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)

/// ローカル環境なら _in.txt から入力を受ける
fn read_input() -> String {
    use std::fs::File;
    use std::io::Read;
    let mut s = String::new();
    match option_env!("LOCAL") {
        Some(_) => File::open("src/_in.txt")
            .expect("File not found")
            .read_to_string(&mut s)
            .unwrap(),
        None => std::io::stdin().read_to_string(&mut s).unwrap(),
    };
    s
}

fn main() {
    let s = read_input();
    let mut ws = s.split_whitespace();
    let in_n: i32 = ws.next().unwrap().parse().unwrap();
    let mut txy: Vec<(i32, i32, i32)> = (0..in_n)
        .map(|_| {
            let t: i32 = ws.next().unwrap().parse().unwrap();
            let x: i32 = ws.next().unwrap().parse().unwrap();
            let y: i32 = ws.next().unwrap().parse().unwrap();
            (t, x, y)
        })
        .collect();
    txy.insert(0, (0, 0, 0));

    let mut ok = true;
    for window in txy.windows(2) {
        let ((t1, x1, y1), (t2, x2, y2)) = (window[0], window[1]);
        let dt = t2 - t1;
        let d = (x1 - x2).abs() + (y1 - y2).abs();
        ok &= dt >= d && (dt - d) % 2 == 0
    }
    println!("{}", if ok { "Yes" } else { "No" });
}