output_description: Print 2^N lines. The (i+1)-th line (0 \leq i \leq 2^N-1) should contain the
  expected number of operations until X becomes i, modulo 998244353.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N
      A_0 A_1 \cdots A_{2^N-1}
attempt: print("wakaranai")
  
problem_description: Statement
  
  Snuke found a random number generator. It generates an integer between 0 and
  2^N-1 (inclusive). An integer sequence A_0, A_1, \cdots, A_{2^N-1} represents
  the probability that each of these integers is generated. The integer i (0
  \leq i \leq 2^N-1) is generated with probability A_i / S, where S =
  \sum_{i=0}^{2^N-1} A_i. The process of generating an integer is done
  independently each time the generator is executed.
  
  Snuke has an integer X, which is now 0. He can perform the following operation
  any number of times:
  
    * Generate an integer v with the generator and replace X with X \oplus v, where \oplus denotes the bitwise XOR.
  
  For each integer i (0 \leq i \leq 2^N-1), find the expected number of
  operations until X becomes i, and print it modulo 998244353. More formally,
  represent the expected number of operations as an irreducible fraction P/Q.
  Then, there exists a unique integer R such that R \times Q \equiv P \mod
  998244353,\ 0 \leq R < 998244353, so print this R.
  
  We can prove that, for every i, the expected number of operations until X
  becomes i is a finite rational number, and its integer representation modulo
  998244353 can be defined.
samples: [{"input": "2\n    1 1 1 1", "output": "0\n    4\n    4\n    4\n    \n\nX=0 after zero operations, so the expected number of operations until X\nbecomes 0 is 0.\n\nAlso, from any state, the value of X after one operation is 0, 1, 2 or 3 with\nequal probability. Thus, the expected numbers of operations until X becomes 1,\n2 and 3 are all 4.\n\n* * *"}, {"input": "2\n    1 2 1 2", "output": "0\n    499122180\n    4\n    499122180\n    \n\nThe expected numbers of operations until X becomes 0, 1, 2 and 3 are 0, 7/2, 4\nand 7/2, respectively.\n\n* * *"}, {"input": "4\n    337 780 799 10 796 875 331 223 941 67 148 483 390 565 116 355", "output": "0\n    468683018\n    635850749\n    96019779\n    657074071\n    24757563\n    745107950\n    665159588\n    551278361\n    143136064\n    557841197\n    185790407\n    988018173\n    247117461\n    129098626\n    789682908"}]