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<cmath>
#include<string>
#include<cstdlib>
#include<ctime>
#include<map>
#include<vector>
#include<list>
#include<set>
using namespace std;

#define ll long long
#define uint unsigned int
#define alloc(n,type) (type*)calloc(n,sizeof(type))
#define MODULE 1
#define RAND(min,max) (rand()%(max-min+1)+min)
#define repeat(i,condition) for(int i = 0; condition; i++)
#define LOG(log) cout<<#log<<" : "<<log<<'\n'
#define DEBUG() {cout<<"DEBUG "<<num_debug<<'\n'; num_debug++;}
int num_debug = 0;
bool* IsPrime;
vector<int> Prime;

int compare_int(const void* a, const void* b);
class Math {
public:
	template<typename T> static T Fac(int n) {
		T ans = 1;
		for (int i = 2; i <= n; i++) {
			ans *= i;
		}
		return ans;
	}
public :
	template<typename T> static T P(int n, int r) {
		T ans = 1;
		for (int i = 0; i < r; i++) {
			ans *= n - i;
		}
		return ans;
	}
public:
	template<typename T>static T C(int n, int r) {
		T nmr = 1;
		T dnm = 1;
		if (n - r < r)
			r = n - r;
		for (int i = 0; i < r; i++) {
			nmr *= n - i;
			dnm *= r - i;
		}
		return nmr / dnm;
	}
};
class Module_int {
public:
	static const int mod = MODULE;

public:
	static int add(int a, int b) {
		int ans = a + b;
		if (ans < 0)
			ans += mod;
		ans %= mod;
		return ans;
	}
public:
	static int mult(int a, int b) {
		return (a * b) % mod;
	}

public:
	static int Pow(int a, int b) {
		int base = a % mod;
		if (mod / 2 < abs(base))
			if (base < 0) {
				base += mod;  //negative
			}
			else {
				base -= mod;  //positive
			}

		return pow(base, b);
	}
};


int main(void) {
	srand((unsigned)time(NULL));

	int N;
	cin >> N;
	int buf;
	set<int> L;
	map<int, int> Lm;
	repeat(i, i < N) {
		scanf("%d", &buf);
		L.insert(buf);
		++Lm[buf];
	}

	if (N < 3) {
		cout << 0;
		return 0;
	}

	long ans = 0;
	set<int>::iterator itr,itr2,itr3;
	/*
	for (itr = L.begin(); itr != L.end(); ++itr) {
		cout << *(itr)<<',';
	}
	cout << '\n';
	*/
	for (itr = L.begin(); next(itr,2) != L.end(); itr++) {
		//LOG(*next(itr, 2));
		for (itr2 = next(itr); next(itr2,1) != L.end(); itr2++) {
			for (itr3 = next(itr2); itr3 != L.end(); itr3++) {
				//LOG(*itr);LOG(*itr2);LOG(*itr3);
				if (*itr3 < *itr + *itr2) {
					ans+=Lm[*itr]*Lm[*itr2]*Lm[*itr3];
				}
			}
		}
	}

	cout << ans;

	L.clear();
	Lm.clear();
	return 0;
}


int compare_int(const void* a, const void* b) {
	return *(int*)a - *(int*)b;
}
void PrimeEnable(int n) {
	//initialize IsPrime
	IsPrime = (bool*)calloc(n + 1, sizeof(bool));
	for (int i = 0; i <= n; i++)
		IsPrime[i] = true;

	//IsPrime 
	IsPrime[0] = IsPrime[1] = false;
	for (int i = 2; i * i <= n; i++) {
		if (IsPrime[i])
			for (int j = i; i * j <= n; j++) {
				IsPrime[i * j] = false;
			}
	}

	//push back to Prime
	for (int i = 0; i <= n; i++) {
		if (IsPrime[i])
			Prime.push_back(i);
	}
}