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 C++ (Clang 10.0.0) (judge verdict: Wrong Answer)

//#pragma warning(disable:4996)
#include <iostream>
#include <vector>
#include <limits.h>
#include <algorithm>
#include <string>
#include <math.h>
#include <limits.h>
#include <queue>
#include <map>
#include <set>
#include <iomanip>
#include <bitset>
#include <cassert>
#include <random>
#include <functional>
#include <stack>
#include <iomanip>
#include <cassert>
//#include <boost/multiprecision/cpp_int.hpp>
#include <complex>
#include <cstdio>
#include <list>
#include <bitset>
//#include <stdio.h>

//< in.txt > out.txt
using namespace std;
//std::ios::sync_with_stdio(false);
//std::cin.tie(0);
const long long MOD = 1e9 + 7;
const long long INF = 1e18;
typedef long long LL;
typedef long double LD;
//typedef boost::multiprecision::cpp_int bigint;
typedef pair<LL, LL> PLL;
typedef pair<int, int> PI;
typedef pair<LD, LL> pdl;
typedef pair<LD, LD> pdd;
typedef vector<LL> VLL;
typedef vector<VLL> VVLL;
typedef vector<int> VI;
typedef vector<vector<int>> VVI;
template<class T>
using V = vector<T>;
template<class T>
using VV = vector<vector<T>>;
typedef unsigned long long ULL;

int main() {
	std::cin.tie(0);
	std::ios::sync_with_stdio(false);
	int N;
	cin >> N;
	VI L(N);
	for (int  n = 0; n < N; n++) {
		cin >> L[n];
	}
	LL ans = 0;
	for (int i = 0; i < N; i++) {
		for (int j = i + 1; j < N; j++) {
			for (int k = j+1; k < N; k++) {
				if (L[i] == L[j] || L[j] == L[k] || L[k] == L[i])continue;
				if (
					L[i] <= L[j] + L[k] &&
					L[j] < L[k] + L[i] &&
					L[k] < L[i] + L[j]
					)ans++;
			}
		}
	}
	cout << ans << "\n";
	return 0;
}