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 Scala (2.11.7) (judge verdict: Runtime Error)

import java.io._
import java.util.StringTokenizer
import scala.util.control.Breaks.{breakable,break}

object Main extends App {
  val in = new InputReader(System.in)
  val pw = new PrintWriter(System.out)

  val s = in.next()
  val _x, y = in.next().toInt
  val N = s.length
  var x = _x

  var dir = 0
  var sayuu: List[Int] = Nil
  var updown: List[Int] = Nil

  def calc(com: Char, num: Int): Unit = {
    com match {
      case 'F' =>
        if(dir == 0)
          sayuu = num :: sayuu
        else
          updown = num :: updown
      case 'T' =>
        if(num % 2 == 1)
          dir += 90
        dir %= 180

    }
  }

  var ind = 0
  ////
  breakable {
    while(ind < N) {
      if(s(ind) == 'F') {
        ind += 1
      }
      else
        break
    }
  }

  x -= ind

  while(ind < N) {
    val now = s(ind)
    var r = ind + 1

    breakable {
      while(true) {
        if(r == N || now != s(r)) {
          calc(now, r-ind)
          ind = r
          break
        }
        else {
          r += 1
        }
      }
    }
  }

  // val dplr = new Array[Int](16002)
  // val dpud = new Array[Int](16002)

  var setlr: Set[Int] = Set(0)
  
  for(e <- sayuu) {
    var now = Set(e, -e)

    for(e2 <- setlr) {
      now = now + (e2 + e) + (e2 - e)
    }

    setlr = now
  }

  var setud: Set[Int] = Set(0)
  for(e <- updown) {
    var now = Set(e, -e)

    for(e2 <- setud) {
      now = now + (e2 + e) + (e2 - e)
    }

    setud = now
  }


  if(setlr.contains(x) && setud.contains(y))
    println("Yes")
  else
    println("No")
}


class InputReader(stream: InputStream) {
  private val reader = new BufferedReader(new InputStreamReader(stream))
  private var tokenizer: StringTokenizer = new StringTokenizer(reader.readLine())
  def next(): String = {
    while (!tokenizer.hasMoreTokens()) {
      tokenizer = new StringTokenizer(reader.readLine())
    }
    tokenizer.nextToken()
  }
}