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 Data.Array
import Data.List

main :: IO ()
main = do
  getLine
  ls <- map read . words <$> getLine
  print $ solve ls

-- |
-- >>> solve [4, 4, 9, 7, 5]
-- 5
--
-- >>> solve [4, 5, 4, 3, 3, 5]
-- 8
--
-- >>> solve [9, 4, 6, 1, 9, 6, 10, 6, 6, 8]
-- 39
--
-- >>> solve [1, 1]
-- 0
--
-- prop> solve xs >= 0
--
-- prop> solve xs == solve (reverse xs)
--
-- prop> solve xs == solve (sort xs)
--
solve :: [Int] -> Int
solve ls = length [ (i,j,k) 
                  | i <- [1..n]
                  , j <- [i+1..n]
                  , k <- [j+1..n]
                  , let [a,b,c] = sort [ary!i, ary!j, ary!k]
                  , a < b
                  , b < c
                  , a + b > c
                  ]
 where
  n = length ls
  ary = listArray (1, n) ls