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
2 3 1 2 6 1 1
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
It is impossible to be at $(100,100)$ two seconds after being at $(0,0)$.
2 5 1 1 100 1 1