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 (
  "bufio"
  "fmt"
  "os"
  "strconv"
  "strings"
)
const size = 1000000
var reader = bufio.NewReaderSize(os.Stdin,size)
func NextLine() string {
  var line,buffer []byte
  var isPrefix bool = true
  var err error
  for ;isPrefix; {
    line,isPrefix,err = reader.ReadLine()
    if err != nil { panic(err) }
    buffer = append(buffer,line...)
  }
  return string(buffer)
}
func NextStringArray() []string {
  return strings.Split(NextLine()," ")
}
func NextIntArray() []int {
  var s []string = strings.Split(NextLine()," ")
  var n int = len(s)
  var a []int = make([]int,n)
  for i:=0;i<n;i++ {
    a[i],_ = strconv.Atoi(s[i])
  }
  return a
}

func main() {
  var n,b,min,max,ans,tmp int
  var a []int
  n,_ = strconv.Atoi(NextLine())
  a = NextIntArray()
  b = 0
  min = 1000000001
  max = -1000000001
  for i:=0;i<n;i++ {
    a[i] -= i+1
    b += a[i]
    if min > a[i] { min = a[i] }
    if max < a[i] { max = a[i] }
  }
  b = nint(b,n)
  ans = 0
  for i:=0;i<n;i++ { ans += abs(a[i]-b) }
  for k:=b-1;k>=min;k-- {
    tmp = 0
    for i:=0;i<n;i++ { tmp += abs(a[i]-k) }
    if tmp >= ans { break }
    ans = tmp
  }
  for k:=b+1;k<=max;k++ {
    tmp = 0
    for i:=0;i<n;i++ { tmp += abs(a[i]-k) }
    if tmp >= ans { break }
    ans = tmp
  }
  fmt.Println(ans)
}
func nint(n int,m int) int {
  var f float64 = float64(n)/float64(m)
  return int(f+0.5)
}
func abs(n int) int {
  if n < 0 { return -n }
  return n
}