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 PHP (5.6.30) (judge verdict: Wrong Answer)

<?php

$L = [];
$R = [];
$D = [];
$F = [];

for($i= 1; $i<= $M; $i++){
  $arr = explode(" ",trim(fgets(STDIN)));
  list($L[$i],$R[$i],$D[$i]) = $arr;
  $F[$i] = true; //論理演算をしたかどうかの判定
}

$X = [];

//初期値をセットする
$X[$L[1]] = 0;
$X[$R[1]] = $x[L[1]]+$D[1];

$result = true;

for($i=1;$i<=$M;$i++){
  if(isset($X[$L[$i]]) && isset($X[$R[$i]])){
    if($X[$L[$i]] + $D[$i] != $X[$R[$i]]){
      $result = false;
      break;
    }
  }elseif(isset($X[$L[$i]])){
    $X[$R[$i]] = $X[$L[$i]]+$D[$i];
  }elseif(isset($X[$R[$i]])){
    $X[$L[$i]] = $X[$R[$i]]-$D[$i];
  }else{
    $F[$i] = false;
  }
}

$keys = array_keys(array_filter($F,"getFalse"));

while(count($keys) > 0){
  foreach($keys as $i){ 
   if(isset($X[$L[$i]]) && isset($X[$R[$i]])){
    if($X[$L[$i]]+$X[R[$i]] != $D[$i]){
      $result = false;
      break;
    }
    $F[$i]=true;
   }elseif(isset($X[$L[$i]])){
    $X[$R[$i]] = $X[$L[$i]]+$D[$i];
    $F[$i]=true;
   }elseif(isset($X[$R[$i]])){
    $X[$L[$i]] = $X[$R[$i]]-$D[$i];
    $F[$i]=true;
   }
  }
  $keys = array_keys(array_filter($F,"getFalse"));
}

echo ($result)? "Yes":"No";

function getFalse($elem){
  return $elem == false;
}