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 Rust (1.42.0) (judge verdict: Accepted)

use proconio::input;
use itertools::Itertools;

fn dedup(v: Vec<u64>) -> Vec<(u64, u16)>{
    let mut tmp = vec![];
    for i in v {
        let mut found = false;
        for j in 0..tmp.len() {
            let (t, n) = tmp[j];
            if i == t {
                found = true;
                tmp[j] = (t, n+1)
            }
        }
        if !found { tmp.push((i, 1)) }
    }
    tmp
}

fn count(xs: Vec<(u64, u16)>) -> u64 {
    let mut x_max = 0;
    let mut temp = 1;
    let mut total = 0;
    for (x, n) in xs {
        temp *= n;
        total += x;
        if x > x_max { x_max = x }
    }
    total -= x_max;
    if x_max < total { temp as u64 } else { 0 }
}

fn main() {
    input!(n: i16);
    let mut ls = vec![];
    for _ in 0..n {
        input!(l: u64);
        ls.push(l);
    }
    let ls = dedup(ls);
    let res = ls.into_iter()
                .combinations(3)
                .map(count)
                .sum::<u64>();
    println!("{}", res)
}