Esoswap

AtCoder

IDarc110_f

Time2000ms

Memory256MB

Difficulty—

We have a permutation $P = P_0, P_1, \ldots, P_{N - 1}$ of $0, 1, \ldots, N - 1$. You can do the following operation on $P$ at most $2 \times 10^5$ times: * Announce an integer $i ~ (0 \leq i \leq N - 1)$. Swap $P_i$ and $P_{(i + P_i) \textrm{ mod } N}$. Your task is to sort $P$ in ascending order with this operation. If it is impossible, print `-1` instead. ## Constraints * All values in input are integers. * $2 \leq N \leq 100$ * $P$ is a permutation of $0, 1, \ldots, N - 1$. ## Input Input is given from Standard Input in the following format: $N$ $P_0$ $P_1$ $\ldots$ $P_{N - 1}$ [samples]

Samples

Input #1

8
7 1 2 6 4 0 5 3

Output #1

4
6
0
3
0

This sequence of operations sorts $P$ in ascending order, as follows:

*   First, announce $i = 6$. We swap $P_6 (= 5)$ and $P_{(6 + 5) \textrm{ mod } 8} = P_3 (= 6)$, turning $P$ into $7, 1, 2, 5, 4, 0, 6, 3$.
    
*   Then, announce $i = 0$. We swap $P_0 (= 7)$ and $P_{(0 + 7) \textrm{ mod } 8} = P_7 (= 3)$, turning $P$ into $3, 1, 2, 5, 4, 0, 6, 7$.
    
*   Then, announce $i = 3$. We swap $P_3 (= 5)$ and $P_{(3 + 5) \textrm{ mod } 8} = P_0 (= 3)$, turning $P$ into $5, 1, 2, 3, 4, 0, 6, 7$.
    
*   Finally, announce $i = 0$. We swap $P_0 (= 5)$ and $P_{(0 + 5) \textrm{ mod } 8} = P_5 (= 0)$, turning $P$ into $0, 1, 2, 3, 4, 5, 6, 7$.

API Response (JSON)

{
  "problem": {
    "name": "Esoswap",
    "description": {
      "content": "We have a permutation $P = P_0, P_1, \\ldots, P_{N - 1}$ of $0, 1, \\ldots, N - 1$. You can do the following operation on $P$ at most $2 \\times 10^5$ times: *   Announce an integer $i ~ (0 \\leq i \\leq ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc110_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a permutation $P = P_0, P_1, \\ldots, P_{N - 1}$ of $0, 1, \\ldots, N - 1$.\nYou can do the following operation on $P$ at most $2 \\times 10^5$ times:\n\n*   Announce an integer $i ~ (0 \\leq i \\leq ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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