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.