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 Julia (1.4.0) (judge verdict: Time Limit Exceeded)

parseline(str=readline()) = parse.(Int, split(str))
function binarysearches(arr_, left, right; rev = false)
    arr = rev ? arr_[end:-1:1] : arr_
    r = searchsortedfirst(arr, right, rev=false) - 1
    l = searchsortedlast(arr, left, rev=false) + 1
    ans = r - l + 1
    return max(0, ans)
end
function Triangles()
    N = parse(Int, readline())
    L = sort(parseline(), rev=true)
    ans = 0
    for n in 1:N-1
        for m in n+1:N
            L_ = [L[l] for l in 1:length(L) if l∉[m, n]]
#             println((L[m], L[n]))
#             println(L_)
#             println((L[n]-L[m], L[n]+L[m]))
#             println(binarysearches(L_, L[n]-L[m], L[n]+L[m], rev = true))
#             println("===============")
            ans += binarysearches(L_, L[n]-L[m], L[n]+L[m], rev = true)
        end
    end
    println(ans÷3)
end
Triangles()