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: Wrong Answer)

import java.util.*;

public class Main {
    public static void main(String[] args) throws Exception {

        int result = 0;
        
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int t[] = new int[110000];
        int x[] = new int[110000];
        int y[] = new int[110000];
        
        // 初期位置
        t[0] = 0; x[0] = 0; y[0] = 0;

        // 入力値を代入
        for (int i = 0;i < n; i++){
            t[i+1] = sc.nextInt();
            x[i+1] = sc.nextInt();
            y[i+1] = sc.nextInt();
        }
        
        boolean can = true;
        // 時刻tに点(x,y)に到達できるか探索
		for (int i = 0; i < n; i++) {
		    // 入力値の時刻tから現在の経過時間を引き、制限時間を算出
		    int dt = t[i+1] - t[i];
		    
		    // 入力値の点(x,y)から現在の点(x,y)の値を引いた値の絶対値を足し、移動距離を算出
		    int dist = Math.abs(x[i+1] - x[i]) + Math.abs(y[i+1] - y[i]);
		    
		    // 制限時間より移動距離のほうが大きい場合失敗判定
		    if (dt < dist) can = false;
		    
		    // 制限時間と移動距離が共に偶数または奇数でない場合失敗判定
		    if (dist % 2 != dt % 2) can = false;
		}
        
        if (can) {
            System.out.println("YES");
        } else {
            System.out.println("NO");
        }
        sc.close();
    }
}