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 Ruby (2.3.3) (judge verdict: Accepted)

require 'prime'
require 'set'
require 'tsort'
include Math
ALP = ('a'..'z').to_a
INF = 0xffffffffffffffff
def max(a,b);              a > b ? a : b                              end
def min(a,b);              a < b ?  a : b                             end
def swap(a,b);             a, b = b, a                                end
def gif;                   gets.to_i                                  end
def gff;                   gets.to_f                                  end
def gsf;                   gets.chomp                                 end
def gi;                    gets.split.map(&:to_i)                     end
def gf;                    gets.split.map(&:to_f)                     end
def gs;                    gets.chomp.split.map(&:to_s)               end
def gc;                    gets.chomp.split('')                       end
def pr(num);               num.prime_division                         end
def pr?(num);              Prime.prime?(num)                          end
def digit(num);            num.to_s.length                            end
def array(s,ini=nil);      Array.new(s){ini}                          end
def darray(s1,s2,ini=nil); Array.new(s1){Array.new(s2){ini}}          end
def rep(num);              num.times{|i|yield(i)}                     end
def repl(st,en,n=1);       st.step(en,n){|i|yield(i)}                 end

n = gif

a = gi

b = Hash.new
a.each do |aa|
b[aa] ||= 0
b[aa] += 1
end
ans = 0
b.each do |key,value|
  if value >= key
  ans += value - key
else
  ans += value
end
end

puts ans