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 (1.42.0) (judge verdict: Accepted)

use proconio::input;

fn main() {
    input! {
        n: usize,
        mut p: [(i32, i32, i32); n],
    };
    p.reverse();
    let mut p0 = (0, 0, 0);
    let mut p1 = if let Some(p1) = p.pop() {
        p1
    } else {
        println!("Yes");
        return;
    };
    let mut res = true;
    loop {
        let t = p1.0 - p0.0;
        let xd = p1.1 - p0.1;
        let yd = p1.2 - p0.2;
        if (t % 2 != (xd + yd).abs() % 2) || (xd.abs() + yd.abs() > t) {
            res = false;
            break;
        }
        p0 = p1;
        p1 = if let Some(p1) = p.pop() {
            p1
        } else {
            break;
        };
    };
    if res {
        println!("Yes");
    } else {
        println!("No");
    }
}