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.reverse
count = 0

(N - 2).times do |i|
    j = i + 1
    while j < N - 1 do
        c = L[i] - L[j] + 1
        $ltl, $lrg = j + 1, N - 1
        while $lrg - $ltl >= 0 do
          $mdl = ($ltl + $lrg) / 2
            if c == L[$mdl]
                break
            elsif c > L[$mdl] 
                $lrg = $mdl - 1
            else
                $ltl = $mdl + 1
            end
        end
        if L[$mdl] >= c 
            count += $mdl - j
        end
        j += 1
    end
end

puts count