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::BufRead;

const DEBUG: bool = false;

fn main() {
    let stdin = std::io::stdin();
    let mut stdinlock = stdin.lock();
    let mut n = String::new();
    let _ = stdinlock.read_line(&mut n);
    // let mut path: Vec<(i32, i32, i32)> = Vec::with_capacity((&n).trim().parse().expect("N"));
    let path: Vec<(i32, i32, i32)> = stdinlock
        .lines()
        .map(|l| {
            let lineinfo: Vec<i32> = l
                .expect("line?")
                .trim()
                .split_whitespace()
                .map(|n| n.parse().expect("parse n error"))
                .collect();
            (lineinfo[0], lineinfo[1], lineinfo[2])
        })
        .collect();
    if solve(&path) {
        println!("Yes");
    } else {
        println!("No");
    }
}

fn solve(path: &[(i32, i32, i32)]) -> bool {
    let mut current: (i32, i32, i32) = (0, 0, 0);
    for &(tN, xN, yN) in path {
        if DEBUG {
            println!("{:?}\t---\t{} {} {}", current, tN, xN, yN);
        }
        if !can_go(tN - current.0, xN - current.1, yN - current.2) {
            return false;
        }
        current = (tN, xN, yN);
    }
    true
}

fn can_go(dt: i32, dx: i32, dy: i32) -> bool {
    let dist = dx.abs() + dy.abs();
    if DEBUG {
        println!("dist: {} in dt {}", dist, dt);
    }
    (dist <= dt) && (dt - dist) % 2 == 0
}