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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;
public class Main {

  public static void main(String[] args) { 
      Scanner sc = new Scanner(System.in);
      int n = sc.nextInt();
      int m = sc.nextInt();
      int[] people = new int[n+1];

      Integer[][] arr = new Integer[m][3];
      for(int i = 0; i < m; i++) {
        arr[i][0] = sc.nextInt();
        arr[i][1] = sc.nextInt();
        arr[i][2] = sc.nextInt();
        if(arr[i][0] > arr[i][1]) {
          int t = arr[i][0];
          arr[i][0] = arr[i][1];
          arr[i][1] = t;
          arr[i][2] *= (-1);
        }
      }
      Arrays.sort(arr, (a, b) -> a[0] - b[0]);
      for(int i = 0; i < m; i++) {
        int p1 = arr[i][0];
        int p2 = arr[i][1];
        int dist = arr[i][2];
        if(people[p1] == 0 && people[p2] == 0) {
          people[p1] = 1; people[p2] = people[p1] + dist;
        } else if(people[p1] == 0) {
          people[p1] = people[p2] - dist;
        } else if(people[p2] == 0) {
          people[p2] = people[p1] + dist;
        } else {
          if(people[p2] - people[p1] != dist) {
            System.out.println("No");
            return;
          }
        }
      }

      System.out.println("Yes");
  }
}