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 Ruby (2.3.3) (judge verdict: Wrong Answer)


inputs = gets
arr_size = inputs.to_i
inputs = gets
arr = inputs.split(" ")
arr.map!(&:to_i)
cnt1 = 0
cnt2 = 0

arr_mid = (arr[arr_size-1] - arr[0]).abs
arr_median = (arr.size % 2).zero? ? arr[arr.size/2 - 1, 2].inject(:+) / 2.0 : arr[arr.size/2]


arr_ave = (arr.inject(0.0){|r,i| r+=i }/arr.size).to_i
num1 = arr_ave - arr_mid
num2 = arr_ave - arr_median

arr.each_with_index do |n, i|
  cnt1 += ((num1+i) - n).abs
  cnt2 += ((num2+i) - n).abs 
end

p cnt1 < cnt2 ? cnt1 : cnt2