output_description: Print the number of the pairs of a subset of the rows and a subset of the
  columns that satisfy the condition, modulo 998244353.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N M
      a_{11} ... a_{1M}
      :
      a_{N1} ... a_{NM}
attempt: n, m = map(int, input().split())
  matrix = [list(map(int, input().split())) for i in range(n)]
  
  
  def change(i, j, matrix):
      line = (matrix[i], matrix[j])
      matrix[i] = line[1]
      matrix[j] = line[0]
      return matrix
  
  
  def kbai(i, k, matrix):
      for j in range(len(matrix[0])):
          matrix[i][j] *= k
      return matrix
  
  
  def plus(i, j, k, matrix):
      for _ in range(len(matrix[0])):
          matrix[i][_] += matrix[j][_] * k
      return matrix
  
  
  def rank(n, m, matrix):
      now = 0
      for j in range(m):
          exist = set()
          jiku = -1
          for i in range(n):
              if matrix[i][j] != 0:
                  if jiku == -1 and i >= now:
                      jiku = i
                  else:
                      exist |= {
                          i,
                      }
          if jiku == -1:
              continue
          for x in range(len(exist)):
              y = exist.pop()
              matrix = plus(y, jiku, -1, matrix)
          matrix = change(jiku, now, matrix)
          now += 1
      return now
  
  
  r = rank(n, m, matrix)
  x, y = 0, 0
  num = 1
  for i in range(1, n + m):
      num = num * 2 % 998244353
      if i == n + m - r - 1:
          y = num
      if i == n + m - 1:
          x = num
  print((x - y) % 998244353)
  # https://img.atcoder.jp/yahoo-procon2019-qual/editorial.pdf
  
problem_description: Statement
  
  There is a square grid with N rows and M columns. Each square contains an
  integer: 0 or 1. The square at the i-th row from the top and the j-th column
  from the left contains a_{ij}.
  
  Among the 2^{N+M} possible pairs of a subset A of the rows and a subset B of
  the columns, find the number of the pairs that satisfy the following
  condition, modulo 998244353:
  
    * The sum of the |A||B| numbers contained in the intersection of the rows belonging to A and the columns belonging to B, is odd.
samples: [{"input": "2 2\n    0 1\n    1 0", "output": "6\n    \n\nFor example, if A consists of the first row and B consists of both columns,\nthe sum of the numbers contained in the intersection is 0+1=1.\n\n* * *"}, {"input": "2 3\n    0 0 0\n    0 1 0", "output": "8"}]