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)

$n=gets.to_i
l=gets.split.map(&:to_i).sort
r=0
def tri(i,j,l)
  y=(i-j).abs;x=i+j
  z=l.bsearch_index{|t|t>y}
  return 0 if z.nil?
  w=l.bsearch_index{|t|t>=x}
  return 0 if w==0
  if w.nil?
    w=$n
    mx=l[-1]
  else
    mx=l[w]
  end
  s=w-z
  s-=1 if l[z]<=i and i<=mx
  s-=1 if l[z]<=j and j<=mx
  return s
end
l.combination(2){|i,j|r+=tri(i,j,l)}
puts r/3