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 Control.Monad
import Data.List
import Data.Ord
import qualified Data.ByteString.Char8 as B
import qualified Data.Vector.Storable as V

main=do
    n<-readLn::IO Int
    as<-V.fromList.sort.map (\(i,a)->a-i).zip [1..].unfoldr (B.readInt.B.dropWhile(==' ')) <$> B.getLine::IO(V.Vector Int)
    print $ tsearch (f as) (0,n-1)

-- 三分探索 (最小値)
-- b<-[l..r]において最小のf bを求める
tsearch f (l,r)
    | (r-l)<3  = minimum $ map f [l..r]
    | c1 < c2  = tsearch f (l,b2)
    | c1 == c2 = tsearch f (b1,b2)
    | c1 > c2  = tsearch f (b1,r)
    where
        c1 = f b1
        c2 = f b2
        b1 = l+(r-l)`div`3
        b2 = l+((r-l)`div`3)*2

f as b = V.sum $ V.map (\a->abs $ a-e) as
        where e = as V.! b