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;
using System.Linq;
using System.Collections.Generic;

class Program
{
    static void Main(string[] args)
    {
        bool result = true;
        int count = int.Parse(Console.ReadLine().Split()[1]);
        var _list = new HashSet<Dictionary<int, int>>();
        const int MAX = 1000000000;
        for (int i = 0; i < count; ++i)
        {
            var sp = Console.ReadLine().Split();
            if (!result) continue;
            int left = int.Parse(sp[0]);
            int right = int.Parse(sp[1]);
            int diff = int.Parse(sp[2]);
            var dicL = _list.FirstOrDefault(d => d.ContainsKey(left));
            var dicR = _list.FirstOrDefault(d => d.ContainsKey(right));
            if (dicL == null)
            {
                if (dicR == null)
                {
                    _list.Add(new Dictionary<int, int>() { { left, 0 }, { right, diff } });
                }
                else
                {
                    dicR[left] = dicR[right] - diff;
                }
            }
            else
            {
                if (dicR == null)
                {
                    int tmp = dicL[left] + diff;
                    if (MAX < tmp) result = false;
                    dicL[right] = tmp;
                }
                else if (dicL == dicR)
                {
                    result &= (dicL[left] + diff == dicL[right]);
                }
                else
                {
                    int move = dicL[left] + diff - dicR[right];
                    foreach (var pair in dicR)
                    {
                        if (dicL.ContainsKey(pair.Key))
                        {
                            if (dicL[pair.Key] != pair.Value + move)
                            {
                                result = false;
                                break;
                            }
                        }
                        else
                        {
                            int tmp = pair.Value + move;
                            if (MAX < tmp) result = false;
                            dicL[pair.Key] = tmp;
                        }
                    }
                    _list.Remove(dicR);
                }
            }
        }
        if (result)
        {
            foreach(var dic in _list)
            {
                int min = int.MaxValue, max = 0;
                foreach(var val in dic.Values)
                {
                    min = Math.Min(min, val);
                    max = Math.Max(max, val);
                }
                if (max - min > 1000000000)
                {
                    result = false;
                    break;
                }
            }
        }
        Console.WriteLine(result ? "YES" : "NO");
    }
}