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 Kotlin (1.3.71) (judge verdict: Accepted)

import java.util.*

fun main(args: Array<String>) {
  val sc = Scanner(System.`in`)
  val n = sc.nextInt()
  val l = (1..n).map { sc.nextInt() }.sorted()
  val d = l.map { it.toDouble() }

  var count = 0L
  for (i in 0..n-3) {
    val a = l[i]
    for (j in i+1..n-2) {
      val b = l[j]
      val ab = a + b
      val from = j + 1
      var r = d.binarySearch(element = ab.toDouble() - 0.1, fromIndex = from, toIndex = n -1)
      if (r < 0) r = r.inv()
      if (ab > l[r]) r++
      count += Math.max(0, r-from)
    }
  }


  println(count)

}