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 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))
        var pos = lowerBound(lines, j, lines.size, lines(i)+lines(j))
        val legals = pos - (j+1)
        // printf("%d:%d -> %d, %d\n", lines(i), lines(j), /*lines.deep,*/ pos, legals)
        sum += legals
      }
    }
    println(sum)
  }
  def lowerBound(ar: Array[Int], start:Int, end:Int, v:Int) :Int = {
    var ub = end
    var lb = start
    while(ub - lb > 1) {
      val mid = (ub + lb) / 2
      // printf("ub:%d, lb:%d, mid:%d\n", ub, lb, mid)
      if(ar(mid) >= v){
        //midが条件を満たせば、解の存在範囲は(lb,mid]
        ub = mid;
      } else {
        //midが条件を満たさなければ、解の存在範囲は(mid,ub]
        lb = mid;
      }
    }
    ub
  }
}