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)

def bsearch(ary, s, n, t)
  r = n
  l = s
  c = (s + n) / 2
  return 0 if ary[s] >= t
  return n-s if ary[n-1] < t
  until ary[c-1] <= t && ary[c] > t
    if ary[c] < t
      l = c
    else
      r = c
    end
    c = (l + r) / 2
  end
  c-s
end

n = gets.to_i
l = gets.split.map(&:to_i).sort
count = 0
(0...n-2).each do |a|
  (a+1...n-1).each do |b|
    count += bsearch(l, b+1, n,  l[a] + l[b])
  end
end
  
puts count