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 Triangles()
    N = parse(Int, readline())
    L = sort(parseline())
    ans = Array{Int, 1}[]
    for m in 1:N-2
        for n in m+2:N
            for l in L[m+1:n-1]
                if (L[n] - L[m]) < l < (L[n] + L[m])
                    push!(ans, sort([L[m], l, L[n]]))
                end
            end
        end
    end
    println(length(unique(ans)))
end
Triangles()