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: Time Limit Exceeded)

package main

import (
	"fmt"
)

func qs(A []int, n int, k int) int {
	i, j, l, pivot := 0, 0, 0, A[k/2]
	for ; i+l < n; i++ {
		if A[i] < pivot {
			A[j], A[i] = A[i], A[j]
			j++
		} else if A[i] > pivot {
			A[n-l-1], A[i] = A[i], A[n-l-1]
			i--
			l++
		}
	}

	if k < j {
		return qs(A, j, k)
	} else if n-l < k {
		return qs(A[n-l:], l, k-n+l)
	} else {
		return pivot
	}
}

func main() {
	var N int
	fmt.Scanf("%d", &N)
	A := make([]int, N)
	for i := 0; i < N; i++ {
		fmt.Scanf("%d", &A[i])
		A[i] -= i + 1
	}
	mid := qs(A, N, N/2)
	ans := 0
	for i := 0; i < N; i++ {
		sub := A[i] - mid
		if sub >= 0 {
			ans += sub
		} else {
			ans -= sub
		}
	}

	fmt.Printf("%d\n", ans)
	return
}