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)

import java.util.*

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

    var ans = 0

    for (i in 0 until n - 2) {
        val a = xs[i]
        for (j in i + 1 until n - 1) {
            val b = xs[j]

            ans += xs.binarySearch(a + b, Comparator { o1, o2 -> if (o1 >= o2) 1 else -1 }, j + 1)
                    .let { -(it + 1) - 1 }
                    .let { it - j }
        }
    }

    println(ans)
}