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)

L.sort!

def bsearch(array, value)
  return nil if array.first >= value
  left = 0
  right = array.size
  while left + 1 < right do
    idx = left + (right - left) / 2
    if array[idx] < value then
      left = idx
    else
      right = idx
    end
  end
  left
end

sum = 0
(0..L.size-1).each do |ai|
  (ai+1..L.size-2).each do |bi|
    next if ai == bi
    a = L[ai]
    b = L[bi]
    # p "a = #{a}, b = #{b}, a + b = #{a + b}, l = #{L}"
    # p bsearch(L, a + b)
    i = bsearch(L, a + b)
    next if i == nil
    sum += (i - bi)
  end
end

puts sum