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 buble(int a, int b[200]){
   int j,i,tmp;
  for(i=0;i<a;i++){
 	 for(j=0;j<a;j++){
   		 if(b[i]>b[j]){
  	   	   tmp=b[i];
   		   b[i]=b[j];
   		   b[j]=tmp;    
		  }
 	 }
  }
   return b;
  }
int main(){
  int N=0,L[200]={},p=0,d=0,e=0,f=0,count=0;
  scanf("%d",&N);
  for(p=0;p<=N;p++){
  scanf("%d",&L[p]);
  }
  L[200]=buble(N,L);
  p=(N*N*N-3*N*N+2*N)/6;
  for(d=0;d<N;d++){
    for(e=d+1;e<N;e++){
      for(f=e+1;f<N;f++){
  if(L[d]>=L[e]+L[f]||L[d]==L[e]||L[e]==L[f]){
    count++;
  }
      }
    }
  }
  count=p-count;
  printf("%d",count);
  return 0;
}