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>
#define mod 1000000007
#define int long long int
#define phi 1.6180339
#define rep(i,n) for(auto i=0;i<(n);i++)
#define endl "\n"
#define For(i,a,b) for(auto i=(a);i<(b);i++)
#define op1 cin.tie(NULL)
#define op2 cout.tie(NULL)
#define op3 std::ios_base::sync_with_stdio(false)
#define MAXX 1000001
using namespace std;
vector<int> arr(MAXX);
void trozen()
{
    int n;
    cin>>n;
    vector<int> v1(n);
    for(auto &i:v1) cin>>i;
    int ans=0;
    for(int i=0;i<n;i++)
    {
        for(int j=i+1;j<n;j++)
        {
            for(int k=j+1;k<n;k++)
            {
                if((v1[i]+v1[j])>v1[k]&&(v1[k]+v1[j])>v1[i]&&(v1[i]+v1[k])>v1[j]&&v1[i]!=v1[j]&&v1[j]!=v1[k]&&v1[i]!=v1[k]) ans++;
            }
        }
    }
    cout<<ans<<endl;
}
int32_t main()
{
    op1;op2;op3;
    /*#ifndef ONLINE_JUDGE
    freopen("input.txt","r",stdin);
    freopen("output.txt","w",stdout);
    #endif*/
    trozen();
    return 0;
}