Many Swaps Sorting

AtCoder

IDasaporo2_b

Time2000ms

Memory256MB

Difficulty—

Snuke has a sequence $p$, which is a permutation of $(0,1,2, ...,N-1)$. The $i$\-th element ($0$\-indexed) in $p$ is $p_i$. He can perform $N-1$ kinds of operations labeled $1,2,...,N-1$ any number of times in any order. When the operation labeled $k$ is executed, the procedure represented by the following code will be performed: for(int i=k;i<N;i++) swap(p\[i\],p\[i-k\]); He would like to sort $p$ in increasing order using between $0$ and $10^{5}$ operations (inclusive). Show one such sequence of operations. It can be proved that there always exists such a sequence of operations under the constraints in this problem. ## Constraints * $2 \leq N \leq 200$ * $0 \leq p_i \leq N-1$ * $p$ is a permutation of $(0,1,2,...,N-1)$. ## Input Input is given from Standard Input in the following format: $N$ $p_0$ $p_1$ $...$ $p_{N-1}$ ## Partial Scores * In the test set worth $300$ points, $N \leq 7$. * In the test set worth another $400$ points, $N \leq 30$. [samples]

Samples

Input #1

5
4 2 0 1 3

Output #1

4
2
3
1
2

*   Each operation changes $p$ as shown below:

![image](https://atcoder.jp/img/asaporo2/9f3b51eb1fe742848f407bdeb7b772e1.png)

Input #2

9
1 0 4 3 5 6 2 8 7

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Many Swaps Sorting",
    "description": {
      "content": "Snuke has a sequence $p$, which is a permutation of $(0,1,2, ...,N-1)$. The $i$\\-th element ($0$\\-indexed) in $p$ is $p_i$. He can perform $N-1$ kinds of operations labeled $1,2,...,N-1$ any number of",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "asaporo2_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Snuke has a sequence $p$, which is a permutation of $(0,1,2, ...,N-1)$. The $i$\\-th element ($0$\\-indexed) in $p$ is $p_i$.\nHe can perform $N-1$ kinds of operations labeled $1,2,...,N-1$ any number of...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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