Linear Approximation

AtCoder

IDarc100_a

Time2000ms

Memory256MB

Difficulty—

Snuke has an integer sequence $A$ of length $N$. He will freely choose an integer $b$. Here, he will get sad if $A_i$ and $b+i$ are far from each other. More specifically, the _sadness_ of Snuke is calculated as follows: * $abs(A_1 - (b+1)) + abs(A_2 - (b+2)) + ... + abs(A_N - (b+N))$ Here, $abs(x)$ is a function that returns the absolute value of $x$. Find the minimum possible sadness of Snuke. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $1 \leq A_i \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $...$ $A_N$ [samples]

Samples

Input #1

5
2 2 3 5 5

Output #1

2

If we choose $b=0$, the sadness of Snuke would be $abs(2-(0+1))+abs(2-(0+2))+abs(3-(0+3))+abs(5-(0+4))+abs(5-(0+5))=2$. Any choice of $b$ does not make the sadness of Snuke less than $2$, so the answer is $2$.

Input #2

9
1 2 3 4 5 6 7 8 9

Output #2

Input #3

6
6 5 4 3 2 1

Output #3

Input #4

7
1 1 1 1 2 3 4

Output #4

API Response (JSON)

{
  "problem": {
    "name": "Linear Approximation",
    "description": {
      "content": "Snuke has an integer sequence $A$ of length $N$. He will freely choose an integer $b$. Here, he will get sad if $A_i$ and $b+i$ are far from each other. More specifically, the _sadness_ of Snuke is ca",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc100_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Snuke has an integer sequence $A$ of length $N$.\nHe will freely choose an integer $b$. Here, he will get sad if $A_i$ and $b+i$ are far from each other. More specifically, the _sadness_ of Snuke is ca...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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