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 List<Int>.indexOfFirstBinary(value: Int): Int {
    var low = 0
    var high = lastIndex
    if (value > get(high)) return size
    if (value <= get(low)) return 0

    while (low <= high) {
        val mid = (low + high).ushr(1) // safe from overflows
        val midVal = get(mid)
        val cmp = midVal - value
        if (cmp < 0)
            low = mid + 1
        else (cmp >= 0)
            high = mid - 1
    }
    return low
}

fun calc143D(Ls: List<Int>): Int {
    val sorted = Ls.sorted()
    var ans = 0
    for (i in 0..sorted.lastIndex) {
        for (j in (i + 1)..sorted.lastIndex) {
            val subList = sorted.subList(j + 1, sorted.size)
            if (subList.isEmpty()) continue
            val count = subList.indexOfFirstBinary(sorted[i] + sorted[j])
            ans += count
        }
    }
    return ans
}

fun main(args: Array<String>) {
    val N = readLine()!!
    val s = readLine()!!.split(" ").map { it.toInt() }
    println(calc143D(s))
}