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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

function is_possible_trip(prev, next){
  prev_array = prev.split(' ');
  next_array = next.split(' ');
  time_distance = next_array[0] - prev_array[0];
  x_distance = next_array[1] - prev_array[1];
  if(x_distance < 0){x_distance = -1*x_distance;}
  y_distance = next_array[2] - prev_array[2];
  if(y_distance < 0){y_distance = -1*y_distance;}
  distance = x_distance + y_distance;
  
  if((time_distance - distance) < 0){return false;}
  
  if((time_distance - distance)%2!=0){return false;}
  
  return true;
}

function main(input) {
  input_array = input.split('\n');
  count = input_array[0];
  
  if(count==1){
    if(!is_possible_trip('0 0 0',input_array[1])){
      console.log('NO');
      return;
    }    
  }
  
  for(i=1; i < count;i++){
    if(!is_possible_trip(input_array[i],input_array[i+1])){
      console.log('NO');
      return;
    }
  }
  console.log('YES');
}
 
main(require('fs').readFileSync('/dev/stdin', 'utf8'));