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 (2.7.1) (judge verdict: Accepted)

n = gets.to_i
arr = gets.chomp.split(' ').map(&:to_i)
k = 1
while k <= n
  arr[k-1] -= k
  k += 1
end
arr.sort!
if n % 2 == 0
  a = arr[(n + 1)/2]
  b = arr[(n - 1)/2]
else
  a = arr[n/2]
  b = arr[n/2]
end
sum_a = 0
sum_b = 0
k = 1
while k <= n
  sum_a += (arr[k-1] - a).abs
  k += 1
end
while k <= n
  sum_b += (arr[k-1] - b - k).abs
  k += 1
end
if sum_a < sum_b
  puts sum_b
else
  puts sum_a
end