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: Wrong Answer)

fun main(args: Array<String>) {
    val n = readLine()?.toInt() ?: return
    val l = readLine()?.split(" ")?.map(String::toInt)?.sortedDescending() ?: return
    var total = 0L
    0.until(n).forEach { i ->
        (i + 1).until(n).forEach loop@{ j ->
            if (l[j] * 2 < n) {
                return@loop
            }
            (j + 1).until(n).forEach { k ->
                val a = l[i]
                val b = l[j]
                val c = l[k]
                if (a < b + c) {
                    total++
                } else {
                    return@loop
                }
            }
        }
    }
    println(total.toString())
}