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: Accepted)

import qualified Data.ByteString.Char8 as BS
import Data.Maybe (fromJust)
import Data.List
import Data.Array.IArray
import Control.Monad

lowerBound:: (Integral i, Ix i, Ord e, IArray a e) => e -> a i e -> i
lowerBound x a =
    let (b,e) = bounds a in bsearch b (e + 1)
  where
    bsearch b e
      | e == b    = b
      | x <= a!p  = bsearch b p
      | otherwise = bsearch (p + 1) e
      where p = (b + e) `div` 2

main :: IO ()
main = do
    _ <- getLine
    l <- map (fst . fromJust . BS.readInt)
        . BS.words <$> BS.getLine :: IO [Int]
    let sl = listArray (0,length l - 1) $ sort l :: Array Int Int
    print $ sum
        [ let c = lowerBound ((sl!a)+(sl!b)) sl
           in c - (b+1)
          | a <- [0..length sl - 1], b <- [(a+1)..length sl - 1]
        ]