Sort from 1 to 4

AtCoder

IDabc302_g

Time2000ms

Memory256MB

Difficulty—

You are given a sequence $A=(A_1,A_2,\ldots,A_N)$ of length $N$, consisting of integers between $1$ and $4$. Takahashi may perform the following operation any number of times (possibly zero): * choose a pair of integer $(i,j)$ such that $1\leq i<j\leq N$, and swap $A_i$ and $A_j$. Find the minimum number of operations required to make $A$ non-decreasing. A sequence is said to be non-decreasing if and only if $A_i\leq A_{i+1}$ for all $1\leq i\leq N-1$. ## Constraints * $2 \leq N \leq 2\times 10^5$ * $1\leq A_i \leq 4$ * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\ldots$ $A_N$ [samples]

Samples

Input #1

6
3 4 1 1 2 4

Output #1

3

One can make $A$ non-decreasing with the following three operations:

*   Choose $(i,j)=(2,3)$ to swap $A_2$ and $A_3$, making $A=(3,1,4,1,2,4)$.
*   Choose $(i,j)=(1,4)$ to swap $A_1$ and $A_4$, making $A=(1,1,4,3,2,4)$.
*   Choose $(i,j)=(3,5)$ to swap $A_3$ and $A_5$, making $A=(1,1,2,3,4,4)$.

This is the minimum number of operations because it is impossible to make $A$ non-decreasing with two or fewer operations.  
Thus, $3$ should be printed.

Input #2

4
2 3 4 1

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Sort from 1 to 4",
    "description": {
      "content": "You are given a sequence $A=(A_1,A_2,\\ldots,A_N)$ of length $N$, consisting of integers between $1$ and $4$. Takahashi may perform the following operation any number of times (possibly zero): *   cho",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc302_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a sequence $A=(A_1,A_2,\\ldots,A_N)$ of length $N$, consisting of integers between $1$ and $4$.\nTakahashi may perform the following operation any number of times (possibly zero):\n\n*   cho...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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