output_description: 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.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N
attempt: import math
  from functools import reduce
  
  def gcd(*numbers):
      return reduce(math.gcd, numbers)
  
  N = int(input())
  if N <= 5:
      if N == 3: print('2 5 63')
      elif N == 4: print('2 5 20 63')
      elif N == 5: print('2 5 20 30 63')
  else:
      flag = 0
      S = 0
      k = 0
      retList = list()
      Q = N // 4
      R = N % 4
      for q in range(Q):
          S += 4*6*q + 15
          retList.append(str(6*q+2))
          retList.append(str(6*q+3))
          retList.append(str(6*q+4))
          retList.append(str(6*q+6))
      if R == 0:
          pass
      elif R == 1:
          S += 6*Q + 2
          retList.append(str(6*Q + 2))
      elif R == 2:
          S += 2*6*Q + 5
          retList.append(str(6*Q + 2))
          retList.append(str(6*Q + 3))
      elif R == 3:
          S += 3*6*Q + 9
          retList.append(str(6*Q + 2))
          retList.append(str(6*Q + 3))
          retList.append(str(6*Q + 4))
  
      if S%6 == 0:
          pass
      elif S%6 == 2:
          retList.remove('8')
          S -= 8
          S += 6*(Q+1) + 6
          retList.append(str(6*Q + 6))
      elif S%6 == 3:
          retList.remove('9')
          S -= 9
          S += 6*(Q+1) + 6
          if 6*
          retList.append(str(6*Q + 6))
      elif S%6 == 5:
          retList.remove('9')
          S -= 9
          S += 6*(Q+1) + 4
          retList.append(str(6*Q + 4))
      # print(S%6)
      # print(len(retList))
      # retIntList = list(map(int, retList))
      # for a in retIntList:
      #     if gcd(S, a) <= 1:
      #         print(S)
      #         print(a)
      print(' '.join(retList))
      # print(gcd(*retIntList))
problem_description: 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.
samples: [{"input": "3", "output": "2 5 63\n    \n\n\\\\{2, 5, 63\\\\} is special because gcd(2, 5 + 63) = 2, gcd(5, 2 + 63) = 5,\ngcd(63, 2 + 5) = 7. Also, gcd(2, 5, 63) = 1. Thus, this set satisfies all the\ncriteria.\n\nNote that \\\\{2, 4, 6\\\\} is not a valid solution because gcd(2, 4, 6) = 2 > 1.\n\n* * *"}, {"input": "4", "output": "2 5 20 63\n    \n\n\\\\{2, 5, 20, 63\\\\} is special because gcd(2, 5 + 20 + 63) = 2, gcd(5, 2 + 20 +\n63) = 5, gcd(20, 2 + 5 + 63) = 10, gcd(63, 2 + 5 + 20) = 9. Also, gcd(2, 5,\n20, 63) = 1. Thus, this set satisfies all the criteria."}]