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 (1.14.1) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"os"
	"sort"
	"strconv"
)

func main() {
	sc.Split(bufio.ScanWords)

	n := nextInt()
	m := nextInt()

	g := make([][]Edge, n+1)
	for i := 0; i < m; i++ {
		l := nextInt()
		r := nextInt()
		d := nextInt()
		if l > r {
			l, r = r, l
		}
		g[l] = append(g[l], Edge{r, d})
	}

	for k := range g {
		sort.Sort(SortBy(g[k]))
	}

	done := make(map[int]bool)
	ans := true
	ds := make([]int, n+1)

	var dfs func(i int)
	dfs = func(u int) {
		for _, e := range g[u] {
			v := e.index
			d := e.dist
			done[u] = true

			if !done[v] {
				ds[v] = ds[u] + d
				done[v] = true
			} else if ds[v] != ds[u]+d {
				ans = false
				return
			}
		}
	}

	for i := 1; i <= n; i++ {
		dfs(i)
	}

	mx := 0
	for i := 1; i <= n; i++ {
		mx = max(mx, ds[i-1])
		if done[i] && mx > ds[i] {
			ans = false
			break
		}
	}

	if ans {
		fmt.Println("Yes")
	} else {
		fmt.Println("No")
	}
}

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

// Edge .
type Edge struct {
	index, dist int
}

// SortBy .
type SortBy []Edge

func (a SortBy) Len() int      { return len(a) }
func (a SortBy) Swap(i, j int) { a[i], a[j] = a[j], a[i] }
func (a SortBy) Less(i, j int) bool {
	return a[i].index < a[j].index
}

var sc = bufio.NewScanner(os.Stdin)

func nextInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}