Modulo Matrix

AtCoder

IDagc027_d

Time2000ms

Memory256MB

Difficulty—

You are given an integer $N$. Construct any one $N$\-by-$N$ matrix $a$ that satisfies the conditions below. It can be proved that a solution always exists under the constraints of this problem. * $1 \leq a_{i,j} \leq 10^{15}$ * $a_{i,j}$ are pairwise distinct integers. * There exists a positive integer $m$ such that the following holds: Let $x$ and $y$ be two elements of the matrix that are vertically or horizontally adjacent. Then, ${\rm max}(x,y)$ ${\rm mod}$ ${\rm min}(x,y)$ is always $m$. ## Constraints * $2 \leq N \leq 500$ ## Input Input is given from Standard Input in the following format: $N$ [samples]

Samples

Input #1

Output #1

4 7
23 10

*   For any two elements $x$ and $y$ that are vertically or horizontally adjacent, ${\rm max}(x,y)$ ${\rm mod}$ ${\rm min}(x,y)$ is always $3$.

API Response (JSON)

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  "problem": {
    "name": "Modulo Matrix",
    "description": {
      "content": "You are given an integer $N$. Construct any one $N$\\-by-$N$ matrix $a$ that satisfies the conditions below. It can be proved that a solution always exists under the constraints of this problem. *   $",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
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    "difficulty": "None",
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    "is_sync": true,
    "sync_url": null,
    "sign": "agc027_d"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given an integer $N$.\nConstruct any one $N$\\-by-$N$ matrix $a$ that satisfies the conditions below. It can be proved that a solution always exists under the constraints of this problem.\n\n*   $...",
      "is_translate": false,
      "language": "English"
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