Revenge of BBuBBBlesort!

AtCoder

IDarc102_d

Time2000ms

Memory256MB

Difficulty—

You are given a permutation of $1,2,...,N$: $p_1,p_2,...,p_N$. Determine if the state where $p_i=i$ for every $i$ can be reached by performing the following operation any number of times: * Choose three elements $p_{i-1},p_{i},p_{i+1}$ ($2\leq i\leq N-1$) such that $p_{i-1}>p_{i}>p_{i+1}$ and reverse the order of these three. ## Constraints * $3 \leq N \leq 3 × 10^5$ * $p_1,p_2,...,p_N$ is a permutation of $1,2,...,N$. ## Input Input is given from Standard Input in the following format: $N$ $p_1$ $:$ $p_N$ [samples]

Samples

Input #1

Output #1

Yes

The state where $p_i=i$ for every $i$ can be reached as follows:

*   Reverse the order of $p_1,p_2,p_3$. The sequence $p$ becomes $1,2,5,4,3$.
*   Reverse the order of $p_3,p_4,p_5$. The sequence $p$ becomes $1,2,3,4,5$.

Input #2

Output #2

No

Input #3

Output #3

Yes

Input #4

Output #4

No

API Response (JSON)

{
  "problem": {
    "name": "Revenge of BBuBBBlesort!",
    "description": {
      "content": "You are given a permutation of $1,2,...,N$: $p_1,p_2,...,p_N$. Determine if the state where $p_i=i$ for every $i$ can be reached by performing the following operation any number of times: *   Choose ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc102_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a permutation of $1,2,...,N$: $p_1,p_2,...,p_N$. Determine if the state where $p_i=i$ for every $i$ can be reached by performing the following operation any number of times:\n\n*   Choose ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments