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 Rust (1.42.0) (judge verdict: Accepted)

use proconio::{input, fastout};
use proconio::marker::{Chars};
use std::cmp::*;

macro_rules! debug {
      ($($a:expr),*) => {
          eprintln!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
    }
}

#[fastout]
fn main() {
    input!{
        n: usize,
    }

    let mut t: Vec<usize> = vec![0;1];
    let mut ords: Vec<(usize,usize)> = vec![(0,0);1];
    for i in 0..n {
        input!{
            t_tmp: usize,
            x: usize,
            y: usize,
        }
        t.push(t_tmp);
        ords.push((x,y));
    }
    debug!(ords);
    debug!(t);
    for i in 0..n {
        let dis = (ords[i+1].0 as i64 - ords[i].0 as i64).abs()
                 +(ords[i+1].1 as i64 - ords[i].1 as i64).abs();
        let time = t[i+1]-t[i];
        debug!(dis);
        debug!(time);
        if time as i64 >=dis && (time as i64 - dis)%2==0{
            continue;
        } else {
            println!("No");
            return;
        }
    }

    println!("Yes");

}