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)

import math
n = int(input())
a = [int(x) for x in input().split()]
a2 = [0] * n
plus = []
minus = []
for i in range(n):
    a2[i] = a[i] - (i+1)
    if a2[i] > 0:
        plus.append(a2[i])
    elif a2[i] < 0:
        minus.append(a2[i])
mean =  sum(a2)//n
if len(plus) > 0:
    b1 = sum(plus)//len(plus)
else:
    b1 = mean
if len(minus)> 0:
    b2 = sum(minus)//len(minus)
else:
    b2 = mean

#print(b1, b2, mean)
#print(a2)
res = [0] * n
res2 = [0] * n
res3 = [0] * n
for i in range(n):
    res[i] = (abs(a2[i] - b1))
    res2[i] = (abs(a2[i] - b2))
    res3[i] = (abs(a2[i] - mean))

print(min(min(sum(res), sum(res2)),sum(res3)))