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::Read;

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

    // 標準入力から全部bufに読み込む
    std::io::stdin().read_to_string(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    let n: u32 = iter.next().unwrap().parse().unwrap();
    let number_tuple: Vec<(i32, i32, i32)> = (0..n)
        .map(|_| {
            (
                iter.next().unwrap().parse().unwrap(),
                iter.next().unwrap().parse().unwrap(),
                iter.next().unwrap().parse().unwrap(),
            )
        })
        .collect();

    let mut prev_numbers = (0, 0, 0);
    let mut result = "Yes";
    for numbers in number_tuple {
        let time_diff = numbers.0 - prev_numbers.0;
        let x_diff = i32::abs(numbers.1 - prev_numbers.1);
        let y_diff = i32::abs(numbers.2 - prev_numbers.2);
        if time_diff < x_diff + y_diff {
            result = "No";
            break;
        }
        if (time_diff % 2 == 0 && (x_diff + y_diff) % 2 != 0)
            || (time_diff % 2 != 0 && (x_diff + y_diff) % 2 == 0)
        {
            result = "No";
            break;
        }
        prev_numbers = numbers;
    }
    println!("{}", result);
}