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)

f :: [String] ->[(Int,Int,Int)]
f []=[]
f (x:xs)=let (t1:x1:y1:[])=map read (words x)::[Int]
         in (t1,x1,y1):f xs

f2 ::(Int,Int,Int)->[(Int,Int,Int)]->String
f2 _ [] = "Yes"
f2 (t0,x0,y0) ((t1,x1,y1):xs) = let d = abs(x0-x1)+abs(y0-y1)
                                in if t1-t0>=d && (t1-t0-d) `mod` 2==0 then f2 (t1,x1,y1) xs else "No"

main = do
      e<-getLine
      xs<-getContents
      let ys=f (lines xs)
      putStrLn $ f2 (0,0,0) ys