Problem:
Score : 200 points

Problem Statement

We have sticks numbered 1, \cdots, N. The length of Stick i (1 \leq i \leq N) is L_i.

In how many ways can we choose three of the sticks with different lengths that can form a triangle?

That is, find the number of triples of integers (i, j, k) (1 \leq i < j < k \leq N) that satisfy both of the following conditions:

L_i, L_j, and L_k are all different.

There exists a triangle whose sides have lengths L_i, L_j, and L_k.

Constraints

1 \leq N \leq 100

1 \leq L_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
L_1 L_2 \cdots L_N

Output

Print the number of ways to choose three of the sticks with different lengths that can form a triangle.

Sample Input 1

5
4 4 9 7 5

Sample Output 1

5

The following five triples (i, j, k) satisfy the conditions: (1, 3, 4), (1, 4, 5), (2, 3, 4), (2, 4, 5), and (3, 4, 5).

Sample Input 2

6
4 5 4 3 3 5

Sample Output 2

8

We have two sticks for each of the lengths 3, 4, and 5. To satisfy the first condition, we have to choose one from each length.

There is a triangle whose sides have lengths 3, 4, and 5, so we have 2 ^ 3 = 8 triples (i, j, k) that satisfy the conditions.

Sample Input 3

10
9 4 6 1 9 6 10 6 6 8

Sample Output 3

39

Sample Input 4

2
1 1

Sample Output 4

0

No triple (i, j, k) satisfies 1 \leq i < j < k \leq N, so we should print 0.

Solution in Haskell (GHC 8.8.3) (judge verdict: Accepted)

import qualified Data.Text as T
import qualified Data.Text.IO as T
import qualified Data.Text.Read as T
import Data.List (sort)
import qualified Data.Vector.Unboxed as VU
import Data.Bool (bool)

main :: IO ()
main = do
  n <- unsafeTextToInt <$> T.getLine :: IO Int
  ls <- map unsafeTextToInt . T.words <$> T.getLine :: IO [Int]
  let
    ls' = VU.fromList . sort $ls :: VU.Vector Int
    m = VU.length ls' :: Int
    xs = do
      i <- [0..(m - 3)]
      j <- [(i + 1)..(m - 2)]
      k <- [(j + 1)..(m - 1)]
      let
        li = ls' VU.! i
        lj = ls' VU.! j
        lk = ls' VU.! k
      bool [] [()] $ li < lj && lj < lk && ls' VU.! k < ls' VU.! i + ls' VU.! j
  print . length $ xs

unsafeTextToInt :: T.Text -> Int
unsafeTextToInt s = case T.signed T.decimal s of
  Right (n, _) -> n
{-# INLINE unsafeTextToInt #-}