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: Wrong Answer)

program main
     implicit none
     integer n,i,sumv1,sumv2,b1,b2
     integer,allocatable,dimension(:)::a
     read(*,*)n
     allocate(a(n))
     read(*,*)a
     do i=1,n
          a(i)=a(i)-i
     enddo
     sumv1=0;sumv2=0
     b1=sum(a)/n
     b2=b1-1
     do i=1,n
          sumv1=sumv1+abs(b1-a(i))
          sumv2=sumv2+abs(b2-a(i))
     enddo
     write(*,*)min(sumv1,sumv2)
     
end program main