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: Accepted)

object Main extends App {
 val n = readInt
 val input = readLine.split(" ").map(_.toInt).sorted
 var ans = 0
 def count(l:Array[Int],k:Int, ans:Int, ab:Int):Int = {

   if(l.length <= k)
     ans
   else if(l(k) >= ab)
     ans
   else
     count(l, k + 1, ans + 1, ab)
 }  
   
 for(i <- 0 until n) {
   for(j <- i + 1 until n) {
     var ab = input(i) + input(j)
     ans = count(input,j + 1, ans, ab)
   }
 }
  println(ans)  
}