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>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename key>
using ordered_set = tree<key, null_type, less<key>, rb_tree_tag, tree_order_statistics_node_update>;
#define F first
#define S second
#define T second.first
#define D second.second
#define FIO ios_base::sync_with_stdio(0);cin.tie(0);
#define all(v) v.begin(),v.end()
#define OO 0x3f3f3f3fLL
#define INF 0x3f3f3f3f3f3f3f3fLL
#define sz(s) (int)(s.size())
#define RT(s) return cout<<s,0
typedef long long ll;
typedef long double ld;
typedef pair<ll, ll> pii;
typedef pair<ll,pair<ll,ll>> piii;
const int N = 2e5+5, M= 20, mod = 1000000000;
const double EPS = 1e-10;


int main(){
    FIO
//    freopen("input.txt", "r", stdin);
//    freopen("output.txt", "w", stdout);
    int n;
    cin>>n;
    ll A[n];
    for(int i=0; i<n; i++){
        cin>>A[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(A[i]+A[j]>A[k] && A[i]+A[k]>A[j] && A[k]+A[j]>A[i] && A[i]!=A[j] && A[i]!=A[k] && A[k] != A[j])
                    ans++;
            }
        }
    }
    cout<<ans;
}