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)

# -*- coding: utf-8 -*-

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

subA = []
sub_dic = {}
for i in range(N):
    tmp = An[i]-(i+1)
    subA.append(tmp)
    if tmp in sub_dic:
        sub_dic[tmp] += 1
    else:
        sub_dic[tmp] = 1

subB = {}
for k,v in sub_dic.items():
    subB[k] = abs(k*v)
# print(subA)
# print(sub_dic)

if max(sub_dic.values()) == 1:
    min_v = 0
    for v in subA:
        min_v += abs(v)
    print(min_v)

else:

    max_sub_k = max([(v,k) for k,v in subB.items()])[1]

    min_v = 0
    for k,v in sub_dic.items():
        min_v += (k - max_sub_k) * v

    print(abs(min_v))