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 (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func nextInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

func nextFloat64() float64 {
	sc.Scan()
	i, e := strconv.ParseFloat(sc.Text(), 64)
	if e != nil {
		panic(e)
	}
	return i
}

func nextString() string {
	sc.Scan()
	return sc.Text()
}

func Max(x, y int) int {
	if x > y {
		return x
	} else {
		return y
	}
}

func Max3(x, y, z int) int {
	if m := Max(x, y); m > z {
		return m
	} else {
		return z
	}
}

func main() {
	sc.Split(bufio.ScanWords)
	//sc.Buffer(nil, 100000000)

	n := nextInt()

	l := make([]int, n)
	for i := 0; i < n; i++ {
		l[i] = nextInt()
	}

	ans := 0
	for i := 0; i < n-2; i++ {
		for j := i + 1; j < n-1; j++ {
			if l[i] == l[j] {
				continue
			}
			for k := j + 1; k < n; k++ {
				if l[i] == l[k] || l[j] == l[k] {
					continue
				}
				max := Max3(l[i], l[j], l[k])
				if l[i] == max {
					if max >= l[j]+l[k] {
						continue
					}
				} else if l[j] == max {
					if max >= l[i]+l[k] {
						continue
					}

				} else {
					if max >= l[i]+l[j] {
						continue
					}
				}

				ans += 1
			}
		}
	}

	fmt.Println(ans)
}