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 (
	"bufio"
	"fmt"
	"io"
	"math"
	"os"
	"strconv"
)

var (
	readString func() string
	stdout     *bufio.Writer
)

func init() {
	readString = newReadString(os.Stdin)
	stdout = bufio.NewWriter(os.Stdout)
}

func newReadString(ior io.Reader) func() string {
	r := bufio.NewScanner(ior)
	r.Buffer(make([]byte, 1024), int(1e+11))
	r.Split(bufio.ScanWords)

	return func() string {
		if !r.Scan() {
			panic("Scan failed")
		}
		return r.Text()
	}
}

func readInt() int {
	return int(readInt64())
}

func readInt64() int64 {
	i, err := strconv.ParseInt(readString(), 0, 64)
	if err != nil {
		panic(err.Error())
	}
	return i
}

func readIntSlice(n int) []int {
	b := make([]int, n)
	for i := 0; i < n; i++ {
		b[i] = readInt()
	}
	return b
}

func readLengthAndSlice() []int {
	n := readInt()
	return readIntSlice(n)
}

func printf(f string, args ...interface{}) (int, error) {
	return fmt.Fprintf(stdout, f, args...)
}

func println(args ...interface{}) (int, error) {
	return fmt.Fprintln(stdout, args...)
}

func vi(n int, args ...int) []int {
	res := make([]int, n)
	if len(args) == 0 {
		return res
	}
	v := args[0]
	if v == 0 {
		return res
	}
	for i := 0; i < n; i++ {
		res[i] = v
	}
	return res
}

func vvi(n int, args ...int) [][]int {
	res := make([][]int, n)
	m := n
	if len(args) > 0 {
		m = args[0]
	}
	v := 0
	if len(args) > 1 {
		v = args[1]
	}
	for i := 0; i < n; i++ {
		res[i] = vi(m, v)
	}
	return res
}

// readString() string
// readInt() int
// readIntSlice(n int) []int
// readLengthAndSlice() []int
func max(a, b int64) int64 {
	if a < b {
		return b
	}
	return a
}

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

func abs(a int64) int64 {
	if a < 0 {
		return -a
	}
	return a
}

func main() {
	defer stdout.Flush()
	n := readInt()
	a := make([]int64, n)
	avg := float64(0)
	for i := 0; i < n; i++ {
		a[i] = readInt64() - int64(i+1)
		avg += float64(a[i]) / float64(n)
	}
	var ans int64 = math.MaxInt64
	for i := int64(avg - 100); i < int64(avg+100); i++ {
		sum := int64(0)
		for j := 0; j < n; j++ {
			sum += abs(a[j] - i)
		}
		if sum < ans {
			ans = sum
		}
	}

	println(ans)

}