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)

import scala.io.StdIn

object Main extends App {
  val n = StdIn.readLine()
  val l :Array[Int] = StdIn.readLine().split(" ").map(_.toInt)
  var ans = 0

  l.zipWithIndex.foreach {i =>
    l.drop(i._2 + 1).zipWithIndex.foreach { j =>
      ans = l.drop(i._2 + 1 + j._2 + 1).filter{
        k => (k < (i._1 + j._1)) && (j._1 < (k + i._1)) && (i._1 < (j._1 + k))}.length +  ans
    }
  }

  println(ans)
}