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;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var tx = Console.ReadLine().Split(' ');
            var N = int.Parse(tx[0]);
            var M = int.Parse(tx[0]);
            var LRD = new List<int[]>();
            for (int i = 0; i < M; i++)
            {
                LRD.Add(Console.ReadLine().Split(' ').Select(xx => int.Parse(xx)).ToArray());
            }
            var x = new Dictionary<int, int>();
            if (LRD.Count > 0)
            {
                x[LRD[0][0]] = 0;

            }
            while (LRD.Count > 0)
            {
                var rmvlist = new List<int>();
                for (int i = 0; i < LRD.Count; i++)
                {
                    var l = LRD[i][0];
                    var r = LRD[i][1];
                    var d = LRD[i][2];

                    if (x.ContainsKey(l) && !x.ContainsKey(r))
                    {
                        x[r] = x[l] + d;
                        rmvlist.Add(i);
                    }
                    else if (x.ContainsKey(r) && !x.ContainsKey(l))
                    {
                        x[l] = x[r] - d;
                        rmvlist.Add(i);
                    }
                    else if (x.ContainsKey(l) && x.ContainsKey(r))
                    {
                        if (x[l] + d != x[r])
                        {
                            Console.WriteLine("No");
                            return;
                        }
                        else
                        {
                            rmvlist.Add(i);
                        }
                    }

                }
                if (rmvlist.Count == 0)
                {
                    x[LRD[0][0]] = 0;
                }
                else
                {
                    rmvlist.Reverse();
                    foreach (var i in rmvlist)
                    {
                        LRD.RemoveAt(i);
                    }
                }
            }
            Console.WriteLine("Yes");
        }
    }
}