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) {
  input = input.split("\n");
  const n = parseInt(input[0],10);
  const txy = [];
  const changeInt = (n) => {
    return parseInt(n, 10);
  };
  for (var i = 0; i < n; i++) {
    txy.push(input[i+1].split(' ').map(changeInt));
  }
  console.log(travelcheck(n,txy)? "Yes":"No")
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));

function travelcheck(n,txy) {
  let dt = 0;
  let dist = 0;
  for (var t_i = 0; t_i < n; t_i++) {
    if (t_i === 0) {
      dt = txy[t_i][0];
      dist = txy[t_i][1] + txy[t_i][2];
    } else {
      dt = txy[t_i][0] - txy[t_i-1][0];
      dist = Math.abs(txy[t_i][1] - txy[t_i-1][1]) + Math.abs(txy[t_i][2] - txy[t_i-1][2]);
    }
    if (dist > dt) {
      return false;
    } else if (dist % 2 !== dt % 2) {
      return false;
    }
  }
  return true;
}