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: Accepted)

program c

integer(8) :: n,a(200000),nn,ans=0

read(*,*) n
read(*,*) (a(i),i=1,n)

do i=1,n
	a(i) = a(i) - i
enddo

call heapsort(n,a(1:n))
nn = a((n+1)/2)

do i=1,n
	a(i) = abs(a(i) - nn)
enddo

write(*,*) sum(a(1:n))



contains

subroutine heapsort(n,y1)

	implicit none
	integer(8),intent(in) :: n
	integer(8),intent(inout) :: y1(1:n)
	integer(8) :: i,k,j,l
	integer(8) :: t1
	
	l = n/2+1
	k = n

	do while (k /= 1)
		 if(l > 1) then
				l = l-1
				t1 = y1(l)
				
		 else
				t1 = y1(k)
				y1(k) = y1(1)
				k = k-1
				if(k == 1) then
					 y1(1) = t1
					 exit
				endif
		 endif

		 i = l
		 j = l+l

		 do while(j <= k)
				if(j < k) then
					 if(y1(j) < y1(j+1)) j = j+1
				endif
				
				if (t1 < y1(j)) then
					 y1(i) = y1(j)
					 i = j
					 j = j+j
				else
					 j = k+1
				endif
		 
		 enddo
		 
		 y1(i) = t1
	
	enddo
	return

end subroutine heapsort

end program