Choosing Points

AtCoder

IDagc025_d

Time2000ms

Memory256MB

Difficulty—

Takahashi is doing a research on sets of points in a plane. Takahashi thinks a set $S$ of points in a coordinate plane is a _good set_ when $S$ satisfies both of the following conditions: * The distance between any two points in $S$ is not $\sqrt{D_1}$. * The distance between any two points in $S$ is not $\sqrt{D_2}$. Here, $D_1$ and $D_2$ are positive integer constants that Takahashi specified. Let $X$ be a set of points $(i,j)$ on a coordinate plane where $i$ and $j$ are integers and satisfy $0 ≤ i,j < 2N$. Takahashi has proved that, for any choice of $D_1$ and $D_2$, there exists a way to choose $N^2$ points from $X$ so that the chosen points form a good set. However, he does not know the specific way to choose such points to form a good set. Find a subset of $X$ whose size is $N^2$ that forms a good set. ## Constraints * $1 ≤ N ≤ 300$ * $1 ≤ D_1 ≤ 2×10^5$ * $1 ≤ D_2 ≤ 2×10^5$ * All values in the input are integers. ## Input Input is given from Standard Input in the following format: $N$ $D_1$ $D_2$ [samples]

Samples

Input #1

2 1 2

Output #1

0 0
0 2
2 0
2 2

Among these points, the distance between $2$ points is either $2$ or $2\sqrt{2}$, thus it satisfies the condition.

Input #2

3 1 5

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Choosing Points",
    "description": {
      "content": "Takahashi is doing a research on sets of points in a plane. Takahashi thinks a set $S$ of points in a coordinate plane is a _good set_ when $S$ satisfies both of the following conditions: *   The dis",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc025_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi is doing a research on sets of points in a plane. Takahashi thinks a set $S$ of points in a coordinate plane is a _good set_ when $S$ satisfies both of the following conditions:\n\n*   The dis...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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