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
l = gets.chomp.split(" ").map(&:to_i).sort

ans = 0

(2..n-1).each do |i|
  (1..i-1).each do |j|  # l[i] >= l[i]
    l_min = l[i] - l[j] + 1
    # l[k] >= l_min となるkを探索
    left = 0
    right = j - 1
    k = right / 2
    while l[k] != l_min && (right - left) > 1 do
      if l[k] < l_min
        left = k + 1 
      elsif l[k] > l_min
        right = k
      end
      k = (right + left) / 2
    end

    ans += l[k..j-1].uniq.size if l[k] >= l_min
  end
end

puts ans