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 int[nm[1]][];
            for (int i = 0; i < nm[1]; i++)
            {
                lrds[i] = ReadInts();
                if (lrds[i][0] > lrds[i][1])
                {
                    lrds[i][0] += lrds[i][1];
                    lrds[i][1] = lrds[i][0] - lrds[i][1];
                    lrds[i][0] = lrds[i][0] - lrds[i][1];
                    lrds[i][2] *= -1;
                }
            }
            Array.Sort(lrds, (a, b) => a[0] - b[0]);
            var unionFind = new int[nm[0]];
            var diff = new int[nm[0]];
            for (int i = 0; i < nm[0]; i++)
            {
                unionFind[i] = i;
            }
            for (int i = 0; i < nm[1]; i++)
            {
                int x = lrds[i][0] - 1;
                int y = lrds[i][1] - 1;
                //Console.WriteLine(x + " " + y);
                if (IsSame(unionFind, x,y))
                {
                    int weight = Weight(unionFind, diff, y)
                        - Weight(unionFind, diff, x);
                    if (weight != lrds[i][2])
                    {
                        Console.WriteLine("No");
                        return;
                    }
                }
                else
                {
                    Unite(ref unionFind, ref diff,
                        lrds[i][0] - 1, lrds[i][1] - 1, lrds[i][2]);
                }
            }

            for(int i = 0; i < nm[0]; i++)
            {
                //Console.WriteLine(unionFind[i] + " " + diff[i]);
            }

            Console.WriteLine("Yes");
        }

        static int Root(int[] tree, int x)
        {
            while (tree[x] != x)
            {
                x = tree[x];
            }
            return x;
        }

        static int Weight(int[] tree, int[] wTree, int x)
        {
            int weight = 0;
            while (tree[x] != x)
            {
                weight += wTree[x];
                x = tree[x];
            }
            return weight;
        }

        static bool IsSame(int[] tree,int x,int y)
        {
            return Root(tree, x) == Root(tree, y);
        }

        static void Unite(ref int[] tree, ref int[] wTree,
            int x, int y, int diff)
        {
            int rx = Root(tree, x);
            int ry = Root(tree, y);
            if (rx < ry)
            {
                tree[ry] = rx;
                diff += Weight(tree, wTree, x) - Weight(tree, wTree, y);
                wTree[ry] = diff;
            }
            else if (rx > ry)
            {
                tree[rx] = ry;
                diff += Weight(tree, wTree, y) - Weight(tree, wTree, y);
                wTree[rx] = diff;
            }
        }

        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); }
    }
}