x f
  0 0
  1 1
  2 1
  3 0
  4 1
  5 0
  6 0
  7 1
f is balanced
 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 0.25 -0.25 0.25 -0.25 0.25 -0.25 0.25 -0.25 0.25 -0.25 0.25 -0.25 0.25 -0.25 0.25 -0.25
 0.25 -0.25 -0.25 0.25 -0.25 0.25 0.25 -0.25 -0.25 0.25 0.25 -0.25 0.25 -0.25 -0.25 0.25
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
p0 = 0, 1-p0 = 1, f is balanced