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>) {
    abc143d()
}

fun abc143d() {
    val n = readLine()!!.toInt()
    val lines = readLine()!!.split(" ").map { it.toInt() }
        .sorted().toIntArray()

    var answer = 0
    for (ai in 0..lines.size - 2) {
        for (bi in ai + 1..lines.size - 1) {
            val right = lowerBound(lines, lines[ai] + lines[bi])
            val left = bi + 1
            answer += Math.max(0, right - left)
        }
    }

    println(answer)
}

// list must be sorted
// find element's index, greater than or equals key
private fun lowerBound(list: IntArray, key: Int): Int {
    var ng = -1
    var ok = list.size

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