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.Linq;
using System.Text;
using System;
using System.Collections;
using System.Collections.Generic;
using System.Globalization;
using System.IO;
using System.Numerics;

namespace AtCoder
{
    class Program
    {

        const int BiggestMod = 1000000007;
        static Dictionary<int, int>[] pos;
        static int numPerson;

        public static void Main()
        {

            var args = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
            numPerson = args[0];
            var numQuery = args[1];
            pos = new Dictionary<int, int>[numPerson];

            for (int i = 0; i < numPerson; i++)
                pos[i] = new Dictionary<int, int>();

            for (int i = 0; i < numQuery; i++)
            {

                var query = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
                var left = query[0] - 1;
                var right = query[1] - 1;
                var distance = query[2];

                if (!SetPos(left, right, distance))
                {
                    Console.WriteLine("No");
                    return;
                }

                foreach (var position in pos[right])
                    if (!SetPos(left, position.Key, distance - (position.Value)))
                    {
                        Console.WriteLine("No");
                        return;
                    }

                foreach (var position in pos[left])
                    if (!SetPos(right, position.Key, distance - (position.Value)))
                    {
                        Console.WriteLine("No");
                        return;
                    }

            }

            Console.WriteLine("Yes");

        }

        private static bool SetPos(int obj, int sbj, int dis)
        {

            if (Math.Abs(dis) >= numPerson)
                return false;
            if (pos[obj].ContainsKey(sbj))
                if (pos[obj][sbj] != dis)
                    return false;
                else return true;

            pos[obj].Add(sbj, dis);
            if (!pos[obj].ContainsKey(sbj)) pos[sbj].Add(obj, -dis);
            return true;
        }

    }

}