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: Accepted)

n = gets.to_i
l = gets.chop.split.map(&:to_i)

l.sort!
ans = 0

# p l

0.upto(n-3) do |i|
  (i+1).upto(n-2) do |j|
    a_b = l[i] + l[j]

    idx = l.bsearch_index{ |x| x >= a_b }

    # p "i:#{i} j: #{j} a+b:#{a_b} idx: #{idx}"

    if idx.nil?
      ans += n - j - 1
    else
      ans += [idx - 1 - j, 0].max
    end
  end
end

puts ans