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 (1.0.0) (judge verdict: Time Limit Exceeded)

import java.io.PrintWriter
val pw = PrintWriter(System.out)
fun main(args : Array<String>) {
    func()
    pw.flush()
}

fun func() {
    // 回答をここに書く
    val n = nextInt()
    val arr = listOfInt()
    var result = 0
    for(i in 0 until arr.size){
      for(j in i + 1 until arr.size){
        for(k in j + 1 until arr.size){
          if(Math.abs(arr[i] - arr[j]) < arr[k] && arr[k] < arr[i] + arr[j]){
            result += 1
          }
        }
      }
    }
    println(result)
}

// 入力取得
fun next() = readLine()!!
fun nextInt() = next().toInt()
fun nextLong() = next().toLong()
fun nextDouble() = next().toDouble()
fun listOfString() = next().split(" ")
fun listOfInt() =listOfString().map { it.toInt() }
fun listOfLong() =listOfString().map { it.toLong() }
fun listOfDouble() =listOfString().map { it.toDouble() }