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)

function Main(input) {
  let [first, data] = input.trim().split("\n");

  let N = Number(first);
  const arr = [];
  let rst = 0;
  if (first < 3) {
    console.log(0);
  } else {
    data = data.split(" ").map(Number);
    dfs(0, 0);
    console.log(rst);
  }

  function dfs(idx, cnt) {
    if (cnt === 3) {
      const a = data[arr[0]];
      const b = data[arr[1]];
      const c = data[arr[2]];

      if (a !== b && a !== c && b !== c) {
        const [aa, bb, cc] = [a, b, c].sort((a, b) => b - a);
        //삼각혀으이 성립조건
        if (aa < bb + cc) {
          rst++;
        }
      }
      return;
    }

    for (let i = idx; i < N; i++) {
      arr.push(i);
      dfs(i + 1, cnt + 1);
      arr.pop();
    }
  }
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));