Problem:
Score : 400 points

Problem Statement

Takahashi has N sticks that are distinguishable from each other. The length of the i-th stick is L_i.

He is going to form a triangle using three of these sticks. Let a, b, and c be the lengths of the three sticks used. Here, all of the following conditions must be satisfied:

a < b + c

b < c + a

c < a + b

How many different triangles can be formed? Two triangles are considered different when there is a stick used in only one of them.

Constraints

All values in input are integers.

3 \leq N \leq 2 \times 10^3

1 \leq L_i \leq 10^3

Input

Input is given from Standard Input in the following format:

N
L_1 L_2 ... L_N

Constraints

Print the number of different triangles that can be formed.

Sample Input 1

4
3 4 2 1

Sample Output 1

1

Only one triangle can be formed: the triangle formed by the first, second, and third sticks.

Sample Input 2

3
1 1000 1

Sample Output 2

0

No triangles can be formed.

Sample Input 3

7
218 786 704 233 645 728 389

Sample Output 3

23

Solution in Scala (2.11.7) (judge verdict: Time Limit Exceeded)

object Main extends App {
 val n = readInt
 val input = readLine.split(" ").map(_.toInt).sorted.reverse
 var count = 0
 def isVaild(a:Int, b:Int, c:Int):Boolean = a < (b + c) && b < (a + c) && c < (a + b)
 for(i <- 0 until n - 2) {
     val a = input(i)
     val b = input(i + 1)
     val c = input(i + 2)
     if(a < b + c)
       for(j <- i + 1 until n - 1)
         for(k <- j + 1 until n)
           if (isVaild(input(i), input(j), input(k))) {
             count += 1 
           }
 }
  println(count)  
  
}