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 (0.5.0) (judge verdict: Time Limit Exceeded)

parseInt(x) = parse(Int, x)
parseBigInt(x) = parse(BigInt, x)
parseFloat(x) = parse(Float64, x)
parseBigFloat(x) = parse(BigFloat, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)

function main()
    n=parseInt(readline())
    l=sort(parseMap(split(readline())))
    ans=0
    for i in 1:n
        for j in i+1:n
            n1=searchsortedlast(l,l[i]+l[j]-1)
            n2=searchsortedfirst(l,-l[i]+l[j]+1)
            n1,n2=min(n1,n2),max(n1,n2)
            n1,n2=max(n1,j),min(n2,n)
            for k in n1:n2
                if i!=k!=j
                    ans+=1
                end
            end
        end
    end
    println(ans)
end
main()