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: Wrong Answer)

#include <iostream>
#include <string>
#include <math.h>
#include <vector>
#include <algorithm>
#include <iomanip>
#include <set>
#include <queue>
#include <deque>
#include <map>
#include <stack>
#include <cmath>
using namespace std;

#define mod 1000000007
#define ten5 100005
#define ten52 200005
#define ten6 1000005
#define PI 3.1415926
#define pb(x) push_back(x)
#define all(x) x.begin(),x.end()
#define mkpr(x1,x2) make_pair(x1,x2)
typedef long long int ll;


//stack<char> stk;
//set<ll> sll;
//set<pair<ll,ll>> spll;
//map<string,ll> mp;
//map<pair<ll,ll>,ll>::iterator iter;
//map<ll,ll> mp;
//deque<ll> deq;
//vector<ll> vll;
ll num[ten5];
//priority_queue<ll> pq;          //decreasing

int main(void)
{
    ll m,n,i,j,k=0,sum=0;
    string s;
    cin>>n;
    for(i=0;i<n;i++) cin>>num[i];
    for(i=0;i<n;i++)
        for(j=i+1;j<n;j++)
            for(k=j+1;k<n;k++)
    {
        if(num[i]==num[j]||num[i]==num[k]||num[j]==num[k]) continue;
        m=num[i]+num[j]+num[k];
        if(!(num[i]>=(m/2)||num[j]>=(m/2)||num[k]>=(m/2)))
            {
                sum++;
            }
    }
    cout<<sum;
    return 0;
}