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 Scala (2.11.7) (judge verdict: Wrong Answer)

import scala.io.StdIn._
object Main extends App {
  val Array(n, m) = readLine.trim.split(' ').map(_.toInt)
  val person = Array.tabulate(n){_ ⇒ new UnionFind}
  var isNonParadoxical = true
  for (_ ← 0 until m){
    val Array(l, r, d) = readLine.trim.split(' ').map(_.toInt)
    if (person(r - 1).isCompatible(person(l - 1), d)) {
      person(r - 1).setInfo(person(l - 1), d)
    }else {
      isNonParadoxical = false
    }
  }
  println(
    if (isNonParadoxical) "Yes" else "No"
  )

  class UnionFind{
    private var parent = this
    private var size: Int = 1
    private var differ: Long = 0
    private def root: UnionFind = {
      if (parent != this){
        val newRoot = parent.root
        differ += parent.differ
        parent = newRoot
      }
      parent
    }
    private def isSameUnion(that: UnionFind): Boolean = {
      root == that.root
    }
    def isCompatible(that: UnionFind, diff: Int): Boolean = {
      root != that.root || that.differ + diff == differ
    }
    def setInfo(that: UnionFind, diff: Int): Unit = {
      if (!isSameUnion(that)){
        val thisR = root
        val thatR = that.root
        //thisR.differ + differ == thatR.differ + that.differ + diff
        if (thisR.size < thatR.size){
          thisR.differ = that.differ + diff - differ
          thisR.parent = thatR
          thatR.size += thisR.size
        }else {
          thatR.differ = thisR.differ - diff + differ
          thatR.parent = thisR
          thisR.size += thatR.size
        }
      }
    }
  }
}