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C - Traveling

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.

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