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 (1.3.71) (judge verdict: Accepted)

import kotlin.math.max

fun main(args: Array<String>) {
    val n = readInt()
    val L = readIntList().sorted()
    //println(L)

    var ans = 0
    for (b in 0 until n) {
        for (a in 0 until b) {
            val ab = L[a] + L[b]
            var r =
                L.binarySearch(element = ab, comparator = lower).inv()
            //if (r == -1) r = n
            val l = b + 1
            //println("a=$a b=$b ab=$ab l=$l r=$r")
            ans += max(0, r - l)
        }
    }
    println(ans)
}

// Tools
fun readString() = readLine()!!
fun readInt() = readLine()!!.toInt()
fun readLong() = readLine()!!.toLong()
fun readStringList() = readLine()!!.split(" ")
fun readIntList() = readLine()!!.split(" ").map(String::toInt)
fun readLongList() = readLine()!!.split(" ").map(String::toLong)

val lower = Comparator { x: Int, y: Int -> if (x >= y) 1 else -1 }