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, unused_variables, dead_code)]
use std::io::{stdin, Read, StdinLock};
use std::str::FromStr;
use std::fmt::*;
use std::str::*;
use std::cmp::*;
use std::collections::*;

// https://beta.atcoder.jp/contests/arc065/tasks/arc065_b

fn bfs(
    cmap: &Vec<Vec<i32>>,
    start: usize,
    goal: usize
) -> i64 {
    let mut visited: Vec<bool> = vec![false; cmap.len()];
    let mut q: VecDeque<(usize, i64)> = VecDeque::new();
    visited[start] = true;
    q.push_back((start, 0));
    while !q.is_empty() {
        let &(c, cnt) = q.front().unwrap();
        for i in 0..cmap.len() {
            if i == c { continue; }
            if visited[i] { continue; }
            if cmap[c][i] < 0 { continue; }
            if i == goal { return cnt + cmap[c][i] as i64; }
            q.push_back((i, cnt + cmap[c][i] as i64));
            visited[i] = true;
        }
        q.pop_front();
    }
    return -1;
}

fn main() {
    let cin = stdin(); let cin = cin.lock(); let mut sc = Scanner::new(cin);

    let (n, m): (usize, usize) = (sc.read(), sc.read());
    // NxNの２次元配列
    let mut lrd: Vec<Vec<i32>> = vec![vec![-1; n]; n];

    let mut n_set: HashSet<usize> = HashSet::new();
    let mut isno = false;
    for i in 0..m {
        let (l, r, d): (usize, usize, i32) = (sc.read(), sc.read(), sc.read());
        let l = l - 1; let r = r - 1;
        let lex = n_set.contains(&l);
        let rex = n_set.contains(&r);
        if (i == 0) | (!lex & !rex) { 
            lrd[l][r] = d; lrd[r][l] = d;
            n_set.insert(l); n_set.insert(r);    
        } else {
            let start; let goal;
            if lex { start = l; goal = r; }
            else { start = r; goal = l; }
            let cost = bfs(&lrd, start, goal);
            if cost == -1 {
                lrd[l][r] = d; lrd[r][l] = d;
                if lex { n_set.insert(r); }
                else { n_set.insert(l); }
            } else if d as i64 != cost {
                isno = true; break;
            } else if !(lex & rex) {
                lrd[l][r] = d; lrd[r][l] = d;
            }
        }
    }

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

struct Scanner<'a> {
    cin: StdinLock<'a>,
}
impl<'a> Scanner<'a> {
    fn new(cin: StdinLock<'a>) -> Scanner<'a> {
        Scanner { cin: cin }
    }
 
    fn read1<T: FromStr>(&mut self) -> Option<T> {
        let token = self.cin.by_ref().bytes().map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>();
        token.parse::<T>().ok()
    }
 
    fn read<T: FromStr>(&mut self) -> T {
        self.read1().unwrap()
    }
}