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.Collections.Generic;
using System.Text;

namespace AtTest.D_Challenge
{
    class ABC_087
    {
        static void Main(string[] args)
        {
            Method(args);
            Console.ReadLine();
        }

        static void Method(string[] args)
        {
            int[] nm = ReadInts();
            var lrds = new long[nm[1]][];
            for(int i = 0; i < nm[1]; i++)
            {
                lrds[i] = ReadLongs();
                if (lrds[i][0] > lrds[i][1])//swap
                {
                    lrds[i][0] += lrds[i][1];
                    lrds[i][1] = lrds[i][0] - lrds[i][1];
                    lrds[i][0] -= lrds[i][1];
                    lrds[i][2] *= -1;
                }
            }
            Array.Sort(lrds, (a, b) => (int)a[1] - (int)b[1]);
            Array.Sort(lrds, (a, b) => (int)a[0] - (int)b[0]);
            var unionFind = new long[nm[0]];
            var relatePoses = new long[nm[0]];
            for (int i = 0; i < nm[0]; i++)
            {
                unionFind[i] = -1;
            }
            for(int i = 0; i < nm[1]; i++)
            {
                int minIndex = (int)lrds[i][0];
                int maxIndex = (int)lrds[i][1];
                if (unionFind[maxIndex - 1] == -1)
                {
                    unionFind[maxIndex - 1] = minIndex - 1;
                    relatePoses[maxIndex - 1] = lrds[i][2];
                }
            }
            var poses = new long[nm[0]];
            var posSetted = new bool[nm[0]];
            posSetted[0] = true;
            for (int i = 0; i < nm[1]; i++)
            {
                if (!posSetted[lrds[i][1] - 1])
                {
                    poses[lrds[i][1] - 1]
                        = poses[lrds[i][0] - 1] + lrds[i][2];
                    posSetted[lrds[i][1] - 1] = true;
                }
                else if (poses[lrds[i][1] - 1]
                    != poses[lrds[i][0] - 1] + lrds[i][2])
                {
                    Console.WriteLine("No");
                    return;
                }
            }
            Console.WriteLine("Yes");
        }

        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}