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;

class Program
{
    static void Main(string[] args)
    {
        string[] args0 = Console.ReadLine().Split(' ');

        int peopleCount = int.Parse(args0[0]);
        int infoCount = int.Parse(args0[1]);

        //var peoplePositions = new Dictionary<int, int>();
        var peoplePositionsList = new List<Dictionary<int, int>>();

        bool successed = true;

        for (int i = 0; i < infoCount; ++i)
        {
            string[] input = Console.ReadLine().Split(' ');

            int personLeft = int.Parse(input[0]);
            int personRight = int.Parse(input[1]);
            int distance = int.Parse(input[2]);

            Dictionary<int, int> leftExist = null;
            Dictionary<int, int> rightExist = null;

            foreach (var peoplePositions in peoplePositionsList)
            {
                if (peoplePositions.ContainsKey(personLeft))
                {
                    leftExist = peoplePositions;
                }
                if (peoplePositions.ContainsKey(personRight))
                {
                    rightExist = peoplePositions;
                }
            }

            if (leftExist != null && rightExist != null)
            {
                if (leftExist.ContainsKey(personRight))
                {
                    if (leftExist[personRight] - leftExist[personLeft] != distance)
                    {
                        successed = false;
                        break;
                    }
                }
                else
                {
                    leftExist.Add(personRight, leftExist[personLeft] + distance);

                    int offset = rightExist[personRight] - (leftExist[personLeft] + distance);

                    bool flag = Combine(ref leftExist, ref rightExist, offset);

                    if (flag == false)
                    {
                        successed = false;
                        break;
                    }
                }

                if (leftExist != rightExist)
                {
                    peoplePositionsList.Remove(rightExist);
                }
            }
            else if (leftExist != null && rightExist == null)
            {
                leftExist.Add(personRight, leftExist[personLeft] + distance);
            }
            else if (leftExist == null && rightExist != null)
            {
                leftExist.Add(personLeft, rightExist[personRight] - distance);
            }
            else
            {
                var peoplePositions = new Dictionary<int, int>();
                peoplePositions.Add(personLeft, 0);
                peoplePositions.Add(personRight, distance);

                peoplePositionsList.Add(peoplePositions);
            }
        }

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

    static bool Combine(ref Dictionary<int, int> left, ref Dictionary<int, int> right, int distance)
    {
        foreach(var pair in right)
        {
            if (left.ContainsKey(pair.Key))
            {
                if (pair.Value != left[pair.Key] + distance)
                {
                    return false;
                }
                else
                {
                    left.Add(pair.Key, pair.Value + distance);
                }
            }
        }
        return true;
    }

}