import math

def cantorPair((x,y)):
  return int(0.5*(x+y)*(x+y+1)+y)

def cantorPairInverse(z):
  w = math.floor(0.5*(math.sqrt(8*z+1)-1))
  t = (w*w + w)/2
  y = int(z - t)
  x = int(w - y)
  return (x,y)

def cantorTuple(t):
  # return the index in the countable set
  return 0

def cantorTupleInverse(z):
  # return the n-tuple
  return (0,0)

def main():
  print("cantorPair((47,32)) = " + str(cantorPair((47,32))))
  print("cantorPairInverse(3192) = " + str(cantorPairInverse(3192)))
  print("cantorPair((2,3)) = " + str(cantorPair((2,3))))
  print("cantorPairInverse(18) = " + str(cantorPairInverse(18)))

main()