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: Accepted)

n = gets.chomp.to_i
llist = gets.chomp.split.collect{ |item| item.to_i}

llist.sort!
ldata = [0]
be = 0
n.times do |ni|
  nowl = llist[ni]
  if be == nowl
    ldata[nowl] += 1
  else
    (be+1).upto(nowl) do |nii|
      ldata[nii] = ldata[be]
    end
    ldata[nowl] += 1
  end
  be = nowl
end

result = 0
a = 0
b = 0
c = 0
0.upto(n-3) do |ai|
  a = llist[ai]
  (ai+1).upto(n-2) do |bi|
    b = llist[bi]
    cmin = b-a
    cmax = a+b
    maxC = ldata[cmax-1] ? ldata[cmax-1] : ldata[-1]
    maxC -= (bi+1)
    result += maxC 
  end
end
puts result