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)

N = gets.to_i
A = gets.split.map(&:to_i)

if N.odd?
  center = N / 2
  array = ((A.sort[center] - center)..(A.sort[center] + center)).to_a
  ansArray = A.map.with_index {|a, i| (a - array[i]).abs}
  puts ansArray.inject(:+)
else
  centerL = N / 2 - 1
  arrayL = ((A.sort[centerL] - centerL)..(A.sort[centerL] + centerL + 1)).to_a 
  ansArrayL = A.map.with_index {|a, i| (a - arrayL[i]).abs}

  centerR = N / 2
  arrayR = ((A.sort[centerR] - centerR)..(A.sort[centerR] + centerR - 1)).to_a
  ansArrayR = A.map.with_index {|a, i| (a - arrayR[i]).abs}

  sumL = ansArrayL.inject(:+)
  sumR = ansArrayR.inject(:+)
  ans = sumL < sumR ? sumL : sumR
  puts ans
end