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"
	"sort"
	"strconv"
	"strings"
)

var memo map[string]bool
func main() {
	scan_init()
	n := scanInt()
	l := make([]int,n)
	for i:= 0; i<n; i++ {
		l[i] = scanInt()
	}
	sort.Ints(l)
	// a + b > c
	//memo := map[int]int {} //その長さの数
	//for i:= n-1; i>=0; i-- {
	//	if  _,ok := memo[l[i]]; !ok {
	//		memo[l[i]] = 0
	//	}
	//	memo[l[i]] ++
	//}
	memo = map[string]bool{}
	count := 0
	// fmt.Println(memo)
	for i:= n-1;  i>=0; i -- {
		max := l[i]
		for j:= 0; j<i; j++ {
			right := l[j]
			for k:= 0; k<j; k++ {
				left := l[k]
				if (left + right > max && memocheck(i,j,k) && left != right && right != max && max != left) {
					// fmt.Println(i,j,k)
					count ++
				}
			}
		}
	}
	fmt.Println(count)
}

func memocheck (a int, b int, c int) bool {
	check := []int{a,b,c}
	sort.Ints(check)
	stringcheck := ""
	for i:= 0; i<3; i++ {
		take := strconv.Itoa(check[i])
		stringcheck = stringcheck + take
	}
	if _,ok := memo[stringcheck]; ok {
		return false
	} else {
		memo[stringcheck] = true
		return true
	}
}
var sc = bufio.NewScanner(os.Stdin)

func scan_init() {
	sc.Split(bufio.ScanWords)
}
func scanInt() int {
	sc.Scan()
	i, _ := strconv.Atoi(sc.Text())
	return i
}
func scan() string {
	sc.Scan()
	return sc.Text()
}

var rdr = bufio.NewReaderSize(os.Stdin, 200000)

func readLine() string {
	buf := make([]byte, 0, 200000)
	for {
		l, p, e := rdr.ReadLine()
		if e != nil {
			panic(e)
		}
		buf = append(buf, l...)
		if !p {
			break
		}
	}
	return string(buf)
}
func readLineToNumber() int {
	S := readLine()
	number, _ := strconv.Atoi(S)
	return number
}
func readLineToSlice() []string {
	S := readLine()
	list := strings.Split(S, "")
	return list
}
func readLineToNumberSlice(memo map[string]int) []int {
	// err時は-1を代入
	S := readLine()
	intList := make([]int, len(S))
	for i := 0; i < len(S); i++ {
		if val, ok := memo[string(S[i])]; ok {
			intList[i] = val
		} else {
			intList[i] = -1
		}
	}
	return intList
}