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>
#define MAX 500000
#define INF 1073741823
int L[MAX],R[MAX];

void merge(int A[],int left,int mid,int right){
  int n1 = mid - left, n2 = right - mid;
  int i,j,k;
  for(i=0; i<n1; ++i) L[i] = A[left+i];
  for(i=0; i<n2; ++i) R[i] = A[mid+i];
  L[n1] = INF; R[n2] = INF;
  //L[n1] = -INF; R[n2] = -INF;
  i=0; j=0;
  for(k=left; k<right; ++k){
    if(L[i]<=R[j])
    //if(L[i]>=R[j])
    {
      A[k] = L[i++];
    }
    else
    {
      A[k] = R[j++];
    }
  }
}
void mergeSort(int A[],int left,int right){
  /*ソートの順番を変えたいときは、
  コメントアウトしているところを入れ替える*/
  int i,mid;
  if(left+1<right){
    mid = (left+right)/2;
    mergeSort(A,left,mid);
    mergeSort(A,mid,right);
    merge(A,left,mid,right);
  }
}


int main(void) {
  int i,j,n,k,ans,a;
  int l[1000000];
  ans=0;
  scanf("%d",&n);
  for(i=0;i<n;i++)
  {
    scanf("%d",&l[i]);
  }
  mergeSort(l,0,n);
  for(i=0;i<n;i++)
  {
    for(j=0;j<i;j++)
    {
      for(k=0;k<j;k++)
      {
        if(l[k]!=l[j] && l[k]!=l[i] && l[i]!=l[j] && l[k]+l[j]>l[i])
        {
          ans++;
        }
      }
    }   
  }
  printf("%d",ans);
  return 0;
}