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: Wrong Answer)

Scanf.scanf "%d" (fun n ->
    let rec gcd a b = if b = 0 then a else gcd b (a mod b) in
    let lcm a b = a / gcd a b * b in

    let smooth k l =
        let rec loop r mask = function
            | [] -> if r = 1 then mask else 0
            | (hd :: tl) as l ->
                    if r mod hd = 0 then loop (r / hd) (mask lor (1 lsl hd)) l
                                    else loop r mask tl
        in
        loop k 0 l
    in

    let m2prod mask =
        let rec loop r i c =
            if r = 0 then c else
                if r land 1 = 0 then loop (r lsr 1) (i + 1) c
                                else loop (r lsr 1) (i + 1) (c * i)
        in
        loop mask 0 1
    in

    let rec loop i acc sum mask =
        let c =  smooth i [ 2; 3; 5; 7; 11; 13; 17; 19; 23 ] in
        if c > 0 then (
            Printf.printf "%d " i;
            let acc = acc + 1 in
            let sum = sum + i in
            let mask = mask lor c in
            if acc = n - 1 then Printf.printf "%d\n" (lcm sum (m2prod mask) - sum) else loop (i +1) acc sum mask
        ) else loop (i + 1) acc sum mask
    in
    loop 2 0 0 0
)