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: Wrong Answer)

<?php
  $N = trim(fgets(STDIN));
  $current_x = 0;
  $current_y = 0;
  $success = true;
  $pre_time = 0;
  
  for($i = 0; $i < $N; $i++){
    $temp = trim(fgets(STDIN));
    $temp = str_replace(array("\r\n", "\r", "\n"), "", $temp);
    $array = explode(" ", $temp);
    $time = $array[0] - $pre_time;
    $trip_x = $array[1];
    $trip_y = $array[2];
    
    $trip_sum = $trip_x + $trip_y;
    $current_sum = $current_x + $current_y;
    
    $move = abs($current_sum - $trip_sum);

    if(($time - $move) % 2 == 0 && $move <= $time){
      $current_x = $trip_x;
      $current_y = $trip_y;
      $pre_time += $time;
    } else {
      $success = false;
      break;
    }
  }
  
  if($success){
    echo "YES";
  } else {
    echo "NO";
  }
?>