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)

# ai-iの数が一番多いやつをbにすればいけそう（いちばん余剰分を殺せるので） 複数あったら全部試せ
n = int(input())
arr = list(map(int, input().split()))
d = {}
for i in range(n):
    t = arr[i] - (i + 1)
    if t in d:
        d[t] += 1
    else:
        d[t] = 1

d = sorted(d.items(), key=lambda x: x[1], reverse=True)
max_v = d[0][1]
ans = 10 ** 10

for k, v in d:
    if v != max_v:
        break
    tmp = 0
    for i in range(n):
        tmp += abs(arr[i] - (k + i + 1))
    ans = min(ans, tmp)
print(ans)