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: Wrong Answer)

package main

import (
	"fmt"
	"math/bits"
	"sort"
)

func main() {
	var n int
	fmt.Scan(&n)
	if n < 3 {
		fmt.Println(0)
		return
	}
	l := make([]int, n)
	for i := range l {
		fmt.Scan(&l[i])
	}
	var ans int

	x := Combinations(l, 3)
	for _, v := range x {
		sort.Ints(v)
		if !(v[0]+v[1] < v[2]) {
			ans++
		}
	}

	fmt.Println(ans)
}

func Combinations(set []int, n int) (subsets [][]int) {
	length := uint(len(set))

	if n > len(set) {
		n = len(set)
	}

	// Go through all possible combinations of objects
	// from 1 (only first object in subset) to 2^length (all objects in subset)
	for subsetBits := 1; subsetBits < (1 << length); subsetBits++ {
		if n > 0 && bits.OnesCount(uint(subsetBits)) != n {
			continue
		}

		var subset []int

		for object := uint(0); object < length; object++ {
			// checks if object is contained in subset
			// by checking if bit 'object' is set in subsetBits
			if (subsetBits>>object)&1 == 1 {
				// add object to subset
				subset = append(subset, set[object])
			}
		}
		// add subset to subsets
		subsets = append(subsets, subset)
	}
	return subsets
}