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: Wrong Answer)

require 'pp'

s = gets.chomp.split("")
x, y = gets.chomp.split(" ").map(&:to_i)

flag = 0
count = 0
x_list = Array.new
y_list = Array.new
while v = s.shift
    if v == "F"
        count += 1
    else
        if flag == 0
            x_list << count
            flag = 1
        else
            y_list << count
            flag = 0
        end
        count = 0
    end
end
if count != 0
    if flag == 0
        x_list << count
    else
        y_list << count
    end
end

dp_x = Array.new
dp_y = Array.new

dp_x[0] = [0]
dp_y[0] = [0]

x_list.each_with_index do |val, i|
    dp_x[i+1] = Array.new(0)
    dp_x[i].each do |w|
        dp_x[i+1].push(w+val)
        dp_x[i+1].push(w-val)
    end
    dp_x[i+1].uniq!
end

y_list.each_with_index do |val, i|
    dp_y[i+1] = Array.new
    dp_y[i].each do |w|
        dp_y[i+1].push(w+val)
        dp_y[i+1].push(w-val)
    end
    dp_y[i+1].uniq!
end

if dp_x[x_list.size].include?(x) && dp_y[y_list.size].include?(y)
    puts "Yes"
else
    puts "No"
end