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.to_i
L = gets.split.map(&:to_i)

answer = 0

L.each.with_index do |a, a_i|
  if a_i + 2 >= L.length
    break
  end
  (a_i + 1..N - 1).each do |b_i|
    c_min = (a - L[b_i]).abs
    c_max = a + L[b_i]
    (b_i + 1..N - 1).each do |c_i|
      if L[c_i] > c_min && L[c_i] < c_max
        answer += 1
       end
    end
  end
end
p answer