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){
Scanner sc = new Scanner(System.in);
int n=Integer.parseInt(sc.next());
int[] t=new int[n+1];
int[] x=new int[n+1];
int[] y=new int[n+1];
t[0]=0;x[0]=0;y[0]=0;
for(int i=1;i<=n;i++){
t[i]=Integer.parseInt(sc.next());
x[i]=Integer.parseInt(sc.next());
y[i]=Integer.parseInt(sc.next());
}
String ans="";
int count=0;
for(int i=0;i<n;i++){
    int dx=Math.abs(x[i+1]-x[i]);
    int dy=Math.abs(y[i+1]-y[i]);
    int dt=Math.abs(t[i+1]-t[i]);
    System.out.println(dt+":"+dx+":"+dy);
    if(dt%2==dx%2&&dt%2==dy%2){
        if(dx+dy<=dt){count++;}
    }
}
if(count==n){ans="Yes";}else{ans="No";}
System.out.println(ans);
}}