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: Wrong Answer)

#include <stdio.h>

int min2(int a, int b){
    if(a < b) return a;
    else return b;
}

int max2(int a, int b){
    if(a > b) return a;
    else return b;
}

int max3(int a, int b, int c){
    return max2(max2(a, b), max2(b, c));
}

int main(){
    int n;
    int l[1000];

    scanf("%d", &n);
    for(int i = 0; i < n; ++i){
        scanf("%d", &l[i]);
    }

    int max = 0;
    int cnt = 0;
    for(int i = 0; i < n; ++i){
        for(int j = i + 1; j < n; ++j){
            for(int k = j + 1; k < n; ++k){
                max = max3(l[i], l[j], l[k]);
                printf("%d\n", max);
                if(max == l[i]){
                    if(max < (l[j] + l[k]) && l[i] != l[j] && l[j] != l[k] && l[i] != l[k]){
                        cnt++;
                        continue;
                    }
                }
                else if(max == l[j]){
                    if(max < (l[i] + l[k]) && l[i] != l[j] && l[j] != l[k] && l[i] != l[k]){
                        cnt++;
                        continue;
                    }
                }
                else{
                    if(max < (l[i] + l[j]) && l[i] != l[j] && l[j] != l[k] && l[i] != l[k]){
                        cnt++;
                        continue;
                    }
                }
            }
        }
    }

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

    return 0;
}