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: Wrong Answer)

/**
 */

use std::io::*;
use std::str::FromStr;

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")
}

struct Coord{
    time:u32,
    x:u32,
    y:u32
}

fn main() {
    let n: u32 = read();

    if (n < 1) || (100000 < n)
    {
        println!("ERROR!(1)¥n");
        return;
    }

    let mut coord_org = Coord {
        time: 0,
        x: 0,
        y: 0
    };

    let mut can_move: bool = true;

    for _i in 0u32..n
    {
        // println!("Now pos:({},{})", coord_org.x, coord_org.y);

        let coord_new = Coord {
            time: read(),
            x: read(),
            y: read()
        };

        if can_move
        {
            let mut coord_calc = Coord{
                time: coord_org.time,
                x: coord_org.x,
                y: coord_org.y
            };

            for j in coord_org.time..coord_new.time
            {
                if coord_calc.x < coord_new.x
                {
                    coord_calc.x += 1;
                }
                else if coord_calc.x > coord_new.x
                {
                    coord_calc.x -= 1;
                }
                else
                {
                    // xが同じ
                    if coord_calc.y < coord_new.y
                    {
                        coord_calc.y += 1;
                    }
                    else if coord_calc.y > coord_new.y
                    {
                        coord_calc.y -= 1;
                    }
                    else
                    {
                        // xもyも同じ
                        coord_calc.x += 1;
                    }
                }

                // println!("Calc pos({}):({},{})", j, coord_calc.x, coord_calc.y);
            }

            if (coord_calc.x == coord_new.x) && (coord_calc.y == coord_new.y)
            {
                coord_org.time = coord_new.time;
                coord_org.x = coord_new.x;
                coord_org.y = coord_org.y;
            }
            else
            {
                can_move = false;
            }
        }
    }

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