Traveling

AtCoder

IDarc089_a

Time2000ms

Memory256MB

Difficulty—

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: $N$ $t_1$ $x_1$ $y_1$ $t_2$ $x_2$ $y_2$ $:$ $t_N$ $x_N$ $y_N$ [samples]

Samples

Input #1

2
3 1 2
6 1 1

Output #1

Yes

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

Input #2

1
2 100 100

Output #2

No

It is impossible to be at $(100,100)$ two seconds after being at $(0,0)$.

Input #3

2
5 1 1
100 1 1

Output #3

No

API Response (JSON)

{
  "problem": {
    "name": "Traveling",
    "description": {
      "content": "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",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc089_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "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...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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