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: n = int(input())
  x = input()
  x_10 = int(x, 2)
  cnt = x_10 + 1
  ans = 0
  n_copy = n
  for i in range(3, n + 1, 2):
      if n % i == 0:
          p = int(x[0 : n // i], 2)
          if x_10 >= sum(p << ((n // i) * j) for j in range(0, i, 2)) + sum(
              (2 ** (n // i) - p - 1) << ((n // i) * j) for j in range(1, i, 2)
          ):
              cnt -= p + 1
              ans += (p + 1) * 2 * (n // i)
          else:
              cnt -= p
              ans += p * 2 * (n // i)
  ans += n * 2 * cnt
  print(ans % 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"}]