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)

get_some :: Int -> [Int] -> [[Int]]

get_some 0 _ = [[]]
get_some 1 x = map (\a -> [a]) x
get_some n (x:xs) = (map (\a -> (x:a)) (get_some (n - 1) xs)) ++ (get_some n xs)
get_some _ [] = []

judge :: [Int] -> Bool
judge x = (a + b > c) && (b + c > a) && (c + a > b) where
    a = x !! 0
    b = x !! 1
    c = x !! 2

main = do
    getLine
    getLine >>= putStrLn . show . length . (filter judge) . (get_some 3) . (map read) . words