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: Accepted)

fun main(args: Array<String>) {
    val n = readLine()!!.toInt()
    val k = readLine()!!.split(" ").map { it.toInt() }.sorted()

    var r = 0

    (0 until n).forEach { a ->
        (a + 1 until n).forEach { b ->
            val index = binarySearch(k, k[a] + k[b])
            r += Math.max(0, (index - b))
        }
    }
    println(r)
}

fun binarySearch(list: List<Int>, k: Int): Int {
    var begin = 0
    var end = list.size - 1
    while (begin < end) {
        val mid = (begin + end) / 2 + 1
        if (list[mid] >= k) end = mid - 1
        else begin = mid
    }
    return end
}