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: Accepted)

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

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

macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

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

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

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

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}
use std::collections::HashMap;
use std::collections::hash_map::Entry::{Occupied, Vacant};

fn main() {
    input! {
        n:usize, m:usize,
        lrd: [(usize1,usize1,i64); m]
    };
    
    let mut grp: HashMap<usize, Vec<(usize, i64)>> = HashMap::new();
    for &(l,r,d) in &lrd {
        match grp.entry(l) {
            Vacant(e) => { e.insert(vec![(r,d)]); },
            Occupied(mut e) => e.get_mut().push((r,d))
        };
        match grp.entry(r) {
            Vacant(e) => { e.insert(vec![(l,d * -1)]); },
            Occupied(mut e) => e.get_mut().push((l,d * -1))
        };
    };

    let mut chk: Vec<bool> = vec![false;n];
    let mut dst: Vec<i64> = vec![0;n];

    let ans = (0..n).fold(true, |ac, i| {
        if !chk[i] {
            ac && dfs(&grp ,&mut chk, &mut dst, i, 0)
        } else {
            ac
        }
    });

    if ans { println!("Yes") } else { println!("No") }
}

fn dfs(grp:&HashMap<usize, Vec<(usize, i64)>>, chk:&mut Vec<bool> , dst: &mut Vec<i64>, i:usize, d:i64) -> bool {
    let di = dst[i];
    if chk[i] {
        di == d
     } else {
        chk[i] = true;
        dst[i] = d;
        match grp.get(&i) {
            None => true,
            Some(e) => e.iter().fold(true, |ac, &(n,vv)| {
                    ac && dfs(grp, chk, dst, n, vv+d)
                })
        }
    }
}