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)

import scala.io.StdIn._

object Main extends App {
  val n = readInt
  val sticks = readLine.split(" ").map(_.toInt).sorted

  def binSearch(n: Int, min: Int, max: Int): Int = {
    if (max - min <= 1) min
    else {
      val mid = (min + max) / 2
      if (sticks(mid) < n) binSearch(n, mid, max)
      else binSearch(n, min, mid)
    }
  }

  val result = for {
    i <- 0 until n
    j <- (i + 1) until n
  } yield binSearch(sticks(j) + sticks(i), j, n) - j
  println(result.sum)
}