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::*;
use std::str::FromStr;

pub fn read<T: FromStr>() -> T {
  let stdin = stdin();
  let stdin = stdin.lock();
  let token: String = stdin
    .bytes()
    .map(|c| c.expect("failed to read char") as char)
    .skip_while(|c| c.is_whitespace())
    .take_while(|c| !c.is_whitespace())
    .collect();
  token.parse().ok().expect("failed to parse token")
}

use std::cmp::{max, min};
use std::collections::HashMap;

fn gcd(a: i64, b: i64) -> i64 {
  if a % b == 0 {
    b
  } else {
    gcd(b, a % b)
  }
}

fn lcm(a: i64, b: i64) -> i64 {
  a * b / gcd(a, b)
}

fn main() {
  let n = read::<i64>();
  let mut vec: Vec<Vec<i64>> = vec![];
  let mut s_x = 0;
  let mut s_y = 0;
  let mut time = 0;
  let mut ans = "Yes";

  for _ in 0..n {
    let t = read::<i64>();
    let x = read::<i64>();
    let y = read::<i64>();
    vec.push(vec![t, x, y]);
  }

  for i in vec {
    let t = i[0];
    let x = i[1];
    let y = i[2];
    let d_x = (s_x - x).abs();
    let d_y = (s_y - y).abs();
    let d_time = (time - t).abs();

    if (d_x + d_y) % 2 != d_time % 2 || d_time < d_x + d_y {
      ans = "No";
      break;
    }
    s_x = x;
    s_y = y;
    time = t;
  }

  println!("{}", ans);
}