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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {
    public static void main(String[] args) {
        try {
            // 標準入力
            InputStreamReader isr = new InputStreamReader(System.in);
            BufferedReader br = new BufferedReader(isr);
            int n = Integer.parseInt(br.readLine());
            int x = 0;
            int y = 0;
            boolean flag = true;
            for (int i = 0; i < n; i++) {
                String str[] = br.readLine().split(" ");
                int t = Integer.parseInt(str[0]);
                int xi = Integer.parseInt(str[1]);
                int yi = Integer.parseInt(str[2]);
                int temp = Math.abs(x - xi) + Math.abs(y - yi);
                if (temp > t) {
                    flag = false;
                    break;
                }
                if (temp % 2 == 0 && t % 2 == 0) {
                    continue;
                } else if (temp % 2 != 0 && t % 2 != 0) {
                    continue;
                } else {
                    flag = false;
                    break;
                }
            }
            if (flag) {
                System.out.println("Yes");
            } else {
                System.out.println("No");
            }
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

}