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)

#![allow(unused_macros, unused_imports, dead_code)]

use std::io;
use std::process;

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

macro_rules! read {
    ($($t:ty),+) => {
        {
            let line = read_line();
            let mut it = line.trim().split_whitespace();
            let result = (
                $(it.next().unwrap().parse::<$t>().unwrap(),)+
            );
            assert!(it.next().is_none());
            result
        }
    };
}

fn read_vec() -> Vec<i64> {
    let line = read_line();
    let it = line.trim().split_whitespace();
    it.map(|s| s.parse().unwrap()).collect()
}

fn dist((x, y): (i32, i32), (z, w): (i32, i32)) -> i32 {
    (z - x).abs() + (w - y).abs()
}

fn main() {
    let (N,) = read!(usize);
    let (mut s, mut z, mut w) = (0, 0, 0);
    for _ in 0..N {
        let (t, x, y) = read!(i32, i32, i32);
        let (dt, d) = (t - s, dist((x, y), (z, w)));
        if dt < d || (d - dt) % 2 != 0 {
            println!("No");
            process::exit(0);
        }
        s = t;
        z = x;
        w = y;
    }

    println!("Yes");    
}