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: Wrong Answer)

package main

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

type Info struct {
	L int
	R int
	D int
}

type InfoList []Info

func (n InfoList) Len() int {
	return len(n)
}

func (n InfoList) Swap(i, j int) {
	n[i], n[j] = n[j], n[i]
}

func (n InfoList) Less(i, j int) bool {
	return n[i].L < n[j].L
}

func main() {
	s := IOInitialize()
	Int(s)
	M := Int(s)
	infoList := scanInfoList(s, M)
	sort.Sort(infoList)
	peopleMap := map[int]int{}
	peopleGroupMap := map[int]int{}
	group := map[int][]int{}
	for _, info := range infoList {
		var lPos int
		var rPos int
		_, hasLPos := peopleMap[info.L]
		_, hasRPos := peopleMap[info.R]
		if hasLPos && hasRPos {
			lPos = peopleMap[info.L]
			rPos = peopleMap[info.R]
			//isSameGroup := (peopleGroupMap[info.L] == peopleGroupMap[info.R])
			if rPos-lPos != info.D && isSameGroup(peopleGroupMap[info.L], group[peopleGroupMap[info.R]], peopleGroupMap) {
				fmt.Println("No")
				return
			}
			var people []int
			var aGroup int
			var distance int
			if len(group[peopleGroupMap[info.L]]) > len(group[peopleGroupMap[info.R]]) {
				people = group[peopleGroupMap[info.R]]
				aGroup = peopleGroupMap[info.L]
				distance = info.D
			} else {
				people = group[peopleGroupMap[info.L]]
				aGroup = peopleGroupMap[info.R]
				distance = -info.D
			}
			for _, person := range people {
				peopleMap[person] += distance
				peopleGroupMap[person] = aGroup
				group[aGroup] = append(group[aGroup], person)
			}
		} else if !hasLPos && !hasRPos {
			peopleMap[info.L] = 0
			lPos = 0
			peopleMap[info.R] = info.D
			groupNum := len(group) + 1
			group[groupNum] = []int{info.L, info.R}
			peopleGroupMap[info.R] = groupNum
			peopleGroupMap[info.L] = groupNum
		} else {
			lPos = peopleMap[info.L]
			peopleMap[info.R] = lPos + info.D
			peopleGroupMap[info.R] = peopleGroupMap[info.L]
			group[peopleGroupMap[info.L]] = append(group[peopleGroupMap[info.L]], info.R)
		}
	}
	fmt.Println("Yes")
}

func isSameGroup(groupNum int, people []int, peopleGroupMap map[int]int) bool {
	for _, person := range people {
		if groupNum == peopleGroupMap[person] {
			return true
		}
	}
	return false
}

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

func Int(s *bufio.Scanner) int {
	if !s.Scan() {
		panic("scan error")
	}

	value, err := strconv.Atoi(s.Text())
	if err != nil {
		panic("text to int error")
	}
	return value
}

func scanInfoList(s *bufio.Scanner, len int) (nums InfoList) {
	for i := 0; i < len; i++ {
		l := Int(s)
		r := Int(s)
		d := Int(s)
		if r < l {
			tmp := r
			r = l
			l = tmp
		}
		nums = append(nums, Info{L: l, R: r, D: d})
	}
	return
}