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;
#define booster ios_base::sync_with_stdio(false); cin.tie(NULL);


void solve() {

     int n;
     cin>>n;
     vector<long long int>a(n);

     for(int i=0;i<n;i++) {
         cin>>a[i];
     }

     if(n<=2)  { cout<<"0"<<endl; return ;}

     long long int ans=0;
     sort(a.begin(),a.end());

     for(int i=0;i<=n-3;i++) {
         for(int j=i+1;j<=n-2;j++) {
             for(int k=j+1;k<=n-1;k++) {
                 if(a[i]!=a[j] && a[j]!=a[k] && a[i]!=a[k]) {
                     if(a[i]+a[j] > a[k]) ans++;
                 }
             }
         }
     }
     cout<<ans<<endl;




}


int main() {

    booster;
#ifndef ONLINE_JUDGE

    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
#endif


    int t;
    t = 1;


    while (t--) solve();


    return 0;
}