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: Runtime Error)

using System;
using System.Collections;
class Program
{
    public static int n;
    public static int[,] G;
    public static bool[] isVisited;
    public static int[] x;
    public static bool answer = true;
    static int[] GetConnected(int s)
    {
        ArrayList list = new ArrayList();
        for (int i = 0; i < n; i++)
            if (G[s, i] != int.MaxValue)
                list.Add(i);
        return (int[])list.ToArray(typeof(int));
    }
    static void DepthFirstSearch(int v)
    {
        if (isVisited[v] == false)
        {
            isVisited[v] = true;
            { // 処理内容
                x[v] = (x[v] == int.MaxValue) ? 0 : x[v];
                for (int i = 0; i < n; i++)
                {
                    if (G[v, i] != int.MaxValue)
                    {
                        if (x[i] == int.MaxValue)
                            x[i] = x[v] + G[v, i];
                        else if (x[i] != x[v] + G[v, i])
                            answer = false;
                    }
                }
            }
            foreach (int i in GetConnected(v))
                if (!isVisited[i])
                    DepthFirstSearch(i);
        }
    }
    public static void Main()
    {
        string[] imp = Console.ReadLine().Split(' ');
        int m;
        n = int.Parse(imp[0]);
        m = int.Parse(imp[1]);
        G = new int[n, n];
        isVisited = new bool[n];
        x = new int[n];
        for (int i = 0; i < n; i++)
            x[i] = int.MaxValue;
        for (int i = 0; i < n; i++)
            for (int j = 0; j < n; j++)
                G[i, j] = int.MaxValue;
        for (int i = 0; i < m; i++) //G[i,j]はi+1からj+1への有向距離、int.MaxValueなら接続なし
        {
            imp = Console.ReadLine().Split(' ');
            int l, r, d;
            l = int.Parse(imp[0]);
            r = int.Parse(imp[1]);
            d = int.Parse(imp[2]);
            G[l - 1, r - 1] = d;
            G[r - 1, l - 1] = -d;
        }
        for (int i = 0; i < n; i++)
            DepthFirstSearch(i);
        Console.WriteLine(answer ? "Yes" : "No");
    }
}