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<stdio.h>
#include<string.h>
#include<math.h>
#include<stdlib.h>
int cmp(const void* a, const void* b)
{
	return*(int*)a - *(int*)b;
}
int main()
{
	int i, j, n, a[110], num = 0,k;
	scanf("%d", &n);
	for (i = 0; i < n; i++)
	{
		scanf("%d", &a[i]);
	}
	qsort(a, n, sizeof(a[0]), cmp);
	if (n < 3)
	{
		printf("0");
	}
	else
	{
		for (i = 0; i < n - 2; i++)
		{
			for (j = i + 1; j < n - 1; j++)
			{
				if (a[i] != a[j])
				{
					for (k = j + 1; k < n; k++)
					{
						if (a[j]!=a[k]&&a[i] + a[j] > a[k])
						{
							num++;
						}
					}
				}
			}
		}
		printf("%d", num);
	}
	return 0;
}