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: Runtime Error)

def BinSearch(A, hi, lo):
    b = (hi + lo) // 2
    tmp0 = FindAns(A, b - 1)
    tmp1 = FindAns(A, b)
    if hi == lo:
        tmp2 = FindAns(A, b + 1)
        return min(tmp0, tmp1, tmp2)
    if tmp0 < tmp1:
        return BinSearch(A, b - 1, lo)
    else:
        return BinSearch(A, hi, b + 1)
    
def FindAns(A, b):
    ans = 0
    for a in A:
        ans += abs(a - b)
    return ans

n = int(input())
A = list(map(int, input().split()))
for i in range(n):
    A[i] -= i + 1
A = sorted(A)
hi = A[int(len(A) / 2 + 1) if int(len(A) / 2 + 1) <  len(A)  else int(len(A) / 2)]
lo = A[int(len(A) / 2 - 1) if int(len(A) / 2 - 1) >= 0 else int(len(A) / 2)]

print(BinSearch(A, hi, lo))