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;

class Program{

    const int INT_MAX = 2147483647;
    static void Main(string[] args)
    {
        bool flag = true;
        int[] nm = Scan.IntArray(2);
        UnionFind uf = new UnionFind();
        uf.Init(nm[0]);
        for (int i = 0; i < nm[1]; i++)
        {
            int[] lrd = Scan.IntArray(3);
            if(uf.Same(lrd[0], lrd[1]))
            {
                // 判定
                if(lrd[2] == uf.Diff(lrd[0], lrd[1]))
                {
                    // OK
                }
                else
                {
                    flag = false;
                }
            }
            else
            {
                // 併合する
                uf.Unite(lrd[0], lrd[1], lrd[2]);
            }
        }
        Out.YesNo(flag);
    }
}

public class Scan
{
    public static int Int()
    {
        return int.Parse(Console.ReadLine());
    }

    public static long Long()
    {
        return long.Parse(Console.ReadLine());
    }

    public static string[] StringArray(int lines)
    {
        string[] str = new string[lines];
        for (int i = 0; i < lines; i++)
        {
            str[i] = Console.ReadLine();
        }
        return str;
    }

    public static int[] IntArray(int t)
    {
        string[] str = Console.ReadLine().Split(' ');
        int[] ar = new int[t];
        for (int i = 0; i < t; i++)
        {
            ar[i] = int.Parse(str[i]);
        }
        return ar;
    }

    public static string[] StringArrayInLine(int t)
    {
        string[] str = Console.ReadLine().Split(' ');
        return str;
    }

    public static Tuple<int, int> ScanTuple()
    {
        int[] tmp = Scan.IntArray(2);
        return new Tuple<int, int>(tmp[0], tmp[1]);
    }

    public static long[] LongArray(int t)
    {
        string[] str = Console.ReadLine().Split(' ');
        long[] ar = new long[t];
        for (int i = 0; i < t; i++)
        {
            ar[i] = long.Parse(str[i]);
        }
        return ar;
    }

    public static double[] DoubleArray(int t)
    {
        string[] str = Console.ReadLine().Split(' ');
        double[] ar = new double[t];
        for (int i = 0; i < t; i++)
        {
            ar[i] = double.Parse(str[i]);
        }
        return ar;
    }

    public static int[,] IntSquareArray(int h, int w)
    {
        int[,] resAr = new int[h, w];
        for (int i = 0; i < h; i++)
        {
            int[] ar = Scan.IntArray(w);
            for (int j = 0; j < w; j++)
            {
                resAr[i, j] = ar[j];
            }
        }
        return resAr;
    }
}

public class Out
{
    public static void YesNo(bool f)
    {
        Console.WriteLine(f ? "Yes" : "No");
    }
    public static void Num<T>(T a)
    {
        Console.WriteLine(a);
    }
    public static void Array<T>(T[] a)
    {
        for (int i = 0; i < a.Length; i++)
        {
            Console.Write(a[i]);
            if(i != a.Length - 1)
            {
                Console.Write(" ");
            }
        }
        Console.WriteLine("");
    }

    public static void List<T>(List<T> a)
    {
        for (int i = 0; i < a.Count; i++)
        {
            Console.Write(a[i]);
            if (i != a.Count - 1)
            {
                Console.Write(" ");
            }
        }
        Console.WriteLine("");
    }

}

public class UnionFind
{
    public int[] parent;
    public int[] rank;
    public int[] weightDiff;

    public void Init(int size)
    {
        parent = new int[size + 5];
        rank = new int[size + 5];
        weightDiff = new int[size + 5];
        for (int i = 0; i < size; i++)
        {
            parent[i] = i;
            rank[i] = 0;
            weightDiff[i] = 0;
        }
    }

    public int Root(int index)
    {
        if(parent[index] == index)
        {
            return index;
        }
        else
        {
            weightDiff[index] += weightDiff[parent[index]];
            return parent[index] = Root(parent[index]);
        }
    }

    public void Unite(int x, int y, int w) // Add edge x <- y (weight: w)
    {
        w = w + GetWeight(x) - GetWeight(y);
        int rx = Root(x);
        int ry = Root(y);
        if(rx != ry)
        {
            if(rank[rx] < rank[ry])
            {
                int tmp = rx;
                rx = ry;
                ry = tmp;
                w *= -1;
            }else if(rank[x] == rank[y])
            {
                rank[x]++;
            }
            weightDiff[ry] = w;
            parent[ry] = rx;
        }
    }

    public bool Same(int x, int y)
    {
        return Root(x) == Root(y);
    }

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

    public int Diff(int x, int y) // x -> y
    {
        return GetWeight(y) - GetWeight(x);
    }



}