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-----
2
3 1 2
6 1 1

-----Sample Output-----
Yes

For example, he can travel as follows: (0,0), (0,1), (1,1), (1,2), (1,1), (1,0), then (1,1).

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