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

main = do
  n <- read <$> getLine :: IO Int
  txys <- replicateM n $
    (\(t:x:[y]) -> (t,x,y)) . map readInt . words <$> getLine
  printAnsLn $  solve $ (0,0,0) : txys

solve (_:[]) = True
solve txys @ ((t1,x1,y1):(t2,x2,y2):_) =
--  traceShow (txys,difft,dist) $
  if isPossible then solve (tail txys)
  else False
  where
    difft = t2 - t1
    dist = x2-x1 + y2-y1
    isPossible = difft>=dist && ((dist-difft) `mod` 2==0)
    
  
readInt :: String -> Int
readInt = read

printAnsLn b = putStrLn $ if b then "Yes" else "No"