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.*;
import java.util.Arrays;

public class Main {
  // final String testCase = "[[\"2\\n3 1 2\\n6 1 1\",\"Yes\"],[\"1\\n2 100 100\",\"No\"],[\"2\\n5 1 1\\n100 1 1\",\"No\"]]";
  public static void main(String[] args) {
    new Main().run();
  }

  public void run() {
    try(BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out)) {
      
      int n = Integer.parseInt(in.readLine());
      int[][] table = new int[n][3];
      
      String[] lines;
      for(int i=0; i<n; i++) {
        lines = in.readLine().split(" ");
        for(int j=0; j<3; j++)
          table[i][j] = Integer.parseInt(lines[j]);
      }

      final int t = 0;
      final int x = 1;
      final int y = 2;
      int ct,cx,cy; ct = cx = cy = 0;
      boolean isPossible = true;
      for(int i=0; i<n; i++) {
        int d = Math.abs(table[i][x] - cx) + Math.abs(table[i][y] - cy);
        int time = table[i][t] - ct;
        if(time < d || (time-d) % 2 != 0) {
          isPossible = false;
          break;
        }
      }

      String ans = isPossible ? "Yes" : "No";
      System.out.println(ans);
    }
    catch(IOException e) {
      System.err.println(e);
    }
  }
}