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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

$n = gets.chomp.to_i
$rod = gets.chomp.split(" ").map(&:to_i).sort
ans = 0

def binary_search(key)
    left = -1
    right = $n
    while right - left > 1 do
        mid = left + (right - left) / 2
        if $rod[mid] >= key then
            right = mid
        else
            left = mid
        end
    end
    return left
end

$n.times do |a|
    (a+1).upto($n-1) do |b|
        tmp = $rod[a] + $rod[b]
        c = binary_search(tmp)
        ans += c-b if b-a < c
    end
end

puts ans