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 PyPy2 (5.6.0) (judge verdict: Wrong Answer)

N=input()
A=map(int, raw_input().split())
B=range(1,N+1)
 
C=[]
for x,y in zip(A,B):
	C.append(x-y)
 
K=set(C)
L=list(K)
L.append(0)
L.sort()
 
h=len(L)
l=0
 
 
ans=float("inf")
 
for j in range(100):
	m=(h+l)/2
	x=L[m]
	t=0
	for y in C:
		t+=abs(-1*x+y)
 
	if 0<=t<ans:
		ans=t
		h=m
	else:
		l=m
	ans=min(ans,t)
 
print ans