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.IO;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using Debug = System.Diagnostics.Debug;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;


static class P
{
    static void Main()
    {
        WeightedUnionFind<long> uf = new WeightedUnionFind<long>(Read(), (x, y) => x + y, x => -x, 0);
        var m = Read();
        for (int i = 0; i < m; i++)
        {
            if (!uf.TryUnite(Read() - 1, Read() - 1, Read()))
            {
                Console.WriteLine("No");
                throw new Exception();
                return;
            }
        }
        Console.WriteLine("Yes");
    }

    static readonly TextReader In = Console.In;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    static int Read()
    {
        int res = 0;
        int next = In.Read();
        while (48 > next || next > 57) next = In.Read();
        while (48 <= next && next <= 57)
        {
            res = res * 10 + next - 48;
            next = In.Read();
        }
        return res;
    }
}


class WeightedUnionFind<T> where T : IEquatable<T>
{
    public int Size { get; private set; }
    public int GroupCount { get; private set; }
    List<int> Sizes;
    List<int> Parent;
    List<T> Value;

    Func<T, T, T> Operate;
    Func<T, T> Inverse;
    T IdentityElement;
    public WeightedUnionFind(int count, Func<T, T, T> operate, Func<T, T> inverse, T identityElement)
    {
        Size = 0;
        GroupCount = 0;
        Parent = new List<int>(count);
        Sizes = new List<int>(count);
        Value = new List<T>(count);
        Operate = operate;
        Inverse = inverse;
        IdentityElement = identityElement;
        ExtendSize(count);
    }

    public bool TryUnite(int x, int y, T distance)
    {
        int xp = Find(x);
        int yp = Find(y);

        //        
        //   (xp|yp) <---.
        //      ^        |
        // v[x] |        | v[y]
        //      |        |
        //      x  ----> y
        //         dist
        if (yp == xp) return Operate(distance, Value[y]).Equals(Value[x]);

        if (Sizes[xp] < Sizes[yp])
        {
            var tmp = xp;
            xp = yp;
            yp = tmp;
            tmp = x;
            x = y;
            y = tmp;
        }
        else
        {
            distance = Inverse(distance);
        }
        GroupCount--;

        //
        //(xp|x) <--- (yp|y)
        //       dist

        //        v[yp]  -v[y] + dist + v[x]
        //      xp <--- yp
        //      ^       ^
        // v[x] |       | v[y]
        //      |       |
        //      x  <--- y
        //         dist
        Value[yp] = Operate(Operate(Inverse(Value[y]), distance), Value[x]);
        Parent[yp] = xp;
        Sizes[xp] += Sizes[yp];
        return true;
    }

    public IEnumerable<int> AllRepresents => Parent.Where(x => x == Parent[x]);
    public int GetSize(int x) => Sizes[Find(x)];
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public int Find(int x)
    {
        while (x != Parent[x])
        {
            //  xpp       xpp
            //  ^         ^
            //  | v[px]   |
            //  |         |
            //  xp        | v[x]+v[px]
            //  ^         |
            //  | v[x]    |
            //  |         |
            //  x         x
            Value[x] = Operate(Value[x], Value[Parent[x]]);
            Parent[x] = Parent[Parent[x]];
            x = Parent[x];
        }
        return x;
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public void ExtendSize(int treeSize)
    {
        if (treeSize <= Size) return;
        Parent.Capacity = treeSize;
        Sizes.Capacity = treeSize;
        Value.Capacity = treeSize;
        while (Size < treeSize)
        {
            Parent.Add(Size);
            Sizes.Add(1);
            Value.Add(IdentityElement);
            Size++;
            GroupCount++;
        }
    }
}