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)

import java.util.Scanner

val sc = Scanner(System.`in`)

fun main(args : Array<String>) {
    val n = sc.nextInt()
    val ll = listOfInt(n)

    var count = 0
    for(i in 0 until ll.size-2) {
        for(j in i+1 until ll.size-1) {
            for(k in j+1 until ll.size) {
                val ii = ll[i]
                val jj = ll[j]
                val kk = ll[k]
                if (ii < jj+kk && jj < ii+kk && kk < ii+jj) count++
            }
        }
    }

    println(count)

    /*
    val ll = mutableMapOf<Int, Int>()
    repeat(n) {
        var num = sc.nextInt()
        if (ll[num] == null) {
            ll[num] = 1
        } else {
            ll[num]?.plus(1)
        }
    }

    var count = 0
    val keys = ll.keys.toList()

    for(i in 0 until keys.size-2) {
        for(j in i+1 until keys.size-1) {
            for(k in j+1 until keys.size) {
                val ii = keys[i]
                val jj = keys[j]
                val kk = keys[k]
                if (ii < jj+kk && jj < ii+kk && kk < ii+jj) count++
            }
        }
    }

    val ll2 = ll.filter { entry -> entry.value == 2 }
    ll2.forEach { entry ->
        for (i in keys.indices) {
            if (keys[i] != entry.key && keys[i] < entry.key*2) count++
        }
    }

    val ll3 = ll.filter {entry -> entry.value >= 3 }
    count += ll3.keys.size

    println(count)
    */
}

fun listOfInt(n: Int) = (1..n).map { sc.nextInt() }.toList()