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.Collections.max

fun main(args: Array<String>) {
    readLine()
    val inp = readLine()!!.split(" ").map { it.toLong() }
    var ans = 0
    for(i in 0 until inp.size){
        for(j in i until inp.size){
            for(k in j until inp.size){
                if(!(i == j || j == k || k == i)) {
                    if (canMakeTriangle(inp[i], inp[j], inp[k])) ans ++
                }
            }
        }
    }
    println(ans)
}

fun canMakeTriangle(a: Long, b: Long, c: Long): Boolean{
    return 2*max(listOf(a, b, c)) < a + b + c
}