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: Wrong Answer)

<body>
<?php
$N = trim(fgets(STDIN));
$a = [];
$cnt = 0;

for ($i=0; $i<$N; $i++) {
    array_push($a, array_map('intval', explode(' ', fgets(STDIN))));
}

foreach ($a as $i) {
    if ($cnt==0) {
        if ($i[0]!==$i[1]+$i[2]){
            break;
        }
    } else {
        $sec = $i[0]-$a[$cnt-1][0];
        $point = ($i[1]+$i[2])-($a[$cnt-1][1]+$a[$cnt-1][2]);
        if (($sec%2!==$point%2)or($sec<$point)) {
            break;
        }
    }

    $cnt ++;
}

echo $cnt==count($a) ? 'Yes': 'No';