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: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Text;


public class Exp
{
	public int L { get; private set; }
	public int R { get; private set; }
	public int D { get; private set; }

	public Exp(int l, int r, int d)
	{
		L = l;
		R = r;
		D = d;
	}
}


public class D
{
	public static void Main()
	{
		string[] args;
		
		args = Console.ReadLine().Split(' ');
		int N = Int32.Parse(args[0]);
		int M = Int32.Parse(args[1]);

		List<Exp> exps = new List<Exp>(M);
		for(int i = 0; i < M; i++)
		{
			args = Console.ReadLine().Split(' ');
			int l = Int32.Parse(args[0]);
			int r = Int32.Parse(args[1]);
			int d = Int32.Parse(args[2]);
			exps.Add(new Exp(l,r,d));
		}
		exps.Sort((a,b) => a.L - b.L);

		bool isCorrect = true;
		if(M > 0)
		{
			int[] x = new int[N+1];
			bool[] decided = new bool[N+1];
			x[exps[0].L] = 0;
			decided[exps[0].L] = true;
			for(int i = 0; i < M; i++)
			{
				Exp exp = exps[i];
				int tmp = x[exp.L] + exp.D;
				if(!decided[exp.R])
				{
					x[exp.R] = tmp;
					decided[exp.R] = true;
				}
				else if(tmp != x[exp.R])
				{
					isCorrect = false;
					break;
				}
			}
		}

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