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 Go (1.6) (judge verdict: Accepted)

package main

import "fmt"

func abs_sum(input []int) int{
	var ans int
	for i := range input {
		if input[i] > 0 {
			ans += input[i]
		} else {
			ans -= input[i]
		}
	}
	return ans
}

func merge(left, right []int) (ret []int) {
	ret = []int{}
	for len(left) > 0 && len(right) > 0 {
		var x int
		if right[0] > left[0] {
			x, left = left[0], left[1:]
		} else {
			x, right = right[0], right[1:]
		}
		ret = append(ret, x)
	}
	ret = append(ret, left...)
	ret = append(ret, right...)
	return
}

func sort(left, right []int) (ret []int) {
	if len(left) > 1 {
		l, r := split(left)
		left = sort(l, r)
	}
	if len(right) > 1 {
		l, r := split(right)
		right = sort(l, r)
	}

	ret = merge(left, right)
	return
}

func split(values []int) (left, right []int) {
	left = values[:len(values) / 2]
	right = values[len(values) / 2:]
	return
}

func Sort(values []int) (ret []int) {
	left, right := split(values)
	ret = sort(left, right)
	return
}

func main(){
	var n int
	fmt.Scanf("%d",&n)
	a := make([]int,n)
	for i := range a {
		var b int
		fmt.Scanf("%d",&b)
		a[i] = b - i - 1
	}

	c := Sort(a)

	result := make([]int,n)
	for i := range result {
		result[i] = c[i]-c[n/2]
	}

	fmt.Println(abs_sum(result))
}