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 JavaScript (Node.js 12.16.1) (judge verdict: Accepted)

"use strict";
    
const main = arg => {
    arg = arg.trim().split("\n");
    const N = parseInt(arg[0].split(" ")[0]);
    const A = arg[1].split(" ").map(n=>parseInt(n));
    
    let answer = 0;
    
    for(let i=0; i<N; i++) {
        for(let j=i+1; j<N; j++) {
            for(let k=j+1; k<N; k++) {
                if(A[i] === A[j] || A[j] === A[k] || A[i] === A[k]) {
                    continue;
                }
                
                if(A[i] + A[j] > A[k] && A[j] + A[k] > A[i] && A[k] + A[i] > A[j]) {
                    answer++;   
                    
                    // console.log("A[i]:" + A[i]);
                    // console.log("A[j]:" + A[j]);
                    // console.log("A[k]:" + A[k]);
                    // console.log("---")
                }
            }
        }
    }

    console.log(answer);
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));