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.chomp.split(" ").map(&:to_i);

results = []
i = 0
while i < n
	j = i + 1
	while j < n
		k = j + 1
		while k < n
			if l[k] < l[i] + l[j] then
				if l[j] < l[k] + l[i] then
					if l[i] < l[j] + l[k] then
						ret = [l[i], l[j], l[k]].sort
						results.push(ret)
					else
						k = k + 1
						next
					end
				else
					k = k + 1
					next
				end
			else
				k = k + 1
				next
			end
			k = k + 1
		end
		j = j + 1
	end
	i = i + 1
end
print results.uniq.length