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)

#[allow(unused_imports)]
use proconio::marker::{Bytes, Chars};
use proconio::{fastout, input};
#[fastout]
fn main() {
    input! {
        n: usize,
        t: [(usize, usize, usize); n],

    }
    // |xi - xi+1| + |yi - yi+1|がt2-t1より大きく、かつ偶奇が一致していればいい
    let t0: (isize, isize, isize) = (0, 0, 0);
    let mut ans = true;
    let distance =
        (t[0].1 as isize - t0.1 as isize).abs() + (t[0].2 as isize - t0.2 as isize).abs();
    if distance > t[0].0 as isize - t0.0 || distance % 2 != (t[0].0 as isize - t0.0) % 2 {
        ans = false;
    }
    for i in 0..(n - 1) {
        let distance = (t[i + 1].1 as isize - t[i].1 as isize).abs()
            + (t[i + 1].2 as isize - t[i].2 as isize).abs();
        if distance as usize > t[i + 1].0 - t[i].0
            || distance as usize % 2 != (t[i + 1].0 - t[i].0) % 2
        {
            ans = false;
            break;
        }
    }
    if ans {
        println!("Yes");
    } else {
        println!("No");
    }
}