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 Go (1.6) (judge verdict: Time Limit Exceeded)

// Package main provides
//
// File:  d.go
// Author: ymiyamoto
//
// Created on Mon Dec 31 17:24:07 2018
//
package main

import "fmt"

type vertex struct {
	from, to, dist int
}

var vs []int
var graph [][]vertex

func dfs(from int) bool {
	for i := range graph[from] {
		if graph[from][i].dist == 0 {
			continue
		}

		to := graph[from][i].to
		dist := vs[from] + graph[from][i].dist
		graph[from][i].dist = 0
		if vs[to] == 1<<60 {
			vs[to] = dist
		}

		if vs[to] != dist {
			return false
		}

		if !dfs(to) {
			return false
		}
	}

	return true
}

func main() {
	var N, M int
	fmt.Scan(&N, &M)

	graph = make([][]vertex, N+1)
	for i := 0; i < M; i++ {
		var l, r, d int
		fmt.Scan(&l, &r, &d)
		graph[l] = append(graph[l], vertex{from: l, to: r, dist: d})
		graph[r] = append(graph[r], vertex{from: r, to: l, dist: -d})
	}

	vs = make([]int, N+1)
	for i := range vs {
		vs[i] = 1 << 60
	}

	for i := 1; i < len(graph); i++ {
		if vs[i] != 1<<60 {
			continue
		}

		vs[i] = 0
		if !dfs(i) {
			fmt.Println("No")
			return
		}
	}

	fmt.Println("Yes")
}