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)

#include<bits/stdc++.h>
using namespace std;
using ll=long long;
const int mod=1e9+7;
const int N = 2e5+5;


vector<ll>ans,veca,vecb;
vector<int>adj[N];
vector<double>aka;
vector<pair<int,double>>dp[N];
vector<bool>vis;


void init(int n){
    ans.clear();veca.clear();aka.clear();vis.clear();ans.resize(n);
    vecb.clear(),vecb.resize(n);veca.resize(n);vis.resize(n);
    for (int i = 0; i <n; i++) {
        vis[i]=0;
    }
    for (int i = 0; i<=n; i++) {
        adj[i].clear();
    }
    for (int i = 0; i <=n; i++) {
        dp[i].clear();
    }
    for (int i = 0; i < n; i++) {
        ans[i]=0;
    }
}

int check(int a,int b,int c){
    int res=0;
    if(a+b>c) res=1;
    return res;
    
}
bool valid(int a,int b,int c){
    if((a<b)&&(b<c)) return 0;
    return 1;
}
void solve(){
    int n,flag=0;
    cin>>n;
    init(n);
    for (int i = 0; i <n; i++) {
        cin>>veca[i];
    }
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            for (int k = 0; k < n; k++) {
                if(!valid(i,j,k)){
                    set<int>st;vector<int>vec;
                    st.insert(veca[i]);st.insert(veca[j]);st.insert(veca[k]);
                    vec.push_back(veca[i]);vec.push_back(veca[j]);vec.push_back(veca[k]);
                    if(st.size()==3){
                        sort(vec.begin(),vec.end());
                        flag+=check(vec[0],vec[1],vec[2]);
                    }
                }
            }
        }
    }
    cout<<flag<<"\n";
    
}

int main(){
   
   
    ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
    int T=1;
    //cin>>T;
    while(T--){
        solve();
    }
        
        
    return 0;
}