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 Python (3.4.3) (judge verdict: Accepted)

# coding: utf-8
# Your code here!
import statistics

N=int(input())
S=list(map(int,input().split()))

S1=[]
for i in range(N):
    S1.append(S[i]-i)
S1.sort()
chuouchi=statistics.median_high(S1)
chuouchi2=statistics.median_low(S1)
chuouchi3=statistics.median(S1)
ans=10**20
ansj=0
A=chuouchi-4
B=chuouchi+4
C=chuouchi2-4
D=chuouchi2+4
E=int(chuouchi3)-4
F=int(chuouchi3)+4
for i in range(A,B):
    goukei=0
    for j in range(N):
        goukei+=abs(S[j]-(i+j+1))
        
    if ans>goukei:
        ans=goukei
        
for i in range(C,D):
    goukei=0
    for j in range(N):
        goukei+=abs(S[j]-(i+j+1))
        
    if ans>goukei:
        ans=goukei

for i in range(E,F):
    goukei=0
    for j in range(N):
        goukei+=abs(S[j]-(i+j+1))
        
    if ans>goukei:
        ans=goukei        
        
print(ans)