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 C++14 (Clang 3.8.0) (judge verdict: Accepted)

#include <iostream>
#include <vector>
#include <utility>
using namespace std;


struct vertex {
  vector<int> w;
  vector<int> e;
  bool f = false;
  int v;
};

vector<struct vertex> G;

bool dfs(int i) {
  for(int j=0; j<G[i].e.size(); j++) {
    int v = G[i].e[j];
    if(G[v].f == false) {
      G[v].f = true;
      G[v].v = G[i].v + G[i].w[j];
      if(!dfs(v)) return false;
    } else {
      if(G[v].v - G[i].v != G[i].w[j]) return false;
    }
  }
  return true;
}

int main() {
  int n, m; cin >> n >> m;
  G.resize(n+1);
  for(int i=1; i<=m; i++) {
    int l, r, d;
    cin >> l >> r >> d;
    G[l].e.push_back(r);
    G[l].w.push_back(d);
    G[r].e.push_back(l);
    G[r].w.push_back(-d);
  }
  for(int i=1; i<=n; i++) {
    if(G[i].f == false) {
      G[i].f = true;
      G[i].v = 0;
      if(!dfs(i)) { cout << "No" << endl; return 0; }
    }
  }
  
  cout << "Yes" << endl;
  return 0;
}