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 Fortran (gfortran v4.8.4) (judge verdict: Time Limit Exceeded)

program linear
  implicit none
  integer(8) :: n, i, ans, j, k, loc(1)
  integer(8),allocatable :: a(:),flag(:)
!  logical,allocatable :: m(:)

  read *, n
  allocate(a(n))
  allocate(flag(n))
  flag = 0
  read *, a
  do i = 1, n
    a(i) = a(i) - i
  end do
!  print *, a
  do j = 1, (n+1)/2
!    if (minval(a, mask = (flag == 0)) > 0) then
      loc = minloc(a,mask = (flag == 0))
      a = a - minval(a,mask = (flag == 0))
      flag(loc(1)) = 1
!    else
!      flag(minloc(a,mask = (flag == 0))) = 1
!    end if
  end do
!  print *, a
  ans = 0
  do k = 1, n
    ans = ans + abs(a(k))
  end do
  print '(i0)', ans
  stop
end program linear