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: Accepted)

#include<iostream>
#include<vector>
#include<algorithm>
#define F(i,n) for(int i=0;i<n;i++)
#define lli long long int
#define vi vector<int> v
#define vpb(x) v.push_back(x)
#define spb(x) s.push_back(x)
using namespace std;
int ans(vi, int n)
{
    int count=0;
sort(v.begin(),v.end());
for(int i=0;i<n-1;i++)
{
    for(int j=i+1;j<n;j++)
    {
        for(int k=j+1;k<n;k++)
        {
            if(v[i]+v[j]>v[k] and v[i]!= v[j] and v[j]!=v[k])
            {
                // cout<<v[i]<<" "<<v[j]<<" "<<v[k]<<endl;
                count++;
            }
        }
    }
}
return count;
}
int main()
{
   int n; 
   cin>>n;
   if(n<3)
   {cout<<"0";
   exit(0);}
   vi;
   F(i,n)
   {
       int x; cin>>x;
       vpb(x);
   }
   cout<<ans(v,n);
}