Arrange Your Balls

AtCoder

IDagc059_b

Time2000ms

Memory256MB

Difficulty—

You have $N$ balls of colors $C_1, C_2, \ldots, C_N$. Here, all colors are represented by an integer between $1$ and $N$ inclusive. You want to arrange the balls on a circle. After you do that, you will count the number of pairs of colors $(X, Y)$ such that $X < Y$ and there exist two adjacent balls of colors $X$ and $Y$. Find an arrangement that minimizes the number of such pairs. If there are many such arrangements, find any of them. For example, for balls of colors $1, 1, 2, 3$, if we arrange them as $1, 1, 2, 3$, we get $3$ pairs: $(1, 2), (2, 3), (1, 3)$. If we arrange them as $1, 2, 1, 3$, we get only $2$ pairs: $(1, 2), (1, 3)$. Solve $T$ test cases for each input file. ## Constraints * $1 \le T \le 5 \cdot 10^4$ * $3 \le N \le 2 \cdot 10^5$ * $1 \le C_i \le N$ * The sum of $N$ in one input file doesn't exceed $2\cdot 10^5$. * All values in the input are integers. ## Input Input is given from Standard Input in the following format: $T$ $case_1$ $case_2$ $\vdots$ $case_T$ Each case is in the following format: $N$ $C_1$ $C_2$ $\ldots$ $C_N$ [samples]

Samples

Input #1

Output #1

1 2 3 
2 1 3 1 
3 3 2 5 2

API Response (JSON)

{
  "problem": {
    "name": "Arrange Your Balls",
    "description": {
      "content": "You have $N$ balls of colors $C_1, C_2, \\ldots, C_N$. Here, all colors are represented by an integer between $1$ and $N$ inclusive. You want to arrange the balls on a circle. After you do that, you wi",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc059_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You have $N$ balls of colors $C_1, C_2, \\ldots, C_N$. Here, all colors are represented by an integer between $1$ and $N$ inclusive. You want to arrange the balls on a circle. After you do that, you wi...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments