Make it Palindrome

AtCoder

IDabc290_e

Time2000ms

Memory256MB

Difficulty—

For a sequence $X$, let $f(X) =$ (the minimum number of elements one must modify to make $X$ a palindrome). Given a sequence $A$ of length $N$, find the sum of $f(X)$ over all **contiguous** subarrays of $A$. Here, a sequence $X$ of length $m$ is said to be a palindrome if and only if the $i$\-th and the $(m+1-i)$\-th elements of $X$ are equal for all $1 \le i \le m$. ## Constraints * All values in the input are integers. * $1 \le N \le 2 \times 10^5$ * $1 \le A_i \le N$ ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\dots$ $A_N$ [samples]

Samples

Input #1

5
5 2 1 2 2

Output #1

9

*   $f(5) = 0$
*   $f(2) = 0$
*   $f(1) = 0$
*   $f(2) = 0$
*   $f(2) = 0$
*   $f(5,2) = 1$
*   $f(2,1) = 1$
*   $f(1,2) = 1$
*   $f(2,2) = 0$
*   $f(5,2,1) = 1$
*   $f(2,1,2) = 0$
*   $f(1,2,2) = 1$
*   $f(5,2,1,2) = 2$
*   $f(2,1,2,2) = 1$
*   $f(5,2,1,2,2) = 1$

Therefore, the sought answer is $9$.

API Response (JSON)

{
  "problem": {
    "name": "Make it Palindrome",
    "description": {
      "content": "For a sequence $X$, let $f(X) =$ (the minimum number of elements one must modify to make $X$ a palindrome). Given a sequence $A$ of length $N$, find the sum of $f(X)$ over all **contiguous** subarrays",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc290_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "For a sequence $X$, let $f(X) =$ (the minimum number of elements one must modify to make $X$ a palindrome).\nGiven a sequence $A$ of length $N$, find the sum of $f(X)$ over all **contiguous** subarrays...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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