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 std::io;

fn main() {
    let n = get_num();
    let mut points: Vec<Vec<i32>> = Vec::new();
    for _i in 0..n {
        let point = read_line();
        points.push(point);
    }

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

    for i in 0..points.len() {
        if possible(points[i][0] - t, x, y, points[i][1], points[i][2]) {
            t = points[i][0];
            x = points[i][1];
            y = points[i][2];
        } else {
            possibility = false;
            break;
        }
    }

    if possibility {
        println!("Yes");
    } else {
        println!("No");
    }
}

fn possible(time: i32, from_x:i32, from_y:i32, to_x:i32, to_y:i32) -> bool {
    let need_time = (from_x - to_x).abs() + (from_y - to_y).abs();
    println!("{}, {}, {}, {}, {}: {}", time, from_x, from_y, to_x, to_y, need_time);
    if need_time <= time && need_time % 2 == time % 2 {
        true
    } else {
        false
    }
}

fn read_line() -> Vec<i32> {

    let input_str = get_input();
    let vec: Vec<&str> = input_str.trim().split_whitespace().collect();

    let mut int_vec: Vec<i32> = Vec::new();
    for v in vec {
        int_vec.push(to_i(v));
    }

    int_vec
}

fn get_num() -> i32 {
    to_i(&get_input())
}

fn to_i(s: &str) -> i32 {
    let input_num: i32 = match s.trim().parse() {
        Ok(num) => num ,
        Err(_)  => panic!("input wrong number."),
    };
    input_num
}

fn get_input() -> String {
    let mut input_str = String::new();
    io::stdin().read_line(&mut input_str)
        .expect("Failed to read line")
        ;
    input_str
}