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) {
    var num = parseInt(input.split("\n")[0]);
    var sideLength = input.split("\n")[1].split(" ");
    
    for(var a=0; a<num; a++){
        sideLength[a] = parseInt(sideLength[a]);
    }
   
   sideLength.sort(
       function(a,b){
           if(a>b){
               return 1;
           }else if(a<b){
               return -1;
           }else{
               return 0;
           }
       }
   )
   
   var count = 0;
   
   if(num<3){
       console.log(0);
   }else{
       for(var i=0; i<num; i++){
           for(var j=i+1; j<num; j++){
               for(var k=j+1; k<num; k++){
                   if(sideLength[i]!=sideLength[j] && sideLength[j]!=sideLength[k] && sideLength[i]!=sideLength[k]){
                       if(sideLength[i]+sideLength[j]>sideLength[k]){
                           count = count + 1;
                       }
                   }
               }
           }
       }
   }
   if(count!==0){
        console.log(count);
   }
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));