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;
using System.Text;
using System.Threading.Tasks;

namespace abc087d
{
    class Program
    {
        static void Main(string[] args) {
            var buffer =Console.ReadLine().Split();
            var N = int.Parse(buffer[0]);
            var M = int.Parse(buffer[1]);
            var revealed = new bool[N + 1];
            var position = new int[N + 1];
            for(var i = 1; i <= M; ++i) {
                buffer = Console.ReadLine().Split();
                var L = int.Parse(buffer[0]);
                var R = int.Parse(buffer[1]);
                var D = int.Parse(buffer[2]);
                if(!revealed[L] && !revealed[R]) {
                    position[L] = 0;
                    position[R] = position[L] + D;
                    revealed[L] = revealed[R] = true;
                } else if(!revealed[L] && revealed[R]) {
                    if(R - D < 0) {
                        var shiftToRight = D - R;
                        for(var j = 1; j <= N; ++j) {
                            if(revealed[j]) { position[j] += shiftToRight; }
                        }
                    }
                    position[L] = 0;
                    revealed[L] = true;
                }else if(revealed[L] && !revealed[R]) {
                    position[R] = position[L] + D;
                    revealed[R] = true;
                } else {
                    if(position[L] + D != position[R]) {
                        Console.WriteLine("No");
                        return;
                    }
                }
            }
            Console.WriteLine("Yes");
        }
    }
}