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>
int main(void){
  long int length[100];
  int N;
  int i;
  scanf("%d",&N);
  for(i=0;i<N;i++){
    scanf("%ld",&length[i]);
  }
  int count=0;
  int j;
  int k;
  int max=0;
  int longest;
  for(i=0;i<N;i++){
    for(j=i;j<N;j++){
      for(k=j;k<N;k++){
        if(length[i]!=length[j]&&length[i]!=length[k]&&length[j]!=length[k]){
          	max=length[i];
          	longest=i;
        	if(length[j]>max){
             max=length[j];
              longest=j;
            }
          	if(max<length[k]){
            	max=length[k];
              longest=k;
            }
          	if(max<length[i]+length[j]+length[k]-length[longest]){
              count++;
            }
        }
      }
    }
  }
  printf("%d",count);
}