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.to_i
L = gets.split.map(&:to_i).sort
# p L

ans = 0

0.upto(N - 3) do |i|
  a = L[i]
  (i + 1).upto(N - 2) do |j|
    b = L[j]
    left = [a - b, b - a].max
    right = a + b
    l_i = L.bsearch_index { |l| l > left }
    l_i = N if l_i.nil?
    l_i = [j + 1, l_i].max
    r_i = L.bsearch_index { |l| l >= right }
    r_i = N if r_i.nil?
    # p "a:#{a}, b:#{b}, left:#{left}, right:#{right}, l_i:#{l_i}, r_i#{r_i}"
    add = r_i - l_i
    # add -= 1 if left < a && a < right
    # add -= 1 if left < b && b < right
    # add -= j - l_i if j - l_i > 0
    # p add
    ans += [add, 0].max
  end
end

puts ans