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

//$_input = explode(
//    "\n",
//    '2
//3 1 2
//6 1 1
//
//'
//);

function getNext() {
    return trim(
        isset($GLOBALS['_input'])
            ? array_shift($GLOBALS['_input'])
            : fgets(STDIN)
    );
}

$planCount = (int) getNext();

$lastTime = 0;
$lastPosX = 0;
$lastPosY = 0;

for ($i = 0; $i < $planCount; ++$i) {
    $temp = explode(' ', getNext());
    $plan = [
        't' => (int) $temp[0],
        'x' => (int) $temp[1],
        'y' => (int) $temp[2],
    ];

    $diffTime = $plan['t'] - $lastTime;
    $diffX = abs($plan['x'] - $lastPosX);
    $diffY = abs($plan['y'] - $lastPosY);

    if (
        $diffX + $diffY > $diffTime
        ||  ($diffTime - ($diffX + $diffY)) % 2 === 1
    ) {
        echo "No\n";
        exit();
    }

    $lastTime = $plan['t'];
    $lastPosX = $plan['x'];
    $lastPosY = $plan['y'];
}

echo "Yes\n";