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 Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

import Data.List

main :: IO ()
main = do
    l1 <- getLine
    l2 <- getLine
    let l = map read $ words l2 :: [Int]

    print $ f l

f l = g n (sort l) 1
    where n = length l

g n l j
    | n == 0 = 0
    | j == n = g (n-1) (tail l) 1
    | otherwise = length (takeWhile (< a+b) $ drop j l) - 1 + g n l (j+1)
        where a = head l
              b = l !! j