Score : 300 points
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.
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
If AtCoDeer can carry out his plan, print Yes
; if he cannot, print No
.
2 3 1 2 6 1 1
Yes
For example, he can travel as follows: (0,0), (0,1), (1,1), (1,2), (1,1), (1,0), then (1,1).
1 2 100 100
No
It is impossible to be at (100,100) two seconds after being at (0,0).
2 5 1 1 100 1 1
No