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;
#ifdef _DEBUG
  #include "_DEBUG.hpp"
#endif
#define int long long
const int INF = 1LL << 60;

signed main(){

  int n; cin >> n;
  vector<int> 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++){
        int Min = min({a[i], a[j], a[k]});
        int Max = max({a[i], a[j], a[k]});
        int Mid = (a[i] + a[j] + a[k]) - Min - Max;
        if(Min == Mid || Mid == Max) continue;
        if(Max < Min + Mid && Mid - Min < Max) ans++;
      }
    }
  }
  cout << ans << endl;

  return 0;
}