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: Accepted)

use std::io::prelude::*;
use std::str::FromStr;
pub struct Scanner<R: Read>(R);
impl<R: Read> Scanner<R> {
    pub fn new(reader: R) -> Self {
        Self(reader)
    }
    pub fn read<T: FromStr>(&mut self) -> T {
        let token = self
            .0
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| (b as char).is_whitespace())
            .take_while(|&b| !(b as char).is_whitespace())
            .collect::<Vec<u8>>();
        unsafe { std::str::from_utf8_unchecked(token.as_slice()) }
            .parse()
            .ok()
            .expect("Can't parse it.")
    }
    pub fn vec<T: FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}
fn main() {
    let (stdin, stdout) = (std::io::stdin(), std::io::stdout());
    let mut sc = Scanner::new(stdin.lock());
    let mut out = std::io::BufWriter::new(stdout.lock());
    solve(&mut sc, &mut out);
    out.flush().ok().unwrap();
}
fn solve(sc: &mut Scanner<std::io::StdinLock>, out: &mut std::io::BufWriter<std::io::StdoutLock>) {
    let N: usize = sc.read();
    let mut A = Vec::new();
    for _ in 0..N {
        let tup: (i32, i32, i32) = (sc.read(), sc.read(), sc.read());
        A.push(tup);
    }

    let mut ans = true;
    let mut ct = 0;
    let mut cx = 0;
    let mut cy = 0;
    for &(t, x, y) in A.iter() {
        let dist = (x - cx).abs() + (y - cy).abs();
        ans &= dist <= t - ct && ((t - ct) & 1) == (dist & 1);
        ct = t;
        cx = x;
        cy = y;
    }
    println!("{}", if ans { "Yes" } else { "No" });
}