Problem:
Score : 300 points

Problem Statement

AtCoDeer the deer is going on a trip in a two-dimensional plane.
In his plan, he will depart from point (0, 0) at time 0, then for each i between 1 and N (inclusive), he will visit point (x_i,y_i) at time t_i.

If AtCoDeer is at point (x, y) at time t, he can be at one of the following points at time t+1: (x+1,y), (x-1,y), (x,y+1) and (x,y-1).
Note that he cannot stay at his place.
Determine whether he can carry out his plan.

Constraints

1 ≤ N ≤ 10^5

0 ≤ x_i ≤ 10^5

0 ≤ y_i ≤ 10^5

1 ≤ t_i ≤ 10^5

t_i < t_{i+1} (1 ≤ i ≤ N-1)

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
t_1 x_1 y_1
t_2 x_2 y_2
:
t_N x_N y_N

Output

If AtCoDeer can carry out his plan, print Yes; if he cannot, print No.

Sample Input 1

2
3 1 2
6 1 1

Sample Output 1

Yes

For example, he can travel as follows: (0,0), (0,1), (1,1), (1,2), (1,1), (1,0), then (1,1).

Sample Input 2

1
2 100 100

Sample Output 2

No

It is impossible to be at (100,100) two seconds after being at (0,0).

Sample Input 3

2
5 1 1
100 1 1

Sample Output 3

No

Solution in PHP (5.6.30) (judge verdict: Accepted)

<?php

$is_honban = 1;

if ($is_honban) {
  //----------------------------------------------------------------------------------
  // Input for honban
  //----------------------------------------------------------------------------------
  $sc = new Scanner();
  $n = $sc->nextInt();

  $t = array();
  $x = array();
  $y = array();
  for ($i = 0; $i < $n; $i++) {
    $t[] = $sc->nextInt();
    $x[] = $sc->nextInt();
    $y[] = $sc->nextInt();
  }



} else {
  //----------------------------------------------------------------------------------
  // Input for test
  //----------------------------------------------------------------------------------
  error_reporting(E_ERROR | E_WARNING | E_PARSE);

  $n = 2;
  $t = array(3,6);
  $x = array(1,1);
  $y = array(2,1);



}
//----------------------------------------------------------------------------------
// Main
//----------------------------------------------------------------------------------

$ans = 0;

$ans = 'Yes';
$x0 = 0;
$y0 = 0;
$t0 = 0;
for ($i = 0; $i < $n; $i++) {
  if ($i > 0) {
    $x0 = $x[$i-1];
    $y0 = $y[$i-1];
    $t0 = $t[$i-1];
  }
  $x1 = $x[$i];
  $y1 = $y[$i];
  $t1 = $t[$i];

  $x_dist = abs($x1 - $x0);
  $y_dist = abs($y1 - $y0);
  $t_dist = abs($t1 - $t0);

  $a = $t_dist - ($x_dist + $y_dist);

  if ($a >= 0 && $a % 2 == 0) { continue; }
  else { $ans = 'No'; break; }
}



//----------------------------------------------------------------------------------
// Output
//----------------------------------------------------------------------------------
out::println($ans);



//----------------------------------------------------------------------------------
// Ref: https://qiita.com/yoshikyoto/items/6924478283dbdd549e4b
//----------------------------------------------------------------------------------
class Scanner {
  private $arr = array();
  private $count = 0;
  private $pointer = 0;
  public function next() {
    if($this->pointer >= $this->count) {
      $str = trim(fgets(STDIN));
      $this->arr = explode(' ', $str);
      $this->count = count($this->arr);
      $this->pointer = 0;
    }
    $result = $this->arr[$this->pointer];
    $this->pointer++;
    return $result;
  }
  public function hasNext() {
    return $this->pointer < $this->count;
  }
  public function nextInt() {
    return (int)$this->next();
  }
  public function nextDouble() {
    return (double)$this->next();
  }
}

class out {
  public static function println($str = "") {
    echo $str . PHP_EOL;
  }
}

?>