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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
fscanf(STDIN, '%d', $n);
$tarray[0] = 0;
$xarray[0] = 0;
$yarray[0] = 0;
for($i = 1; $i <= $n; $i++){
    fscanf(STDIN, '%d %d %d', $t, $x, $y);
    $tarray[$i] = $t;
    $xarray[$i] = $x;
    $yarray[$i] = $y;
}
$ans = 'Yes';
for($i = 1; $i <= $n; $i++){
    $d = ($tarray[$i] - $tarray[$i-1]) -(($xarray[$i] - $xarray[$i-1]) + ($yarray[$i] - $yarray[$i-1]));
    if(($d < 0) | ($d % 2 != 0)){
        $ans = 'No';
        break;
    }
}
print $ans;