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
a = gets.split.map &:to_i
a.sort!

def count(lo,hi,ok)
  while hi - lo > 1
    mid = (hi + lo) / 2
    ok[mid] ? lo = mid : hi = mid
  end
  lo
end

ans = 0
(n-2).times do |i|
  (i+1).upto(n-2) do |j|
    k = a[i] + a[j]
    ok = -> mid { a[mid] < k }
    ans += count(j,n,ok) - j
  end
end

puts ans