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 mut buf: String = String::new();
    let n: i32 = if io::stdin().read_line(&mut buf).is_ok() {
        buf.trim().parse::<i32>().unwrap()
    } else { 0 };
    let mut v: Vec<(i32, i32, i32)> = Vec::new();
    v.push((0,0,0));
    for _ in 0..n {
        buf = String::new();
        io::stdin().read_line(&mut buf).unwrap();
        let mut iter = buf.trim().split_whitespace();
        v.push(
            (
                iter.next().unwrap().parse::<i32>().unwrap(),
                iter.next().unwrap().parse::<i32>().unwrap(),
                iter.next().unwrap().parse::<i32>().unwrap()
            )
        );
    }
    v.sort_by_key(|t| t.0);
    for i in 0..(v.len() - 1) {
        let dist = (v[i+1].1 - v[i].1).abs() + (v[i+1].2 - v[i].2).abs();
        let turn = v[i+1].0 - v[i].0;
        if dist > turn {
            println!("No");
            return;
        } else if (dist - turn).abs() % 2 == 1 {
            println!("No");
            return;
        }
    }
    println!("Yes");
}