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)

#[allow(unused_macros)]
macro_rules! get {
    ([$t:ty] ; $n:expr) => {
        (0..$n)
        .map(|_| get!([$t])).collect::<Vec<_>>()
    };
    ($($t:ty),+ ; $n:expr) => {
        (0..$n).map(|_| get!($($t),+)).collect::<Vec<_>>()
    };
    ([$t:ty]) => {
        rl().split_whitespace()
        .map(|x| x.parse().unwrap())
        .collect::<Vec<$t>>()
    };
    ($t:ty) => {
        rl().parse::<$t>().unwrap()
    };
    ($($t:ty),*) => {
        {
            let line =rl();
            let mut iter = line.split_whitespace();
            ($(iter.next().unwrap().parse::<$t>().unwrap()),*)
        }
    };
}
fn rl() -> String {
    let mut line = String::new();
    std::io::stdin().read_line(&mut line).unwrap();
    line.trim().to_string()
}

struct UnionFindWeighted {
    par: Vec<usize>,
    rank: Vec<usize>,
    weight: Vec<i64>,
}
impl UnionFindWeighted {
    fn new(n: usize) -> UnionFindWeighted {
        let mut par = Vec::with_capacity(n);
        let mut rank = Vec::with_capacity(n);
        let mut weight = Vec::with_capacity(n);
        for i in 0..n {
            par.push(i);
            rank.push(0);
            weight.push(0);
        }
        UnionFindWeighted {
            par: par,
            rank: rank,
            weight: weight,
        }
    }
    fn root(&mut self, x: usize) -> usize {
        if self.par[x] == x {
            x
        } else {
            let par = self.par[x];
            let ppar = self.root(par);
            self.weight[x] += self.weight[par] as i64;
            self.par[x] = ppar;
            ppar
        }
    }
    fn same(&mut self, x: usize, y: usize) -> bool {
        return self.root(x) == self.root(y);
    }
    fn unite(&mut self, x: usize, y: usize, w: i64) {
        let px = self.root(x);
        let py = self.root(y);
        if px == py {
            return;
        }
        if self.rank[px] < self.rank[py] {
            self.par[px] = py;
            self.weight[px] = w - self.weight[x] + self.weight[y];
        } else {
            self.par[py] = px;
            self.weight[py] = -w - self.weight[y] + self.weight[x];
            if self.rank[px] == self.rank[py] {
                self.rank[px] += 1;
            }
        }
    }
    fn diff(&mut self, x: usize, y: usize) -> i64 {
        return self.weight[x] - self.weight[y];
    }
}
fn main() {
    let (n, m) = get!(usize, usize);
    let mut ufw = UnionFindWeighted::new(n);
    for _ in 0..m {
        let mut tmp = get!(usize, usize, i64);
        tmp.0 -= 1;
        tmp.1 -= 1;
        if ufw.same(tmp.0, tmp.1) {
            //eprintln!("tmp.0: {}, tmp.1: {}", tmp.0, tmp.1);
            //eprintln!(
            //    "weight[tmp.0]: {}, weight[tmp.1]: {}",
            //    ufw.weight[tmp.0], ufw.weight[tmp.1]
            //);
            if ufw.diff(tmp.0, tmp.1) != tmp.2 {
                println!("No");
                return;
            }
        }
        ufw.unite(tmp.0, tmp.1, tmp.2);
    }
    println!("Yes");
}