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: Wrong Answer)

use std::io;

fn main() {
    let n = input_ways_count();
    let ways = input_ways(n);

    let mut current_time = 0;
    let mut current_place = (0, 0);
    for way in ways.iter() {
        let time_diff = way.0 - current_time;

        let x = (way.1 - current_place.0).abs();
        let y = (way.2 - current_place.1).abs();
        let distance = x + y;

        if time_diff < distance {
            println!("NO");
            return;
        }

        if time_diff != distance && time_diff % 3 != 0 {
            println!("NO");
            return;
        }

        current_time = way.0;
        current_place = (way.1, way.2);
    }

    println!("YES")
}


fn input() -> String {
    let mut s = String::new();
    io::stdin().read_line(&mut s).expect("panic read line");
    s
}

fn input_ways_count() -> i32 {
    let n = input();
    let n: i32 = n.trim().parse().expect("panic parse");
    n
}

fn input_ways(count: i32) -> Vec<(i32, i32, i32)> {
    let mut ways: Vec<(i32, i32, i32)> = Vec::new();
    for _ in 0..count {
        ways.push(input_way())
    }

    ways
}

fn input_way() -> (i32, i32, i32) {
    let mut s = String::new();
    io::stdin().read_line(&mut s).expect("panic read line");
    let way: Vec<i32> = s.split_whitespace()
                    .map(|s| s.parse().expect("panic parse"))
                    .collect();

    (way[0], way[1], way[2])
}