Problem:
Score : 400 points

Problem Statement

Snuke has decided to play a game using cards.
He has a deck consisting of N cards. On the i-th card from the top, an integer A_i is written.

He will perform the operation described below zero or more times, so that the values written on the remaining cards will be pairwise distinct. Find the maximum possible number of remaining cards. Here, N is odd, which guarantees that at least one card can be kept.

Operation: Take out three arbitrary cards from the deck. Among those three cards, eat two: one with the largest value, and another with the smallest value. Then, return the remaining one card to the deck.

Constraints

3 ≦ N ≦ 10^{5}

N is odd.

1 ≦ A_i ≦ 10^{5}

A_i is an integer.

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 A_3 ... A_{N}

Output

Print the answer.

Sample Input 1

5
1 2 1 3 7

Sample Output 1

3

One optimal solution is to perform the operation once, taking out two cards with 1 and one card with 2. One card with 1 and another with 2 will be eaten, and the remaining card with 1 will be returned to deck. Then, the values written on the remaining cards in the deck will be pairwise distinct: 1, 3 and 7.

Sample Input 2

15
1 3 5 2 1 3 2 8 8 6 2 6 11 1 1

Sample Output 2

7

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Control.Monad
import qualified Data.ByteString.Char8 as BS
import Data.Maybe (fromJust)
import Debug.Trace
import Data.List

getEachNumberCount :: [Int] -> [Int]
getEachNumberCount = map length . group . sort

countDuplicated :: [Int] -> Int
countDuplicated [] = 0
countDuplicated (x:xs) = (x - 1) + (countDuplicated xs)

solve:: [Int] -> Int
solve arr = ans
    where
        countArr = getEachNumberCount arr
        dup = countDuplicated countArr
        cardNum = length countArr
        ans = if dup `mod` 2 == 0 then cardNum else cardNum - 1

main :: IO ()
main = do
    n <- (fst . fromJust . BS.readInt) <$> BS.getLine
    a <- map (fst . fromJust . BS.readInt) . BS.words <$> BS.getLine
    print $ solve a