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 Common Lisp (SBCL 2.0.3) (judge verdict: Time Limit Exceeded)

(let* ((n (read))
       (l (make-array (list n)))
       (ans 0))
  (loop :for i :from 0 :to (1- n)
        :do (setf (aref l i) (read)))
  (setf l (sort l #'<))
  (loop :for i :from 0 :to (- n 3)
        :for a := (aref l i)
        :do (loop :for j :from (+ i 1) :to (- n 2)
                  :for b := (aref l j)
                  :do (loop :for k :from (+ j 1) :to (- n 1)
                            :for c := (aref l k)
                            :if (< c (+ a b))
                            :do (incf ans))))
  (format t "~A~%" ans))