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
arr = gets.split.map(&:to_i)
h = {}

diff = 0
1.upto(N) do |i|
  # puts "i:#{i}, arr[#{i-1}]=#{arr[i-1]}, diff += #{arr[i-1] - i}"
  diff = arr[i-1] - i
  # p diff
  # p h.has_key?(diff.to_s)
  if h.has_key?(diff.to_s)
    h[diff.to_s] += 1
  else
    h.store(diff.to_s, 1)
  end
  # p h
end

bb = h.max { |a, b| a[1] <=> b[1] }
b = bb[1]==1 ? 0 : bb[0].to_i 
# p b

sum = 0
0.upto(N-1) do |item|
  # puts "item:#{item}, arr[#{item}]=#{arr[item]}"
  sum += (arr[item] - (item+1) - b).abs
end

p sum