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.to_i
Ls = gets.split.map &:to_i

ll = Array.new(1000, 0)
Ls.each{ |x|
	ll[x - 1] += 1
}

sums = Array.new(1000, 0)

sum = 0

ll.reverse.each_with_index{ |l, i|
	sum += l
	sums[sums.size - i - 1] = sum
}

max = N * (N - 1) * (N - 2) / (3 * 2)

Lsuni = Ls.uniq

Lsuni.combination(2).each{ |a| max -= ll[a[0] - 1] * ll[a[1] - 1] * sums[[a[0] + a[1] - 1, 999].min] }

puts [max, 0].max - ll.inject(0, :+) + ll.size