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 Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

quicksort :: (Ord a) => [a] -> [a]
quicksort [] = []
quicksort (x:xs) =
  let small = [a | a <- xs , a <= x]
      large = [a | a <- xs , a > x]
  in quicksort small ++ [x] ++ quicksort large

subi :: [Int] -> Int -> [Int]
subi [] _ = []
subi (x:xs) n = (x-n) : subi xs (n-1)

main = do
  n <- (read :: String -> Int) <$> getLine
  x <- map (read :: String -> Int) . words <$> getLine
  let y = subi (reverse x) n
      b = head $ drop (div n 2) $ quicksort y
      ans = foldl (\acc t -> (acc + abs(t-b))) 0 y
  putStrLn $ show ans