output_description: Print the number of choices of K in which N becomes 1 in the end.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N
attempt: n = int(input())
  a = [int(i + 2) for i in range(n - 1)]
  for i, ai in enumerate(a):
      m = n
      while m % ai == 0:
          if m >= ai and m % ai == 0:
              m = m / ai
      if m % ai != 1:
          a[i] = 0
  b = set(a)
  print(len(b) - 1)
  
problem_description: Statement
  
  Given is a positive integer N.
  
  We will choose an integer K between 2 and N (inclusive), then we will repeat
  the operation below until N becomes less than K.
  
    * Operation: if K divides N, replace N with N/K; otherwise, replace N with N-K.
  
  In how many choices of K will N become 1 in the end?
samples: [{"input": "6", "output": "3\n    \n\nThere are three choices of K in which N becomes 1 in the end: 2, 5, and 6.\n\nIn each of these choices, N will change as follows:\n\n  * When K=2: 6 \\to 3 \\to 1\n  * When K=5: 6 \\to 1\n  * When K=6: 6 \\to 1\n\n* * *"}, {"input": "3141", "output": "13\n    \n\n* * *"}, {"input": "314159265358", "output": "9"}]