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)

readArray::IO String -> IO[Int]
readArray = fmap $ map read . words

difList::[Int] -> [Int] -> [Int] -> [Int]
difList (x:xs) (y:ys) sumList
    |xs == [] = sumList++[x-y]
    |otherwise = difList xs ys (sumList ++ [x-y])
    
absDif x y
    | x > y = x - y
    |otherwise = y - x
qSort::[Int] -> [Int]
qSort [] = []
qSort (x:xs)
    | xs == [] = [x]
    | otherwise = qSort [y|y<-xs, y < x] ++ [x] ++ qSort [z|z<-xs, z >= x]

median::[Int] -> Int
median xs = 
    let l = length xs
        n = div l 2
        ms = qSort xs
    in if mod l 2 == 0 then
        div ((ms !! (n - 1)) + (ms !! n)) 2
    else
        (ms !! n)
        
main = do
    getLine
    a <- readArray getLine
    let len = length a
    let b = difList a [1..len] []
    print $  sum $ map (absDif $ median b) (qSort b)