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: Wrong Answer)

package main

import "fmt"

func main() {
	var N int = 0
	fmt.Scan(&N)
	A := make([]int64, 0, N)
	for i := 0; i < N; i++ {
		var Ai int64
		fmt.Scan(&Ai)
		A = append(A, Ai)
	}

	additional := int64(-1)
	r := int64(0x7FFFFFFFFFFFFFFF)
	for b := int64(0); ; b += additional {
		tmp := f(A, b)
		if tmp < r {
			r = tmp
		} else if additional == -1 {
			additional = 1
		} else {
			break
		}
	}

	fmt.Println(r)
}

func abs(x int64) int64 {
	if x < 0 {
		return x * -1
	}
	return x
}

func f(A []int64, b int64) int64 {
	n := int64(0)
	for i := 0; i < len(A); i++ {
		n += abs(A[i] - (b + int64(i) + 1))
	}
	return n
}