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 OCaml (4.02.3) (judge verdict: Accepted)

let () = Scanf.scanf "%d\n" @@ fun n ->
  Array.init n (fun _ ->
    Scanf.scanf "%d %d %d\n" @@ fun t x y -> t, x, y)
  |> Array.fold_left (fun (acc, txy') txy -> ((txy', txy) :: acc, txy)) ([], (0, 0, 0))
  |> fst
  |> List.for_all (fun ((t, x, y), (t', x', y')) ->
      let d = abs (x - x') + abs (y - y') in
      let dt = t' - t in
      d <= dt && (d - dt) mod 2 = 0)
  |> (function true -> "Yes" | false -> "No")
  |> print_endline