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: Wrong Answer)

"use strict";

function main(input) {
  input = input.trim().split("\n");
  let ans = [];
  let line_two = input[1].split(" ");
  line_two = Array.from(line_two, (x) => parseInt(x)).sort();
  for (let i = 0; i < line_two.length; i++) {
    for (let j = i + 1; i < line_two.length; i++) {
      for (let n = j + 1; n < line_two.length; n++) {
        if (triangle(line_two[i], line_two[j], line_two[n])) {
          ans.push([i + 1, j + 1, n + 1]);
        }
      }
    }
  }
  console.log(ans.length);
}

function triangle(a, b, c) {
  if (a == b || b == c || c == a) return false;
  if (a + b > c) {
    return true;
  } else {
    return false;
  }
}

function numberSort(array) {
  array.sort(f);
  return array;
}

var f = function (a, b) {
  return a - b;
};

main(require("fs").readFileSync("/dev/stdin", "utf-8"));