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)

# frozen_string_literal: true

Inf = 100_000_000_000
$n = gets.chomp.to_i
$a = gets.split.map(&:to_i)
def limits(b)
  min = Inf
  max = -Inf
  $n.times do |i|
    diff = $a[i] - (b + i + 1)
    min = diff if diff < min
    max = diff if diff > max
  end
  [min, max]
end

def diff(b)
  sum = 0
  $n.times do |i|
    sum += ($a[i] - (b + i + 1)).abs
  end
  sum
end
lower, upper = limits(0)
s_lower = diff(lower)
s_upper = diff(upper)
if s_lower < s_upper
  min = s_lower
  upper = (lower + upper) / 2
else
  min = s_upper
  lower = (lower + upper) / 2
end
loop do
  if (lower - upper).abs <= 1
    puts [diff(lower), diff(upper)].min
    exit
  end
  s_lower = diff(lower)
  s_upper = diff(upper)
  if s_lower < s_upper
    min = s_lower
    upper = (lower + upper) / 2
  else
    min = s_upper
    lower = (lower + upper) / 2
  end
end