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: Wrong Answer)

N = gets.to_i
ls = gets.split(' ').map(&:to_i).sort
count = 0
(0..(N - 3)).each do |a|
  if a > 501
    count += (N - a) * (N - a - 1) * (N - a - 2) / 6
    break
  end
  ((a + 1)..(N - 2)).each do |b|
    if ls[a] + ls[b] > 1000
      count += (N - b) * (N - b - 1) / 2 
      break
    end
    i = ls.bsearch_index { |c| c >= ls[a] + ls[b] } || N
    count += i - (b + 1)
  end
end
p count