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: Accepted)

import qualified Data.ByteString.Char8 as BC
import qualified Data.Sequence as S
import qualified Data.IntMap as M
import Data.Maybe (fromJust)
import Data.List

main = do
  n <- readLn :: IO Int
  t <- map (\[x,y,z] -> (x,y,z)) <$> getInt2DListBC
  if solve (0, 0, 0) t
    then putStrLn "Yes"
    else putStrLn "No"

solve :: (Int, Int, Int) -> [(Int, Int, Int)] -> Bool
solve (_, _, _) [] = True
solve (t1, x1, y1) ((t2, x2, y2):s) =
  let t = t2 - t1
      x = abs $ x2 - x1
      y = abs $ y2 - y1
  in if t < x + y || mod (t-(x+y)) 2 /= 0
       then False
       else solve (t2, x2, y2) s


bsToInt :: BC.ByteString -> Int
bsToInt = fst . fromJust . BC.readInt

getInt2DListBC :: IO [[Int]]
getInt2DListBC = map (map bsToInt . BC.words) . BC.lines <$> BC.getContents