Problem:
Score : 600 points

Problem Statement

Nagase is a top student in high school. One day, she's analyzing some properties of special sets of positive integers.

She thinks that a set S = \{a_{1}, a_{2}, ..., a_{N}\} of distinct positive integers is called special if for all 1 \leq i \leq N, the gcd (greatest common divisor) of a_{i} and the sum of the remaining elements of S is not 1.

Nagase wants to find a special set of size N. However, this task is too easy, so she decided to ramp up the difficulty. Nagase challenges you to find a special set of size N such that the gcd of all elements are 1 and the elements of the set does not exceed 30000.

Constraints

3 \leq N \leq 20000

Input

Input is given from Standard Input in the following format:

N

Output

Output N space-separated integers, denoting the elements of the set S. S must satisfy the following conditions :

The elements must be distinct positive integers not exceeding 30000.

The gcd of all elements of S is 1, i.e. there does not exist an integer d > 1 that divides all elements of S.

S is a special set.

If there are multiple solutions, you may output any of them. The elements of S may be printed in any order. It is guaranteed that at least one solution exist under the given contraints.

Sample Input 1

3

Sample Output 1

2 5 63

\{2, 5, 63\} is special because gcd(2, 5 + 63) = 2, gcd(5, 2 + 63) = 5, gcd(63, 2 + 5) = 7. Also, gcd(2, 5, 63) = 1. Thus, this set satisfies all the criteria.

Note that \{2, 4, 6\} is not a valid solution because gcd(2, 4, 6) = 2 > 1.

Sample Input 2

4

Sample Output 2

2 5 20 63

\{2, 5, 20, 63\} is special because gcd(2, 5 + 20 + 63) = 2, gcd(5, 2 + 20 + 63) = 5, gcd(20, 2 + 5 + 63) = 10, gcd(63, 2 + 5 + 20) = 9. Also, gcd(2, 5, 20, 63) = 1. Thus, this set satisfies all the criteria.

Solution in Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

n = gets.chomp.to_i

if n == 3
  puts '2 5 63'
elsif n == 4
  puts '2 5 20 63'
elsif n <= 15000
  0.step do |k|
    answer = nil
    [15000, (n - 1)].min.downto(1) do |l2|
      next if l2 % 3 == 1
      l3 = n - l2 + k
      next if l3 > 10000 || l3 % 4 == 1 || l3 % 4 == 2
      l6 = [l2 / 3, l3 / 2].min
      if n == l2 + l3 - l6
        answer = ((1..l2).map{ |i| i * 2 } + (1..l3).map{ |i| i * 3 }).uniq.join(' ')
        puts answer
        break
      end
      break if answer
    end
    break if answer
  end
else
  0.step do |k|
    l2 = 15000
    l3 = n - l2 + k
    next if l3 > 10000 || l3 % 4 == 1 || l3 % 4 == 2
    l6 = [l2 / 3, l3 / 2].min
    if n == l2 + l3 - l6
      answer = ((1..l2).map{ |i| i * 2 } + (1..l3).map{ |i| i * 3 }).uniq.join(' ')
      puts answer
      break
    end
    break if answer
  end
end