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"
	"sort"
)

func main() {
	var N int
	fmt.Scan(&N)
	A := make([]int, N)
	total := int(0)

	for i := range A {
		var a int
		fmt.Scan(&a)
		A[i] = a - int(i) - int(1)
		total += A[i]
	}
	sort.Ints(A)

	abe1 := A[N/2]
	abe2 := abe1 + 1
	abe3 := abe1 - 1

	r1 := int(0)
	r2 := r1
	r3 := r1
	for _, i := range A {
		r1 += abs(i - abe1)
		r2 += abs(i - abe2)
		r3 += abs(i - abe3)
	}

	fmt.Println(min(r3, min(r1, r2)))

}

func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}

func max(a, b int64) int64 {
	if a < b {
		return b
	}
	return a
}

func min(a, b int) int {
	if a > b {
		return b
	}
	return a
}