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)

use std::io::stdin;

fn main() {
    let mut s = String::new();

    stdin().read_line(&mut s).ok();
    let n: i32 = s.trim().parse().unwrap();
    s.clear();

    let mut former_t = 0;
    let mut former_travel_plan = vec![0, 0, 0];
    let mut travel_plan: Vec<i32>;

    let mut res = "Yes";

    for _i in 0..n {
        stdin().read_line(&mut s).ok();
        travel_plan = s
            .trim()
            .split_whitespace()
            .map(|x| x.parse().unwrap())
            .collect();

        let t_diff = travel_plan[0] - former_t;
        let place_diff = (travel_plan[1] - former_travel_plan[1]).abs()
            + (travel_plan[2] - former_travel_plan[2]).abs();
        if (t_diff >= place_diff) & ((t_diff - place_diff) % 2 == 0){
            former_t = travel_plan[0];
            former_travel_plan = travel_plan;
            s.clear();
        } else {
            res = "No";
            break;
        }
    }

    println!("{}", res);
//     let mut travel_plan = Vec::<(i32, i32, i32)>::new();
//     travel_plan.push((0, 0, 0));
// 
//     for _i in 0..n {
//         stdin().read_line(&mut s).ok();
//         let travel_plan_unit: Vec<i32> = s
//             .trim()
//             .split_whitespace()
//             .map(|x| x.parse().unwrap())
//             .collect();
//         travel_plan.push((
//             travel_plan_unit[0],
//             travel_plan_unit[1],
//             travel_plan_unit[2],
//         ));
//         s.clear();
//     }
}