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::{ self, Write };
use std::str::FromStr;
use std::cmp::{ min, max };
use std::collections::{ BinaryHeap, VecDeque, HashMap };

#[allow(unused_macros)]
macro_rules! trace {
    ($var:expr) => {
        let _ = writeln!(&mut std::io::stderr(), ">>> {} = {:?}", stringify!($var), $var);
    };
    ($($args:expr),*) => { trace!(($($args),*)) }
}

#[allow(unused_macros)]
macro_rules! put {
    ($var:expr) => {
        let _ = writeln!(&mut std::io::stdout(), "{}", $var);
    };
    ($var:expr, $($args:expr),*) => {
        let _ = write!(&mut std::io::stdout(), "{} ", $var);
        put!($($args),*);
    };
}

type Length = i64;

#[derive(Debug)]
struct Topological(Vec<usize>);

impl Topological {

    fn visit(u: usize, mut used: &mut Vec<bool>, rd: &Vec<Vec<usize>>, mut ord: &mut Vec<usize>) {
        if used[u] { return }
        used[u] = true;
        for &v in rd[u].iter() {
            Self::visit(v, &mut used, &rd, &mut ord);
        }
        ord.push(u);
    }

    fn new(neigh: &Vec<Vec<usize>>) -> Self {
        let n = neigh.len();
        let mut rd = vec![vec![]; n];
        for u in 0..n {
            for &v in neigh[u].iter() {
                rd[v].push(u);
            }
        }
        // sort
        let mut used = vec![false; n];
        let mut ord = vec![];
        for u in 0..n { Self::visit(u, &mut used, &rd, &mut ord); }
        Topological(ord)
    }
}

fn main() {
    let mut sc = Scanner::new();
    let n: usize = sc.cin();
    let m: usize = sc.cin();

    let mut cost = HashMap::new();
    let mut neigh = vec![vec![]; n];

    for _ in 0..m {
        let u = sc.cin::<usize>() - 1;
        let v = sc.cin::<usize>() - 1;
        let d: Length = sc.cin();
        cost.insert((u, v), d);
        neigh[u].push(v);
    }

    let Topological(ord) = Topological::new(&neigh);
    // trace!(ord);

    let mut xs: Vec<Option<Length>> = vec![None; n];

    for &u in ord.iter() {

        if xs[u] == None { xs[u] = Some(0); }

        let mut stack = vec![u];
        while let Some(u) = stack.pop() {
            let x_u = xs[u].unwrap();
            for &v in neigh[u].iter() {
                let d = cost[&(u, v)];
                stack.push(v);
                trace!(u, x_u, v, xs[v], d);
                match xs[v] {
                    None => {
                        xs[v] = Some(x_u + d);
                    },
                    Some(x) => {
                        if x != x_u + d {
                            put!("No");
                            return;
                        }
                    }
                }
            }
        }
    }

    put!("Yes");

}

#[allow(dead_code)]
struct Scanner { stdin: io::Stdin, buffer: VecDeque<String>, }
#[allow(dead_code)]
impl Scanner {
    fn new() -> Scanner { Scanner { stdin: io::stdin(), buffer: VecDeque::new() } }
    fn reserve(&mut self) {
        while self.buffer.len() == 0 {
            let mut line = String::new();
            let _ = self.stdin.read_line(&mut line);
            for w in line.split_whitespace() {
                self.buffer.push_back(String::from(w));
            }
        }
    }
    fn cin<T: FromStr>(&mut self) -> T {
        self.reserve();
        match self.buffer.pop_front().unwrap().parse::<T>() {
            Ok(a) => a,
            Err(_) => panic!("parse err")
        }
    }
}