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: Wrong Answer)

def Asum(A,b):
    sumA = 0
    for i in range(len(A)):
        sumA += abs(A[i] - i - b - 1)
    return sumA

def aveA(A):
    return sum(A)/len(A)


N = int(input())
ip = input().split()

A = []
for i in ip:
    A.append(int(i))

for i in range(N):
    A[i] -= i + 1

b1 = aveA(A)
b2 = b1 + 1
b3 = b1 - 1

ans = min(Asum(A,b1),Asum(A,b2),Asum(A,b3))

print(ans)
#buf = Asum(A,max(A))
#for i in range(max(A)-1,min(A)-N,-1):
#    if buf > Asum(A,i):
#        buf = Asum(A,i)
#    else:
#        break

print(Asum(A,i-1))