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 12.16.1) (judge verdict: Accepted)

function main(input) {
  const args = input.split('\n');
  var int = [];
  for(let i=0;i<args.length;i++){
    int.push(args[i].split(' '));
  }
  var times = parseInt(int[0][0]);
  var points = [];
  for(let j=1;j<=times;j++){
    var point = [parseInt(int[j][0]),parseInt(int[j][1]),parseInt(int[j][2])];
    points.push(point);
  }
  points.unshift([0,0,0])
  for(let k=0;k<times;k++){
    var judge_time = points[k+1][0]-points[k][0];
    var judge_point = (points[k+1][1]-points[k][1])+(points[k+1][2]-points[k][2]);
    if(Math.abs(judge_point)<= judge_time && (judge_time-judge_point)%2 === 0){
      var result = 'Yes';
    }else{
      var result = 'No';
      break;
    }
  }
  console.log(result);
}

main(require('fs').readFileSync('/dev/stdin', 'utf8'));