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 = {
    val sc = new java.util.Scanner(System.in)
    val N = sc.nextInt()
    val L = Array.fill(N)(sc.nextInt()).sorted(Ordering.Int.reverse)

    def binarySearch(a: Int, b: Int): Int = {
      def recursive(l: Int, r: Int): Int =
        if (r - l > 1) {
          val m = l + (r - l) / 2
          if (L(m) <= L(a) - L(b)) recursive(l, m)
          else recursive(m, r)
        } else l
      recursive(b, N)
    }

    var triangles = 0
    var a = 0
    while (a < N -2) {
      var b = a + 1
      while (b < N - 1) {
        val cMin = binarySearch(a, b)
        triangles += cMin - b
        b += 1
      }
      a += 1
    }

    println(triangles)
  }

}