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)

input = require("fs").readFileSync("/dev/stdin", "utf8").trim();
input = input.split('\n');
function abs(x){
  if (x > 0){
    return x;
  }
  else{
    return -x;
  }
}
let n = parseInt(input[0]);
input[1] = input[1].split(' ');
a = new Int32Array(n);
for (i=0;i<n;i++){
  a[i] = input[1][i];
}
if (n < 3){
  console.log(0);
}
else{
  cnt = 0;
  for (i=0;i<n-2;i++){
    for (j=i+1;j<n-1;j++){
      for (k=j+1;k<n;k++){
        if (a[k] < a[i] + a[j] && a[k] > abs(a[i] - a[j])){
          if (a[i] != a[j] && a[j] != a[k] && a[k] != a[i]){
            cnt += 1;
          }
        }
      }
    }
  }
  console.log(cnt);
}