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.ArrayDeque;
import java.util.Arrays;
import java.util.Queue;
import java.util.Scanner;

public class Main {
    private static class Edge {
        int l, r;
        int x[];

        public Edge(int l, int r, int x[]) {
            this.l = l;
            this.r = r;
            this.x = x;
        }
    }

    public void main(Scanner sc) {
        int n = sc.nextInt();
        int m = sc.nextInt();
        int data[][] = new int[n][n];
        for (int i = 0; i < m; i++) {
            int l = sc.nextInt();
            int r = sc.nextInt();
            int d = sc.nextInt();
            data[l - 1][r - 1] = d;
            data[r - 1][l - 1] = -d;
        }

        Queue<Edge> queue = new ArrayDeque<>();
        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                if (data[i][j] != 0) {
                    boolean isAdd = true;
                    for (int k = 0; k < j; k++) {
                        if (i != k && data[j][k] != 0) {
                            isAdd = false;
                            break;
                        }
                    }

                    if (isAdd) {
                        int x[] = new int[n];
                        x[i] = 0;
                        x[j] = data[i][j];
                        queue.add(new Edge(i, j, x));
                    }
                }
            }
        }

        boolean flg = true;
        LOOP: while (!queue.isEmpty()) {
            Edge e = queue.poll();
            System.out.println(Arrays.toString(e.x));
            for (int i = e.r + 1; i < n; i++) {
                if (data[e.r][i] != 0) {
                    if (e.x[i] != 0) {
                        if (e.x[i] - e.x[e.r] != data[e.r][i]) {
                            flg = false;
                            break LOOP;
                        }
                    } else {
                        e.x[i] = e.x[e.r] + data[e.r][i];
                        queue.add(new Edge(e.r, i, e.x));
                    }
                }
            }
        }
        System.out.println(flg ? "Yes" : "No");
    }

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