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)

struct Place {
    t: i32,
    x: i32,
    y: i32
}

impl Place {
    fn from_vec(vec: Vec<&str>) -> Place{
        Place {
            t: vec[0].parse::<i32>().unwrap(),
            x: vec[1].parse::<i32>().unwrap(),
            y: vec[2].parse::<i32>().unwrap()
        }
    }
}

fn c_can_move(place:&Place, goal:&Place) -> bool {
    let dt = place.t - goal.t; 
    let dx = place.x - goal.x; 
    let dy = place.y - goal.y;
    if ( dt.abs() - dx.abs() - dy.abs() ) % 2 == 0  && dt.abs() > dx.abs() + dy.abs() {
        true
    } else {
        false
    }
}

fn c() {
    let mut can_traveling = true;
    let mut line = String::new();
    let _ = std::io::stdin().read_line(&mut line);
    let n = line.trim().parse::<i32>().unwrap();
    let mut place = Place{ t: 0, x: 0, y: 0 };
    for _ in 0..n {
        line = String::new();
        let _ = std::io::stdin().read_line(&mut line);
        let vec: Vec<&str> = line.split_whitespace().collect();
        let goal = Place::from_vec(vec);
        if c_can_move(&place, &goal) {
            place = goal;
        } else {
            can_traveling = false;
            break;
        }
    }
    if can_traveling {
        print!("Yes");
    } else {
        print!("No");
    }
}

fn main() {
    c();
}