Problem:
Score: 400 points

Problem Statement

Print a sequence a_1, a_2, ..., a_N whose length is N that satisfies the following conditions:

a_i (1 \leq i \leq N) is a prime number at most 55 555.

The values of a_1, a_2, ..., a_N are all different.

In every choice of five different integers from a_1, a_2, ..., a_N, the sum of those integers is a composite number.

If there are multiple such sequences, printing any of them is accepted.

Notes

An integer N not less than 2 is called a prime number if it cannot be divided evenly by any integers except 1 and N, and called a composite number otherwise.

Constraints

N is an integer between 5 and 55 (inclusive).

Input

Input is given from Standard Input in the following format:

N

Output

Print N numbers a_1, a_2, a_3, ..., a_N in a line, with spaces in between.

Sample Input 1

5

Sample Output 1

3 5 7 11 31

Let us see if this output actually satisfies the conditions.

First, 3, 5, 7, 11 and 31 are all different, and all of them are prime numbers.

The only way to choose five among them is to choose all of them, whose sum is a_1+a_2+a_3+a_4+a_5=57, which is a composite number.

There are also other possible outputs, such as 2 3 5 7 13, 11 13 17 19 31 and 7 11 5 31 3.

Sample Input 2

6

Sample Output 2

2 3 5 7 11 13

2, 3, 5, 7, 11, 13 are all different prime numbers.

2+3+5+7+11=28 is a composite number.

2+3+5+7+13=30 is a composite number.

2+3+5+11+13=34 is a composite number.

2+3+7+11+13=36 is a composite number.

2+5+7+11+13=38 is a composite number.

3+5+7+11+13=39 is a composite number.

Thus, the sequence 2 3 5 7 11 13 satisfies the conditions.

Sample Input 3

8

Sample Output 3

2 5 7 13 19 37 67 79

Solution in Ruby (2.3.3) (judge verdict: Accepted)

# 素数探索（エラトステネスの篩）
# - 2の倍数を最初から除外してみた
# @param limit 探索する範囲（最大の整数）
# @return [Array] 素数配列
def eratosthenes(limit)
  # 探索リスト
  search_list = []
  3.upto limit do |i|
    search_list << i if i.odd?
  end
  # p search_list

  # 探索結果（素数配列）
  primes = [2]

  # 最後に見つかった素数がコレを越えたら探索終了（残りは全て素数）
  root_limit = Math.sqrt(limit)

  while (prime = search_list.shift) do
    # 探索リストの先頭は必ず素数
    primes << prime

    # primeが√limit を越えたら、残りは全て素数
    if root_limit < prime
      primes.concat(search_list)
      break
    end

    # primeの倍数を全て除去
    search_list.reject! { |i| i % prime == 0 }
  end

  primes
end


num = gets.chomp.to_i

# 『5で割って余り1』になる素数だけを集める
# ※55555までだと該当するのが1408個もある。該当数を55個見つければOKなので。
prime_numbers = eratosthenes(1500).select {|n| n % 5 == 1}
# puts "Len: #{prime_numbers.length}"
# puts prime_numbers

# 先頭から必要な数の部分配列を返す
ans_nums = prime_numbers[0, num]
puts ans_nums.join(" ")