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.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ABC087_D
{
    class Program
    {
        class Node
        {
            public int Parent;
            public int Position;

            public Node(int parent, int position)
            {
                Parent = parent;
                Position = position;
            }
        }


        static void Main(string[] args)
        {
            string[] strs = Console.ReadLine().Split(' ');
            int n = int.Parse(strs[0]);
            int m = int.Parse(strs[1]);

            bool flag = true;


            Node[] position = new Node[n + 1];
            Queue<int>[] axis = new Queue<int>[n + 1];

            for (int i = 0; i < m; ++i)
            {
                string[] strs2 = Console.ReadLine().Split(' ');
                int l = int.Parse(strs2[0]);
                int r = int.Parse(strs2[1]);
                int d = int.Parse(strs2[2]);

#if false
                if (l > r)
                {
                    int tmp = l;
                    l = r;
                    r = tmp;
                    d = -d;
                }
#endif


                if (position[l] == null)
                {
                    if (position[r] == null)
                    {
                        position[l] = new Node(l, 0);

                        position[r] = new Node(l, d);
                        axis[l] = new Queue<int>();
                    }
                    else
                    {
                        int rParent = position[r].Parent;
                        int rPosition = position[r].Position;

                        position[l] = new Node(rPosition - d, rParent);
                        axis[rParent].Enqueue(l);
                    }
                }
                else
                {
                    int lParent = position[l].Parent;
                    int lPosition = position[l].Position;

                    // lの人が既に登録されていたら
                    if (position[r] == null)
                    {
                        position[r] = new Node(lParent, lPosition + d);
                        axis[lParent].Enqueue(r);
                    }
                    else
                    {
                        int rParent = position[r].Parent;
                        int rPosition = position[r].Position;

                        // lの人もrの人も既に登録されていたら
                        if (lParent == rParent)
                        {
                            // lとrの総親が同じな場合、座標が食い違っていないかを確認する
                            if (rPosition - lPosition != d)
                            {
                                flag = false;
                                break;
                            }
                        }
                        else
                        {
                            // lとrの総親が異なる場合、座標系を合体させる
                            // 子供が少ないほうの総親の子供の情報を書き換える
                            Queue<int> src;
                            Queue<int> dst;
                            int parent;
                            int diffPosition;
                            if (axis[lParent].Count < axis[rParent].Count)
                            {
                                dst = axis[lParent];
                                src = axis[rParent];
                                axis[lParent] = null;
                                parent = rParent;
                                diffPosition = (rPosition - d) - lPosition;
                            }
                            else
                            {
                                dst = axis[rParent];
                                src = axis[lParent];
                                axis[rParent] = null;
                                parent = lParent;
                                diffPosition = (lPosition + d) - rPosition;
                            }


                            foreach (int index in dst)
                            {
                                position[index].Parent = parent;
                                position[index].Position += diffPosition;
                            }

                            src.Concat(dst);

                            //必要？
                            //dst.Clear();
                        }

                    }
                }
            }

            Console.WriteLine("{0}", flag ? "Yes" : "No");
        }
    }
}