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: Runtime Error)

#include <bits/stdc++.h>
using namespace std;
#define rep(i,a,n) for (int i=a;i<n;i++)
#define per(i,a,n) for (int i=n-1;i>=a;i--)
#define pb push_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define sz(x) ((int)(x).size())
typedef vector<int> vi;
typedef long long ll;
typedef pair<int,int> pii;
typedef double db;
const ll mod=1000000007;
ll powmod(ll a,ll b) {ll res=1;a%=mod;assert(b>=0);for(;b;b>>=1){if(b&1)res=res*a%mod;a=a*a%mod;}return res;}
ll gcd(ll a,ll b) { return b?gcd(b,a%b):a;}
// head
int n;
vector<pii>values;
int createTriangles(){
	int ret = 0;
	for (int i = 0; i < n; i++){
		//n^2 time 
		int t;
		cin>>t;
		bool found = false;
		for(int i = 0; i < values.size(); i++){
			if (values[i].first == t){
				values[i].second++;
				found = true;
			}
		}
		if (!found){
			values.pb(pii(t,1));
		}
	}
	sort(values.begin(),values.end());
	for(int i = 0; i < values.size(); i++){
		for(int j = i + 1; j < values.size(); j++){
			if(values[i].first+values[j].first<values[j+1].first)
				break;
			for(int k = j +1; k < values.size(); k++){
				if(values[i].first+values[j].first>values[k].first){
					int value = values[i].second*values[j].second*values[k].second;
					ret+=value;
				}
				else{
					break;
				}
			}
		}
	}
	cout<<ret;
}
int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	cin >>n;
	if (n < 3){
		cout<<0;
		return 0;
	}
	createTriangles();
	return 0;
}