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)

fun main(args: Array<String>) {

    val n = readLine()!!.toInt()
    val ds = readLine()!!.split(" ").take(n).map { it.toInt() }.sorted().toIntArray()

    var count = 0
    for (ai in (0 until ds.size - 2)) {
        for (bi in (ai + 1 until ds.size - 1)) {


            val cs = ds.sliceArray((bi + 1) until ds.size)
            val values = cs.binarySearch(ds[ai] + ds[bi])

            count += if (values >= 0) {
                cs.lastIndexOf(values) + 1
            } else {
                -values - 1
            }
        }
    }

    print(count)
}