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
sticks = gets.split.map(&:to_i).sort
memo = Array.new(2002, 0)
sticks.each do |stick|
  memo[stick] = 1
end
sum = 0
memo.each_with_index do |m, index|
  sum += m
  memo[index] = sum
end

ans = 0
sticks.each_with_index do |stick1, index1|
  sticks[index1 + 1..-1].each_with_index do |stick2, index2|
    max = stick1 + stick2
    min = [stick1, stick2].max - [stick1, stick2].min
    increment = memo[max - 1] - memo[min]
    increment -= 1 if stick1 < max && stick1 > min
    increment -= 1 if stick2 < max && stick2 > min
    ans += increment if increment > 0
  end
end
puts ans / 3