Problem:
Score : 300 points

Problem Statement

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

Output

Print the minimum possible sadness of Snuke.

Sample Input 1

5
2 2 3 5 5

Sample 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.

Sample Input 2

9
1 2 3 4 5 6 7 8 9

Sample Output 2

0

Sample Input 3

6
6 5 4 3 2 1

Sample Output 3

18

Sample Input 4

7
1 1 1 1 2 3 4

Sample Output 4

6

Solution in Kotlin (1.0.0) (judge verdict: Wrong Answer)

import java.util.Scanner
import java.util.Arrays

fun main(args: Array<String>) {
  val cin = Scanner(System.`in`)
  val n = cin.nextInt()


  var a = IntArray(n)
  for (i in 0 until n) {
    a[i] = cin.nextInt()
    a[i] -= (i + 1)
  }

  Arrays.sort(a)
  var b = -1
  var ct = 0
  var tmpCt = 0
  for (i in 1 until n) {
    if (a[i] == a[i - 1]) {
      tmpCt++
    } else {
      tmpCt = 0
    }
    if (ct < tmpCt) {
      ct = tmpCt
      b = a[i]
    }
  }

  var res = 0
  for (i in 0 until n) {
    res += Math.abs(a[i] - b)
  }

  println(res)

  cin.close()
}