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 (4.10.0) (judge verdict: Accepted)

open Core

let n = Scanf.scanf "%d" ident

let plans =
  List.init n (fun _ -> Scanf.scanf " %d %d %d" (fun t x y -> (t, x, y)))
  |> List.rev

let reachable np p =
  let nt, nx, ny = np in
  let t, x, y = p in
  let d1 = abs (nx - x) + abs (ny - y) in
  let dt = nt - t in
  if d1 <= dt && d1 mod 2 = dt mod 2 then true else false

let rec solve p = function
  | [] ->
      true
  | np :: rest ->
      if reachable np p then solve np rest else false

let str = if solve (0, 0, 0) plans then "Yes" else "No"

let () = print_endline str