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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Convert;
using static System.Math;
//using static System.Globalization.CultureInfo;

class Program
{
    class P
    {
        public int index;
        public List<int> ad;
        public Dictionary<int, int> weights;
        public P(int index)
        {
            this.index = index;
            ad = new List<int>();
            weights = new Dictionary<int, int>();
        }
    }
    private static bool Imp = false;
    static void Main(string[] args)
    {
        var nm = Array.ConvertAll(ReadLine().Split(' '), int.Parse);
        var ps = new P[nm[0]];
        for (var i = 0; i < nm[0]; i++)
            ps[i] = new P(i);
        for(var i = 0; i < nm[1]; i++)
        {
            var input = Array.ConvertAll(ReadLine().Split(' '), int.Parse);
            for(var j = -1; j < 2; j+=2)
            {
                ps[input[(j + 1) / 2] - 1].ad.Add(input[(2 - j) / 3] - 1);
                ps[input[(j + 1) / 2] - 1].weights[input[(2 - j) / 3] - 1] = -j * input[2];
            }
        }
        var set = new HashSet<int>();
        for (var i = 0; i < nm[0]; i++)
            if (!set.Contains(i))
                dfs(ps, i, set, new int[nm[0]]);
        WriteLine(Imp ? "No" : "Yes");
    }
    private static void dfs(P[] ps,int index,HashSet<int> set,int[] val)
    {
        set.Add(index);
        foreach (var ad in ps[index].ad)
        {
            if (!set.Contains(ad)&&!Imp)
            {
                val[ad] = val[index] + ps[index].weights[ad];
                dfs(ps, ad, set, val);
            }
            if (val[ad] != val[index] + ps[index].weights[ad])
                Imp = true;
        }
    }
    private const string ALFA = "abcdefghijklmnopqrstuvwxyz";
    private const int MOD = 1000000007;
}