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)

function Main(input){
  input = input.split("\n");//[N, L L L L L,]
  //const N = parseInt(input[0], 10);
  const hairetu = input[1].split("");//[L,L,L,L,L,]
  let result = 0;

  for(let i = 0; i < hairetu.length; i++){
   for(let j = i+1; j < hairetu.length; j++){
    for(let k = j +1; k < hairetu.length; k++){
      if(hairetu[i] < hairetu[j] + hairetu[k] &&
        hairetu[j] < hairetu[i] + hairetu[k]&&
        hairetu[k] < hairetu[i] + hairetu[j]
        && hairetu[i] !== hairetu[j] && hairetu[j] !== hairetu[k] && hairetu[i] !== hairetu[k]){
             result++;}//要素3つが三角形の成立条件を満たしているか
      }
    }
   }
    console.log(result);
  }
  Main(require("fs").readFileSync("/dev/stdin", "utf8"));