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: Accepted)

import Debug.Trace

solve0 as b = sum $ zipWith (\a i->abs (a-(b+i))) as [1,2..]

solve as minB maxB
  | abs(minB - maxB) < 3 = minimum $ map (solve0 as) [minB, minB+1, minB+2]
  | lbs < rbs = solve as minB rb
  | otherwise = solve as lb maxB
  where lb = (minB*2+maxB)`div`3
        rb = (minB+maxB*2)`div`3
        lbs = solve0 as lb
        rbs = solve0 as rb

main :: IO ()
main = do
  _ <- read <$> getLine :: IO Int
  as <- map read.words <$> getLine :: IO [Int]
  let bs = zipWith (-) as [1..]
      maxB = maximum bs
      minB = minimum bs
  print $ solve as minB maxB