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)

#! /usr/bin/env python3

import math

n = int(input())
a = [int(i) for i in input().split()]
b = [0 for i in range(n)]
b_sum = 0

for i in range(n):
    b[i] = a[i] - (i + 1)

b.sort()
median = b[int(n / 2)]

res = 10**16

tmp = median

while True:
    if tmp >= n:
        break
    v = 0
    for i in range(n):
        v += abs(b[i] - tmp)
    if v < res:
        res = v
    elif v > res:
        break
    tmp += 1

tmp = median - 1

while True:
    if tmp < 0:
        break
    v = 0
    for i in range(n):
        v += abs(b[i] - tmp)
    if v < res:
        res = v
    elif v > res:
        break
    tmp -= 1

print(res)