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.Collections

fun main(args: Array<String>) {
    val N = readInputLine().toInt()
    val Ls = readInputLine().split(" ").map { it.toInt() }.sorted()
    val LsArr = Ls.toIntArray()
    
    var ans = 0
    
    for (mid in N - 1 downTo 0) {
        for (low in mid - 1 downTo 0) {
            ans += lowerBound(Ls, LsArr[mid] + LsArr[low]) - 1 - mid
        }
    }
    
    println(ans)
}

fun readInputLine(): String {
    return readLine()!!
}

fun <T: Comparable<T>> lowerBound(list: List<T>, value: T): Int {
    return Collections.binarySearch(list, value, {x, y -> if (x >= y) 1 else -1}).inv()
}