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)


fn main() {
  
  let n = read::<usize>()[0];
  let (mut px, mut py, mut pt) = (0, 0, 0);
  for _ in 0..n {
    let txy = read::<i64>();
    let (t, x, y) = (txy[0], txy[1], txy[2]);
    let dx = (px - x).abs() + (py - y).abs();
    let dt = t - pt;
    if dt < dx || (dt - dx) % 2 != 0 {
      println!("No");
      return;
    };
    px = x;
    py = y;
    pt = t;
  };
  println!("Yes");
}

fn read<T: std::str::FromStr>() -> Vec<T> {
  gets().split_whitespace().filter_map(|s|s.parse().ok()).collect()
}

fn gets() -> String {
  let mut line = String::new();
  std::io::stdin().read_line(&mut line).ok();
  line.trim().to_string()
}