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 (1.42.0) (judge verdict: Runtime Error)

use std::cmp::max;
use std::collections::BinaryHeap;
fn main() {
    input! {
        n: usize,
        m: usize,
        lrd: [(usize, usize, usize); m]
    }

    let D_MAX = 10005;

    let mut not_in_nodes = vec![true; n];
    let mut edges = vec![vec![]; n];
    let mut mat: Vec<Vec<i64>> = vec![vec![D_MAX; n]; n];
    for i in 0..n {
        mat[i][i] = 0 as i64;
    }
    for &(l, r, d) in lrd.iter() {
        let r = r - 1;
        let l = l - 1;
        edges[r].push(l);
        edges[l].push(r);
        mat[r][l] = d as i64;
        mat[l][r] = -(d as i64);
    }

    let mut visited = vec![false; n];
    let mut dists = vec![0; n];
    for i in 0..n {
        if visited[i] {
            continue;
        }
        let mut stack = vec![];
        dists[i] = 0;
        stack.push(i);
        while let Some(current) = stack.pop() {
            visited[current] = true;
            for &nc in &edges[current] {
                let dist = dists[current] + mat[current][nc];
                if visited[nc] && dists[nc] != dist {
                    print!("No");
                    return;
                }
                if !visited[nc] {
                    dists[nc] = dist;
                    stack.push(nc);
                }
            }
        }
    }

    println!("Yes");
}

fn dfs(v: usize, edges: &Vec<Vec<usize>>, visited: &mut Vec<bool>) -> bool {
    visited[v] = true;
    for &edge in &edges[v] {
        if visited[edge] {
            return false;
        }
        if !dfs(edge, &edges, visited) {
            return false;
        }
    }
    return true;
}

#[macro_export(local_inner_maccros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let mut s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}
#[macro_export(lcal_inner_macros)]
macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

#[macro_export(lcal_inner_macros)]
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}