Problem:
Score : 700 points

Problem Statement

We have N cards numbered 1, 2, ..., N.
Card i (1 \leq i \leq N) has an integer A_i written in red ink on one side and an integer B_i written in blue ink on the other side.
Initially, these cards are arranged from left to right in the order from Card 1 to Card N, with the red numbers facing up.

Determine whether it is possible to have a non-decreasing sequence facing up from left to right (that is, for each i (1 \leq i \leq N - 1), the integer facing up on the (i+1)-th card from the left is not less than the integer facing up on the i-th card from the left) by repeating the operation below. If the answer is yes, find the minimum number of operations required to achieve it.

Choose an integer i (1 \leq i \leq N - 1).
Swap the i-th and (i+1)-th cards from the left, then flip these two cards.

Constraints

1 \leq N \leq 18

1 \leq A_i, B_i \leq 50 (1 \leq i \leq N)

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N
B_1 B_2 ... B_N

Output

If it is impossible to have a non-decreasing sequence, print -1.
If it is possible, print the minimum number of operations required to achieve it.

Sample Input 1

3
3 4 3
3 2 3

Sample Output 1

1

By doing the operation once with i = 1, we have a sequence [2, 3, 3] facing up, which is non-decreasing.

Sample Input 2

2
2 1
1 2

Sample Output 2

-1

After any number of operations, we have the sequence [2, 1] facing up, which is not non-decreasing.

Sample Input 3

4
1 2 3 4
5 6 7 8

Sample Output 3

0

No operation may be required.

Sample Input 4

5
28 15 22 43 31
20 22 43 33 32

Sample Output 4

-1

Sample Input 5

5
4 46 6 38 43
33 15 18 27 37

Sample Output 5

3

Solution in Haskell (GHC 7.10.3) (judge verdict: Runtime Error)

import qualified Data.Text as T
import qualified Data.Text.IO as T
import qualified Data.Text.Read as T
import Data.List (sortBy, groupBy)
import Data.Tuple (swap)
import Data.Function (on)

main :: IO ()
main = do
  (n : _) <- map unsafeSignedDecimal . T.words <$> T.getLine :: IO [Int]
  xls <- sequence . replicate n $ unsafeListToTuple . map unsafeSignedDecimal . T.words <$> T.getLine :: IO [(Int, Int)]
  let
    lrs :: [(Int, Int)]
    lrs = sortBy (compare `on` snd) . map bound $ xls
    step :: (Int, Int) -> (Int, Int) -> (Int, Int)
    step acc@(s, r0) (l, r) | r0 <= l   = (succ s, r)
                            | otherwise = acc
  print . fst . foldl step (0, -(10 ^ 9)) $ lrs

bound :: (Int, Int) -> (Int, Int)
bound (x, l) = (x - l, x + l)

unsafeListToTuple :: [Int] -> (Int, Int)
unsafeListToTuple (x : y : _) = (x, y)

unsafeSignedDecimal :: T.Text -> Int
unsafeSignedDecimal s = case T.signed T.decimal s of
  Right (n, _) -> n