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: Wrong Answer)

import scala.math.min
import java.util.Arrays.binarySearch
object Main {
  def main(args:Array[String]) = {
    val sc = new java.util.Scanner(System.in)
    val n = sc.nextInt
    val lines = Array.fill(n)(sc.nextInt).sorted
    var sum = 0
    for(i <- 0 to lines.size-3) {
      for(j <- i+1 to lines.size-2) {
        var pos = binarySearch(lines, j+1, lines.size, lines(i)+lines(j))
        if (pos < 0) pos = ~pos // 挿入点
        val legals = pos - (j+1)
        //(pos match {
          //case 0 => 0// 辺全滅
          //case v => v-(j+1) // 開始地点～挿入点までの要素がOK
        //})
        //printf("%d:%d |%s| -> %d, %d\n", lines(i), lines(j), lines.deep, pos, legals)
        sum += legals
      }
    }
    println(sum)
  }
}