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: Wrong Answer)

N = gets.to_i

if N <= 5
  puts [
    [2, 5, 20, 30, 63],
    [2, 5, 20, 63],
    [2, 5, 63],
  ][5 - N].join(' ')
else
  list2 = [*1..3 * N].map { |x| 2 * x }
  list3 = [*1..3 * N].map { |x| 3 * x }

  list2.delete_if { |x| x % 6 == 0 }
  list3.delete_if { |x| x % 6 == 0 }

  rui2 = [0]
  rui3 = [0]

  (1..N).each do |i|
    rui2[i] = rui2[i - 1] + list2[i - 1]
    rui3[i] = rui3[i - 1] + list3[i - 1]
  end

  (1..N).each do |a|
    b = N - a

    next if rui2[a] % 3 > 0
    next if rui3[b] % 2 > 0

    puts (list2.take(a) + list3.take(b)).join(' ')

    break
  end
end