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++ (GCC 9.2.1) (judge verdict: Accepted)

/*
    @uthor: Amit Kumar
    user -->GitHub: drviruses ; CodeChef: dr_virus_ ; Codeforces,AtCoder,Hackerearth,Hakerrank: dr_virus;
*/
#include <bits/stdc++.h>
#include <chrono>
using namespace std;
using namespace std::chrono;
//#include <boost/multiprecision/cpp_int.hpp>
//namespace mp = boost::multiprecision;
//#define ln mp::cpp_int;
#define ll    long long
#define ld    long double
#define ull   unsigned long long
#define endl "\n"
ll google_itr = 1;
#define google(x) cout<<"Case #"<<x<<":"
#define pi 3.14159265358979323846264338327950L

const ll mod = 1e9+7;
const ll inf = 1e18;

ll popcount(ll num){
    num = num - ((num >> 1) & 0x55555555);
    num = (num & 0x33333333) + ((num >> 2) & 0x33333333);
    return ((num + (num >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
}

vector<pair<ll,ll>> factor_arr;

void myfactor(ll num){ 
    ll count = 0;   
    while (!(num % 2)) { 
        num >>= 1; count++; 
    }  
    if (count) factor_arr.push_back({2,count}); 
    for (auto i = 3; i <= sqrt(num); i += 2) { 
        count = 0; 
        while (num % i == 0) { 
            count++; 
            num /= i; 
        } 
        if (count) factor_arr.push_back({i,count}); 
    } 
    if (num > 2) factor_arr.push_back({num,1});
}

void virus(){
        ll len;
        cin>>len;
        vector<ll> arr(len);
        for(auto &i:arr) cin>>i;
        sort(arr.begin(),arr.end());
        set<ll> uniq;
        ll cnt = 0;
        for(auto i=0; i<len; i++){
            for(auto j=i; j<len; j++){
                for(auto k=j; k<len; k++){
                    uniq.insert(arr[i]); uniq.insert(arr[j]); uniq.insert(arr[k]);
                    if(uniq.size() == 3){
                        vector<ll> temp(uniq.begin(),uniq.end());
                        sort(temp.begin(),temp.end());
                        if(temp[0]+temp[1] > temp[2]) cnt++;
                        uniq.clear();
                    }
                    else{
                        uniq.clear();
                    }
                }
                uniq.clear();
            }
            uniq.clear();
        }
        cout<<cnt<<endl;
}


int32_t main(){
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    
  /*#ifndef ONLINE_JUDGE
    freopen("input.txt","r",stdin);
    freopen("output.txt","w",stdout);
    #endif*/

    ll t = 1;
    //cin>>t;
    while(t--){
           auto start = high_resolution_clock::now();
           virus();
           auto stop = high_resolution_clock::now();
           auto duration = duration_cast<seconds>(stop - start);
         //cout << "Time: "<<duration.count()<<endl;
        //your code goes here
    }
    return 0;
}