true;
            for &(m, diff) in &full_mat[n] {
                let pos_m = positions[n].unwrap() + diff;
                if let Some(current_pos_m) = positions[m] {
                    if current_pos_m != pos_m {
                        return false;
                    }
                    // Already pushed
                    continue;
                }

                positions[m] = Some(pos_m);
                stack.push(m);
            }
        }
    }

    return true;
}

fn main() {
    println!("{}", match execute() {
        false => "No",
        true => "Yes",
    });
}