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 Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

import Control.Monad

tdiff xy1 xy2 =       (xy2 !! 0) - (xy1 !! 0)
xdiff xy1 xy2 = abs $ (xy2 !! 1) - (xy1 !! 1)
ydiff xy1 xy2 = abs $ (xy2 !! 2) - (xy1 !! 2)

movable xy1 xy2 =
  let t = tdiff xy1 xy2
      x = xdiff xy1 xy2
      y = ydiff xy1 xy2
  in x + y <= t && (t - x - y) `mod` 2 == 0
  

main = do
  n <- readLn
  ls <- replicateM n getLine
  let xys = [0, 0, 0] : (map (map read . words) $ ls)
  putStrLn $ if all (\x -> x) $ [ movable (xys !! (i-1)) (xys !! i) | i<-[1..length xys -1 ] ]
             then "Yes"
             else "No"