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.Linq;
using static System.Console;

class Program
{
    static void Main()
    {
        var NM = ReadLine().Split().Select(int.Parse).ToArray();
        var N = NM[0];
        var M = NM[1];
        var L = new int[M];
        var R = new int[M];
        var D = new int[M];
        for (int i = 0; i < M; i++)
        {
            var LRD = ReadLine().Split().Select(int.Parse).ToArray();
            L[i] = LRD[0] - 1;
            R[i] = LRD[1] - 1;
            D[i] = LRD[2];
        }
        var uf = new WeightedMeguruUnionFind(N);
        for (int i = 0; i < M; i++)
        {
            if (uf.Same(L[i], R[i]))
            {
                if (D[i] != uf.Diff(L[i], R[i]))
                {
                    WriteLine("No");
                    return;
                }
            }
            else
            {
                uf.Unite(L[i], R[i], D[i]);
            }
        }
        WriteLine("Yes");
    }
}

class WeightedMeguruUnionFind
{
    int[] parent;
    int[] weightDiff;
    int count;

    public WeightedMeguruUnionFind(int size)
    {
        var b = new int[size];
        for (int i = 0; i < b.Length; i++)
        {
            b[i] = -1;
        }
        parent = b;
        weightDiff = new int[size];
        count = size;
    }

    int Root(int x)
    {
        if (parent[x] < 0)
        {
            return x;
        }
        else
        {
            var r = Root(parent[x]);
            weightDiff[x] += weightDiff[parent[x]];
            return parent[x] = r;
        }
    }

    int Weight(int x)
    {
        Root(x);
        return weightDiff[x];
    }

    public int Diff(int x, int y) => Weight(y) - Weight(x);

    public bool Same(int x, int y) => Root(x) == Root(y);

    public void Unite(int x, int y, int w)
    {
        w += weightDiff[x] - weightDiff[y];
        x = Root(x);
        y = Root(y);
        if (x == y) return;
        count--;
        if (parent[x] > parent[y])
        {
            parent[y] += parent[x];
            parent[x] = y;
            weightDiff[x] = -w;
        }
        else
        {
            parent[x] += parent[y];
            parent[y] = x;
            weightDiff[x] = w;
        }
    }

    public int Size(int x) => -parent[Root(x)];

    public int Count() => count;
}