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 {
  def main(args: Array[String]): Unit = {
    solve
  }

  def solve(): Unit = {
    val sc = new java.util.Scanner(System.in)
    val n = sc.nextInt
    val l = new Array[Int](n)
    for (i <- 0 until n) {
      l(i) = sc.nextInt
    }
    val sortedL = l.sorted

    var count = 0
    for (i <- 0 until n - 2; j <- i + 1 until n - 1) {
      val a = sortedL(i)
      val b = sortedL(j)

      var flg = true
      var k = n - 1
      while (flg && k >= j + 1) {
        val c = sortedL(k)
        if (c < a + b) {
          flg = false
        } else {
          k -= 1
        }
      }
      count += k - j
    }
    println(count)
  }
}