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;

class Program
{
    static string InputPattern = "InputX";

    static List<string> GetInputList()
    {
        var WillReturn = new List<string>();

        if (InputPattern == "Input1") {
            WillReturn.Add("3 3");
            WillReturn.Add("1 2 1");
            WillReturn.Add("2 3 1");
            WillReturn.Add("1 3 2");
            //Yes
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("3 3");
            WillReturn.Add("1 2 1");
            WillReturn.Add("2 3 1");
            WillReturn.Add("1 3 5");
            //No
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("4 3");
            WillReturn.Add("2 1 1");
            WillReturn.Add("2 3 5");
            WillReturn.Add("3 4 2");
            //Yes
        }
        else if (InputPattern == "Input4") {
            WillReturn.Add("10 3");
            WillReturn.Add("8 7 100");
            WillReturn.Add("7 9 100");
            WillReturn.Add("9 8 100");
            //No
        }
        else if (InputPattern == "Input5") {
            WillReturn.Add("100 0");
            //Yes
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    struct LRInfoDef
    {
        internal long L;
        internal long R;
        internal long D;
    }

    static void Main()
    {
        List<string> InputList = GetInputList();

        long[] wkArr = { };
        Action<string> SplitAct = pStr =>
            wkArr = pStr.Split(' ').Select(X => long.Parse(X)).ToArray();

        var LRList = new List<LRInfoDef>();
        foreach (string EachStr in InputList.Skip(1)) {
            SplitAct(EachStr);
            LRInfoDef WillAdd;
            WillAdd.L = wkArr[0];
            WillAdd.R = wkArr[1];
            WillAdd.D = wkArr[2];
            LRList.Add(WillAdd);
        }
        LRList = LRList.OrderBy(X => Math.Min(X.L, X.R)).ToList();

        bool IsOK = true;
        var HaitiDict = new Dictionary<long, long>();
        foreach (LRInfoDef EachLRInfo in LRList) {
            long CurrL = EachLRInfo.L;
            long CurrR = EachLRInfo.R;
            long CurrD = EachLRInfo.D;

            bool ConTainsL = HaitiDict.ContainsKey(CurrL);
            bool ConTainsR = HaitiDict.ContainsKey(CurrR);

            if (ConTainsL == false && ConTainsR == false) {
                HaitiDict[CurrL] = 0;
                HaitiDict[CurrR] = CurrD;
            }

            if (ConTainsL == false && ConTainsR) {
                HaitiDict[CurrL] = HaitiDict[CurrR] - CurrD;
            }
            if (ConTainsL && ConTainsR == false) {
                HaitiDict[CurrR] = HaitiDict[CurrL] + CurrD;
            }
            if (ConTainsL && ConTainsR) {
                if (HaitiDict[CurrL] + CurrD != HaitiDict[CurrR]) {
                    IsOK = false;
                }
            }
        }
        Console.WriteLine(IsOK ? "Yes" : "No");
    }
}