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: Time Limit Exceeded)

const input = require("fs").readFileSync("/dev/stdin", "utf8")
;(input => {
  
    const lines = input.split('\n')
    const N = lines[0] - 0

    const T = []
    for (let i = 1; i <= N; i++) {
         T.push(lines[i].split(' ').map(Number))
    }
  
    const f = (a, b) => {
      const dist = Math.abs(a[1] + a[2] - b[1] - b[2])
      const t = b[0] - a[0]
      if (t < dist) {
        return false
      } else if ((t - dist) % 2) {
        return false
      }
      return true
    }
    
    let ans = 'Yes'
    let t = null
    let p = [0, 0, 0]
    while (t = T.shift()) {
	    if (f(p, t)) {
            p = t
        } else {
            ans = 'No'
            break
        }
    }

    console.log(ans)
  
})(input)