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 OCaml (4.02.3) (judge verdict: Accepted)

module IntSet = Set.Make (struct
  type t = int
  let compare = compare
end)

let () = Scanf.scanf "%d" @@ function
  | 3 -> print_endline "2 5 63\n"
  | 4 -> print_endline "2 5 20 63\n"
  | 5 -> print_endline "2 5 20 30 63\n"
  | n ->
      let s =
        IntSet.of_list @@
        Array.to_list @@
        Array.init n @@ fun i ->
          i / 4 * 6 + [| 2; 3; 4; 6 |].(i mod 4) in
      let maximum = IntSet.max_elt s in
      IntSet.iter (Printf.printf "%d ")
        begin match IntSet.fold (fun x y -> (x + y) mod 6) s 0 with
        | 0 -> s
        | 2 -> IntSet.add (maximum - maximum mod 6 + 6) @@ IntSet.remove 8 s
        | 3 -> IntSet.add (maximum - maximum mod 6 + 6) @@ IntSet.remove 9 s
        | 5 -> IntSet.add (maximum - maximum mod 6 + if maximum mod 6 < 4 then 4 else 10) @@ IntSet.remove 9 s
        end;
      print_newline ()