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.chomp.to_i
lines = gets.chomp.split.map(&:to_i).sort.reverse

count = 0
(N-2).times do |i|
  found = false
  a = lines[i]
  bclines =  lines[(i+1)..N].reverse
  bclines.each_with_index do |b, j|
    clines =  bclines[(j+1)..N]
    clines.each_with_index do |c, k|
      if a < b + c
        count += clines.length - k
        found = true
        break
      end
    end
    if found
      nokori = bclines.length - 1
      count += nokori * (nokori - 1)
      break
    end
  end
  if found
    break
  end
end
puts count