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 (2.4.0) (judge verdict: Wrong Answer)

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

aa = [ai - i-1 for i,ai in enumerate(a)]

def tri_search(f:"f(x:float)->float", left, right, iter=100)->float:
    for _ in range(iter):
        ml = (left*2 + right) / 3
        mr = (left + right*2) / 3
        if f(ml) < f(mr):
            right = mr
        else:
            left = ml
    # print(left, right)
    return (right + left) / 2

def f(x):
    ret = 0
    x = int(x+0.5)
    for aai in aa:
        ret += abs(aai - x)
    return ret

b = tri_search(f, -10**9, 10**9)
print(f(b))