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::{self, BufRead};

fn main() {
    let si = io::stdin();
    let triplets = si.lock().lines().skip(1).map(|l| {
        let l = l.unwrap();
        let mut ns = l.split_whitespace().map(|s| s.parse::<u32>().unwrap());
        (ns.next().unwrap(), ns.next().unwrap(), ns.next().unwrap())
    });
    let (mut t, mut x, mut y) = (0, 0, 0);
    for (ti, xi, yi) in triplets {
        let d = sub_abs(xi, x) + sub_abs(yi, y);
        let dt = ti - t;
        if dt < d || (dt - d) % 2 == 1 {
            println!("No");
            return;
        }
        t = ti;
        x = xi;
        y = yi;
    }
    println!("Yes");
}

fn sub_abs(a: u32, b: u32) -> u32 {
    if a > b {
        a - b
    } else {
        b - a
    }
}