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.*;
import java.util.function.Consumer;

import static java.util.stream.Collectors.toList;

public class Main {
    private static final Scanner scanner = new Scanner(System.in);
    private static final Consumer<List<String>> consumer = solve();

    public static void main(String[] args) {
        consumer.accept(readInput());
    }

    private static List<String> readInput() {
        final List<String> lineList = new ArrayList<>();
        while (scanner.hasNextLine()) {
            lineList.add(scanner.nextLine());
        }
        return lineList;
    }

    private static Consumer<List<String>> solve() {
        return args -> {
            final List<List<Integer>> inputLineList =
                    args.stream()
                            .skip(1)
                            .map(line -> Arrays.stream(line.split(" ")).map(Integer::valueOf).collect(toList()))
                            .collect(toList());

            final Map<Integer, Map<Integer, Integer>> dest2Src2Cost = new HashMap<>();
            Boolean flag = true;
            for (List<Integer> line: inputLineList) {
                final Integer left = line.get(0);
                final Integer right = line.get(1);
                final Integer cost = line.get(2);
                if (dest2Src2Cost.containsKey(left)) {
                    if (dest2Src2Cost.get(left).containsKey(right) && !dest2Src2Cost.get(left).get(right).equals(cost)) {
                        flag = false;
                        break;
                    }
                } else {
                    dest2Src2Cost.put(left, new HashMap<>());
                    dest2Src2Cost.get(left).put(right, cost);
                    if (dest2Src2Cost.containsKey(right)) {
                        for (Map.Entry<Integer, Integer> entry: dest2Src2Cost.get(right).entrySet()) {
                            dest2Src2Cost.get(left).put(entry.getKey(), cost + entry.getValue());
                        }
                    }
                }
                if (dest2Src2Cost.containsKey(right)) {
                    if (dest2Src2Cost.get(right).containsKey(left) && !dest2Src2Cost.get(right).get(left).equals(cost)) {
                        flag = false;
                        break;
                    }
                } else {
                    dest2Src2Cost.put(right, new HashMap<>());
                    dest2Src2Cost.get(right).put(left, cost);
                    if (dest2Src2Cost.containsKey(left)) {
                        for (Map.Entry<Integer, Integer> entry: dest2Src2Cost.get(left).entrySet()) {
                            dest2Src2Cost.get(right).put(entry.getKey(), cost + entry.getValue());
                        }
                    }
                }
            }

            if (flag) {
                System.out.println("Yes");
            } else {
                System.out.println("No");
            }

        };
    }

}