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: Runtime Error)

import           Control.Monad
import           Control.Monad.ST
import qualified Data.Array                  as A
import qualified Data.Array.ST               as ST
import qualified Data.Array.Unboxed          as AU
import           Data.Bits
import qualified Data.ByteString.Char8       as BS
import           Data.Char
import           Data.Int
import qualified Data.IntMap                 as IM
import           Data.List
import qualified Data.Map                    as M
import           Data.Maybe
import           Data.Ord
import qualified Data.Set                    as S
import           Data.Time
import qualified Data.Vector                 as V
import qualified Data.Vector.Mutable         as VM
import qualified Data.Vector.Unboxed         as VU
import qualified Data.Vector.Unboxed.Mutable as VUM

readInt :: IO [Int]
readInt = map (fst . fromJust . BS.readInt) . BS.words <$> BS.getLine

readInts :: Int -> IO [[Int]]
readInts n = replicateM n readInt

readInteger :: IO [Integer]
readInteger = map (fst . fromJust . BS.readInteger) . BS.words <$> BS.getLine

readIntegers :: Int -> IO [[Integer]]
readIntegers n = replicateM n readInteger

readString :: IO [String]
readString = map BS.unpack . BS.words <$> BS.getLine

readStrings :: Int -> IO [[String]]
readStrings n = replicateM n <$> readString

toPair :: [a] -> (a, a)
toPair [x, y] = (x, y)

count :: Eq a => a -> [a] -> Int
count a as = length $ filter (== a) as

main = do
  [n] <- readInt
  a <- readInt
  b <- readInt
  c <- readInt
  let (a', b', c') = (sort a, sort b, sort c)
   in print $ solve a b c

solve a b c = ans
  where
    a' = V.fromList a
    b' = V.fromList b
    c' = V.fromList c
    ans = sum $ map (\bb -> f bb a' * g bb c') b

f bb a = ff bb a 0 (V.length a - 1) (V.length a)
  where
    ff bb as s e len
      | m == 0 && as V.! m >= bb = 0
      | m == len - 2 && as V.! (m + 1) < bb = len
      | as V.! m < bb && as V.! (m + 1) >= bb = m + 1
      | as V.! m >= bb = ff bb as s m len
      | as V.! (m + 1) < bb = ff bb as m e len
      where
        m = (s + e) `div` 2

g bb c = gg bb c 0 (V.length c - 1) (V.length c)
  where
    gg bb cs s e len
      | m == 0 && cs V.! m <= bb = 0
      | m == len - 2 && cs V.! (m + 1) > bb = len
      | cs V.! m > bb && cs V.! (m + 1) <= bb = m + 1
      | cs V.! m <= bb = gg bb cs s m len
      | cs V.! (m + 1) > bb = gg bb cs m e len
      where
        m = (s + e) `div` 2