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>) {
    abc143d()
}

fun abc143d() {
    var result = 0

    val n = readLine()!!
    val lList = readLine()!!.split(" ").map(String::toInt)

    for (i1 in lList.indices) {
        val l1 = lList[i1]

        for (i2 in (i1 + 1) until lList.size) {
            val l2 = lList[i2]

            val high = l1 + l2
            val low = Math.max(l2 - l1, l1 - l2)

            if (low < 1) {
                continue
            }

            for (i3 in (i2 + 1) until lList.size) {
                val l3 = lList[i3]

                if (l3 !in (low + 1) until high) {
                    continue
                }

//                println("l1 -> $l1 l2 -> $l2 l3 -> $l3")
                result++
            }
        }
    }
    println(result)
}