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 java.util.Collections

import scala.io.StdIn

object Main {
  def main(args: Array[String]) = {
    val N = StdIn.readLine.toInt
    val L = StdIn.readLine.split(" ").map(l => l.toInt).sorted
    var ans = 0
    for (i <- 0 until N-2) {
      for (j <- i + 1 until N-1) {
        var low = j
        var high = N
        while(high - low > 1) {
          val mid = (high + low) / 2
          if (L(mid) < L(i) + L(j)) {
            low = mid
          } else {
            high = mid
          }
        }
        ans += low - j
      }
    }

    println(ans)
  }
}