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: Runtime Error)

package atcoder.ABC087;

import java.util.ArrayList;
import java.util.Arrays;
import java.util.LinkedList;
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();
        ArrayList<LinkedList<Tuple>> list = new ArrayList<>();
        for(int i = 0; i <= n; i++) list.add(new LinkedList<Tuple>());
        int[] memo = new int[3];
        for (int i = 0; i < m; i++) {
            ArrayList<ArrayList<Integer>> memo2 = new ArrayList<>();
            memo[0] = sc.nextInt();
            memo[1] = sc.nextInt();
            memo[2] = sc.nextInt();
            for (Tuple t2 : list.get(memo[1])) {
                list.get(memo[0]).add(new Tuple(memo[1], memo[2] + t2.y));
                memo2.add(new ArrayList<Integer>(Arrays.asList(memo[1], memo[0], t2.y - memo[2])));
            }
            for (ArrayList<Integer> m2 : memo2) {
                list.get(m2.get(0)).add(new Tuple(m2.get(1), m2.get(2)));
            }
            list.get(memo[0]).add(new Tuple(memo[1], memo[2]));
            list.get(memo[1]).add(new Tuple(memo[0], -memo[2]));
            for (Tuple t : list.get(memo[0])) {
                if (t.x == memo[1] && t.y != memo[2]) {
                    System.out.println("No");
                    return;
                }
            }
        }
        System.out.println("Yes");
    }
    static class Tuple {
        public final int x;
        public final int y;
        public Tuple(int x, int y) {
            this.x = x;
            this.y = y;
        }
    }
}