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 (Clang 10.0.0) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>
#include<stdbool.h>
#include<string.h>
#include<math.h>
#include<ctype.h>

#define rep(i,n) for(int i=0;i<n;i++)

typedef long long ll;

ll gcd(ll a, ll b) { if (b == 0) return a; return gcd(b, a % b); }

ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }

int asc(const void* a, const void* b) { return *(int*)a - *(int*)b; }

ll dsc(const void* a, const void* b) { return *(ll*)b - *(ll*)a; }

bool used[100];
ll perm[100];

void permutation(int pos, int n) {
    if (pos == n) return;
    for (int i = 0; i < n; ++i) {
        if (!used[i]) {
            perm[pos] = i;
            used[i] = true;
            permutation(pos + 1, n);
            used[i] = false;
        }
    }
}

int main() {
    ll n, l[100];
    scanf("%lld", &n);
    for (int i = 0; i < n; i++) {
        scanf("%lld", &l[i]);
    }
    qsort(l, n, sizeof(ll), asc);
    ll ans = 0;
    for (int i = 0; i < n-2; i++) {
        for (int j = i + 1; j < n-1; j++) {
            for (int k = j + 1; k < n; k++) {
                if (l[i] == l[j] || l[j] ==l[k] || l[k] == l[i]) continue;
                if (l[i] + l[j] > l[k] && l[k] > l[j] - l[i]) ans++;
            }
        }
    }
    printf("%lld", ans);

    return 0;
}