Rearranging

AtCoder

IDabc317_g

Time2000ms

Memory256MB

Difficulty—

There is a grid with $N$ rows and $M$ columns. The square at the $i$\-th row from the top and the $j$\-th column from the left contains the integer $A_{i,j}$. Here, the squares contain $M$ occurrences of each of $1,\ldots,N$, for a total of $NM$ integers. You perform the following operations to swap the numbers written on the squares. * For $i=1,\ldots,N$ in this order, do the following. * Freely rearrange the numbers written in the $i$\-th row. That is, freely choose a permutation $P=(P_{1},\ldots,P_{M})$ of $1,\ldots,M$, and replace $A_{i,1},\ldots,A_{i,M}$ with $A_{i,P_{1}},\ldots,A_{i,P_{M}}$ simultaneously. Your goal is to perform the operations so that each column contains each of $1,\ldots,N$ once. Determine if this is possible, and if so, print such a resulting grid. ## Constraints * $1 \leq N,M \leq 100$ * $1 \leq A_{i,j} \leq N$ * All input values are integers. * The $NM$ numbers $A_{1,1},\ldots,A_{N,M}$ contain exactly $M$ occurrences of each of $1,\ldots,N$. ## Input The Input is given from Standard Input in the following format: $N$ $M$ $A_{1,1}$ $\ldots$ $A_{1,M}$ $\vdots$ $A_{N,1}$ $\ldots$ $A_{N,M}$ [samples]

Samples

Input #1

Output #1

Yes
1 1
3 2
2 3

Also, the following output is accepted.

Yes
1 1
2 3
3 2

Input #2

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Rearranging",
    "description": {
      "content": "There is a grid with $N$ rows and $M$ columns. The square at the $i$\\-th row from the top and the $j$\\-th column from the left contains the integer $A_{i,j}$.   Here, the squares contain $M$ occurrenc",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc317_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a grid with $N$ rows and $M$ columns. The square at the $i$\\-th row from the top and the $j$\\-th column from the left contains the integer $A_{i,j}$.  \nHere, the squares contain $M$ occurrenc...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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