Sorting a Grid

AtCoder

IDagc037_d

Time2000ms

Memory256MB

Difficulty—

We have a grid with $N$ rows and $M$ columns of squares. Each integer from $1$ to $NM$ is written in this grid once. The number written in the square at the $i$\-th row from the top and the $j$\-th column from the left is $A_{ij}$. You need to rearrange these numbers as follows: 1. First, for each of the $N$ rows, rearrange the numbers written in it as you like. 2. Second, for each of the $M$ columns, rearrange the numbers written in it as you like. 3. Finally, for each of the $N$ rows, rearrange the numbers written in it as you like. After rearranging the numbers, you want the number written in the square at the $i$\-th row from the top and the $j$\-th column from the left to be $M\times (i-1)+j$. Construct one such way to rearrange the numbers. The constraints guarantee that it is always possible to achieve the objective. ## Constraints * $1 \leq N,M \leq 100$ * $1 \leq A_{ij} \leq NM$ * $A_{ij}$ are distinct. ## Input Input is given from Standard Input in the following format: $N$ $M$ $A_{11}$ $A_{12}$ $...$ $A_{1M}$ $:$ $A_{N1}$ $A_{N2}$ $...$ $A_{NM}$ [samples]

Samples

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API Response (JSON)

{
  "problem": {
    "name": "Sorting a Grid",
    "description": {
      "content": "We have a grid with $N$ rows and $M$ columns of squares. Each integer from $1$ to $NM$ is written in this grid once. The number written in the square at the $i$\\-th row from the top and the $j$\\-th co",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc037_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a grid with $N$ rows and $M$ columns of squares. Each integer from $1$ to $NM$ is written in this grid once. The number written in the square at the $i$\\-th row from the top and the $j$\\-th co...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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