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)

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

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")
    };
}

use std::collections::VecDeque;

fn main() {
    input!{
        n: i32,
        m: i32,
        lrd:[[i32;3];m]
    }

    let mut offsets: Vec<Option<i32>> = vec![];
    offsets.resize(n as usize, None);

    let mut edges: VecDeque<(usize, usize, i32)> = VecDeque::new();

    for c in &lrd {
        let l = (c[0] - 1) as usize;
        let r = (c[1] - 1) as usize;
        let d = c[2];
        edges.push_back((l, r, d));
    }

    let pop = |edges: &mut VecDeque<(usize, usize, i32)>, offs: &Vec<Option<i32>>| {
        let mut search = 0;
        while let Some(edge) = edges.pop_front() {
            let ol = offs[edge.0];
            let or = offs[edge.1];
            if ol != None || or != None {
                return Some(edge);
            } else {
                edges.push_back(edge);
            }
            search = search + 1;
            if (search >= edges.len()) {
                break;
            }
        }
        return None;
    };

    while let Some(start) = edges.pop_front() {
        offsets[start.0] = Some(0);
        offsets[start.1] = Some(start.2);
        while let Some(edge) = pop(&mut edges, &offsets) {
            let ol = offsets[edge.0];
            let or = offsets[edge.1];
            if ol != None && or != None {
                if (or.unwrap() - ol.unwrap()) != edge.2 {
                    println!("No");
                    std::process::exit(0);
                }
            } else if ol != None {
                offsets[edge.1] = Some(ol.unwrap() + edge.2);
            } else if or != None {
                offsets[edge.0] = Some(or.unwrap() - edge.2);
            }
        }
    }
    println!("Yes");
}