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;
class Program{
	public static void Main(){
		string[] str = Console.ReadLine().Split(' ');
		int N = int.Parse(str[0]);
		int M = int.Parse(str[1]);
		if (M == 0)
			Console.WriteLine("Yes");
		else{
			int[][] LRD = new int[2 * M][];
			for (int i = 0 ;i < M ;i++ ){
				str = Console.ReadLine().Split(' ');
				LRD[i] = new int[3]{int.Parse(str[0]) ,int.Parse(str[1]) ,int.Parse(str[2])};
				LRD[i + M] = new int[3]{int.Parse(str[1]) ,int.Parse(str[0]) ,-int.Parse(str[2])};
			}
			Array.Sort(LRD, (a, b) => a[0] - b[0]);
			int[] x = new int[N];
			for (int l = 0 ;l < N ;l++ )
			x[l] = 0;
			int f = 0;
			int y, z, w;
			for (int p = 0 ;p < 2 * M ;p++ ){
				y = LRD[p][1];
				z = LRD[p][0];
				w = LRD[p][2];
				if (x[y - 1] == 0)
				x[y - 1] = x[z - 1] + w;
				else if (x[y - 1] != x[z - 1] + w){
					f = 1;
					break;
				}
			}
			if (f == 0)
				Console.WriteLine("Yes");
			else
				Console.WriteLine("No");
		}
	}
}