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)

# frozen_string_literal: true

n = gets.to_i
l = gets.split.map(&:to_i).sort
count = 0
0.upto(n - 3) do |i|
  a = l[i]
  b_lower = l.bsearch_index { |e| a + e > l[i + 2] }
  b_lower = i + 1 if b_lower <= i
  b_lower.upto(n - 2) do |j|
    b = l[j]
    c_upper = l.bsearch_index { |e| a + b <= e }
    next if c_upper == n - 1

    c_lower = l.bsearch_index { |e| e + a > b }
    next if c_lower.nil?

    c_upper = n if c_upper.nil?
    c_upper -= 1
    c_lower = j + 1 if c_lower <= j
    next if c_upper < c_lower

    count += [c_upper - c_lower, 0].max + 1
  end
end

puts count