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: Wrong Answer)

/*
2
3 1 2
6 1 1
*/
fn main() {
    // let n = 2;
    // let vt = vec![0, 3, 6];
    // let vx = vec![0, 1, 1];
    // let vy = vec![0, 2, 1];
    let n = read();
    let vec = read_lines(n);
    let mut vt = vec![0];
    let mut vx = vec![0];
    let mut vy = vec![0];
    for v in vec {
        vt.push(v[0]);
        vx.push(v[1]);
        vy.push(v[2]);
    }

    for i in 1..(n + 1) as usize {
        let dt: i32 = vt[i] - vt[i - 1];
        let dx = ((vx[i] - vx[i - 1]) as i32).abs();
        let dy = ((vy[i] - vy[i - 1]) as i32).abs();
        let div = (dx + dy - dt).abs();

        // debug
        println!("{} {} {} {}", dt, dx, dy, div);

        if dt < (dx + dy) {
            println!("NO");
            return;
        }
        if div < 0 {
            println!("NO");
            return;
        }
        if div % 2 == 1 {
            println!("NO");
            return;
        }
    }

    println!("YES");
}

fn read() -> i32 {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_lines(n: i32) -> Vec<Vec<i32>> {
    let mut v2 = Vec::new();
    for _ in 0..n {
        let mut s = String::new();
        std::io::stdin().read_line(&mut s).ok();
        let v = s.trim()
            .split_whitespace()
            .map(|e| e.parse().ok().unwrap())
            .collect();
        v2.push(v);
    }
    v2
}