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 (
	"fmt"
	"io"
	"os"
)

type data struct {
	l, r, d int
}

func parse(r io.Reader) (int, []data) {
	var N, M int
	fmt.Fscan(r, &N, &M)
	d := make([]data, M)
	for i := range d {
		fmt.Fscan(r, &d[i].l, &d[i].r, &d[i].d)
	}
	return N, d
}

func calc(N int, d []data) string {
	x := make([]int, N+1)
	for i := range x {
		x[i] = -1
	}
	for _, d := range d {
		if x[d.l] != -1 && x[d.r] != -1 {
			if x[d.r]-x[d.l] != d.d {
				return "No"
			}
			continue
		}
		if x[d.l] == -1 && x[d.r] != -1 {
			x[d.l] = x[d.r] - d.d
			continue
		}
		if x[d.l] != -1 && x[d.r] == -1 {
			x[d.r] = x[d.l] + d.d
		}
		if x[d.l] == -1 && x[d.r] == -1 {
			x[d.l] = 1e+10
			x[d.r] = x[d.l] + d.d
		}
	}
	return "Yes"
}

func main() {
	fmt.Println(calc(parse(os.Stdin)))
}