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)

use scanner::Scanner;

fn main() {
    let mut sc = Scanner::new();
    let n: usize = sc.read();
    let mut txy: Vec<(i64, i64, i64)> = (0..n).map(|_| (sc.read(), sc.read(), sc.read())).collect();
    txy.sort_by_key(|k| k.0);

    for i in 1..n {
        let time = txy[i].0 - txy[i - 1].0;
        let dis = (txy[i].1 - txy[i - 1].1).abs() + (txy[i].2 - txy[i - 1].2).abs();
        if time >= dis && time % 2 == dis % 2 {
            println!("Yes");
            return;
        }
    }
    println!("No");
}


mod scanner {
    pub struct Scanner<'a> {
        s: String,
        words: ::std::str::SplitWhitespace<'a>,
    }

    impl<'a> Scanner<'a> {
        pub fn new() -> Scanner<'a> {
            let s = String::new();
            let words = unsafe { ::std::mem::transmute(s.split_whitespace()) };
            Scanner { s: s, words: words }
        }

        pub fn read<T: ::std::str::FromStr>(&mut self) -> T {
            match self.words.next() {
                Some(x) => x.parse().ok().unwrap(),
                None => {
                    self.load();
                    self.read()
                }
            }
        }

        fn load(&mut self) {
            self.s.clear();
            ::std::io::stdin().read_line(&mut self.s).unwrap();
            self.words = unsafe { ::std::mem::transmute(self.s.split_whitespace()) };
        }
    }
}