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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
#include<stdlib.h>
 
int main(){
 
  int N, i, a, b, c, t, h, v;
  int x[100001], y[100001], n[100001];
  x[0]=0; y[0]=0; n[0]=0;
  scanf("%d", &N);
  for(i=0; i<N; i++){
    scanf(" %d %d %d", &c, &a, &b);
    n[i+1]=c; x[i+1]=a; y[i+1]=b;
  }

  for(i=0; i<N; i++){
    t=n[i+1];
    h=(x[i]>x[i+1]?x[i]-x[i+1]:x[i+1]-x[i]);
    v=(y[i]>y[i+1]?y[i]-y[i+1]:y[i+1]-y[i]);
    if(h+v>t){
      printf("No\n"); break;
    }else if(h+v==t){
      if(i==N-1){
        printf("Yes\n"); break;
      }else
        continue;
    }else{
      if(i==N-1){
         if((t-(h+v))%2){
           printf("No\n"); break;
         }else{
           printf("Yes\n"); break;
         }
      }else{
         if((t-(h+v))%2){
           printf("No\n"); break;
         }else
           continue;
      }
    }
  }

}