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>) {
    abc143d()
}

fun abc143d() {
    val n = readLine()!!.toInt()
    val lines = readLine()!!.split(" ").map { it.toInt() }
        .toIntArray()

    var answer = 0
    for (ai in 0..lines.size - 3) {
        for (bi in ai + 1..lines.size - 2) {
            for (ci in bi + 1..lines.size - 1) {
                val a = lines[ai]
                val b = lines[bi]
                val c = lines[ci]

                if (a < b + c && b < a + c && c < a + b) answer++
            }
        }
    }

    println(answer)
}