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: Accepted)

using System;
using System.Collections.Generic;
class Program{
	static long[] h;
	static List<int[]>[] li;
	static string ans="Yes";
	static void Main(){
		int[] s=Array.ConvertAll(Console.ReadLine().Split(),int.Parse);
		h=new long[s[0]+1];
		li=new List<int[]>[s[0]+1];
		for(int i=1;i<=s[0];i++){
			h[i]=long.MinValue;
			li[i]=new List<int[]>();
		}
		for(int i=0;i<s[1];i++){
			int[] q=Array.ConvertAll(Console.ReadLine().Split(),int.Parse);
			li[q[0]].Add(new int[]{q[1],q[2]});
			li[q[1]].Add(new int[]{q[0],-q[2]});
		}
		for(int i=1;i<=s[0]&&ans=="Yes";i++){
			if(h[i]==long.MinValue){
				h[i]=0;
				fu(i);
			}
		}
		Console.WriteLine("{0}",ans);
	}
	static void fu(int a){
		for(int i=0;i<li[a].Count&&ans=="Yes";i++){
			if(h[li[a][i][0]]==long.MinValue){
				h[li[a][i][0]]=h[a]+li[a][i][1];
				fu(li[a][i][0]);
			}
			else if(h[li[a][i][0]]!=h[a]+li[a][i][1]){
				ans="No";
				break;
			}
		}
	}
}