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)

{-# LANGUAGE OverloadedStrings #-}
import Data.Char
import Data.List
import Data.Maybe
import qualified Data.ByteString.Char8 as BS
import qualified Data.Vector.Unboxed as UV

main :: IO()
main = do
  n <- readLn
  ns <- UV.fromList . sort <$> getIntList
  let f x k = (subtract k) . fst . bisearch ((< x) . (ns UV.!)) $ (k, n) 
  print . sum $ [ f x j | i <- [0..n-3], j <- [i+1..n-2], let x = (ns UV.! i) + (ns UV.! j)]


readInt :: BS.ByteString -> Maybe (Int, BS.ByteString)
readInt = BS.readInt . BS.dropWhile isSpace

getIntList :: IO [Int]
getIntList = map (fst . fromJust . BS.readInt) . BS.words <$> BS.getLine


-- 二分探索(整数)
bisearch :: (Int -> Bool) -> (Int, Int) -> (Int, Int)
bisearch check (left, right) = go (left, right)
 where
  go (l, r) | r - l == 1 = (l, r)
            | check mid  = go (mid, r)
            | otherwise  = go (l, mid)
    where mid = l + (r - l) `div` 2