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 Control.Monad
import Debug.Trace

data Travel = Travel {
    time  :: Int,
    x :: Int,
    y :: Int
    } deriving (Show, Eq)

main :: IO ()
main = do
    n <- read <$> getLine :: IO Int
    travel <- forM [1..n] ( \_ -> do
            [t, x, y] <- map read . words <$> getLine :: IO [Int]
            return $ Travel t x y
        )
    putStrLn $ if move travel $ Travel 0 0 0 then "Yes" else "No"

move :: [Travel]
     -> Travel -- current status
     -> Bool
move [] _ = True
move ((Travel time x y):xs) (Travel ctime cx cy) = let
    canMove = let a = (time - ctime) - (abs (x - cx) + abs (y - cy)) :: Int
        in a >= 0 && even a  :: Bool
    nextStates = Travel time x y :: Travel
    in canMove && move xs nextStates