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 Perl (v5.18.2) (judge verdict: Accepted)

use strict;
use warnings;

my $n = <STDIN>;
chomp $n;
my (@t, @x, @y);
{
    for (my $i=0; $i<$n; $i++)
    {
        my $in = <STDIN>;
        ($t[$i], $x[$i], $y[$i]) = split(" ", $in);
    }
}
my ($t0, $x0, $y0) = (0, 0, 0);
my $ans = "Yes";
for (my $i=0; $i<$n; $i++)
{
    my $x1 = $x[$i];
    my $y1 = $y[$i];
    my $diff = $x1 - $x0 + $y1 - $y0;
    my $ditt = $t[$i] - $t0;
    $ans = "No" if $diff>$ditt || ($diff%2)!=($ditt%2);
    last if $diff<$ditt || ($diff%2)!=($ditt%2);
    ($t0, $x0, $y0) = ($t[$i], $x[$i], $y[$i]);
}

print "$ans\n";