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)

import Control.Monad
import Data.List
import Data.Ord
import qualified Data.ByteString.Char8 as B
import qualified Data.IntMap as M

main=do
    n<-readLn::IO Int
    as<-map (\(i,a)->a-i).zip [1..].unfoldr (B.readInt.B.dropWhile(==' ')) <$> B.getLine::IO[Int]
    let (ms,ps) = partition (<0) as
    let mm = if null ms then 0 else minimum ms
    let ma = if null ms then 0 else maximum ms
    let pp = if null ps then 0 else minimum ps
    let pa = if null ps then 0 else maximum ps
    --
    print $ minimum [sum $ map abs as, sum $ map (\a->abs$a-mm) as, sum $ map (\a->abs$a-pp) as, sum $ map(\a->abs$a-ma)as, sum$map(\a->abs$a-pa)as]