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 quick_sorts(int *x, int left, int right){
    if(left >=right)return;
    int i = left,j = right, pivot = x[i];
    while(x[i]>pivot)i++;
    while(x[j]<pivot)j--;
    while(i < j){
        int tmp = x[i];
        x[i] = x[j];
        x[j] = tmp;
        i++;
        j--;
        while(x[i]>pivot)i++;
        while(x[j]<pivot)j--;
    }
    quick_sorts(x,left,i-1);
    quick_sorts(x,j+1,right);
}

int main(){
    int N;
    scanf("%d%*c",&N);
    int *L = (int *)malloc(N * sizeof(int));
    char *s = (char *)malloc(11 * N * sizeof(char));
    char *ms = s;
    fgets(s,11 * N,stdin);
    for(int i = 0; i < N; i++){
        for(int j = 0; j < 11; j++){
            if(s[j] == ' '||s[j] == '\n'){
                s[j] = '\0';
                L[i] = atoi(s);
                s = &s[j+1];
                break;
            }
        }
    }

    quick_sorts(L,0,N-1);
    int count = 0;
    for(int i = 0;i < N; i++){
        for(int j = 0;j < i; j++){
            for(int k = 0; k < j; k++){
                if(L[i]!=L[j]&&L[j]!=L[k]&&L[k]!=L[i]&&L[k]<L[j]+L[i]){
                    count++;
                }
            }
        }
    }
    free(L);
    free(ms);
    printf("%d\n",count);
    return 0;
}