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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Arrays;
import java.util.Comparator;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();
        int m = sc.nextInt();
        int[][] l = new int[m][3];
        int[] x = new int[n];

        for(int i=0; i<m; i++){
            l[i][0] = sc.nextInt()-1;
            l[i][1] = sc.nextInt()-1;
            l[i][2] = sc.nextInt();
        }

        //Comparatorインターフェイスを実装したクラスを作成
        Comp comp = new Comp();

        for(int i=0; i<m; i++){
            if(l[i][0] > l[i][1]){
                int tmp = l[i][0];
                l[i][0] = l[i][1];
                l[i][1] = tmp;
                l[i][2] = -l[i][2];
            }
        }

        //2次元目のインデックス0番でソート
        comp.set_index(0);
        //Arraysクラスのsort()を実行する
        Arrays.sort(l, comp);

        Arrays.fill(x, -1000000007);

        

        for(int i=0; i<m; i++){
            if(x[l[i][0]] == -1000000007 && x[l[i][1]] == -1000000007){
                x[l[i][0]] = 0;
                x[l[i][1]] = x[l[i][0]] + l[i][2];
            }else if(x[l[i][1]] == -1000000007){
                x[l[i][1]] = x[l[i][0]] + l[i][2];
            }else if(x[l[i][0]] == -1000000007){
                x[l[i][0]] = x[l[i][1]] - l[i][2];
            }else if(x[l[i][1]] - x[l[i][0]] != l[i][2]){
                System.out.println("No");
                return;
            }
        }
        System.out.println("Yes");
    }
}

class Comp implements Comparator {

    int index = 0;

    public void set_index (int i) {
        index = i;
    }

    public int compare (Object a, Object b) {
        int[] int_a = (int[]) a;
        int[] int_b = (int[]) b;
        return (int_a[index] - int_b[index]);
    }

}