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 li long long int

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    int t;
    t=1;
    while(t--)
    {
       
       int n;
       cin>>n;
       li a[n];
       for(int i=0;i<n;i++)
       cin>>a[i];
       sort(a,a+n);
      
       int cnt=0;
       for(int i=0;i<n-2;i++)
       {
           for(int j=i+1;j<n-1;j++)
           {
               for(int k=j+1;k<n;k++)
               {
                   if(a[k]<(a[j]+a[i]) && a[k]!=a[j] && a[k]!=a[i] && a[j]!=a[i])
                   {
                    // cout<<i<<" "<<j<<" "<<k<<endl;
                      cnt++;
                   }
                   
               }
           }
       }
       cout<<cnt;
      
       
    }
}