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 id x = x in
let n = Scanf.scanf "%d\n" id in
let list =  (0,0,0) :: (Array.to_list @@ Array.init n (fun _ ->
    Scanf.scanf "%d %d %d\n" (fun a b c-> a, b, c))) in
   
let rec check : (int*int*int) list -> string =
  fun list ->
  match list with
  | [] -> "Yes"
  |  _ :: [] -> "Yes"
  | (t, x, y) :: ((t', x', y') as next) :: rest ->
     let dift=t'-t in
     let difd=x'-x+(y'-y) in
     if (dift+difd) mod 2 = 0 && difd<=dift
     then check (next :: rest)
     else "No" in

print_string (check list)
;;