KAIBUNsyo

AtCoder

IDabc206_d

Time2000ms

Memory256MB

Difficulty—

You are given a sequence of $N$ positive integers: $A=(A_1,A_2, \dots A_N)$. You can do the operation below zero or more times. At least how many operations are needed to make $A$ a palindrome? * Choose a pair $(x,y)$ of positive integers, and replace every occurrence of $x$ in $A$ with $y$. Here, we say $A$ is a palindrome if and only if $A_i=A_{N+1-i}$ holds for every $i$ ($1 \le i \le N$). ## Constraints * All values in input are integers. * $1 \le N \le 2 \times 10^5$ * $1 \le A_i \le 2 \times 10^5$ ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\dots$ $A_N$ [samples]

Samples

Input #1

8
1 5 3 2 5 2 3 1

Output #1

2

*   Initially, we have $A=(1,5,3,2,5,2,3,1)$.
*   After replacing every occurrence of $3$ in $A$ with $2$, we have $A=(1,5,2,2,5,2,2,1)$.
*   After replacing every occurrence of $2$ in $A$ with $5$, we have $A=(1,5,5,5,5,5,5,1)$.

In this way, we can make $A$ a palindrome in two operations, which is the minimum needed.

Input #2

7
1 2 3 4 1 2 3

Output #2

Input #3

1
200000

Output #3

0

$A$ may already be a palindrome in the beginning.

API Response (JSON)

{
  "problem": {
    "name": "KAIBUNsyo",
    "description": {
      "content": "You are given a sequence of $N$ positive integers: $A=(A_1,A_2, \\dots A_N)$. You can do the operation below zero or more times. At least how many operations are needed to make $A$ a palindrome? *   C",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc206_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a sequence of $N$ positive integers: $A=(A_1,A_2, \\dots A_N)$. You can do the operation below zero or more times. At least how many operations are needed to make $A$ a palindrome?\n\n*   C...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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