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 Go (1.14.1) (judge verdict: Accepted)

package main

import (
	"fmt"
	"sort"
)

func main() {
	var n int
	fmt.Scan(&n)
	ls := make([]int, n)
	lm := make(map[int]int)
	for i := range ls {
		fmt.Scan(&ls[i])
		lm[ls[i]]++
	}
	ks := make([]int, 0)
	for k := range lm {
		ks = append(ks, k)
	}
	sort.Ints(ks)

	if n < 3 {
		fmt.Println(0)
		return
	}

	count := 0
	for i := 0; i < len(ks)-2; i++ {
		for j := i + 1; j < len(ks)-1; j++ {
			for k := j + 1; k < len(ks); k++ {
				if ks[i]+ks[j] > ks[k] {
					count += lm[ks[i]] * lm[ks[j]] * lm[ks[k]]
				}
			}
		}
	}
	fmt.Println(count)

}