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 (Clang 10.0.0) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>
#include<string.h>

int is_it_triangle(int a, int b, int c) {
	if(a == b || b == c || c == a) {//shant be isosceles nor equilateral triangle
		return 0;
	} else if(a + b > c && b + c > a && c + a > b) {
		return 1;
	} else {
		return 0;
	}
}

int main(void) {
	int i, j, k;
	int N;
	int ans;
	int *L;
	char buf[128], *ch;
	char *g_buf;

	fgets(buf, sizeof(buf), stdin);
	ch = strtok(buf, " ");
	N = atoi(ch);
	L = (int *)calloc(N, sizeof(double));
	g_buf = (char *)calloc(N*16, sizeof(double));

	fgets(g_buf, N*16, stdin);
	ch = strtok(g_buf, " ");
	L[0] = atoi(ch);
	for(i = 1; i < N; i += 1) {
		ch = strtok(NULL, " ");
		L[i] = atoi(ch);
	}

	ans = 0;
	for(i = 0; i < N; i += 1) {
		for(j = 0; j < i; j += 1) {
			for(k = 0; k < j; k += 1) {
				ans += is_it_triangle(L[i], L[j], L[k]);
			}
		}
	}

	printf("%d\n", ans);

	free(g_buf);
	free(L);
	return 0;
}