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)

@nums = []
A.each_with_index do |num, i|
  @nums << (num - i - 1)
end

@nums.sort!
@sum = @nums.reduce(:+)

def score(b)
  score = @nums.map{|n| (n - b).abs }.reduce(:+)
  score
end

min = nil
current = score(@nums[0])
@nums.each_with_index do |b, i|
  next if i == 0 || i == N
  diff = @nums[i] - @nums[i - 1]
  s = current + i * diff - (N - i) * diff
  min = [min, s].compact.min
  current = s
end
puts min