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: Accepted)

// weighted union findわかりません

package main

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

type Node struct {
	to, cost int
}

var sc = bufio.NewScanner(os.Stdin)
var out = bufio.NewWriter(os.Stdout)

func main() {
	buf := make([]byte, 1024*1024)
	sc.Buffer(buf, bufio.MaxScanTokenSize)
	sc.Split(bufio.ScanWords)
	defer out.Flush()

	N, M := nextInt(), nextInt()
	T := make([][]Node, N+1)
	for i := 0; i <= N; i++ {
		T[i] = []Node{}
	}
	for i := 0; i < M; i++ {
		L, R, D := nextInt(), nextInt(), nextInt()
		T[L] = append(T[L], Node{to: R, cost: D})
		T[R] = append(T[R], Node{to: L, cost: -D})
	}

	passed := make([]bool, N+1)
	dist := make([]int, N+1)

	// nodeを出発して通りがかりのcostをもちつつ全探索
	var dfs func(i, j int) bool
	dfs = func(node, d int) bool {
		if passed[node] {
			if dist[node] != d {
				return false
			} else {
				return true
			}
		}
		// 未踏
		passed[node] = true
		dist[node] = d
		for i, nexNode := range T[node] {
			if !dfs(nexNode.to, d+T[node][i].cost) {
				return false
			}
		}
		return true
	}

	// 1orderにしてるんでね
	for i := 1; i <= N; i++ {
		if passed[i] {
			continue
		}
		if !dfs(i, 0) {
			fmt.Fprintln(out, "No")
			return
		}
	}
	fmt.Fprintln(out, "Yes")
}

func next() string {
	sc.Scan()
	return sc.Text()
}

func nextInt() int {
	a, _ := strconv.Atoi(next())
	return a
}