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 qualified Data.ByteString.Char8 as BS
import Data.Maybe (fromJust)
import Data.List (tails)

combinations :: Int -> [a] -> [[a]]
combinations 0 _  = [[]]
combinations n xs = [ y:ys | y:xs' <- tails xs
                           , ys <- combinations (n-1) xs' ]

main :: IO ()
main = do
    n <- readLn :: IO Int
    l <- map (fst . fromJust . BS.readInt)
        . BS.words <$> BS.getLine :: IO [Int]
    let cmb = combinations 3 l
    -- print cmb
    print . sum $ [1 | [a,b,c] <- cmb,
        (b-c)^2 < a^2 && a < b + c ]