output_description: Print the sum of the answers to the questions for the integers between 0 and X
  (inclusive), modulo 998244353.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N
      X
attempt: import sys
  
  N = int(input())
  X = int(input(), 2)
  
  
  def proc(x):
      if x % 2 == 1:
          return x >> 1
      else:
          return (x >> 1) + int("1" + "0" * (N - 1), 2)
  
  
  total = 0
  MAX_TRY = 1000
  for k in range(X + 1):
      p = k
      for num_calc in range(1, MAX_TRY):
          p = proc(p)
          if p == k:
              total += num_calc
              break
          if num_calc == MAX_TRY - 1:
              print("-1")
              sys.exit(0)
  
  print(total % 998244353)
  
problem_description: Statement
  
  Given are integers N and X. For each integer k between 0 and X (inclusive),
  find the answer to the following question, then compute the sum of all those
  answers, modulo 998244353.
  
    * Let us repeat the following operation on the integer k. Operation: if the integer is currently odd, subtract 1 from it and divide it by 2; otherwise, divide it by 2 and add 2^{N-1} to it. How many operations need to be performed until k returns to its original value? (The answer is considered to be 0 if k never returns to its original value.)
samples: [{"input": "3\n    111", "output": "40\n    \n\nFor example, for k=3, the operation changes k as follows: 1,0,4,6,7,3.\nTherefore the answer for k=3 is 6.\n\n* * *"}, {"input": "6\n    110101", "output": "616\n    \n\n* * *"}, {"input": "30\n    001110011011011101010111011100", "output": "549320998"}]