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 PyPy3 (7.3.0) (judge verdict: Accepted)

N = int(input())
A = list(map(int,input().split()))
for i in range(N):
  A[i] -= i+1
#print(A)
A.sort()
dic = {}
for x in A:
  if x not in dic:
    dic[x] = 1
  else:
    dic[x] += 1
S = list(dic.keys())
now = 0
for x in A:
  now += abs(A[0]-x)
#print(now)
prev = A[0]
left = dic[S[0]]; right = N- left
for i in range(1,len(S)):
  dif = (left-right)*(S[i]-S[i-1])
  if dif < 0:
    now += dif
  left += dic[S[i]]
  right -= dic[S[i]]
print(now)