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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] t = new int[n];
        int[] x = new int[n];
        int[] y = new int[n];
        for (int i = 0; i < n; i++) {
            t[i] = sc.nextInt();
            x[i] = sc.nextInt();
            y[i] = sc.nextInt();
        }
        boolean flag = true;
        if (t[0] < x[0] + y[0]) {
            flag = false;
        }
        if (t[0] % 2 != (x[0] + y[0]) % 2) {
            flag = false;
        }
        if (n >= 2) {
            for (int i = 0; i < n - 1; i++) {
                int deltaT = t[i + 1] - t[i];
                int deltaX = Math.abs(x[i + 1] - x[i]);
                int deltaY = Math.abs(y[i + 1] - y[i]);
                int deltaPos = deltaX + deltaY;
                if (deltaT < deltaPos) {
                    flag = false;
                }
                if (deltaT % 2 != deltaPos % 2) {
                    flag = false;
                }
            }
        }
        System.out.println(flag ? "Yes" : "No");
    }
}