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: Wrong Answer)

fun main(args: Array<String>) {
    val N = nextInt()
    val L = listOfInt().sorted()
        var ans = 0
        for (i in 0 until N - 2) {
            for (j in i + 1 until N - 1) {
                // k in j + 1 until N
                val k = j + 1
                val P = L[i] + L[j]  // > L[k]
                var r = L.binarySearch(P, k, N)
                if (r < 0) r = r.inv() - 1
                if (k <= r && P > L[r]) ans += (r - j)
            }
        }
        println(ans)
}
fun next() = readLine()!!
fun nextInt(delta: Int = 0) = Integer.parseInt(next()) + delta
fun listOfString() = next().split(" ")
fun listOfInt(delta: Int = 0) = listOfString().map { Integer.parseInt(it) + delta }