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 (1.15.1) (judge verdict: Accepted)

use std::io;

fn main() {
  let n = read_values::<usize>()[0];
  let mut cur = (0, 0);
  let mut time = 0;

  for _ in 0..n {
    let (t, x, y) = {
      let v = read_values::<i64>();
      (v[0], v[1], v[2])
    };

    let duration = t - time;
    let (cx, cy) = cur;
    let length = (cx - x).abs() + (cy - y).abs();

    if length > duration {
      println!("No");
      return;
    }
    if (duration - length) % 2 != 0 {
      println!("No");
      return;
    }

    time = t;
    cur = (x, y);
  }
  println!("Yes");
}

fn read_line() -> String {
  let stdin = io::stdin();
  let mut buf = String::new();
  stdin.read_line(&mut buf).unwrap();
  buf
}

fn read_values<T>() -> Vec<T> where T: std::str::FromStr, T::Err: std::fmt::Debug {
  read_line()
    .split(' ')
    .map(|a| a.trim().parse().unwrap())
    .collect()
}