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 
fscanf(STDIN, "%d", $n);
for ($i=1; $i < $n+1; $i++) {
  fscanf(STDIN, "%d %d %d", ${"t".$i}, ${"x".$i}, ${"y".$i});
}
$t0 = 0;
$x0 = 0;
$y0 = 0;
$flag = 0;
for ($i=0; $i < $n ; $i++) {
  $j = $i+1;
  $tdiff = ${"t".$j} - ${"t".$i};
  $xdiff = abs(${"x".$j} - ${"x".$i});
  $ydiff = abs(${"y".$j} - ${"y".$i});
  if($tdiff == $xdiff + $ydiff){
    $flag = "0";
  }elseif ($tdiff < $xdiff + $ydiff) {
    $flag = "1";
    echo "No";
    break;
  }elseif ($tdiff > $xdiff + $ydiff) {
    if($tdiff % 2 == ($xdiff + $ydiff) % 2){
      $flag = "0";
    }else {
      $flag = "2";
      echo "No";
      break;
    }
  }
}
if($flag == 0){
  echo "Yes";
}

 ?>