Problem:
Score : 300 points

Problem Statement

You are given a sequence of positive integers of length N, a = (a_1, a_2, ..., a_N).
Your objective is to remove some of the elements in a so that a will be a good sequence.

Here, an sequence b is a good sequence when the following condition holds true:

For each element x in b, the value x occurs exactly x times in b.

For example, (3, 3, 3), (4, 2, 4, 1, 4, 2, 4) and () (an empty sequence) are good sequences, while (3, 3, 3, 3) and (2, 4, 1, 4, 2) are not.

Find the minimum number of elements that needs to be removed so that a will be a good sequence.

Constraints

1 \leq N \leq 10^5

a_i is an integer.

1 \leq a_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the minimum number of elements that needs to be removed so that a will be a good sequence.

Sample Input 1

4
3 3 3 3

Sample Output 1

1

We can, for example, remove one occurrence of 3. Then, (3, 3, 3) is a good sequence.

Sample Input 2

5
2 4 1 4 2

Sample Output 2

2

We can, for example, remove two occurrences of 4. Then, (2, 1, 2) is a good sequence.

Sample Input 3

6
1 2 2 3 3 3

Sample Output 3

0

Sample Input 4

1
1000000000

Sample Output 4

1

Remove one occurrence of 10^9. Then, () is a good sequence.

Sample Input 5

8
2 7 1 8 2 8 1 8

Sample Output 5

5

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

import Control.Applicative
import Control.Monad
import System.IO.Unsafe
import Control.Monad.ST
import Data.Functor
import Data.Function
import Data.Monoid
import Data.Maybe
import Data.List
import Data.Foldable (foldMap)
import Data.List.Split
import Data.Bits
import Data.Char
import Data.Ix
import Data.Ratio
import Data.Ord
import Data.Tuple
import Data.Array
import Data.Array.IO
import Data.Array.ST
import Data.IORef
import Data.STRef
 
readInt = read :: String -> Int
readDouble = read :: String -> Double
getInt = readLn :: IO Int
getInts = map readInt . words <$> getLine
getDouble = readLn :: IO Double
sjoin :: (Show a) => [a] -> String
sjoin = unwords . map show
cond :: a -> a -> Bool -> a
cond t f c = if c then t else f
apply2 :: (a -> a -> b) -> [a] -> b
apply2 f [x,y] = f x y
apply3 :: (a -> a -> a -> b) -> [a] -> b
apply3 f [x,y,z] = f x y z
fnBin :: (b -> c -> d) -> (a -> b) -> (a -> c) -> a -> d
fnBin op f g x = op (f x) $ g x
fnTuple :: (a -> b, a -> c) -> a -> (b, c)
fnTuple (f,g) a = (f a, g a)
replace :: (Eq a) => a -> a -> [a] -> [a]
replace x y = map (\z -> if z==x then y else z)
modifyArray :: (Ix i, MArray a e m) => a i e -> i -> (e -> e) -> m ()
modifyArray arr ix f = readArray arr ix >>= writeArray arr ix . f
-- end of templete


main = getLine >> getInts >>= print . sum . map (\xs -> let x = head xs in let l = length xs in if x<=l then l-x else l) . group . sort