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)

main = do
    n <- getLine >>= return . read 
    strlist <- sequence (take n (repeat getLine))
    let ans = solve n strlist
    putStrLn ans

solve :: Int -> [String] -> String
solve _ strings = if subA strings then "Yes" else "No"

subA :: [String] -> Bool
subA strings = and $ map subB tuples
    where tuples = subC $ map subE strings

subB :: (Int,Int,Int) -> Bool
subB (t,x,y) = t >= x+y && mod (x+y-t) 2 == 0

subC :: [(Int,Int,Int)] -> [(Int,Int,Int)]
subC = \xs -> zipWith subD xs ((0,0,0):xs)

subD ::  (Int,Int,Int) -> (Int,Int,Int) -> (Int,Int,Int)
subD (x,y,z) (a,b,c) = (x-a,y-b,z-c)

subF :: String -> [Int]
subF = map read . words

subE :: String -> (Int,Int,Int)
subE string = (\[a,b,c] -> (a,b,c)) (subF string)