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
l=gets.chomp.split(' ').map(&:to_i)
cnt=0
l2=l.sort
h={}
l2.each_with_index do |a,i|
  failed=0
  l2.each_with_index do |b,j|
    next if i==j
    break if failed > b
    ab=a+b
    l2.each_with_index do |c,k|
      key=[i,j,k].sort
      next if h[key]
      h[key] = true
      next if i == k || k == j
      if ab<c || a>b+c || b>a+c
        failed = c
        break
      end
      if ab>c && a+c>b&& b+c>a
        cnt+=1
      end
    end
  end
end

puts cnt