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)

package main

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

type edge struct {
	to    int
	value int
}

var edges [][]edge
var vertex []int
var visited []bool

func fillNumber(x int) bool {
	visited[x] = true
	for _, e := range edges[x] {
		if !visited[e.to] {
			vertex[e.to] = vertex[x] + e.value
			if !fillNumber(e.to) {
				fmt.Println("No")
				os.Exit(0)
			}
		} else if vertex[e.to] != vertex[x]+e.value {
			return false
		}
	}
	return true
}

func main() {
	in := IOInitialize()
	n, m := Int(in), Int(in)

	if m == 0 || m == 1 {
		fmt.Println("Yes")
		return
	}

	edges = make([][]edge, n)
	for i := range edges {
		edges[i] = make([]edge, 0, 32)
	}

	for i := 0; i < m; i++ {
		l, r, d := Int(in)-1, Int(in)-1, Int(in)
		edges[l] = append(edges[l], edge{to: r, value: d})
		edges[r] = append(edges[r], edge{to: l, value: -d})
	}

	vertex = make([]int, n)
	visited = make([]bool, n)

	for i := range visited {
		if !visited[i] {
			visited[i] = true
			if !fillNumber(i) {
				fmt.Println("No")
				return
			}
		}
	}
	fmt.Println("Yes")
}

//////////
//
//

func IOInitialize() *bufio.Scanner {
	t := bufio.NewScanner(os.Stdin)
	t.Split(bufio.ScanWords)
	return t
}

func Int(s *bufio.Scanner) int {
	if !s.Scan() {
		panic("\t\tThere is a FALSE not to want.")
	}

	value, err := strconv.Atoi(s.Text())
	if err != nil {
		panic("\t\tError:Failed to convert text to int,")
	}
	return value
}

func IntArray(s *bufio.Scanner, size int) []int {
	deepArray := make([]int, size)
	for i := range deepArray {
		deepArray[i] = Int(s)
	}
	return deepArray
}

func GraphSetByEdge(s *bufio.Scanner, v int) [][]int {
	g := make([][]int, v)
	for i := range g {
		g[i] = make([]int, 0)
	}
	for xxNonUsedInLoopI := 0; xxNonUsedInLoopI < v-1; xxNonUsedInLoopI++ {
		a, b := Int(s)-1, Int(s)-1
		g[a] = append(g[a], b)
		g[b] = append(g[b], a)
	}

	return g
}