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::*;

fn read<T: FromStr>(s: &mut StdinLock) -> Option<T> {
    let s = s.by_ref()
        .bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect::<String>();
    s.parse::<T>().ok()
}

fn is_reachable(targets: Vec<(u32, (i32, i32))>) -> bool {
    let mut step = 0;
    let mut start = (0, 0);
    for target in targets {
        let limit = target.0 - step;
        let len = ((target.1).0 - start.0).abs() + ((target.1).1 - start.1).abs();
        let len = len as u32;

        if limit < len || limit % 2 != len % 2 {
            return false;
        }

        step = target.0;
        start = target.1;
    }

    return true;
}

pub fn main() {
    let stdin = stdin();
    let mut stdin = stdin.lock();

    let n: u32 = read(&mut stdin).unwrap();
    let targets: Vec<(u32, (i32, i32))> = (0..n)
        .map(|_x| {
            (
                read(&mut stdin).unwrap(),
                (read(&mut stdin).unwrap(), read(&mut stdin).unwrap()),
            )
        })
        .collect();

    if is_reachable(targets) {
        println!("Yes");
    } else {
        println!("No");
    }
}