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 Scala (2.11.7) (judge verdict: Accepted)

object Main extends App {
	val n = scala.io.StdIn.readInt
	var a = scala.io.StdIn.readLine.split(" ").map(_.toLong)

	for(i<-0 until n){
		a(i) -= i.toLong + 1L
	}

//	println(a.mkString(" "))

	a = a.sorted

	var ans = 0L

	val t = n/2

	if(n%2 == 1){
		val b = a(t)

		for(x<-a){
			ans += math.abs(x - b)
		}
		println(ans)

	}else{
		val b1 = a(t)
		val b2 = a(t-1)

		var ans1 = 0L

		for(x<-a){
			ans += math.abs(x - b1)
			ans1 += math.abs(x - b2)
		}
		println(math.min(ans, ans1))
	}
}