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)

fun c102(args: Array<String>) {
    val numList = args[1].split(" ")
            .map { it.toInt() }
            .mapIndexed { index, i -> i - (index + 1) }
            .sorted()
    if (numList.size % 2 == 1) {
        val med = numList[(numList.size - 1) / 2]
        println(numList.map { Math.abs(it - med) }.sum())
    } else {
        val med1 = numList[(numList.size - 1) / 2]
        val med2 = numList[((numList.size - 1) / 2) + 1]
        println(Math.min(
                numList.map { Math.abs(it - med1) }.sum(),
                numList.map { Math.abs(it - med2) }.sum()))
    }
}

fun main(args: Array<String>) {
    c102(readLineList())
}

fun readLineList(): Array<String> {
    val lineList = mutableListOf<String>()
    while (true) {
        val line = readLine()
        if (line.isNullOrBlank()) {
            break
        } else {
            lineList.add(line!!)
        }
    }
    return lineList.toTypedArray()
}