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)

fn solve(rs: Vec<(i32, i32, i32)>) -> String {
    for i in 0..rs.len() - 1 {
        let (t1, x1, y1) = rs[i];
        let (t2, x2, y2) = rs[i + 1];
        let t = t2 - t1;
        let dist = (x2 - x1).abs() + (y2 - y1).abs();

        if t % 2 != dist % 2 || t < dist {
            return "No".to_string();
        }
    }
    "Yes".to_string()
}

fn main() {
    let n = read_1();
    let mut rs = vec!((0, 0, 0));
    rs.append(&mut read_tup3_n(n));

    println!("{}", solve(rs));
}

fn read_1<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_tup3_n<T: std::str::FromStr + Copy>(n: usize) -> Vec<(T, T, T)> {
    let mut ss = String::new();
    for _ in 0..n {
        std::io::stdin().read_line(&mut ss).ok();
    }
    let mut v = ss.split("\n").collect::<Vec<&str>>();
    v.pop();
    v.iter()
        .map(
            |s| {
                let v = s.trim().split_whitespace()
                    .map(|c| c.parse().ok().unwrap())
                    .collect::<Vec<T>>();
                (v[0], v[1], v[2])
            }
        )
        .collect()
}