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)

require 'pp'
$DEBUG ? define_method(:dpp){|e|pp e} : define_method(:dpp){|e|}

# [a, b].min が遅いので
def min(a, b)
  return a < b ? a : b
end

# [a, b].max が遅いので
def max(a, b)
  return a > b ? a : b
end

# Nと空白区切の入力値を数値の配列で返却する
def gets_n_and_i_list()
  return gets.chomp.to_i, gets.chomp.split(" ").map(&:to_i).sort
end
N, l_list = gets_n_and_i_list

total = 0

0.upto(N-3) do |i|
  a = l_list[i]
  (i+1).upto(N-2) do |j|
    b = l_list[j]
    c_list = l_list[(j+1)..(N-1)]
    total += c_list.count do |c|
      c < a + b
    end
  end
end


puts total