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: Time Limit Exceeded)

#!/usr/bin/env php
<?php
const YES = "Yes";
const NO = "No";

function solve($N, array $t, array $x, array $y) {
    $pre_x = 0;
    $pre_y = 0;
    $pre_t = 0;
    foreach ($t as $time) {
        $cur_x = array_shift($x);
        $cur_y = array_shift($y);
        $move_t = $time - $pre_t;
        $move_s = abs($cur_x - $pre_x) + abs($cur_y - $pre_y);
        if ($move_s > $move_t) {
            echo NO.PHP_EOL;
            return;
        }
        if (($move_s % 2) != ($move_t % 2)) {
            echo NO.PHP_EOL;
            return;
        }

        $pre_x = $cur_x;
        $pre_y = $cur_y;
        $pre_t = $time;
    }
    echo YES.PHP_EOL;
}

function getInputs() {
    while(($input = fgets(STDIN)) !== false) {
        foreach (explode(' ', $input) as $v) {
            yield $v;
        }
    }
}

$gen = getInputs();
$N = $gen->current();
$gen->next();
for ($i = 0; $i < $N; $i++) {
    $t[] = $gen->current(); $gen->next();
    $x[] = $gen->current(); $gen->next();
    $y[] = $gen->current(); $gen->next();
}
solve($N, $t, $x, $y);