from itertools import combinations

def latexifyCondition(condition):
  return condition[0] if condition[1] else f'\\overline{{{condition[0]}}}'

def latexify(listOfConditions): # [(str,bool)]
  lines = []
  for n in range(1, len(listOfConditions) + 1):
    line = []
    for x in combinations(listOfConditions, n):
      line.append(''.join(latexifyCondition(c) for c in x))
    lines.append(line)
  
  linestrs = []
  for line in lines:
    linestr = ' + '.join(f'N({x})' for x in line)
    if len(line) > 1:
      linestr = f'\\left[ {linestr} \\right]'
    linestrs.append(linestr)

  b = False
  result = '\\begin{align*}\nN'
  for l in linestrs:
    result += ' &+ ' if b else ' &- '
    result += l + ' \\\\\n'
    b = not b
  result += '\\end{align*}' 
  return result

def parseInput(string):
  result = []
  for x in string.split(' '):
    if x.startswith('!'):
      result.append((x[1:], False))
    else:
      result.append((x, True))
  return result

def processFileContent(raw):
  listOfConditions = parseInput(raw)
  content = latexify(listOfConditions)
  return content

if __name__ == '__main__':
  pass