Problem:
Score : 300 points

Problem Statement

The season for Snuke Festival has come again this year. First of all, Ringo will perform a ritual to summon Snuke. For the ritual, he needs an altar, which consists of three parts, one in each of the three categories: upper, middle and lower.

He has N parts for each of the three categories. The size of the i-th upper part is A_i, the size of the i-th middle part is B_i, and the size of the i-th lower part is C_i.

To build an altar, the size of the middle part must be strictly greater than that of the upper part, and the size of the lower part must be strictly greater than that of the middle part. On the other hand, any three parts that satisfy these conditions can be combined to form an altar.

How many different altars can Ringo build? Here, two altars are considered different when at least one of the three parts used is different.

Constraints

1 \leq N \leq 10^5

1 \leq A_i \leq 10^9(1\leq i\leq N)

1 \leq B_i \leq 10^9(1\leq i\leq N)

1 \leq C_i \leq 10^9(1\leq i\leq N)

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 ... A_N
B_1 ... B_N
C_1 ... C_N

Output

Print the number of different altars that Ringo can build.

Sample Input 1

2
1 5
2 4
3 6

Sample Output 1

3

The following three altars can be built:

Upper: 1-st part, Middle: 1-st part, Lower: 1-st part

Upper: 1-st part, Middle: 1-st part, Lower: 2-nd part

Upper: 1-st part, Middle: 2-nd part, Lower: 2-nd part

Sample Input 2

3
1 1 1
2 2 2
3 3 3

Sample Output 2

27

Sample Input 3

6
3 14 159 2 6 53
58 9 79 323 84 6
2643 383 2 79 50 288

Sample Output 3

87

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

{-# LANGUAGE BangPatterns #-}
import           Control.Exception           (assert)
import           Control.Monad
import           Control.Monad.Primitive
import qualified Control.Monad.ST            as ST
import qualified Data.Array.IO               as IO
import qualified Data.Array.ST               as ST
import qualified Data.Array.Unboxed          as A
import           Data.Bits
import qualified Data.ByteString.Char8       as BS
import           Data.Char
import           Data.Foldable
import           Data.List
import           Data.Maybe
import qualified Data.Sequence               as Seq
import qualified Data.Set                    as Set
import qualified Data.Vector.Unboxed         as V
import qualified Data.Vector.Unboxed.Mutable as VM
import           Debug.Trace

readInt = fst . fromJust . BS.readInt
readIntList = map readInt . BS.words
getInt = readInt <$> BS.getLine
getIntList = readIntList <$> BS.getLine
getIntVec n = V.unfoldrN n (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine

readInteger = fst . fromJust . BS.readInteger
readIntegerList = map readInteger . BS.words
getInteger = readInteger <$> BS.getLine
getIntegerList = readIntegerList <$> BS.getLine

quickSortVec l u arr
  | l >= u    = return ()
  | otherwise = do
      VM.unsafeSwap arr l ((u+l)`div`2)
      t <- VM.unsafeRead arr l
      let i = l
          j = u + 1
      nj <- loopVec t u i j arr
      VM.unsafeSwap arr l nj
      quickSortVec l (nj-1) arr
      quickSortVec (nj+1) u arr

loopVec !t !u !i !j arr = do
  ni <- doWhile i (+1)         (< t)
  nj <- doWhile j (subtract 1) (> t)
  if ni > nj
    then return nj
    else do VM.unsafeSwap arr ni nj
            loopVec t u ni nj arr
              where
                {-# INLINE doWhile #-}
                doWhile k op p
                  | nk > u    = return nk
                  | otherwise = do
                      x <- VM.unsafeRead arr nk
                      if p x then
                        doWhile nk op p
                        else
                        return nk
                        where
                          nk = op k

bisectRight :: Ord a => (Int -> a) -> a -> Int -> Int -> Int
bisectRight f x lo hi
  | lo >= hi  = lo
  | x < f mid = bisectRight f x lo mid
  | otherwise = bisectRight f x (mid+1) hi
  where
    mid = lo + (hi - lo) `div` 2

bisectLeft :: Ord a => (Int -> a) -> a -> Int -> Int -> Int
bisectLeft f x lo hi
  | lo >= hi  = lo
  | f mid < x = bisectLeft f x (mid+1) hi
  | otherwise = bisectLeft f x lo mid
  where
    mid = lo + (hi - lo) `div` 2

main = do
  n <- getInt
  as <- getIntVec n
  bs <- getIntVec n
  cs <- getIntVec n

  as' <- V.thaw as
  cs' <- V.thaw cs
  quickSortVec 0 (n-1) as'
  quickSortVec 0 (n-1) cs'
  va <- V.freeze as'
  vc <- V.freeze cs'

  let solve' b = let i = bisectLeft (va V.!) b 0 n
                     i' = if i == n || (va V.! i) >= b then i - 1 else i
                     k = bisectRight (vc V.!) b 0 n
                     k' = if k < n && (vc V.! k) <= b then k + 1 else k
                 in (i' + 1) * (n - k')

      solve j res | j == n = res
                  | otherwise = solve (j+1) (res + solve' (bs V.! j))

  print $ solve 0 0