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.to_i
hen = gets.split(' ').map(&:to_i)
hen.sort!
 
triangle_total = 0
a = 0
 
while a < N - 2 do
    b = a + 1
 
    while b < N - 1 do 

        check_num = hen[a] + hen[b]
        
        if check_num <= hen[b + 1]
        elsif check_num > hen[N - 1]
            triangle_total = triangle_total + N - 1 - b
        else
            
            head = b + 1
            tail = N - 1
 
            while head <= tail
                center = (head + tail) / 2   
                
                if hen[center] >= check_num
                    tail = center - 1
                elsif hen[center] < check_num
                    if check_num <= hen[center + 1] 
                        triangle_total = triangle_total + center - b
                        break
                    else 
                        head = center + 1
                    end
                end

            end
 
        end
 
        b = b + 1
 
    end
    a = a + 1
 
end
 
p triangle_total