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 Control.Monad
import Data.Maybe
import qualified Data.ByteString.Char8 as BS
import Data.List
import qualified Data.Vector.Unboxed as VU

readInt = fst . fromJust . BS.readInt
readIntList = map readInt . BS.words
getInt = readInt <$> BS.getLine
getIntList = readIntList <$> BS.getLine

main = do
    n <- getInt
    ls <- VU.fromList . sort <$> getIntList
    print $ sum [(binom (j+1) (n-1)  (ls VU.! i) (ls VU.! j) ls) - j | i <- [0..(n-3)], j <- [(i+1)..(n-2)]]

binom m1 m2 a b ls | m1 == m2 && tri a b (ls VU.! m1) = m1
                   | m1 == m2 = m1 - 1
                   | tri a b c = binom m' m2 a b ls
                   | otherwise = binom m1 (m' - 1) a b ls
    where m' = (m1 + m2) `div` 2 + 1
          c = ls VU.! m'

tri a b c | a + b > c && b + c > a && c + a > b = True
          | otherwise = False