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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

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

import java.util.Arrays;
import java.util.Collections;
import java.util.ArrayList;
import java.util.List;
import java.util.HashSet;
import java.io.PrintWriter;
import java.io.OutputStream;

public class Main {
    // 標準入力
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

    // 標準入力数値配列用 int
    static int[] inputval() throws Exception {
        String[] strarray = br.readLine().trim().split(" ");
        int[] intarray = new int[strarray.length];
        for (int i = 0; i < intarray.length; i++) {
            intarray[i] = Integer.parseInt(strarray[i]);
        }
        return intarray;
    }

    // 標準入力数値配列用 integer ソート用
    static Integer[] inputvalInteger() throws Exception {
        String[] strarray = br.readLine().trim().split(" ");
        Integer[] intarray = new Integer[strarray.length];
        for (int i = 0; i < intarray.length; i++) {
            intarray[i] = Integer.parseInt(strarray[i]);
        }
        return intarray;
    }

    public static void main(String[] args) throws Exception {
        // write your code here
        int n = Integer.parseInt(br.readLine().trim());
        int oldx = 0;
        int oldey = 0;
        int oldt = 0;
        for (int i=0;i<n;i++){
            int [] inputval = inputval();
            int t = inputval[0] - oldt;
            int x = inputval[1];
            int y = inputval[2];
            int dist = Math.abs((x+y)-(oldx+oldey));
            if (dist > t || (t-dist) % 2 !=0){
                System.out.println("No");
                return;
            }
            oldx = x;
            oldey = y;
            oldt = t;

        }

        System.out.println("Yes");
    }

}