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)

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

#[allow(dead_code)]
fn read_vec2<T: std::str::FromStr>(n: u32) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

fn cango(t: i32, x: i32, y: i32) -> bool {
    println!("{}, {}, {}", t, x, y);
    let xab = if x >= 0 { x } else { -x };
    let yab = if y >= 0 { y } else { -y };
    if xab + yab > t {
        return false
    }

    (xab + yab) % 2 == t % 2
}

fn main() {
    let n = read::<i32>();
    let mut v = vec![];
    for _ in 0..n {
        v.push(read_vec::<i32>());
    }

    let mut vs: Vec<(i32, i32, i32)> = vec![];
    for (i, vi) in v.iter().enumerate() {
        if i == 0 {
            vs.push((vi[0], vi[1], vi[2]));
        } else {
            vs.push((vi[0]-v[i-1][0], vi[1]-v[i-1][1], vi[2]-v[i-1][2]));
        }
    }

    let mut retb = true;
    for vi in vs {
        if !cango(vi.0, vi.1, vi.2) {
            retb = false;
            break;
        }
    }
    if retb {
        println!("Yes");
    } else {
        println!("No");
    }
}