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)

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

    var cnt = 0L
    for (i in 0..n-3) {
        for (j in i+1..n-2) {
            val idx = lowerBound(ll, ll[i]+ll[j], j+1, n-1)
            cnt += idx-(j+1)
        }
    }

    println(cnt)
}

fun lowerBound(list: IntArray, key: Int, start: Int, end: Int): Int {
    var minIdx = start-1
    var maxIdx = end+1

    while (maxIdx - minIdx > 1) {
        val mid = minIdx + (maxIdx - minIdx)/2
        if (list[mid] >= key) {
            maxIdx = mid
        } else {
            minIdx = mid
        }
    }

    return maxIdx
}