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: Wrong Answer)

{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE BangPatterns #-}

import Control.Applicative
import Control.Monad
import Control.Arrow
import Data.List
import Data.Maybe
import Data.Char
import qualified Data.ByteString.Char8 as B
import Text.Printf

readInt = ( readLn :: IO Int )
readInts = map ( read :: String -> Int ) . words <$> getLine

getList = map ( fst . fromJust . B.readInteger ) . B.words <$> B.getLine

which a b f = if f then a else b
mp [ a, b ] = ( a, b )

main = do
	n <- readLn
	as <- zipWith (-) [ 1 .. ] <$> getList
	let
		b1 = sum as `div` n
	print $ minimum $ map ( sum . map abs ) $ map ( \b -> map ( (-) b ) as ) [ b1 - 3 .. b1 + 3 ]