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# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
class Program
{

static string[] input = Console.ReadLine().Split(' ');
static int n = int.Parse(input[0]);
static int m = int.Parse(input[1]);
static int[,] parents = new int[n,2];//親と、親から右への距離
static bool answer = true;
  
	static void Main()
	{
    for(int i = 1; i < n; i++)
    {
    parents[i,0] = i;
    parents[i,1] = 0;
    }
    
    for(int i = 0; i < m; i++)
    {
    int[] nums = Array.ConvertAll(Console.ReadLine().Split(' '),int.Parse);

      if(whatParent(nums[0]) == whatParent(nums[1]))
      {
        if(parents[nums[1], 1] - parents[nums[0], 1] != nums[2]) answer = false;
          //グループ内の距離が矛盾でfalse
      }
      else
      {
         parents[nums[0], 0] = whatParent(nums[1]);//親の統一
         parents[nums[0], 1] = parents[nums[1], 1] - nums[2];//親との距離
      }
    }

    Console.WriteLine((answer) ? "Yes" : "No");
    
	}

  static int whatParent(int child)
  {
    if(parents[child,0] == child) return child;
    else return child = whatParent(parents[child,0]);
  }
  
}