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<iostream>
#include<vector>
#include<string>
#include<algorithm>
#include<queue>
#include<deque>
#include<cmath>
#include<map>
#include<unordered_map>
#include<set>
#include<cstring>
#include<iomanip> //cout << fixed << setprecision(15) << x << endl;

using namespace std;
typedef long long ll;
const ll INF = 1e9 + 8;
const ll MOD = 1e9 + 7;
const ll LLINF = 1e18;
#define Pint pair<int, int>
#define rng(i, a, b) for(int i = int(a); i < int(b); i++)
#define rnr(i, a, b) for(int i = int(a); i >= int(b); i--)
#define rep(i, b) rng(i, 0, b)
#define pb push_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
/* -- template -- */

bool isRectangle(int a, int b, int c) {
    return (a + b > c) && (b + c > a) && (c + a > b);
}

bool isDifferent(int a, int b, int c) {
    return a != b && a != c && b != c;
}

int main() {
    int n; cin >> n;
    ll l[n]; rep(i, n) cin >> l[i];
    sort(l, l + n);
    //sort不要かも
    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(isRectangle(l[i], l[j], l[k]) && isDifferent(l[i], l[j], l[k]))
                    ++ans;
            }
        }
    }
    cout << ans << endl;
}