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::*;
use std::str::FromStr;
use std::collections::HashMap;
use std::collections::BTreeSet;
use std::collections::HashSet;
use std::cmp;
use std::f64::consts;

fn main() {
    let num: i32 = read();
    let mut vec: Vec<(i32, i32, i32)> = Vec::new();

    for i in 0..num {
        let each_vec: (i32,i32,i32) = (read(),read(),read());
        vec.push(each_vec);
    }

    let mut t = 0;
    let mut x = 0;
    let mut y = 0;

    let mut ans = "Yes";

    for &i in vec.iter() {
        let target_t = i.0;
        let target_x = i.1;
        let target_y = i.2;

        let diff = calc_distance(x,y,target_x,target_y);
        let time_diff = (target_t - t).abs();

        if diff > time_diff {
            ans = "No";
            break;
        }

        if (time_diff - diff) % 2 != 0 {
            ans = "No";
            break;
        }

        t = target_t;
        x = target_x;
        y = target_y;
    }

    println!("{}", ans);
}

fn calc_distance(x: i32, y: i32, target_x: i32, target_y: i32) -> i32 {
    let diff_x = (target_x - x).abs();
    let diff_y = (target_y - y).abs();

    return diff_x + diff_y;
}

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

// 最大公約数
fn gcd(a: i32, b: i32) -> i32 {
    match b {
        0 => a,
        _ => gcd(b, a % b)
    }
}

// 最小公倍数
fn lcm(a: i32, b: i32) -> i32 {
    a * b / gcd(a, b)
}

// 階乗
fn kaijou(n: i32)->i32 {
    if n == 1 {
        return n;
    }
    return n * kaijou(n-1);
}