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 <stdlib.h>

void sort(int *a,int n);

int main(void)
{
	int n;
	int *a;
	
	scanf("%d",&n);
	a=(int *)malloc(sizeof(int)*n);
	int i;
	for(i=0;i<n;i++)
	{
		scanf("%d",&a[i]);
	}
	
	
	int check;
	int count=0;
	int j,k;
	for(i=0;i<n;i++)
	{
		for(j=i+1;j<n;j++)
		{
			if(a[i]==a[j])
			{
				;
			}
			else
			{
				for(k=j+1;k<n;k++)
				{
					if(a[j]==a[k])
					{
						;
					}
					else if(a[i]==a[k])
					{
						;
					}
					else
					{
						check=0;
						if(a[i]+a[j]>a[k])
						{
							check++;
						}
						if(a[j]+a[k]>a[i])
						{
							check++;
						}
						if(a[k]+a[i]>a[j])
						{
							check++;
						}
						if(check==3)
						{
							count++;
						}
					}
				}
			}
		}
	}
	printf("%d",count);
	return 0;
}

void sort(int *a,int n)
{
	int i,j;
	int tmp;
	for(i=0;i<n;i++)
	{
		for(j=i+1;j<n;j++)
		{
			if(a[i]>a[j])
			{
				tmp=a[i];
				a[i]=a[j];
				a[j]=tmp;
			}
		}
	}
}